Go Math Grade 7 Answer Key Chapter 12 Experimental Probability

go-math-grade-7-chapter-12-experimental-probability-answer-key

Go Math Grade 7 Answer Key Chapter 12 Experimental Probability helps the students to score best in the examinations. Download Go Math Answer Key Chapter 12 Experimental Probability for free. We provide a detailed explanation for all the questions which makes students understand the concepts in an easy manner. Students feel that probability is difficult among all the chapters but it is an interesting and easy chapter. Refer Go Math Grade 7 Answer Key Chapter 12 Experimental Probability while doing your homework.

Go Math Grade 7 Answer Key Chapter 12 Experimental Probability

Below we have provided the links according to the list of the chapters. Get the solutions for all Guided Practice and Independent Practice. Just tap the links and get the answers in Go Math Grade 7 Answer Key Chapter 12 Experimental Probability. Improve your math skills with the help of HMH Go Math Grade 7 Solution Key Chapter 12 Experimental Probability.

Chapter 12– Lesson 1:

Chapter 12– Lesson 2:

Chapter 12– Lesson 3:

Chapter 12– Lesson 4:

 

Guided Practice – Page No. 372

Determine whether each event is impossible, unlikely, as likely as not, likely, or certain. Then, tell whether the probability is 0, close to 0, \(\frac{1}{2}\) , close to 1, or 1.

Question 2.
randomly picking a green card from a standard deck of playing cards
_____

Answer: Probability is 0.

Explanation: A standard deck of play cards does not have green cards, so the probability is 0.

Question 3.
randomly picking a red card from a standard deck of playing cards
_____

Answer: Probability is 1/2.

Explanation: As half of the cards are from a standard deck of playing cards are red, so the probability is 1/2.

Question 4.
picking a number less than 15 from a jar with papers labeled from 1 to 12
_____

Answer: The probability of picking a number less than 15 is 1.

Explanation: All papers have a number less than 15, so the probability of picking a number less than 15 is 1.

Question 5.
picking a number that is divisible by 5 from a jar with papers labeled from 1 to 12
close to _____

Answer: The probability is 1/6.

Explanation: The numbers divisible by 5 from 1 to 12 are 5 and 10, so there are two positive numbers from a total of 12 positive numbers and the probability of picking a number that is divisible by 5 is 2/12= 1/6.

Find each probability. Write your answer in simplest form.

Question 6.
spinning a spinner that has 5 equal sections marked 1 through 5 and landing on an even number
\(\frac{□}{□}\)

Answer: The spinner landing on an even number is 2/5.

Explanation: As there are 5 possible outcomes when spinning the spinner and there are two even numbers on the spinner 2 and 4. So the probability of the spinner landing on an even number is 2/5.

Question 7.
picking a diamond from a standard deck of playing cards which has 13 cards in each of four suits: spades, hearts, diamonds and clubs
\(\frac{□}{□}\)

Answer: The probability is 1/4.

Explanation: As the dek of cards contains 52 cards. so there are 52 possible outcomes in the situation and there are 13 cards with diamonds. So the probability is 13/52= 1/4.

Use the complement to find each probability.

Question 8.
What is the probability of not rolling a 5 on a standard number cube?
\(\frac{□}{□}\)

Answer: The probability of not rolling a 5 is 5/6.

Explanation: A standard number cube has six sides and marked from 1 to 6, so the probability of rolling a 5 is 1/6. And the probability of not rolling a 5 is
P(rolling a 5) + P(not rolling a 5 ) = 1
1/6 + P(not rolling a 5 )= 1
P(not rolling a 5 ) = 1- 1/6
= (6-1)/6
= 5/6.

Question 9.
A spinner has 3 equal sections that are red, white, and blue. What is the probability of not landing on blue?
\(\frac{□}{□}\)

Answer: The probability of not landing on blue is 2/3.

Explanation: As spinner has 3 equal sections, so possible outcomes are 3. The probability of landing on blue is 1/3, so the probability of not landing on blue is
P(landing on blue) + P(not landing on blue ) = 1
1/3 + P(not landing on blue )= 1
P(not landing on blue ) = 1- 1/3
= (3-1)/3
= 2/3.

Question 10.
A spinner has 5 equal sections marked 1 through 5. What is the probability of not landing on 4?
\(\frac{□}{□}\)

Answer:

Explanation: As spinner has 5 equal sections, so possible outcomes are 5. The probability of landing on 4 is 1/5, so the probability of not landing on 4 is
P(landing on 4) + P(not landing on 4 ) = 1
1/5 + P(not landing on blue )= 1
P(not landing on blue ) = 1- 1/5
= (5-1)/5
= 4/5.

Question 11.
There are 4 queens in a standard deck of 52 cards. You pick one card at random. What is the probability of not picking a queen?
\(\frac{□}{□}\)

Answer: The probability of not picking a queen is 12/13.

Explanation: The deck has 52 cards, so there are 52 possible outcomes. And there are 4 queens in the deck, so the probability of picking a queen is 4/52= 1/13. And the probability of not picking a queen is
P(picking queen) + P(not picking queen ) = 1
1/13 + P(not picking queen )= 1
P(not picking queen ) = 1- 1/13
= (13-1)/13
= 12/13.

Essential Question Check-In

Question 12.
Describe an event that has a probability of 0% and an event that has a probability of 100%.

Answer: An event with a probability of 0% would be picking a number card labeled 15 from a standard deck of cards. And an event with a probability of 100% would be picking a red marble from a bowl filled only with red marbles.

Independent Practice – Page No. 373

Question 13.
There are 4 aces and 4 kings in a standard deck of 52 cards. You pick one card at random. What is the probability of selecting an ace or a king? Explain your reasoning.
\(\frac{□}{□}\)

Answer: The probability of selecting an ace or king from the deck is 2/13.

Explanation: There are 52 possible outcomes when picking from a deck of cards and there are 8 cards that have an ace or king, so the probability of selecting an ace or king from the deck is 8/52= 2/13.

Question 14.
There are 12 pieces of fruit in a bowl. Seven of the pieces are apples and two are peaches. What is the probability that a randomly selected piece of fruit will not be an apple or a peach? Justify your answer.
\(\frac{□}{□}\)

Answer: The probability of not picking an apple or a peach is 1/4.

Explanation: There are 12 possible outcomes and 9 out of 12 fruits are apples or peaches, so the probability of picking an apple or a peach is 9/12 = 3/4. And the probability of not picking an apple or a peach is
P(picking an apple or a peach ) + P(not picking an apple or a peach ) = 1
3/4 + P(not picking an apple or a peach)= 1
P(not picking an apple or a peach) = 1- 3/4
= (4-3)/4
= 1/4.

Question 15.
Critique Reasoning
For breakfast, Clarissa can choose from oatmeal, cereal, French toast, or scrambled eggs. She thinks that if she selects a breakfast at random, it is likely that it will be oatmeal. Is she correct? Explain your reasoning.
_____

Answer: Clarissa will unlikely to have oatmeal.

Explanation: As Clarissa has 4 breakfast choices, the probability of choosing oatmeal is 1/4, so it is unlikely that Clarissa will have oatmeal.

Question 16.
Draw Conclusions
A researcher’s garden contains 90 sweet pea plants, which have either white or purple flowers. About 70 of the plants have purple flowers, and about 20 have white flowers. Would you expect that one plant randomly selected from the garden will have purple or white flowers? Explain.
_____

Answer: The one plant randomly selected from the garden will be pruple flowers.

Explanation: The probability of selecting a white flowered plant is 20/90= 2/9 and the probability of selecting purple flowered plant is 70/90= 7/9. So, it is more likely to select a purple plant when randomly choosing from the garden

Question 17.
The power goes out as Sandra is trying to get dressed. If she has 4 white T-shirts and 10 colored T-shirts in her drawer, is it likely that she will pick a colored T-shirt in the dark? What is the probability she will pick a colored T-shirt? Explain your answers.
_____

Answer: The probability of selecting a colored T-shirt is 5/7.

Explanation: The total number of T-shirts in Sandra’s drawer are 14, and the probability of selecting a white T-shirt is 4/14= 2/7. And the probability of selecting a colored T-shirt is 10/14= 5/7. So, it is more likely to choose a colored T-shirt when randomly choosing from the drawer.

Page No. 374

Question 18.
James counts the hair colors of the 22 people in his class, including himself. He finds that there are 4 people with blonde hair, 8 people with brown hair, and 10 people with black hair. What is the probability that a randomly chosen student in the class does not have red hair? Explain.
_____

Answer: The probability that a randomly chosen student in the class does not have red hair is 1.

Explanation: As there is no student with red hair in James class and that means the probability that a randomly chosen student in the class does not have red hair is 1.

Question 19.
Persevere in Problem Solving
A bag contains 8 blue coins and 6 red coins. A coin is removed at random and replaced by three of the other color.
a. What is the probability that the removed coin is blue?
\(\frac{□}{□}\)

Answer: The probability that the blue coin is removed is 8/14= 4/7.

Explanation: The total number of coins in the bag is 14, so there are 14 possible outcomes. As there are 8 blue coins and 6 red coins, so the probability that the blue coin is removed is 8/14= 4/7.

Question 19.
b. If the coin removed is blue, what is the probability of drawing a red coin after three red coins are put in the bag to replace the blue one?
\(\frac{□}{□}\)

Answer: The probability of choosing a red coin is 9/16.

Explanation: The total number of coins in the bag is 14 and one blue coin was removed which means 8-1= 7 and three red coins are added, so 6+3= 9  the total number of coins is 7+9= 16. And there are 7 blue coins and 9 red coins, so the probability of choosing a red coin is 9/16.

Question 19.
c. If the coin removed is red, what is the probability of drawing a red coin after three blue coins are put in the bag to replace the red one?
\(\frac{□}{□}\)

Answer: The probability of choosing a red coin is 5/16.

Explanation: The total number of coins in the bag is 14 and one red coin was removed which means 6-1= 5 and three blue coins are added, so 8+3= 11 the total number of coins is 5+11= 16. And there are 11 blue coins and 5 red coins, so the probability of choosing a red coin is 5/16.

H.O.T.

Focus on Higher Order Thinking

Question 20.
Draw Conclusions
Give an example of an event in which all of the outcomes are not equally likely. Explain.

Answer: A bag of coins with 5 red coins and 11 blue coins are not equally likely.

Explanation: All the outcomes are not equally likely would be having a bag of coins with 5 red coins and 11 blue coins. Since these are not the same number of coins of each color, so the probability of choosing a certain color are not equal.

Question 21.
Critique Reasoning
A box contains 150 black pens and 50 red pens. Jose said the sum of the probability that a randomly selected pen will not be black and the probability that the pen will not be red is 1. Explain whether you agree.

Answer: Jose is correct and the probability of choosing a pen that is not black and the probability of choosing the pen that is not red is 1.

Explanation: Since the pens are either red or black, the probability of choosing a pen that is not black is equal to the probability of choosing a pen that is red and the probability of choosing a pen that is not red is equal to the probability of choosing a pen that is black. So the probability of choosing a pen that is not black and the probability of choosing the pen that is not red is
P(not red)+P(not black)= 150/200 + 50/200
= 200/200
= 1.

Question 22.
Communicate Mathematical Ideas
A spinner has 7 identical sections. Two sections are blue, 1 is red, and 4 of the sections are green. Suppose the probability of an event happening is \(\frac{2}{7}\). What does each number in the ratio represent? What outcome matches this probability?

Answer: The probability outcome match is 2/7.

Explanation: As the spinner has 7 identical sections. The numerator of the ratio represents the number of sections with color and the denominator represents the total number of sections on the spinner. And there are 2 blue sections, so the probability of the spinner landing on the blue is 2/7 matches.

Guided Practice – Page No. 378

Question 1.
A spinner has four sections lettered A, B, C, and D. The table shows the results of several spins. Find the experimental probability of spinning each letter as a fraction in simplest form, a decimal, and a percent.
Go Math Grade 7 Answer Key Chapter 12 Experimental Probability img 1

Answer:
The probability of letter A is 35%.
The probability of letter B is 17.5%.
The probability of letter C is 27.5%.
The probability of letter D is 20%.

Explanation:
The total number of spins is 14+7+11+8= 40.
The probability for the letter A is 14/40= 7/20
= 0.35
= 35%.
The probability for the letter B is 7/40= 0.175
= 17.5%.
The probability for the letter C  is 11/40= 0.275
= 27.5%.
The probability for the letter D is 8/40= 1/5
= 0.2
= 20%.

Question 2.
Rachel’s free-throw average for basketball is 60%. She wants to predict how many times in the next 50 tries she will make a free throw. Describe how she could use 10 index cards to predict the answer.

Answer: As Rachel has a 60%  success rate, she could write Successful on 6 cards and Unsuccesful on 4 cards. She then needs to draw cards at random 50 times and record the number of times she gets a Succesful card.

Essential Question Check-In

Question 3.
Essential Question Follow Up
How do you find an experimental probability of a simple event?

Answer: To find the experimental probability of a simple event, divide the number of successful outcomes by the total number of outcomes in the experiment.

Explanation: To find the experimental probability of a simple event, divide the number of successful outcomes by the total number of outcomes in the experiment. For example, if a person makes 10 free throws out of 18, attempts, the experimental probability of making the next free throw is 10/18 = 5/9.

Independent Practice – Page No. 379

Question 4.
Dree rolls a strike in 6 out of the 10 frames of bowling. What is the experimental probability that Dree will roll a strike in the first frame of the next game? Explain why a number cube would not be a good way to simulate this situation.
\(\frac{□}{□}\)

Answer: The experimental probability is 6/10 = 3/5. And the number of possible outcomes should be a multiple of 5.

Experiment:
The experimental probability is 6/10 = 3/5. As the denominator of the probability is either 5 or 10, a number cube would not be able to represent the outcomes because it has 6 faces.

Question 5.
To play a game, you spin a spinner like the one shown. You win if the arrow lands in one of the areas marked “WIN”. Lee played this game many times and recorded her results. She won 8 times and lost 40 times. Use Lee’s data to explain how to find the experimental probability of winning this game.
Go Math Grade 7 Answer Key Chapter 12 Experimental Probability img 2
\(\frac{□}{□}\)

Answer: The experimental probability is 8/48= 1/6.

Explanation: As Lee won 8 times and lost 40 times, the number of spins that Lee played is 8+40= 48. So the experimental probability is 8/48= 1/6.

Question 6.
The names of the students in Mr. Hayes’ math class are written on the board. Mr. Hayes writes each name on an index card and shuffles the cards. Each day he randomly draws a card, and the chosen student explains a math problem at the board. What is the probability that Ryan is chosen today? What is the probability that Ryan is not chosen today?
Go Math Grade 7 Answer Key Chapter 12 Experimental Probability img 3
Chosen: \(\frac{□}{□}\)

Answer: The probability of the teacher not choosing Ryan is 19/20.

Explanation: As there are 20 students, so possible outcomes are 20. And Ryan is 1 student, the probability of the teacher choosing Ryan is 1/20. And the probability of the teacher not choosing Ryan is
= 1- 1/20
= (20-1)/20
= 19/20.

Question 7.
Critique Reasoning
A meteorologist reports an 80% chance of precipitation. Is this an example of experimental probability, written as a percent? Explain your reasoning.
______

Answer: Yes, the given example is the experimental probability.

Explanation: Experimental probability uses past data to predict future data. The probability that it will rain is based on historical data. So it is an experimental probability written as a percent.

Page No. 380

Question 8.
Mica and Joan are on the same softball team. Mica got 8 hits out of 48 times at bat, while Joan got 12 hits out of 40 times at bat. Who do you think is more likely to get a hit her next time at bat? Explain.
______

Answer: Joan is more likely to get hit her next time at the bat.

Explanation:
As Mica got 8 hits out of 48 times, so the experimental probability of getting a hit is 8/48= 1/6.
And Joan got 12 hits out of 40 times, the experimental probability of getting a hit is 12/40= 3/10.
Therefore Joan is more likely to get hit her next time at the bat.

Question 9.
Make a Prediction
In tennis, Gabby serves an ace, a ball that can’t be returned, 4 out of the 10 times she serves. What is the experimental probability that Gabby will serve an ace in the first match of the next game? Make a prediction about how many aces Gabby will have for the next 40 serves. Justify your reasoning.
\(\frac{□}{□}\)

Answer: The experimental probability of her serving an ace is 2/5. In 40 serves, she will serve an ace about 2/5×40 = 16 times.

Explanation: To find the experimental probability we need to divide the number of tries by the number of aces. As Gabby serves 4 aces out of 10 times, the experimental probability of her serving an ace is 4/10= 2/5. Next, to make a prediction about how many aces Gabby will have for the next 40 serves, we need to multiply the number of servers 40 by the experimental probability. In her next 40 serves, she will serve an ace about 2/5×40 = 16 times.

Question 10.
Represent Real-World Problems
Patricia finds that the experimental probability that her dog will want to go outside between 4 P.M. and 5 P.M. is \(\frac{7}{12}\). About what percent of the time does her dog not want to go out between 4 P.M. and 5 P.M.?
______ %

Answer: 41.67%

Explanation: As the sum of the probabilities of an event and its complement is always equal to 1 and P(dog want to go outside) is \(\frac{7}{12}\).
So P(dog want to go outside)+P(dog does not want to go outside) = 1
\(\frac{7}{12}\) + P(dog does not want to go outside) = 1
P(dog does not want to go outside) = 1-\(\frac{7}{12}\)
= \(\frac{12-7}{12}\)
= \(\frac{5}{12}\)
= 0.4167
= 41.67%

H.O.T.

Focus on Higher Order Thinking

Question 11.
Explain the Error
Talia tossed a penny many times. She got 40 heads and 60 tails. She said the experimental probability of getting heads was \(\frac{40}{60}\). Explain and correct her error.

Answer: Talia is not correct.

Explanation: As Taila got 40 heads and 60 tails, which means that she did 100 tosses of the coin. So the experimental probability of getting heads was \(\frac{40}{100}\)

Question 12.
Communicate Mathematical Ideas
A high school has 438 students, with about the same number of males as females. Describe a simulation to predict how many of the first 50 students who leave school at the end of the day are female.

Answer: Since high school has about the same number of male students as female students, the probability of a student leaving school at the end of the day being female is about 50%. And a possible simulation could be using a coin toss, with heads representing males and tails representing females. Toss the coin 50 times and use the results to make a prediction.

Question 13.
Critical Thinking
For a scavenger hunt, Chessa put one coin in each of 10 small boxes. Four coins are quarters, 4 are dimes, and 2 are nickels. How could you simulate choosing one box at random? Would you use the same simulation if you planned to put these coins in your pocket and choose one? Explain your reasoning.

Answer: A possible simulation could be using 10 index cards. Four of the cards could be labeled as quarters, four as dimes, and two nickels. Then cards can be drawn and recorded to simulate choosing a box at random. This simulation could not be used if you planned to put these coins in your pocket and choose one. This is because the size of the coins vary. As we would be able to tell what coin it was in the pocket by feeling its size. And picking one of out your pocket is different than picking a box out of 10 boxes of the same size.

Guided Practice – Page No. 384

Question 1.
A dentist has 400 male and female patients that range in ages from 10 years old to 50 years old and up as shown in the table. What is the experimental probability that the next patient will be female and in the age range 22–39?
Go Math Grade 7 Answer Key Chapter 12 Experimental Probability img 4
\(\frac{□}{□}\)

Answer: The experimental probability is \(\frac{1}{8}\)

Explanation: The total male and female patients are 400.
The age range 22-39 is 50 females
The experimental probability is \(\frac{50}{400}\)
= \(\frac{1}{8}\).

Question 2.
At a car wash, customers can choose the type of wash and whether to use the interior vacuum. Customers are equally likely to choose each type of wash and whether to use the vacuum. Use a simulation to find the experimental probability that the next customer purchases a deluxe wash and no interior vacuum. Describe your simulation.
Go Math Grade 7 Answer Key Chapter 12 Experimental Probability img 5

Answer: The experimental probability is \(\frac{11}{50}\).

Explanation: A possible simulation could be using a standard cube and flipping a coin. If the number cube rolls 1 or 2 it is recorded as a standard wash, if the number cube rolls 3 or 4 it is recorded as a deluxe wash, if the number cube rolls 5 or 6 it is recorded as a superior wash. For the coin toss, heads count as vacuum and tails count as no vacuum.
For example:

Go Math Grade 7 Answer Key Chapter 12 Experimental Probability

So the experimental probability that the next customer purchases a deluxe and no interior vacuum is \(\frac{11}{50}\).

Essential Question Check-In

Question 3.
How do you find the experimental probability of a compound event?

Answer: To find the experimental probability of a compound event, determine the number of occurrences that satisfies both events and then divide it by the total number of trails.

Independent Practice – Page No. 385

Question 4.
Represent Real-World Problems
For the same food trailer mentioned in Example 1, explain how to find the experimental probability that the next order is two pieces of chicken with a green salad.
Go Math Grade 7 Answer Key Chapter 12 Experimental Probability img 6
\(\frac{□}{□}\)

Answer: The experimental probability is \(\frac{1}{10}\).

Explanation: The total number of orders is 330 and in that 33 orders are with 2 pieces green salad, so the experimental probability is
P(2 pieces + green salad) = \(\frac{33}{330}\)
= \(\frac{1}{10}\).

The school store sells spiral notebooks in four colors and three different sizes. The table shows the sales by size and color for 400 notebooks.
Go Math Grade 7 Answer Key Chapter 12 Experimental Probability img 7

Question 5.
What is the experimental probability that the next customer buys a red notebook with 150 pages?
\(\frac{□}{□}\)

Answer: The experimental probability is \(\frac{3}{20}\).

Experiment: The total number of notebooks sold is 400 and in that, red notebooks with 150 pages sold are 60.
So the experimental probability is \(\frac{60}{400}\)
= \(\frac{3}{20}\).

Question 6.
What is the experimental probability that the next customer buys any red notebooks?
\(\frac{□}{□}\)

Answer: The experimental probability is \(\frac{69}{200}\).

Explanation: The total number of notebooks sold is 400 and in that, red notebooks sold are 138.
So the experimental probability that the next customer buys any red notebooks is \(\frac{138}{400}\)
= \(\frac{69}{200}\).

Question 7.
Analyze Relationships
How many possible combined page count and color choices are possible? How does this number relate to the number of page size choices and to the number of color choices?

Answer: 12 is the product of the number of page size choices and the number of color choices.

Explanation: As there are 12 entries in the table, there are 12 possible page count and color combinations. This number relates to the number of page size choices and to the number of color choices by the fact that there are 3-page count choices and 4 colors.
So 3×4= 12.

A middle school English teacher polled random students about how many pages of a book they read per week.
Go Math Grade 7 Answer Key Chapter 12 Experimental Probability img 8

Question 8.
Critique Reasoning
Jennie says the experimental probability that a 7th grade student reads at least 100 pages per week is \(\frac{16}{125}\). What is her error and the correct experimental probability?
\(\frac{□}{□}\)

Answer: The correct experimental probability \(\frac{17}{50}\).

Explanation:
The total number of students is 24+22+30+18+32+53+22+24+25= 250. And the total number of 7th graders that reads at least 100 pages is 32+53= 85. Jennie’s error not including the 7th-grade students that read 150 pages a week. So the experimental probability is
P(7th grade+ al least 100 pages)= \(\frac{85}{250}\)
= \(\frac{17}{50}\).

Question 9.
Analyze Relationships
Based on the data, which group(s) of students should be encouraged to read more? Explain your reasoning.

Answer: 6th and 8th grade should be encouraged to read more.

Explanation: Based on the data, 6th and 8th grade should be encouraged to read more as 6th and 8th grades read 150 pages per week than 7th grade.

H.O.T. – Page No. 386

Focus on Higher Order Thinking

Question 10.
Make a Conjecture
Would you expect the probability for the simple event “rolling a 6” to be greater than or less than the probability of the compound event “rolling a 6 and getting heads on a coin”? Explain.

Answer: Rolling a 6 to be greater than the probability of the compound event.

Explanation: The simple event would have a greater probability than the probability of the compound event. Because to find a compound event you have to multiply the two probabilities in fraction form. Multiplying two fractions that are less than 1 gives a fraction answer that is smaller than the original two fractions. The probability for the simple event of rolling a 6 is 1/6. The probability of the compound event is 1/6×1/2= 1/12 < 1/6.

Question 11.
Critique Reasoning
Donald says he uses a standard number cube for simulations that involve 2, 3, or 6 equal outcomes. Explain how Donald can do this.

Answer:
If a simulation has two options A and B, Donald can let the even number be A and the odd number be B. If a stimulation has 3 outcomes A, Band C Donald can let 1 and 2 be A, 3 and 4 be B, and 5 and 6 be C. If a stimulation has 6 outcomes A, B, C, D, E, and F Donald can let 1 be A 2 be B, 3 be C 4 be D 5 be E, and 6 be F

Question 12.
Draw Conclusions
Data collected in a mall recorded the shoe styles worn by 150 male and for 150 female customers. What is the probability that the next customer is male and has an open-toe shoe (such as a sandal)? What is the probability that the next male customer has an open-toe shoe? Are the two probabilities the same? Explain.
Go Math Grade 7 Answer Key Chapter 12 Experimental Probability img 9

Answer: The probability of the next customer is male and has an open-toe shoe is 11/300. And the probability of male customers having open-toe shoes is 11/150.

Explanation:
The total number of customers is 300 and 11 male customers are with open-toe shoes. So the probability of the next customer is male and has an open-toe shoe is 11/300. And the probability of male customers having open-toe shoes is 11/150. The probabilities are not the same, the first one being a compound event and the second one being a simple event.

Question 13.
What If?
Suppose you wanted to perform a simulation to model the shoe style data shown in the table. Could you use two coins? Explain.
______

Answer: No, two coins cannot be used.

Explanation: No, coins cannot be used for this simulation. As there are two options male and female, for the type of customers and two options open and close toe for the type of shoe. It is not given that the customers are equally likely to wear each kind of shoe. So a coin can only be used to simulate male or female.

Question 14.
Represent Real-World Problems
A middle school is made up of grades 6, 7, and 8, and has about the same number of male and female students in each grade. Explain how to use a simulation to find the experimental probability that the first 50 students who arrive at school are male and 7th graders.

Answer: A possible simulation could be done using a coin to simulate a male or female and a standard number of the cube to simulate a grade. Let tails be the male and heads be the female. 1 and 2 be 6th grade, 3 and 4 be 7th grade, and 5 and 6 be the 8th grade. After flipping the coin and rolling the number cube 50 times and recording the results each time and count the number of times you got male and 7th grade out of 50 trails.

Guided Practice – Page No. 390

Question 1.
A baseball player reaches first base 30% of the times he is at bat. Out of 50 times at bat, about how many times will the player reach first base?
______

Answer: So 15 times will the player reach the first base.

Explanation: As the baseball player reaches first base at 30% out of 50 times at bat, so
30% of 50= 0.3×50
= 15.
So 15 times will the player reach the first base.

Question 2.
The experimental probability that it will rain on any given day in Houston, Texas, is about 15%. Out of 365 days, about how many days can residents predict rain?
______

Answer: 55 days can residents predict rain.

Explanation: As the experimental probability that it will rain is 15% out of 365 days, so
15% of 365= 0.15×365
= 54.75
= 55 days.
So 55 days can residents predict rain.

Question 3.
A catalog store has 6% of its orders returned for a refund. The owner predicts that a new candle will have 812 returns out of the 16,824 sold. Do you agree with this prediction? Explain.
______

Answer: The prediction is incorrect.

Explanation: As the catalog store has 6% of its order and 16,824 are sold, so
6% of 16,824 = 0.06×16,824
= 1009 will return.
As the owner predicts that a new candle will have an 812 return which is less than 1009, so the prediction is incorrect.

Question 4.
On a toy assembly line, 3% of the toys are found to be defective. The quality control officer predicts that 872 toys will be found defective out of 24,850 toys made. Do you agree with this prediction? Explain.
______

Answer: The prediction is incorrect.

Explanation: As 3% are found defective out of 24,850 toys, so
3% of 24,850 = 0.03×24850
= 746 will be defective.
As the quality control officer predicts that 872 toys will be found defective which is greater than 746, so the prediction is incorrect.

Question 5.
A light-rail service claims to be on time 98% of the time. Jeanette takes the light-rail 40 times one month, how many times can she predict she will be on time? Is the light-rail’s claim accurate if she is late 6 times?
______

Answer: Jeanette will be on time about 39 times.

Explanation: As light-rail service claims to be on time 98%, and Jeanette takes the light-rail 40 times one month. So
98% of 40= 0.98×40
= 39.
So Jeanette will be on time about 39 times. if she is late 6 times, then the claim is not accurate. Being late 6 times means she was on-time 34 times and \(\frac{34}{40}\)= 85% which is not close to 98%.

Question 6.
On average, a college claims to accept 18% of its applicants. If the college has 5,000 applicants, predict how many will be accepted. If 885 applicants are accepted, is the college’s claim accurate?
______

Answer: 900 applicants will be accepted.

Explanation: As the college claims to accept 18% of its applicants of 5000 applicants, so 18% of 5000 is
0.18×5000= 900.
About 900 applicants will be accepted. If 885 applicants are accepted, the claim is accurate because 885 is close to 900.

Essential Question Check-In

Question 7.
How do you make predictions using experimental probability?

Answer: To make a prediction using experimental probability multiply the experimental probability by the number of trails to get the prediction number.

Independent Practice – Page No. 391

The table shows the number of students in a middle school at the beginning of the year and the percentage that can be expected to move out of the area by the end of the year.
Go Math Grade 7 Answer Key Chapter 12 Experimental Probability img 10

Question 8.
How many 7th grade students are expected to move by the end of the year? If 12 students actually moved, did more or fewer 7th grade students move than expected? Justify your answer.
______ students

Answer: 8 students from 7th grade are expected to move by the end of the year.

Explanation: As 4% of 7th grades are expected to move by the end of the year, so 4% of 200 is
0.04×200= 8.
If 12 students actually moved, then more than expected would have moved.

Question 9.
Critique Reasoning
The middle school will lose some of its funding if 50 or more students move away in any year. The principal claims he only loses about 30 students a year. Do the values in the table support his claim? Explain.
______

Answer: Yes, the table supports the principal’s claim of 30 students.

Explanation: 2% of 6th graders and 8% of 8th graders are expected to move. So
2% of 250= 0.02×250
= 5.
8% of 150= 0.08×150
= 12
So in total 5+8+12= 25 students are expected to move. And the table supports the principal’s claim of 30 students.

Question 10.
Represent Real-World Problems
An airline knows that, on average, the probability that a passenger will not show up for a flight is 6%. If an airplane is fully booked and holds 300 passengers, how many seats are expected to be empty? If the airline overbooked the flight by 10 passengers, about how many passengers are expected to show up for the flight? Justify your answer.
______

Answer: The number of passengers expected to show up is then 310-19= 291 passengers.

Explanation: As 6% of the 300 seats are expected to be empty, so
6% of 300 = 0.06×300
= 18.
18 seats are expected to be empty. If the airline overbooked the flight by 10 passengers then 300+10= 310 passengers were booked, then 310×0.06= 18.6
= 19
So the number of passengers expected to show up is then 310-19= 291 passengers.

Question 11.
Draw Conclusions
In a doctor’s office, an average of 94% of the clients pay on the day of the appointment. If the office has 600 clients per month, how many are expected not to pay on the day of the appointment? If 40 clients do not pay on the day of their appointment in a month, did more or fewer than the average not pay?
______

Answer:

Explanation: 94% of the clients pay on the day of the appointment for 600 clients, so
94% of 600= 0.94 × 600
= 564
As 564 clients are expected to pay so 600- 564= 36 clients are expected not to pay on the day of the appointment. So if 40 clients do not pay, then this a little more than the average.

Page No. 392

Question 12.
Counterexamples
The soccer coach claimed that, on average, only 80% of the team come to practice each day. The table shows the number of students that came to practice for 8 days. If the team has 20 members, how many team members should come to practice to uphold the coach’s claim? Was the coach’s claim accurate? Explain your reasoning.
Go Math Grade 7 Answer Key Chapter 12 Experimental Probability img 11

Answer: As all the values in the table are greater than 16 except for one value, the claim is not accurate.

Explanation: As the soccer coach claimed that only 80% of the team come to practice each day, and the team has 20 members. So
80% of 20= 0.8×20
= 16.
So 16 players in the team should come to practice to uphold the coach’s claim. As all the values in the table are greater than 16 except for one value, the claim is not accurate. More than 80% come on average to practice each day and more than 16 members on average come to practice.

Question 13.
What’s the Error?
Ronnie misses the school bus 1 out of every 30 school days. He sets up the proportion \(\frac{1}{30}\) = \(\frac{180}{x}\) to predict how many days he will miss the bus in the 180-day school year. What is Ronnie’s error?

Answer: The proportion he sets up is \(\frac{1}{30}\) = \(\frac{180}{X}\) is Ronnie’s error.

Explanation: As Ronnie misses the school bus 1 out of every 30 school days, and the proportion he sets up is \(\frac{1}{30}\) = \(\frac{180}{X}\) which is incorrect. As it should be \(\frac{1}{30}\) = \(\frac{X}{180}\) to respect the form of \(\frac{number of days missed}{total number of days}\)

H.O.T.

Focus on Higher Order Thinking

Question 14.
Persevere in Problem Solving
A gas pump machine rejects 12% of credit card transactions. If this is twice the normal rejection rate for a normal gas pump, how many out of 500 credit cards transactions would a normal gas pump machine reject?
______

Answer: The normal gas machine rejects 30 transactions.

Explanation: If 12% is twice the normal rate, then the normal rate is 6%, so 6% of 500 is
0.06×500= 30.
So the normal gas machine rejects 30 transactions.

Question 15.
Make Predictions
An airline’s weekly flight data showed a 98% probability of being on time. If this airline has 15,000 flights in a year, how many flights would you predict to arrive on time? Explain whether you can use the data to predict whether a specific flight with this airline will be on time.
______

Answer: 14,700 flights we can predict to arrive on time.

Explanation: The airline’s weekly flight data is a 98% probability of being on time, and there are 15,000 flights in a year. So 98% of 15,000 is 0.98×15000 = 14,700.
So 14,700 flights are expected to be on time and 15,000-14,700= 300 flights will not be on time. And we can use the data to predict whether a specific flight with this airline will be on time by determining the number of flights that have not been on time. If about 300 flights have not been on time then we can predict that the specific flight will be on time. If less than 300 flights have not been on time, then you can’t predict with absolute certainty if the specific flight will be on time.

Question 16.
Draw Conclusions
An average response rate for a marketing letter is 4%, meaning that 4% of the people who receive the letter respond to it. A company writes a new type of marketing letter, sends out 2,400 of them, and gets 65 responses. Explain whether the new type of letter would be considered to be a success.

Answer: As we have received fewer responses than expected and thus a new type of letter would be considered to be not successful.

Explanation: The company sends 2400 letters. And the average response rate for marketing is 4%, so we can expect only a 4% response to the 2400 letters. So
4% of 2400= \(\frac{4}{100}\) × 2400
= 4×24
= 96.
Since 96 is greater than 65, we have received fewer responses than expected and thus a new type of letter would be considered to be not successful. We should receive more responses than expected if the letter was successful.

12.1 Probability – Page No. 393

Question 1.
Josue tosses a coin and spins the spinner at the right. What are all the possible outcomes?
Go Math Grade 7 Answer Key Chapter 12 Experimental Probability img 12

Answer: The possible outcomes are heads and 1, heads and 2, tails and 1, tails and 2.

Explanation: The spinner can land on 1 or 2 so the outcomes for the spinner 1 and 2. So the coin can land on heads or tails so the outcomes for the coin are heads and tails. The outcomes for tossing a coin and spinning the spinner are heads and 1, heads and 2, tails and 1, tails and 2.

12.2 Experimental Probability of Simple Events

Question 2.
While bowling with friends, Brandy rolls a strike in 6 out of 10 frames. What is the experimental probability that Brandy will roll a strike in the first frame of the next game?
\(\frac{□}{□}\)

Answer: The experimental probability is \(\frac{3}{5}\).

Explanation: As there are 10 frames, so possible outcomes are 10. And Brandy rolls a strike in 6, so the experimental probability that Brandy will roll a strike in the first frame of the next game is \(\frac{6}{10}\)= \(\frac{3}{5}\).

Question 3.
Ben is greeting customers at a music store. Of the first 20 people he sees enter the store, 13 are wearing jackets and 7 are not. What is the experimental probability that the next person to enter the store will be wearing a jacket?
\(\frac{□}{□}\)

Answer: The experimental probability \(\frac{13}{20}\).

Explanation: The total number of people is 20, and Ben sees 13 people were wearing jackets. So the experimental probability that the next person to enter the store will be wearing a jacket is \(\frac{13}{20}\).

12.3 Experimental Probability of Compound Events

Question 4.
Auden rolled two number cubes and recorded the results.
Go Math Grade 7 Answer Key Chapter 12 Experimental Probability img 13
What is the experimental probability that the sum of the next two numbers rolled is greater than 5?
\(\frac{□}{□}\)

Answer: The experimental probability is latex]\frac{3}{7}[/latex].

Explanation:
The sum of two numbers for every roll is
Roll #1 is 2+1= 3.
Roll #2 is 4+5= 9.
Roll #3 is 3+2= 5.
Roll #4 is 2+2= 4.
Roll #5 is 1+3= 4
Roll #6 is 6+2= 8.
Roll #7 is 5+3= 8.
As there are 7 rolls, so the possible outcomes are 7, so the experimental probability that the sum of the next two numbers rolled is greater than 5 is \(\frac{3}{7}\).

12.4 Making Predictions with Experimental Probability

Question 5.
A player on a school baseball team reaches first base \(\frac{3}{10}\) of the time he is at bat. Out of 80 times at bat, about how many times would you predict he will reach first base?
______

Answer: We can predict that he will reach first base 24 times out 80 times at the bat.

Explanation:
We need to write a proportion:
latex]\frac{3}{10}[/latex]= latex]\frac{X}{80}[/latex].
10×X= 80×3
10×X= 240
X= 24.
So we can predict that he will reach first base 24 times out 80 times at the bat.

Essential Question

Question 6.
How is experimental probability used to make predictions?

Answer:

Selected Response – Page No. 394

Question 1.
A frozen yogurt shop offers scoops in cake cones, waffle cones, or cups. You can get vanilla, chocolate, strawberry, pistachio, or coffee flavored frozen yogurt. If you order a single scoop, how many outcomes are in the sample space?
Options:
a. 3
b. 5
c. 8
d. 15

Answer: The possible outcomes are 3×5= 15.

Explanation: As there is three option for the scoops are cake cones, waffle cones, or cups. And the five flavors are vanilla, chocolate, strawberry, pistachio, or coffee. So the possible outcomes are 3×5= 15.

Question 2.
A bag contains 7 purple beads, 4 blue beads, and 4 pink beads. What is the probability of not drawing a pink bead?
Options:
a. \(\frac{4}{15}\)
b. \(\frac{7}{15}\)
c. \(\frac{8}{15}\)
d. \(\frac{11}{15}\)

Answer: The probability of not drawing a pink bead is \(\frac{11}{15}\).

Explanation: The total number of beads in the bag are 7+4+4= 15 beads. And the pink beads are 4 beads.
The probability of not drawing a pink bead is
P(pink)+P(not pink)= 1
\(\frac{4}{15}\)+ P(not pink)= 1
P(not pink)= 1- \(\frac{4}{15}\)
= \(\frac{15-4}{15}\)
= \(\frac{11}{15}\).

Question 3.
During the month of June, Ava kept track of the number of days she saw birds in her garden. She saw birds on 18 days of the month. What is the experimental probability that she will see birds in her garden on July 1?
Options:
a. \(\frac{1}{18}\)
b. \(\frac{2}{5}\)
c. \(\frac{1}{2}\)
d. \(\frac{3}{5}\)

Answer: The experimental probability that she will see birds in her garden on July 1 is \(\frac{3}{5}\).

Explanation:
As there are 30 days in the month of June, so if Ava saw birds of those days, the experimental probability that she will see birds in her garden on July 1 is \(\frac{18}{30}\)= \(\frac{3}{5}\).

Question 4.
A rectangle has a width of 4 inches and a length of 6 inches. A similar rectangle has a width of 12 inches. What is the length of the similar rectangle?
Options:
a. 8 inches
b. 12 inches
c. 14 inches
d. 18 inches

Answer: The length is 18 inches.

Explanation: The length of the rectangle is 6 inches and the width is 4 inches and similarly width of the other rectangle is 12 inches so the length is
\(\frac{Length}{Width}\)= \(\frac{6}{4}\)= \(\frac{X}{12}\).
4×X= 12×6
4X= 72
X= 18 inches.

Question 5.
The experimental probability of hearing thunder on any given day in Ohio is 30%. Out of 600 days, on about how many days can Ohioans expect to hear thunder?
Options:
a. 90 days
b. 180 days
c. 210 days
d. 420 days

Answer: The number of days is 180 days.

Explanation: We need to find 30%. Out of 600 days
= 0.3×600
= 180 days.
The number of days is 180 days.

Question 6.
Isidro tossed two coins several times and then recorded the results in the table below.
Go Math Grade 7 Answer Key Chapter 12 Experimental Probability img 14
What is the experimental probability that both coins will land on the same side on Isidro’s next toss?
Options:
a. \(\frac{1}{5}\)
b. \(\frac{2}{5}\)
c. \(\frac{3}{5}\)
d. \(\frac{4}{5}\)

Answer: The experimental probability that both coins will land on the same side on Isidro’s next toss is \(\frac{2}{5}\).

Explanation: As there are 5 tosses and possible outcomes are 5. As the coin was landed twice on the same side, so the experimental probability is \(\frac{2}{5}\).

Mini-Task

Question 7.
Magdalena had a spinner that was evenly divided into sections of red, blue, and green. She spun the spinner and tossed a coin several times. The table below shows the results.
Go Math Grade 7 Answer Key Chapter 12 Experimental Probability img 15
a. What are all the possible outcomes?

Answer: The possible outcomes are RH,RT,BH,BT,GH,GT.

Explanation:
The spinner can land on red, blue, and green and the coin can land heads or tails so the possible outcomes are red and heads, red and tails, blue and heads, blue and tails, green and heads and green and tails.

Question 7.
b. What experimental probability did Magdalena find for spinning blue? Give your answer as a fraction in simplest form, as a decimal, and as a percent.

Answer: The experimental probability is 40%.

Explanation: The total trails are 5 and Magdalena spun blue twice,
so the experimental probability is 2/5 = 0.4
= 40%

Question 7.
c. Out of 90 trials, how many times should Magdalena predict she will spin green while tossing tails?
______ times

Answer: We can predict that she will spin green 36 times.

Explanation: The total trails are 5 and Magdalena spun green twice,
so the experimental probability is 2/5.
And out of 90 trails, we can predict that she will spin green
2/5×90
= 18×2
= 36 times.

Conclusion:

We believe the information provided in this article is helpful for you. Refer Go Math Answer Key Grade 7 Chapter 12 Experimental Probability and enhance your math skills. You can also test your skills by solving the questions which are provided at the end of the chapter. All the Best!!!

Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers

go-math-grade-6-chapter-3-understand-positive-and-negative-numbers-answer-key

Enhance your knowledge by practicing the problems from Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers. You can get the free pdfs of Go Math Grade 6 Chapter 3 Understand Positive and Negative Numbers Solution Key. We have provided the Go Math Grade 6 Answer Key in pdf format so that you can practice online and offline mode. Take the given resources as references and score well in the exams.

Go Math Grade 6 Chapter 3 Understand Positive and Negative Numbers Answer Key

Improve your math skills with the help of Go Math 6th Standard Answer Key Chapter 3 Understand Positive and Negative Numbers. Unlimited practice with all the maths questions and answers along with the practice questions. It is mandatory to practice with the Grade 6 Chapter 3 Solution key to score maximum marks in the exams. Check out the links given the below sections before you start your preparation.

Lesson 1: Understand Positive and Negative Numbers

Lesson 2: Compare and Order Integers

Lesson 3: Rational Numbers and the Number Line

Lesson 4: Compare and Order Rational Numbers

Mid-Chapter Checkpoint

Lesson 5: Absolute Value

Lesson 6: Compare Absolute Values

Lesson 7: Rational Numbers and the Coordinate Plane

Lesson 8: Ordered Pair Relationships

Lesson 9: Distance on the Coordinate Plane

Lesson 10: Problem Solving • The Coordinate Plane

Chapter 3 Review/Test

Share and Show – Page No. 141

Graph the integer and its opposite on a number line.

Question 1.
−7
Type below:
__________

Answer:
7

Explanation:
The opposite number of -7 is 7

Question 2.
9
Type below:
__________

Answer:
-9

Explanation:
The opposite number of 9 is -9

Name the integer that represents the situation, and tell what 0 represents in that situation.
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 1

Question 3.
Type below:
__________

Answer:
Integer: 24
0 represents: neither gaining nor losing points

Explanation:
Kerri gained 24 pounds during a round of the game show. So, he has a positive integer.

Question 4.
Type below:
__________

Answer:
Integer: -5
0 represents: Ben neither gains nor loses during the summer

Explanation:
Ben lost 5 points during the summer. He has a negative integer.

Question 5.
Type below:
__________

Answer:
Integer: 35
0 represents: No changes in her savings account.

Explanation:
Marcy deposited $35 in her savings account. She has a positive integer.

On Your Own

Write the opposite of the integer.

Question 6.
−98
Type below:
__________

Answer:
98

Explanation:
The integer −98 is on the left side of 0.
So, the opposite of -98 is 98

Question 7.
0
Type below:
__________

Answer:
0

Explanation:
Opposite of 0 is 0

Question 8.
−53
Type below:
__________

Answer:
53

Explanation:
The integer −53 is on the left side of 0.
So, the opposite of -53 is 53

Name the integer that represents the situation, and tell what 0 represents in that situation.
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 2

Question 9.
Type below:
__________

Answer:
Integer: $850
0 represents: Desmond neither gains nor loses at his summer job

Question 10.
Type below:
__________

Answer:
Integer: -300
0 represents: No change from his checking point

Question 11.
Type below:
__________

Answer:
Integer: 2
0 represents: No change of protons than electrons

Write the opposite of the opposite of the integer.

Question 12.
−23
Type below:
__________

Answer:
-23

Explanation:
The opposite integer of the -23 is 23
The opposite integer of the 23 is -23.
So, the opposite of the opposite of the integer -23 is -23.

Question 13.
17
Type below:
__________

Answer:
17

Explanation:
The opposite integer of the 17 is -17
The opposite integer of the -17 is 17.
So, the opposite of the opposite of the integer 17 is 17.

Question 14.
−125
Type below:
__________

Answer:
-125

Explanation:
The opposite integer of the -125 is 125
The opposite integer of the 125 is -125.
So, the opposite of the opposite of the integer -125 is -125.

Question 15.
Suppose you know a certain number’s distance from zero on the number line. Explain how you could find the number’s distance from its opposite.
Type below:
__________

Answer:
The distance between a number’s place on the number line and 0 is called the number’s [absolute value]. To write the absolute value of a number, use short vertical lines (|) on either side of the number. For example, the absolute value of −5 is written |−5|

Problem Solving + Applications – Page No. 142

Wind makes the air temperature seem colder. The chart gives the wind chill temperature (what the temperature seems like) at several air temperatures and wind speeds. Use the chart for 16–18.
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 3

Question 16.
At 6 a.m., the air temperature was 20°F and the wind speed was 55 mi/hr. What was the wind chill temperature at 6 a.m.?
Type below:
__________

Answer:
At 6 a.m., the air temperature was 20°F and the wind speed was 55 mi/hr.
The winds chill temperature at 6 a.m. is -4

Question 17.
At noon, the air temperature was 15°F and the wind speed was 45 mi/hr. At what air temperature and wind speed would the wind chill temperature be the opposite of what it was at noon?
Type below:
__________

Answer:
If the air temperature was 15°F and the wind speed was 45 mi/hr, the wind chill temperature is -9. The opposite number of -9 is 9.
So, at the air temperature was 25°F and the wind speed was 25 mi/hr, the wind chill temperature is the opposite of what it was at noon.

Question 18.
The wind was blowing 35 mi/hr in both Ashton and Fenton. The wind chill temperatures in the two towns were opposites. If the air temperature in Ashton was 25°F, what was the air temperature in Fenton?
Type below:
__________

Answer:
The wind was blowing 35 mi/hr in both Ashton and Fenton.
If the air temperature in Ashton was 25°F, the wind chill temperature is 7.
The wind chill temperatures in the two towns were opposites.
So, the wind chill temperature in Fenton is -7. So, the air temperature in Fenton was 15°F.

Question 19.
Sense or Nonsense? Claudia states that the opposite of any integer is always a different number than the integer. Is Claudia’s statement sense or nonsense? Explain.
Type below:
__________

Answer:
Claudia is correct.
Because the opposite of any integer is always a different number than the integer.
Example: The opposite of 7 is -7.

Question 20.
For numbers 20a−20d, choose Yes or No to indicate whether the situation can be represented by a negative number.
20a. Death Valley is located 282 feet below sea level.
20b. Austin’s golf score was 3 strokes below par.
20c. The average temperature in Santa Monica in August is 75°F.
20d. Janai withdraws $20 from her bank account.
20a. __________
20b. __________
20c. __________
20d. __________

Answer:
20a. Yes
20b. Yes
20c. No
20d. Yes

Understand Positive and Negative Numbers – Page No. 143

Graph the integer and its opposite on a number line.

Question 1.
−6
Type below:
__________

Answer:
6
grade 6 chapter 3 image 1

Explanation:
The opposite number of -6 is 6

Question 2.
3
Type below:
__________

Answer:
-3
grade 6 chapter 3 image 2

Explanation:
The opposite number of -3 is 3

Question 3.
10
Type below:
__________

Answer:
-10
grade 6 chapter 3 image 3

Explanation:
The opposite number of 10 is -10

Question 4.
−8
Type below:
__________

Answer:
8
grade 6 chapter 3 image 4

Explanation:
The opposite number of -8 is 8

Name the integer that represents the situation, and tell what 0 represents in that situation
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 4

Question 5.
Type below:
__________

Answer:
Integer: -60
0 represents: No changes in the account balance

Explanation:

Question 6.
Type below:
__________

Answer:
Integer: 12
0 represents: neither gaining nor losing points

Explanation:

Write the opposite of the opposite of the integer.

Question 7.
−20
Type below:
__________

Answer:
-20

Explanation:
The opposite integer of the -20 is 20
The opposite integer of the 20 is -20.
So, the opposite of the opposite of the integer -20 is -20

Question 8.
4
Type below:
__________

Answer:
4

Explanation:
The opposite integer of the 4 is -4
The opposite integer of the -4 is 4.
So, the opposite of the opposite of the integer -4 is 4.

Question 9.
95
Type below:
__________

Answer:
95

Explanation:
The opposite integer of the 95 is -95
The opposite integer of the -95 is 95.
So, the opposite of the opposite of the integer 95 is 95.

Question 10.
−63
Type below:
__________

Answer:
-63

Explanation:
The opposite integer of the -63 is 63
The opposite integer of the 63 is -63.
So, the opposite of the opposite of the integer -63 is -63.

Problem Solving

Question 11.
Dakshesh won a game by scoring 25 points. Randy scored the opposite number of points as Dakshesh. What is Randy’s score?
Type below:
__________

Answer:
Randy’s score -25.

Explanation:
Dakshesh won a game by scoring 25 points. Randy scored the opposite number of points as Dakshesh.
The opposite number of 25 is -25

Question 12.
When Dakshesh and Randy played the game again, Dakshesh scored the opposite of the opposite of his first score. What is his score?
Type below:
__________

Answer:
25 points

Explanation:
When Dakshesh and Randy played the game again, Dakshesh scored the opposite of the opposite of his first score.
The opposite of the 25 is -25.
The opposite of the -25 is 25.
The opposite of the opposite of his first score is 25

Question 13.
Give three examples of when negative numbers are used in daily life.
Type below:
__________

Answer:
1) negative numbers in weather reports and on food packaging. The temperature -5°C is ‘negative five degrees’ and it means 5 degrees below zero.
2) The floors as you go down in a lift, starting on the third floor you’ll see:
3, 2, 1, 0, -1, -2.
In this example building, -2 is the second floor underground
3) When you spend more money than you have in your bank account it shows up as a negative number.

Lesson Check – Page No. 144

Name the integers that represent each situation.

Question 1.
During their first round of golf, Imani was 7 strokes over par and Peter was 8 strokes below par.
Type below:
__________

Answer:
In the first round of golf, Imani has scored 7 strokes over par. So, it is represented by 7.
Peter was scored 8 strokes below par. So, it is represented by -8.
Therefore, the answer is 7 and -8.

Question 2.
Wyatt earned $15 baby-sitting on Saturday. Wilson spent $12 at the movies.
Type below:
__________

Answer:
He has $3 dollars left because you take 12 from 15 and you get 3
$15 – $12 = $3

Spiral Review

Question 3.
Mr. Nolan’s code for his ATM card is a 4-digit number. The digits of the code are the prime factors of 84 listed from least to greatest. What is the code for Mr. Nolan’s ATM card?
Type below:
__________

Answer:
2237

Explanation:
Mr.Nolan’s code for his ATM card is a 4- digit number.
The digits of the code are the prime factors of 84 listed from least to greatest.
In order to find the code, we have to find the prime factors of 84.
The prime factors of 84 are 2,2,3 and 7.
Therefore, the code=2237

Question 4.
Over a four-year period, a tree grew 2.62 feet. If the tree grows at a constant rate, how many feet did the tree grow each year?
Type below:
__________

Answer:
0.655 feet

Explanation:
Each year the tree grows
( 2.62 ÷ 4 ) feet
= 0.655 feet

Question 5.
Omarion has \(\frac{9}{10}\) of the pages in a book remaining to read for school. He reads \(\frac{2}{3}\) of the remaining pages over the weekend. What fraction of the book does Omarion read over the weekend?
Type below:
__________

Answer:
\(\frac{3}{5}\)

Explanation:
Omarion has 9/10 of pages in a book remaining to read for school and he reads 2/3 of the remaining pages over the weekend.
The fraction of the book trade over the weekend = the fraction of the pages read over the weekend multiplied by the fraction of the book that is remaining to be read.
Therefore, the fraction of the book that Omarion trad over the weekend is 2/3 × 9/10 = 3/5
Thus, the required fraction of the book that Omarion trad over the weekend is 3/5

Question 6.
Marianne has \(\frac{5}{8}\) pound of peas. She cooks \(\frac{2}{3}\) of those peas for 5 people. If each person is served an equal amount, how much peas did each person get?
Type below:
__________

Answer:
\(\frac{1}{12}\) pounds

Explanation:
Marianne has \(\frac{5}{8}\) pound of peas. IShe cooks \(\frac{2}{3}\) of those peas for 5 people.
Marianne cooks 5/8 × 2/3 = 5/12 pounds.
(5/12)/5 = 1/12 pounds

the answer is

Share and Show – Page No. 147

Compare the numbers. Write < or >.

Question 1.
8 _____ 6

Answer:
–8 < 6

Explanation:
-8 is to the left of 6 on the number line.
So, -8 is less than 6.

Question 2.
1 _____ 8

Answer:
1 > –8

Explanation:
1 is to the right of -8 on the number line.
So, 1 is greater than -8.

Question 3.
4 _____ 0

Answer:
-4 < 0

Explanation:
-4 is to the left of 0 on the number line.
So, -4 is less than 0.

Question 4.
3 _____ 7

Answer:
3 > -7

Explanation:
3 is to the right of -7 on the number line.
So, 3 is greater than -7.

Order the numbers from least to greatest.

Question 5.
4, 3, 7
Type below:
__________

Answer:
-7, -3, 4

Explanation:
-7 is to the left of -3 on the number line. -3 is to the left of 4 on the number line.
So, -7 < -3 < 4

Question 6.
0, 1, 3
Type below:
__________

Answer:
-1, 0, 3

Explanation:
-1 is to the left of 0 on the number line. 0 is to the left of 3 on the number line.
So, -1 < 0 < 3

Question 7.
5, 3, 9
Type below:
__________

Answer:
-9, -5, -3

Explanation:
-9 is to the left of -5 on the number line. -5 is to the left of -3 on the number line.
So, -9 < -5 < -3

Order the numbers from greatest to least.

Question 8.
1, 4, 2
Type below:
__________

Answer:
2, -1, -4

Explanation:
2 is to the right of -1 on the number line. -1 is to the right of -4 on the number line.
So, 2 > -1 > -4

Question 9.
5, 0, 10
Type below:
__________

Answer:
10, 5, 0

Explanation:
10 is to the right of 5 on the number line. 5 is to the right of 0 on the number line.
So, 10 > 5 > 0

Question 10.
5, 4, 3
Type below:
__________

Answer:
-3, -4, -5

Explanation:
-3 is to the right of -4 on the number line. -4 is to the right of -5 on the number line.
So, -3 > -4 > -5

On Your Own

Order the numbers from least to greatest.

Question 11.
2, 1, 1
Type below:
__________

Answer:
-1, 1, 2

Explanation:
-1 is to the left of 1 on the number line. 1 is to the left of 2 on the number line.
So, -1 < 1 < 2

Question 12.
6, 12, 30
Type below:
__________

Answer:
-12, -6, 30

Explanation:
-12 is to the left of -6 on the number line. -6 is to the left of 30 on the number line.
So, -12 < -6 < 30

Question 13.
15, 9, 20
Type below:
__________

Answer:
-20, -15, -9

Explanation:
-20 is to the left of -15 on the number line. -15 is to the left of -9 on the number line.
So, -20 < -15 < -9

Order the number from greatest to least.

Question 14.
13, 14, 14
Type below:
__________

Answer:
14, -13, -14

Explanation:
14 is to the right of -13 on the number line. -13 is to the right of -14 on the number line.
So, 14 > -13 > -14

Question 15.
20, 30, 40
Type below:
__________

Answer:
-20, -30, -40

Explanation:
-20 is to the right of -30 on the number line. -30 is to the right of -40 on the number line.
So, -20 > -30 > -40

Question 16.
9, 37, 0
Type below:
__________

Answer:
9, 0, -37

Explanation:
9 is to the right of 0 on the number line. 0 is to the right of -37 on the number line.
So, 9 > 0 > -37

Question 17.
Saturday’s low temperature was −6°F. Sunday’s low temperature was 3°F. Monday’s low temperature was −2°F. Tuesday’s low temperature was 5°F. Which day’s low temperature was closest to 0°F?
Type below:
__________

Answer:
Monday’s temperature was closest to 0°F

Explanation:
Saturday’s low temperature was −6°F. Sunday’s low temperature was 3°F. Monday’s low temperature was −2°F. Tuesday’s low temperature was 5°F.
-2 is closest to 0. So, Monday’s temperature was closest to 0°F.

Question 18.
Use Symbols Write a comparison using < or > to show that South America’s Valdes Peninsula (elevation −131 ft) is lower than Europe’s Caspian Sea (elevation −92 ft).
Type below:
__________

Answer:
South America’s Valdes Peninsula < Europe’s Caspian Sea

Explanation:
South America’s Valdes Peninsula (elevation −131 ft) is lower than Europe’s Caspian Sea (elevation −92 ft).
-131 < -92.
So, South America’s Valdes Peninsula < Europe’s Caspian Sea

Problem Solving + Applications – Page No. 148

What’s the Error?

Question 19.
In the game of golf, the player with the lowest score wins. Raheem, Erin, and Blake played a game of miniature golf. The table shows their scores compared to par.
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 5
At the end of the game, they wanted to know who had won.
Look at how they solved the problem. Find their error.
STEP 1: 0 is greater than both −1 and −5. Since Raheem had the highest score, he did not win.
STEP 2: −1 is less than −5, so Blake’s score was less than Erin’s score. Since Blake had the lowest score, he won the game.
Correct the error by ordering the scores from least to greatest.
So, _____ won. _____ came in second. _____ came in third.
Describe the error that the players made.
Type below:
__________

Answer:
Step 2 is wrong.
In step 2, they mentioned that -1 is less than −5. But -1 is greater than -5.
So, Erin won. Blake came in second. Raheem came in third.

Question 20.
Jasmine recorded the low temperatures for 3 cities.
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 6
Draw a dot on the number line to represent the low temperature of each city. Write the letter of the city above the dot.
Type below:
__________

Answer:
grade 6 chapter 3 image 5

Explanation:
6 > 2 > -4

Compare and Order Integers – Page No. 149

Compare the numbers. Write < or >.

Question 1.
4 ____ 5

Answer:
-4 > -5

Explanation:
-4 is to the right of -5 on the number line.
So, -4 is greater than -5.

Question 2.
0 ____ 1

Answer:
0 > -1

Explanation:
0 is to the right of -1 on the number line.
So, 0 is greater than -1.

Question 3.
4 ____ 6

Answer:
4 > -6

Explanation:
4 is to the right of -6 on the number line.
So, 4 is greater than -6.

Question 4.
9 ____ 8

Answer:
-9 < -8

Explanation:
-9 is to the left of -8 on the number line.
So, -9 is less than -8.

Question 5.
2 ____ 10

Answer:
2 > -10

Explanation:
2 is to the right of -10 on the number line.
So, 2 is greater than -10.

Question 6.
12 ____ 11

Answer:
-12 < -11

Explanation:
-12 is to the left of -11 on the number line.
So, -12 is less than -11.

Question 7.
1 ____ 10

Answer:
1 > -10

Explanation:
1 is to the right of -10 on the number line.
So, 1 is greater than -10.

Order the numbers from least to greatest.

Question 8.
3, 2, 7
Type below:
__________

Answer:
-7, -2, 3

Explanation:
-7 is to the left of -2 on the number line. -2 is to the left of 3 on the number line.
So, -7 < -2 < 3

Question 9.
0, 2, 5
Type below:
__________

Answer:
-5, 0, 2

Explanation:
-5 is to the left of 0 on the number line. 0 is to the left of 2 on the number line.
So, -5 < 0 < 2

Question 10.
9, 12, 10
Type below:
__________

Answer:
-12, -10, -9

Explanation:
-12 is to the left of -10 on the number line. -10 is to the left of -9 on the number line.
So, -12 < -10 < -9

Question 11.
2, 3, 4
Type below:
__________

Answer:
-4, -3, -2

Explanation:
-4 is to the left of -3 on the number line. -3 is to the left of -2 on the number line.
So, -4 < -3 < -2

Question 12.
1, 6, 13
Type below:
__________

Answer:
-13, -6, 1

Explanation:
-13 is to the left of -6 on the number line. -6 is to the left of 1 on the number line.
So, -13 < -6 < 1

Question 13.
5, 7, 0
Type below:
__________

Answer:
0, 5, 7

Explanation:
0 is to the left of 5 on the number line. 5 is to the left of 7 on the number line.
So, 0 < 5 < 7

Question 14.
0, 13, 13
Type below:
__________

Answer:
-13, 0, 13

Explanation:
-13 is to the left of 0 on the number line. 0 is to the left of 13 on the number line.
So, -13 < 0 < 13

Question 15.
11, 7, 5
Type below:
__________

Answer:
-11, -5, 7

Explanation:
-11 is to the left of -5 on the number line. -5 is to the left of 7 on the number line.
So, -11 < -5 < 7

Question 16.
9, 8, 1
Type below:
__________

Answer:
-9, -8, 1

Explanation:
-9 is to the left of -8 on the number line. -8 is to the left of 1 on the number line.
So, -9 < -8 < 1

Problem Solving

Question 17.
Meg and Derek played a game. Meg scored 11 points, and Derek scored 4 points. Write a comparison to show that Meg’s score is less than Derek’s score.
Type below:
__________

Answer:
-11 < 4

Explanation:
Meg and Derek played a game. Meg scored -11 points, and Derek scored 4 points.
-11 < 4

Question 18.
Misha is thinking of a negative integer greater than −4. What number could she be thinking of?
Type below:
__________

Answer:
-3, -2, -1

Explanation:
Misha is thinking of a negative integer greater than −4.
-3, -2, -1

Question 19.
Explain how to use a number line to compare two negative integers. Give an example.
Type below:
__________

Answer:
-> On a number line, numbers always increase (become “more positive”) to the right and decrease (become “more negative”) to the left.
-> Numbers to the right are greater than numbers to the left and numbers to the left are less than numbers to the right.
Example: 2 > -10
2 is to the right of -10 on the number line.
So, 2 is greater than -10.

Lesson Check – Page No. 150

Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 7
The chart shows the high temperatures for seven cities on one day in January.

Question 1.
Which city had the lower temperature, Helena or Chicago?
Type below:
__________

Answer:
Helena had a lower temperature

Explanation:
Helena = -1
Chicago = 2
-1 < 2
So, Helena had a lower temperature.

Question 2.
Write the temperatures of the following cities in order from greatest to least: Denver, Helena, Lansing.
Type below:
__________

Answer:
Lansing, Helena, Denver

Explanation:
Denver = -8
Helena = -1
Lansing = 3
3 > -1 > -8
So, Lansing, Helena, Denver is the answer.

Spiral Review

Question 3.
Fiona starts at the beginning of a hiking trail and walks \(\frac{4}{5}\) mile. She counts the mileage markers that are placed every \(\frac{1}{10}\) mile along the trail. How many markers does she count?
______ markers

Answer:
8 markers

Explanation:
Fiona starts at the beginning of a hiking trail and walks \(\frac{4}{5}\) mile. She counts the mileage markers that are placed every \(\frac{1}{10}\) mile along the trail.
Number of markers = (4/5)/(1/10) = 4/5 × 10 = 8

Question 4.
If Amanda hikes at an average speed of 2.72 miles per hour, how long will it take her to hike 6.8 miles?
______ hours

Answer:
2.5 hours

Explanation:
speed times time = distance
distance = 6.8
speed = 2.72
time = s
2.72 times s = 6.8
divide both sides by 2.72
s = 2.5
The answer is 2.5 hours

Question 5.
The area of a rectangle is 5 \(\frac{4}{5}\) square meters. The width of the rectangle is 2 \(\frac{1}{4}\) meter. Which is the best estimate for the length of the rectangle?
______ meters

Answer:
2 \(\frac{26}{45}\) meters

Explanation:
Since the area of a rectangle is, A = l × b
A = 5 \(\frac{4}{5}\) square meters
b = 2 \(\frac{1}{4}\) meter
5 \(\frac{4}{5}\) = l × 2 \(\frac{1}{4}\)
l = \(\frac{29 × 4}{9 × 5}\) = \(\frac{116}{45}\) = 2 \(\frac{26}{45}\)

Question 6.
Lillian bought 2.52 pounds of tomatoes and 1.26 pounds of lettuce to make a salad for 18 people. If each person got the same amount of salad, how much salad did each person get?
______ pounds per person

Answer:
0.21 pounds per person

Explanation:
Lillian bought 2.52 pounds of tomatoes and 1.26 pounds of lettuce to make a salad for 18 people.
2.52 pounds + 1.26 pounds = 3.78 pounds of salad ÷ 18 people = 0.21 pounds of salad per person

Share and Show – Page No. 153

Graph the number on the horizontal number line.

Question 1.
2.25
Type below:
__________

Answer:
grade 6 chapter 3 image 6

Explanation:
-2.25 is in between -2 and -3.
-2.25 is between -2 and -2.5

Question 2.
1 \(\frac{5}{8}\)
Type below:
__________

Answer:
grade 6 chapter 3 image 7

Explanation:
-1 \(\frac{5}{8}\) is in between -1 and -2.
-1 \(\frac{5}{8}\) is closer to -2.

Question 3.
\(\frac{1}{2}\)
Type below:
__________

Answer:
grade 6 chapter 3 image 8

Explanation:
\(\frac{1}{2}\) is in between 0 and 1
\(\frac{1}{2}\) = 0.5

On Your Own

Practice: Copy and Solve Graph the number on a vertical number line.

Question 4.
0.6
Type below:
__________

Answer:
grade 6 chapter 3 image 13

Explanation:
0.6 is in between 0 and 1.
0.6 is closer to 1

Question 5.
1.25
Type below:
__________

Answer:
grade 6 chapter 3 image 10

Explanation:
-1.25 is in between -1 and -2
-1.25 is closer to -1.

Question 6.
1 \(\frac{1}{2}\)
Type below:
__________

Answer:
grade 6 chapter 3 image 11

Explanation:
-1 \(\frac{1}{2}\) is in between -1 and -2
-1 \(\frac{1}{2}\) = -1.5

Question 7.
0.3
Type below:
__________

Answer:
grade 6 chapter 3 image 14

Explanation:
0.3 is in between 0 and 1
0.3 is closer to 0

Question 8.
0.7
Type below:
__________

Answer:
grade 6 chapter 3 image 15

Explanation:
-0.7 is in between 0 and -1
-0.7 is closer to -1

Question 9.
1.4
Type below:
__________

Answer:
grade 6 chapter 3 image 16

Explanation:
1.4 is in between 1 and 2
1.4 is closer to 1

Question 10.
0.5
Type below:
__________

Answer:
grade 6 chapter 3 image 17

Explanation:
−0.5 is in between 0 and -1

Question 11.
− \(\frac{1}{4}\)
Type below:
__________

Answer:
grade 6 chapter 3 image 19

Explanation:
− \(\frac{1}{4}\) is in between 0 and -1
-0.25 is closer to 0

State whether the numbers are on the same or opposite sides of zero.

Question 12.
1.38 and 2.9
Type below:
__________

Answer:
Opposite

Explanation:
-1.38 is a negative number.
2.9 is a positive number.
So, both numbers are on opposite sides of zero.

Question 13.
3 \(\frac{9}{10}\) and 0.99
Type below:
__________

Answer:
Same

Explanation:
−3 \(\frac{9}{10}\) is a negative number.
−0.99 is a negative number.
So, both numbers are on the same sides of zero.

Question 14.
\(\frac{5}{6}\) and 4.713
Type below:
__________

Answer:
Opposite

Explanation:
−4.713 is a negative number.
\(\frac{5}{6}\) is a positive number.
So, both numbers are on opposite sides of zero.

Identify a decimal and a fraction in simplest form for the point.
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 8

Question 15.
Point A
Type below:
__________

Answer:
-1.0

Explanation:
The point A is located at -1.0 = -1

Question 16.
Point B
Type below:
__________

Answer:
0.75 = 3/4

Explanation:
Point B is between 0.5 and 1. It is 0.75

Question 17.
Point C
Type below:
__________

Answer:
-0.25 = 1/4

Explanation:
Point C is in between 0 and -0.5
-0.25

Question 18.
Point D
Type below:
__________

Answer:
-1.25 = 5/4

Explanation:
Point D is in between -1 and -1.5.
-1.25

Question 19.
The roots of 6 corn plants grew to 3.54 feet, 2 \(\frac{4}{5}\) feet, 3.86 feet, 4 \(\frac{1}{8}\) feet, 4.25 feet, and 2 \(\frac{2}{5}\) feet. How many corn plants had roots between 3 and 4 feet deep?
______ plants

Answer:
2 plants

Explanation:
The roots of 6 corn plants grew to −3.54 feet, −2 \(\frac{4}{5}\) feet, −3.86 feet, −4 \(\frac{1}{8}\) feet, −4.25 feet, and −2 \(\frac{2}{5}\) feet.
−3.54 feet, −3.86 feet,
2 corn plants had roots between 3 and 4 feet deep.

Problem Solving + Applications – Page No. 154

A star’s magnitude is a number that measures the star’s brightness. Use the table of star magnitudes for 20–22.
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 9

Question 20.
Between what two integers is the magnitude of Canopus?
Type below:
__________

Answer:
-0.72 is between -0.04 and -1.46

Explanation:
Canopus = -0.72
-0.72 is between -0.04 and -1.46

Question 21.
Model Mathematics
Graph the magnitude of Betelgeuse on the number line.
Type below:
__________

Answer:
grade 6 chapter 3 image 20

Explanation:
Betelgeuse = 0.7

Question 22.
What’s the Error?
Jacob graphed the magnitude of Sirius on the number line. Explain his error. Then graph the magnitude correctly.
Type below:
__________

Answer:
grade 6 chapter 3 image 21

Explanation:
Sirius = -1.46

Question 23.
The flag pole is located at point 0 on a map of Orange Avenue. Other points of interest on Orange Avenue are located on the number line based on their distances, in miles to the right of the flag pole (positive numbers) or to the left of the flag pole (negative numbers). Graph and label each location on the number line.
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 10
Type below:
__________

Answer:
grade 6 chapter 3 image 22

Explanation:
0.4 is the right side of the 0.
1.8 is the right side of the 0.
-1 is the left side of the 0.
-1.3 is the left side of the 0.

Rational Numbers and the Number Line – Page No. 155

Graph the number on the number line.

Question 1.
2 \(\frac{3}{4}\)
Type below:
__________

Answer:
grade 6 chapter 3 Page no. 155 image 1

Explanation:
The number is between the integers -3 and -2.
It is closer to the integer -3.

Question 2.
\(\frac{-1}{4}\)
Type below:
__________

Answer:
grade 6 chapter 3 Page no. 155 image 2

Explanation:
The number is between the integers -0.3 and -0.2.
It is closer to the integer -0.25.

Question 3.
0.5
Type below:
__________

Answer:
grade 6 chapter 3 Page no. 155 image 3JPG

Explanation:
The number is between integers 0 and -1.
It is closer to the integer -0.5.

Question 4.
1.75
Type below:
__________

Answer:
grade 6 chapter 3 Page no. 155 image 4

Explanation:
The number is between integers 1 and 2.
It is closer to the integer 1.75.

Question 5.
1 \(\frac{1}{2}\)
Type below:
__________

Answer:
grade 6 chapter 3 Page no. 155 image 5

Explanation:
The number is between integers 1 and 2.
It is closer to the integer 1.5.

State whether the numbers are on the same or opposite sides of zero.

Question 6.
2.4 and 2.3
Type below:
__________

Answer:
Opposite

Explanation:
-2.4 is a negative number.
2.3 is a positive number.
So, both numbers are on opposite sides of zero.

Question 7.
2 \(\frac{1}{5}\) and 1
Type below:
__________

Answer:
Same

Explanation:
−2 \(\frac{1}{5}\) is a negative number.
-1 is a negative number.
So, both numbers are on the same sides of zero.

Question 8.
0.3 and 0.3
Type below:
__________

Answer:
opposite

Explanation:
-0.3 is a negative number.
0.3 is a positive number.
So, both numbers are on opposite sides of zero.

Question 9.
0.44 and \(\frac{2}{3}\)
Type below:
__________

Answer:
Same

Explanation:
0.44 is a positive number.
\(\frac{2}{3}\) is a positive number.
So, both numbers are on the same sides of zero.

Write the opposite of the number.

Question 10.
5.23
Type below:
__________

Answer:
5.23

Explanation:
The opposite number of -5.23 is 5.23

Question 11.
\(\frac{4}{5}\)
Type below:
__________

Answer:
–\(\frac{4}{5}\)

Explanation:
The opposite number of \(\frac{4}{5}\) is –\(\frac{4}{5}\)

Question 12.
−5
Type below:
__________

Answer:
5

Explanation:
The opposite number of -5 is 5

Question 13.
2 \(\frac{2}{3}\)
Type below:
__________

Answer:
2 \(\frac{2}{3}\)

Explanation:
The opposite number of −2 \(\frac{2}{3}\) is 2 \(\frac{2}{3}\)

Problem Solving

Question 14.
The outdoor temperature yesterday reached a low of −4.5° F. Between what two integers was the temperature?
Type below:
__________

Answer:
An integer is a whole number. -4.5 is not a whole number.
-4.5 is in between -4 and the integer below it is -5.

Question 15.
Jacob needs to graph 6 \(\frac{2}{5}\) on a horizontal number line. Should he graph it to the left or right of 6?
Type below:
__________

Answer:
left

Explanation:
It will on the left because it is negative and on a number line the left side is the least side.

Question 16.
Describe how to plot 3 \(\frac{3}{4}\) on a number line.
Type below:
__________

Answer:
On the number line, negative numbers go to the left. Since -3 3/4 is negative, go 3 spaces to the left.
If there are half marks in between the numbers, plot the point near the half mark. If it’s -3 3/4, count 3 spaces, then go to the half mark of -3 to -4, and plot the 3/4 in between the -3 and -4 half mark. If there is no half mark, place it near the -4 mark.
The red line represents the half mark, the blue line represents where the point would go. Notice how when negative, the numbers go higher as they go left.
grade 6 chapter 3 Page no. 155 image 5

Lesson Check – Page No. 156

Question 1.
What number is the opposite of 0.2?
Type below:
__________

Answer:
-0.2

Explanation:
The opposite of 0.2 is -0.2

Question 2.
Between which two integers would you locate −3.4 on a number line?
Type below:
__________

Answer:
-3.4 is located between -3 and -4

Explanation:
Positive 3.4 lies between 3 and 4 on the number line. It is more than 3 but less than 4. 3.4 is further from 0 than just 3. In the same way and because of the symmetrical arrangement of numbers on the number line, -3.4 lies between -3 and -4.

Spiral Review

Question 3.
Yemi used these pattern blocks to solve a division problem. He found a quotient of 7. Which division problem was he solving?
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 11
Type below:
__________

Answer:
7

Explanation:
3 1/2 ÷ 1/2
First, we transform the mixed number into a fraction, 3 1/2 = 7/2
Then, we divide
7/2 ÷ 1/2 = 7
The quotient of the first division is 7.

Question 4.
Eric had 2 liters of water. He gave 0.42 liter to his friend and then drank 0.32 liter. How much water does he have left?
______ liters

Answer:
1.26 liters

Explanation:
Eric had 2 liters of water. He gave 0.42 liter to his friend and then drank 0.32 liter.
2 – 0.42 – 0.32 = 1.26 L

Question 5.
To pass a math test, students must correctly answer at least 0.6 of the questions. Donald’s score is \(\frac{5}{8}\), Karen’s score is 0.88, Gino’s score is \(\frac{3}{5}\) and Sierra’s score is \(\frac{4}{5}\). How many of the students passed the test?
Type below:
__________

Answer:
4

Explanation:
Donald’s score of 5/8 is equal to 0.625.
Gino scored 3/5 which is 0.6.
Sierra’s score of 4/5 equals 0.8.
Karen’s score is already given, and 0.88 is greater than 0.6.
None of the students obtained lower than 0.6.
If at least does not include scores equal to 0.6, and only scores greater than 0.6, then Gino possibly failed this math test.
If a passing score is equal to or greater than 0.6, then all four students passed the test.

Question 6.
Jonna mixes \(\frac{1}{4}\) gallon of orange juice and \(\frac{1}{2}\) gallon of pineapple juice to make punch. Each serving is \(\frac{1}{16}\) gallon. How many servings can Jonna make?
_____ servings

Answer:
12 servings

Explanation:
The number of a gallon of orange juice is mixed to make punch is given by 1/4
The number of a gallon of pineapple juice is mixed to make punch is given by 1/2
The number of gallon in each serving is given by 1/16
1/4 + 1/2 = 3/4
3/4 ÷ 1/16 = 12
So, there are 12 servings which can be made by Jonna.

Share and Show – Page No. 159

Compare the numbers. Write < or >.

Question 1.
0.3 _____ 0.2

Answer:
-0.3 < 0.2

Explanation:
-0.3 is to the left of 0.2 on the number line.
So, -0.3 is less than 0.2.

Question 2.
\(\frac{1}{3}\) _____ \(\frac{−2}{5}\)

Answer:
\(\frac{1}{3}\) > \(\frac{−2}{5}\)

Explanation:
\(\frac{1}{3}\) is to the right of \(\frac{−2}{5}\) on the number line.
So, \(\frac{1}{3}\) is greater than \(\frac{−2}{5}\).

Question 3.
0.8 _____ 0.5

Answer:
−0.8 < −0.5

Explanation:
-0.8 is to the left of -0.5 on the number line.
So, -0.8 is less than -0.5.

Question 4.
\(\frac{−3}{4}\) _____ −0.7

Answer:
\(\frac{−3}{4}\) < −0.7

Explanation:
\(\frac{−3}{4}\) is to the left of −0.7 on the number line.
So, \(\frac{−3}{4}\) is less than −0.7.

Order the numbers from least to greatest.

Question 5.
3.6, 7.1, 5.9
Type below:
__________

Answer:
-7.1, -5.9, 3.6

Explanation:
-7.1 is to the left of -5.9 on the number line. -5.9 is to the left of 3.6 on the number line.
So, -7.1 < -5.9 < 3.6

Question 6.
\(\frac{-6}{7}, \frac{1}{9}, \frac{-2}{3}\)
Type below:
__________

Answer:
\(\frac{-6}{7}, \frac{-2}{3}, \frac{1}{9}\)

Explanation:
-6/7 = -0.857
1/9 = 0.111
-2/3 = -0.666
-6/7 is to the left of -2/3 on the number line. -2/3 is to the left of 1/9 on the number line.
So, -6/7 < -2/3 < 1/9

Question 7.
5 \(\frac{1}{4}\), 6.5, 5.3
Type below:
__________

Answer:
-6.5, -5.3, −5 \(\frac{1}{4}\)

Explanation:
−5 \(\frac{1}{4}\) = -21/4 = -5.25
-6.5 is to the left of -5.3 on the number line. -5.3 is to the left of -5 \(\frac{1}{4}\) on the number line.
-6.5 < -5.3 < -5.25

On Your Own

Compare the numbers. Write < or >.

Question 8.
\(\frac{−1}{2}\) _____ \(\frac{−3}{7}\)

Answer:
\(\frac{−1}{2}\) < \(\frac{−3}{7}\)

Explanation:
\(\frac{−1}{2}\) = -0.5
\(\frac{−3}{7}\) = -0.428
\(\frac{−1}{2}\) is to the left of \(\frac{−3}{7}\) on the number line.
So, \(\frac{−1}{2}\) is less than \(\frac{−3}{7}\).

Question 9.
23.7 _____ 18.8

Answer:
−23.7 < −18.8

Explanation:
−23.7 is to the left of −18.8 on the number line.
So, −23.7 is less than −18.8.

Question 10.
3 \(\frac{1}{4}\) _____ 4.3

Answer:
−3 \(\frac{1}{4}\) > −4.3

Explanation:
−3 \(\frac{1}{4}\) = -13/4 = -3.25
−3 \(\frac{1}{4}\) is to the right of −4.3 on the number line.
So, −3 \(\frac{1}{4}\) is greater than −4.3.

Order the numbers from greatest to least.

Question 11.
2.4, 1.9, 7.6
Type below:
__________

Answer:
1.9, -2.4, -7.6

Explanation:
1.9 is to the right of -2.4 on the number line. -2.4 is to the right of -7.6 on the number line.
So, 1.9 > -2.4 > -7.6

Question 12.
\(\frac{-2}{5}, \frac{-3}{4}, \frac{-1}{2}\)
Type below:
__________

Answer:
\(\frac{-2}{5}, \frac{-1}{2}, \frac{-3}{4}\)

Explanation:
-2/5 = -0.4; -3/4 = -0.75; -1/2 = -0.5
-2/5 is to the right of -1/2 on the number line. -1/2 is to the right of -3/4 on the number line.
So, -2/5 > -1/2 > -3/4

Question 13.
3, 6 \(\frac{4}{5}\), 3 \(\frac{2}{3}\)
Type below:
__________

Answer:
3, −3 \(\frac{2}{3}\), −6 \(\frac{4}{5}\)

Explanation:
−6 \(\frac{4}{5}\) = -34/5 = -6.8
−3 \(\frac{2}{3}\) = -11/3 = -3.666
3 is to the right of -3 \(\frac{2}{3}\) on the number line. -3 \(\frac{2}{3}\) is to the right of −6 \(\frac{4}{5}\) on the number line.
So, 3 > −3 \(\frac{2}{3}\) > −6 \(\frac{4}{5}\)

Question 14.
Last week, Wednesday’s low temperature was −4.5°F, Thursday’s low temperature was −1.2°F, Friday’s low temperature was −2.7°F, and Saturday’s low temperature was 0.5°F. The average low temperature for the week was −1.5°F. How many of these days had low temperatures less than the average low temperature for the week?
_____ days

Answer:
2 days

Explanation:
Last week, Wednesday’s low temperature was −4.5°F, Thursday’s low temperature was −1.2°F, Friday’s low temperature was −2.7°F, and Saturday’s low temperature was 0.5°F. The average low temperature for the week was −1.5°F.
-4.5 < -1.5; -2.7 < -1.5
2 days had low temperatures less than the average low temperature for the week.

Question 15.
Use Symbols Write a comparison using < or > to show the relationship between an elevation of 12 \(\frac{1}{2}\) ft and an elevation of 16 \(\frac{5}{8}\) ft.
Type below:__________

Answer:
−12 \(\frac{1}{2}\) ft > −16 \(\frac{5}{8}\) ft

Explanation:
−12 \(\frac{1}{2}\) = -25/2 = -12.5
−16 \(\frac{5}{8}\) = -133/8 = -16.625
-12.5 > -16.625

Problem Solving + Applications – Page No. 160

Elevations, in miles, are given for the lowest points below sea level for 4 bodies of water. Use the table for 16–19.
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 12

Question 16.
The lowest point of which has the greater elevation, the Arctic Ocean or Lake Tanganyika?
Type below:
__________

Answer:
Arctic Ocean has the greater elevation

Explanation:
Arctic Ocean = -0.8
Lake Tanganyika = -0.9
-0.8 > -0.9
Arctic Ocean has the greater elevation

Question 17.
Which has a lower elevation, the lowest point of Lake Superior or a point at an elevation of \(\frac{2}{5}\) mi?
Type below:
__________

Answer:
Lake Superior has a lower elevation

Explanation:
Lake Superior = -1/4 = -0.25
\(\frac{2}{5}\) = 0.4
-0.25 < 0.4
Lake Superior has a lower elevation

Question 18.
List the elevations in order from least to greatest.
Type below:
__________

Answer:
-0.9, -0.8, -1/3, -1/4

Explanation:
Article Ocean = -0.8
Lake Superior = -1/4 = -0.25
Lake Tanganyika = -0.9
Red Sea = -1/3 = -0.333
-0.9 < -0.8 < -0.333 < -0.25

Question 19.
A shipwreck is found at an elevation of – 0.75 mile. In which bodies of water could the shipwreck have been found?
Type below:
__________

Answer:
Article Ocean

Explanation:
-0.75 is closer to -0.8
Article Ocean = -0.8

Question 20.
Circle <, >, or =.
20a. \(\frac{−3}{5}\) Ο \(\frac{−4}{5}\)
20b. \(\frac{−2}{5}\) Ο \(\frac{−3}{4}\)
20c. 6.5 Ο 4.2
20d. 2.4 Ο 3.7
\(\frac{−3}{5}\) _____ \(\frac{−4}{5}\)
\(\frac{−2}{5}\) _____ \(\frac{−3}{4}\)
6.5 _____ 4.7
2.4 _____ 3.7

Answer:
\(\frac{−3}{5}\) > \(\frac{−4}{5}\)
\(\frac{−2}{5}\) > \(\frac{−3}{4}\)
−6.5 < −4.7
−2.4 > −3.7

Explanation:
-3/5 = -0.6; -4/5 = -0.8
-0.6 > -0.8
-2/5 = -0.4; -3/4 = -0.75
-0.4 > -0.75
-6.5 < -4.7
-2.4 > -3.7

Compare and Order Rational Numbers – Page No. 161

Compare the numbers. Write < or >.

Question 1.
1\(\frac{1}{2}\) _____ \(\frac{−1}{2}\)

Answer:
−1\(\frac{1}{2}\) < \(\frac{−1}{2}\)

Explanation:
−1\(\frac{1}{2}\) = -3/2 = – 1.5
\(\frac{−1}{2}\) = -0.5
-1.5 < -0.5

Question 2.
0.1 _____ 1.9

Answer:
0.1 > −1.9

Explanation:
0.1 is to the right of -1.9 on the number line.
So, 0.1 is greater than -1.9.

Question 3.
0.4 _____ \(\frac{−1}{2}\)

Answer:
0.4 > \(\frac{−1}{2}\)

Explanation:
0.4 is to the right of \(\frac{−1}{2}\) on the number line.
So, 0.4 is greater than \(\frac{−1}{2}\).

Question 4.
\(\frac{2}{5}\) _____ 0.5

Answer:
\(\frac{2}{5}\) < 0.5

Explanation:
2/5 = 0.4
0.4 < 0.5

Order the numbers from least to greatest.

Question 5.
0.2, 1.7, 1
Type below:
__________

Answer:
-1.7, -1, 0.2

Explanation:
-1.7 is to the left of -1 on the number line. -1 is to the left of 0.2 on the number line.
So, -1.7 < -1 < 0.2

Question 6.
\(2 \frac{3}{4}, \frac{-3}{5}, 1 \frac{3}{4}\)
Type below:
__________

Answer:
\( \frac{-3}{5}, 1\frac{3}{4}, 2 \frac{3}{4}\)

Explanation:
2 3/4 = 11/4 = 2.75
-3/5 = – 0.6
1 3/4 = 7/4 = 1.75
-0.6 < 1.75 < 2.75

Question 7.
0.5, 1 \(\frac{2}{3}\), 2.7
Type below:
__________

Answer:
-2.7, −1 \(\frac{2}{3}\), -0.5

Explanation:
−1 \(\frac{2}{3}\) = -5/3 = -1.666
-2.7 < -1.66, -0.5

Order the numbers from greatest to least.

Question 8.
1, \(\frac{−5}{6}\), 0
Type below:
__________

Answer:
0, \(\frac{−5}{6}\), -1

Explanation:
\(\frac{−5}{6}\) = -0.8333
0 is to the right of \(\frac{−5}{6}\) on the number line. \(\frac{−5}{6}\) is to the right of -1 on the number line.
So, 0 > \(\frac{−5}{6}\) > -1

Question 9.
\(1.82, \frac{-2}{5}, \frac{4}{5}\)
Type below:
__________

Answer:
\(1.82, \frac{4}{5}, \frac{-2}{5}\)

Explanation:
-2/5 = -0.4
4/5 = 0.8
1.82
1.82 > 0.8 > -0.4

Question 10.
2.19, 2.5, 1.1
Type below:
__________

Answer:
1.1, -2.19, -2.5

Explanation:
1.1 is to the right of -2.19 on the number line. -2.19 is to the right of -2.5 on the number line.
So, 1.1 > -2.19 > -2.5

Write a comparison using < or > to show the relationship between the two values.

Question 11.
an elevation of −15 m and an elevation of −20.5 m
Type below:
__________

Answer:
-15m > -20.5m

Explanation:
-15 is to the right of -20.5 on the number line.
-15m > -20.5m

Question 12.
a balance of $78 and a balance of −$42
Type below:
__________

Answer:
$42 < $78

Explanation:
$42 is to the left of $78 on the number line.
So, $42 is less than $78.

Question 13.
a score of −31 points and a score of −30 points
Type below:
__________

Answer:
-31 points < -30 points

Explanation:
-31 is to the left of -30 on the number line.
So, -31 is less than -30.

Problem Solving

Question 14.
The temperature in Cold Town on Monday was 1°C. The temperature in Frosty Town on Monday was −2°C. Which town was colder on Monday?
Type below:
__________

Answer:
Frosty Town

Explanation:
The temperature in Cold Town on Monday was 1°C. The temperature in Frosty Town on Monday was −2°C.
Frosty Town town was colder on Monday.

Question 15.
Stan’s bank account balance is less than −$20.00 but greater than −$21.00. What could Stan’s account balance be?
Type below:
__________

Answer:
From -$20.99 to -$20.01

Explanation:
Stan’s bank account balance is less than −$20.00 but greater than −$21.00. The possible answer is From -$20.99 to -$20.01

Question 16.
Describe two situations in which it would be helpful to compare or order positive and negative rational numbers.
Type below:
__________

Answer:
1) negative numbers in weather reports and on food packaging. The temperature -5°C is ‘negative five degrees’ and it means 5 degrees below zero.
2) When you spend more money than you have in your bank account it shows up as a negative number.

Lesson Check – Page No. 162

Question 1.
The low temperature was —1.8 °C yesterday and −2.1 °C today. Use the symbols < or > to show the relationship between the temperatures.
Type below:
__________

Answer:
The low temperature was —1.8 °C yesterday and −2.1 °C today.
-1.8 > -2.1

Question 2.
The scores at the end of a game are shown. List the scores in order from greatest to least.
Vince: −0.5
Allison: \(\frac{3}{8}\)
Mariah: \(\frac{−7}{20}\)
Type below:
__________

Answer:
\(\frac{3}{8}\), -0.5, \(\frac{−7}{20}\)

Explanation:
\(\frac{3}{8}\) = 0.375
\(\frac{−7}{20}\) = -0.35
-0.5
\(\frac{3}{8}\) > -0.5 > -0.35

Spiral Review

Question 3.
Simone bought 3.42 pounds of green apples and 2.19 pounds of red apples. She used 3 pounds to make a pie. How many pounds of apples are left?
_____ pounds

Answer:
2.61 pounds

Explanation:
She bought 3.42 pounds of green apples, then you can subtract 3 lbs off of that, so she bought .42 lbs of green apples and 2.19 lbs red apples
So now, you just need to add .42 and 2.19
.42 + 2.19 = 2.61, so she has 2.61 lbs of apples left

Question 4.
Kwan bought three rolls of regular wrapping paper with 6.7 square meters of paper each. He also bought a roll of fancy wrapping paper containing 4.18 square meters. How much paper did he have altogether?
_____ square meters

Answer:
24.28 square meters

Explanation:
He bought 3 rolls of regular wrapping paper with 6.7 m². Then the total of this paper is: 3 × 6.7 = 20.1
He also bought a roll of fancy wrapping with 4.18 m². Therefore, to calculate the amount of paper he had together (which you can call ), you must add 20.1 m² and 4.18 m²,
x = 20.1 + 41.8 = 24.28

Question 5.
Eddie needs 223 cups of flour for one batch of pancakes. How much flour does he need for 212 batches?
_____ \(\frac{□}{□}\) cups

Answer:
6\(\frac{4}{6}\) cups

Explanation:
For 1 batch of pancake = 2 2/3 = 8/3 cups
For 2 1/2 = 5/2 pancake = 8/3 × 5/2 = 40/6 cups = 6 4/6 cups

Question 6.
Tommy notices that he reads \(\frac{2}{3}\) page in a minute. At that rate, how long will it take him to read 12 pages?
_____ minutes

Answer:
18 minutes

Explanation:
It will take him 18 minutes.
2/3 of a page in 18 minutes= 12 pages read

Mid-Chapter Checkpoint – Vocabulary – Page No. 163

Choose the best term from the box to complete the sentence.
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 13

Question 1.
Any number that can be written as \(\frac{a}{b}\), where a and b are integers and b≠0 is called a(n) _____.
Type below:
__________

Answer:
rational number

Question 2.
The set of whole numbers and their opposites is the set of _____.
Type below:
__________

Answer:
Integers

Concepts and Skills

Write the opposite of the integer.

Question 3.
72
Type below:
__________

Answer:
72

Explanation:
The integer −72 is on the left side of 0.
So, the opposite of -72 is 72

Question 4.
0
Type below:
__________

Answer:
0

Explanation:

Opposite of 0 is 0

Question 5.
31
Type below:
__________

Answer:
31

Explanation:
The integer −31 is on the left side of 0.
So, the opposite of -31 is 31

Question 6.
27
Type below:
__________

Answer:

Explanation:
The integer 27 is on the right side of 0.
So, the opposite of 27 is -27

Name the integer that represents the situation, and tell what 0 represents in that situation.
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 14

Question 7.
Type below:
__________

Answer:
Integer: 278
0 represents: Neither loses or gains in the video game.

Question 8.
Type below:
__________

Answer:
Integer: -8 degrees
0 represents: No change in the temperature.

Compare the numbers. Write < or >.

Question 9.
3 _____ 4

Answer:
3 > −4

Explanation:
3 is to the right of -4 on the number line.
So, 3 is greater than -4.

Question 10.
6 _____ 5

Answer:
−6 < −5

Explanation:
-6 is to the left of -5 on the number line.
So, -6 is less than -5.

Question 11.
5 _____ 6

Answer:
5 > −6

Explanation:
5 is to the right of -6 on the number line.
So, 5 is greater than -6.

Question 12.
\(\frac{1}{3}\) _____ \(\frac{1}{2}\)

Answer:
\(\frac{1}{3}\) < \(\frac{1}{2}\)

Explanation:
\(\frac{1}{3}\) is to the left of \(\frac{1}{2}\) on the number line.
So, \(\frac{1}{3}\) is less than \(\frac{1}{2}\).

Question 13.
3.1 _____ 4.3

Answer:
−3.1 >−4.3

Explanation:
-3.1 is to the right of -4.3 on the number line.
So, -3.1 is greater than -4.3.

Question 14.
1\(\frac{3}{4}\) _____ 2\(\frac{1}{2}\)

Answer:
1\(\frac{3}{4}\) >−2\(\frac{1}{2}\)

Explanation:
1\(\frac{3}{4}\) is to the right of −2\(\frac{1}{2}\) on the number line.
So, 1\(\frac{3}{4}\) is greater than −2\(\frac{1}{2}\).

Order the numbers.

Question 15.
5, 2, 8
Type below:
__________

Answer:
-8, -2, 5

Explanation:
-8 is to the left of -2 on the number line. -2 is to the left of 5 on the number line.
So, -8 < -2 < 5

Question 16.
0, 3, 1
Type below:
__________

Answer:
-3, 0, 1

Explanation:
-3 is to the left of 0 on the number line. 0 is to the left of 1 on the number line.
So, -3 < 0 < 1

Question 17.
7, 6, 11
Type below:
__________

Answer:
-11, -7, -6

Explanation:
-11 is to the left of -7 on the number line. -7 is to the left of -6 on the number line.
So, -11 < -7 < -6

Question 18.
2.5, 1.7, 4.3
Type below:
__________

Answer:
-4.3, -1.7, 2.5

Explanation:
-4.3 is to the left of -1.7 on the number line. -1.7 is to the left of 2.5 on the number line.
So, -4.3 < -1.7 < 2.5

Question 19.
\(\frac{2}{3} \cdot \frac{1}{4}, \frac{5}{12}\)
Type below:
__________

Answer:
\(\frac{1}{4} \cdot \frac{5}{12}, \frac{2}{3}\)

Explanation:
2/3 = 0.666
1/4 = 0.25
5/12 = 0.4166
1/4 < 5/12 < 2/3

Question 20.
5.2, 3.8, 9.4
Type below:
__________

Answer:
−9.4, −5.2, −3.8

Explanation:
-9.4 is to the left of -5.2 on the number line. -5.2 is to the left of -3.8 on the number line.
So, -9.4 < -5.2 < -3.8

Page No. 164

Question 21.
Judy is scuba diving at −7 meters, Nelda is scuba diving at −9 meters, and Rod is scuba diving at −3 meters. List the divers in order from the deepest diver to the diver who is closest to the surface.
Type below:
__________

Answer:
Judy is scuba diving at −7 meters, Nelda is scuba diving at −9 meters, and Rod is scuba diving at −3 meters.
the higher the value of the negative number, the deepest the diver is.
Nelda (-9)- Judy (-7) -Rod (-3)

Question 22.
A football team gains 8 yards on their first play. They lose 12 yards on the next play. What two integers represent the two plays?
Type below:
__________

Answer:
A football team gains 8 yards on their first play. +8
They lose 12 yards on the next play. -12
The 2 integers are positive 8 and negative 12

Question 23.
The player who scores the closest to 0 points wins the game. The scores of four players are given in the table. Who won the game?
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 15
Type below:
__________

Answer:
Donovan won the game

Explanation:
Donovan because he has-1.5
Myra has -1.93
Amari has -1.66666666
Justine has -1.8
-1.5 is the closest to 0

Question 24.
Which point on the graph represents 3 \(\frac{3}{4}\) ? What number does point C represent?
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 16
Type below:
__________

Answer:
A

Explanation:
−3 \(\frac{3}{4}\) = -15/4 = -3.75
-3.75 is in between -3 and -4.
So, point A is the correct answer

Share and Show – Page No. 167

Find the absolute value.

Question 1.
|2|
Type below:
__________

Answer:
2

Explanation:
The distance from 0 to the point I graphed is 2 units.
|−2| = 2

Question 2.
|6|
Type below:
__________

Answer:
6

Explanation:
The distance from 0 to the point I graphed is 6 units.
|6| = 6

Question 3.
|5|
Type below:
__________

Answer:
5

Explanation:
The distance from 0 to the point I graphed is 6 units.
|-5| = 5

Question 4.
|11|
Type below:
__________

Answer:
11

Explanation:
The distance from 0 to the point I graphed is 6 units.
|-11| = 11

Question 5.
|9|
Type below:
__________

Answer:
9

Explanation:
The distance from 0 to the point I graphed is 6 units.
|9| = 9

Question 6.
|15|
Type below:
__________

Answer:
15

Explanation:
The distance from 0 to the point I graphed is 6 units.
|-15| = 15

On Your Own

Find the absolute value.

Question 7.
|37|
Type below:
__________

Answer:
37

Explanation:
The distance from 0 to the point I graphed is 6 units.
|-37| = 37

Question 8.
|1.8|
Type below:
__________

Answer:
1.8

Explanation:
The distance from 0 to the point I graphed is 6 units.
|1.8| = 1.8

Question 9.
|\(\frac{−2}{3}\)|
Type below:
__________

Answer:
|\(\frac{2}{3}\)|

Explanation:
The distance from 0 to the point I graphed is 6 units.
||\(\frac{−2}{3}\)|| = |\(\frac{2}{3}\)|

Question 10.
|6.39|
Type below:
__________

Answer:
6.39

Explanation:
The distance from 0 to the point I graphed is 6 units.
|-6.39| = 6.39

Question 11.
|5\(\frac{7}{8}\)|
Type below:
__________

Answer:
5\(\frac{7}{8}\)

Explanation:
The distance from 0 to the point I graphed is 5\(\frac{7}{8}\) units.
|−5\(\frac{7}{8}\)| = 5\(\frac{7}{8}\)

Find all numbers with the given absolute value.

Question 12.
13
Type below:
__________

Answer:
13 and -13

Explanation:
13 and -13 are at the same distance from 0.

Question 13.
\(\frac{5}{6}\)
Type below:
__________

Answer:
\(\frac{5}{6}\) and \(\frac{-5}{6}\)

Explanation:
\(\frac{5}{6}\) and \(\frac{-5}{6}\) are at the same distance from 0.

Question 14.
14.03
Type below:
__________

Answer:
14.03 and -14.03

Explanation:
14.03 and -14.03 are at the same distance from 0.

Question 15.
0.59
Type below:
__________

Answer:
0.59 and -0.59

Explanation:
0.59 and -0.59 are at the same distance from 0.

Question 16.
3\(\frac{1}{7}\)
Type below:
__________

Answer:
3\(\frac{1}{7}\) and -3\(\frac{1}{7}\)

Explanation:
3\(\frac{1}{7}\) and -3\(\frac{1}{7}\) are at the same distance from 0.

Use Reasoning Algebra Find the missing number or numbers to make the statement true.

Question 17.
|?| = 10
Type below:
__________

Answer:
10 and -10

Explanation:
|-10| = 10
|10| = 10

Question 18.
|?| = 1.78
Type below:
__________

Answer:
1.78 and -1.78

Explanation:
|-1.78| = 1.78
|1.78| = 1.78

Question 19.
|?| = 0
Type below:
__________

Answer:
0

Explanation:
|0| = 0

Question 20.
|?| = \(\frac{15}{16}\)
Type below:
__________

Answer:
\(\frac{-15}{16}\) and \(\frac{15}{16}\)

Explanation:
|\(\frac{-15}{16}\)| = \(\frac{15}{16}\)
|\(\frac{15}{16}\)| = \(\frac{15}{16}\)

Question 21.
Find all of the integers whose absolute value is less than |–4|.
Type below:
__________

Answer:
3, 2, 1, 0

Explanation:
The absolute value of |–4| = 4.
3, 2, 1, 0 are the integers whose absolute value is less than |–4|.

Unlock The Problem – Page No. 168

Question 22.
The Blue Ridge Trail starts at Park Headquarters in Big Bear Park and goes up the mountain. The Green Creek Trail starts at Park Headquarters and goes down the mountain. The table gives elevations of various points of interest in relation to Park Headquarters. How many points of interest are less than 1 kilometer above or below Park Headquarters?
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 17
a. How can you find how far above or below Park Headquarters a given point of interest is located?
Type below:
__________

Answer:
By knowing the values below 1 km can help you to find how far above or below Park Headquarters a given point of interest is located

Question 22.
b. How can you find the number of points of interest that are less than 1 km above or below Park Headquarters?
Type below:
__________

Answer:
By counting the number of points of interest that are less than 1 km, you can find the number of points of interest that are less than 1 km above or below Park Headquarters.

Question 22.
c. Find how far above or below Park Headquarters each point of interest is located.
Type below:
__________

Answer:
C, D, E, F, G, H

Question 22.
d. How many points of interest are less than 1 kilometer above or below Park Headquarters?
Type below:
__________

Answer:
6

Question 23.
Use Reasoning Name a rational number that can replace ? to make both statements true.
?>3             |?|<|3|
Type below:
__________

Answer:
-2 or -1 >−3          1 or 2 < |−3|

Explanation:
The greatest numbers than -3 are -2 or -1.
|−3| = 3. So, the fewer numbers than 3 are 1, 2

Question 24.
Laila said |4| equals |−4|. Is Laila correct? Use the number line and words to support your answer.
Type below:
__________

Answer:
Laila is correct. The absolute value of |−4| = 4 = |4|

Absolute Value – Page No. 169

Find the absolute value.

Question 1.
|7|
Type below:
__________

Answer:
7

Explanation:

The distance from 0 to the point I graphed is 2 units.
|7| = 7

Question 2.
|8|
Type below:
__________

Answer:
8

Explanation:
The distance from 0 to the point I graphed is 2 units.
|−8| = 8

Question 3.
|16|
Type below:
__________

Answer:
16

Explanation:
The distance from 0 to the point I graphed is 2 units.
|16| = 16

Question 4.
|8.65|
Type below:
__________

Answer:
8.65

Explanation:
The distance from 0 to the point I graphed is 2 units.
|8.65| = 8.65

Question 5.
|4\(\frac{3}{20}\)|
Type below:
__________

Answer:
4\(\frac{3}{20}\)

Explanation:
The distance from 0 to the point I graphed is 2 units.
|4\(\frac{3}{20}\)| = 4\(\frac{3}{20}\)

Question 6.
|5000|
Type below:
__________

Answer:
5000

Explanation:
The distance from 0 to the point I graphed is 2 units.
|−5000| = 5000

Find all numbers with the given absolute value.

Question 7.
12
Type below:
__________

Answer:
12 and -12

Explanation:
12 and -12 are at the same distance from 0.

Question 8.
1.7
Type below:
__________

Answer:
1.7 and -1.7

Explanation:
1.7 and -1.7 are at the same distance from 0.

Question 9.
\(\frac{3}{5}\)
Type below:
__________

Answer:
\(\frac{3}{5}\) and \(\frac{-3}{5}\)

Explanation:
\(\frac{3}{5}\) and \(\frac{-3}{5}\) are at the same distance from 0.

Question 10.
3\(\frac{1}{6}\)
Type below:
__________

Answer:
3\(\frac{1}{6}\) and -3\(\frac{1}{6}\)

Explanation:
3\(\frac{1}{6}\) and -3\(\frac{1}{6}\) are at the same distance from 0.

Question 11.
0
Type below:
__________

Answer:
0

Explanation:
0 is same distance from 0.

Find the number or numbers that make the statement true.

Question 12.
|?| = 17
Type below:
__________

Answer:
17 and -17

Explanation:
|-17| = 17
|17| = 17

Question 13.
|?| = 2.04
Type below:
__________

Answer:
2.04 and -2.04

Explanation:
|-2.04| = 2.04
|2.04| = 2.04

Question 14.
|?| = 1\(\frac{9}{10}\)
Type below:
__________

Answer:
1\(\frac{9}{10}\) and -1\(\frac{9}{10}\)

Explanation:
|-1\(\frac{9}{10}\)| = 1\(\frac{9}{10}\)
|1\(\frac{9}{10}\)| = 1\(\frac{9}{10}\)

Question 15.
|?| = \(\frac{19}{24}\)
Type below:
__________

Answer:
\(\frac{19}{24}\) and \(\frac{-19}{24}\)

Explanation:
|\(\frac{-19}{24}\)| = \(\frac{19}{24}\)
|\(\frac{19}{24}\)| = \(\frac{19}{24}\)

Problem Solving

Question 16.
Which two numbers are 7.5 units away from 0 on a number line?
Type below:
__________

Answer:
7.5 and -7.5 are away from 0 on a number line

Explanation:
|7.5| = 7.5
|-7.5| = 7.5

Question 17.
Emilio is playing a game. He just answered a question incorrectly, so his score will change by −10 points. Find the absolute value of −10.
Type below:
__________

Answer:
10

Explanation:
Emilio is playing a game. He just answered a question incorrectly, so his score will change by −10 points.
|-10| = 10

Question 18.
Write two different real-world examples. One should involve the absolute value of a positive number, and the other should involve the absolute value of a negative number.
Type below:
__________

Answer:
1) If we have a balance of -$35 dollars in an account, we may also choose to represent that as a debt of $35.
2) The temperature of the human body

Lesson Check – Page No. 170

Question 1.
What is the absolute value of \(\frac{8}{9}\)?
Type below:
__________

Answer:
\(\frac{8}{9}\)

Explanation:
|\(\frac{8}{9}\)| = \(\frac{8}{9}\)

Question 2.
What two numbers have an absolute value of 21.63?
Type below:
__________

Answer:
21.63 and -21.63

Explanation:
|-21.63| = 21.63
|21.63| = 21.63

Spiral Review

Question 3.
Rachel earned $89.70 on Tuesday. She spent $55.89 at the grocery store. How much money does she have left?
$ ______

Answer:
$33.81

Explanation:
Rachel earned $89.70 on Tuesday. She spent $55.89 at the grocery store.
89.70 – 55.89 = 33.81
Rachel has $33.81 left

Question 4.
One carton contains \(\frac{17}{20}\) liter of juice. Another carton contains 0.87 liter of juice. Which carton contains the most?
Type below:
__________

Answer:
0.87 is more because 17/20 is 0.85

Explanation:
One carton contains \(\frac{17}{20}\) liter of juice. Another carton contains 0.87 liters of juice.
0.87 is more because 17/20 is 0.85

Question 5.
Maggie jogged \(\frac{7}{8}\) mile on Monday and \(\frac{1}{2}\) of that distance on Tuesday. How far did she jog on Tuesday?
\(\frac{□}{□}\) mile

Answer:
\(\frac{7}{4}\) mile

Explanation:
Maggie jogged \(\frac{7}{8}\) mile on Monday and \(\frac{1}{2}\) of that distance on Tuesday.
\(\frac{7}{8}\) ÷ \(\frac{1}{2}\) = 7/4
7/4 or as a mixed fraction which is 1 3/4 mile

Question 6.
Trygg has \(\frac{3}{4}\) package of marigold seeds. He plants \(\frac{1}{6}\) of those seeds in his garden and divides the rest equally into 10 flowerpots. What fraction of a package of seeds is planted in each flowerpot?
\(\frac{□}{□}\) package

Answer:
\(\frac{1}{16}\) package

Explanation:
He has a 3/4 package and plants 1/6 of the seeds.
3/4 × 1/6 = 1/8
He divides the rest equally into 10 flowerpots.
Subtract 1/8 from 3/4.
The common denominator of 4 and 8 is 8.
Multiply the numerator 3 × 2= 6 with a denominator of 8.
3/4 – 1/8 = 6/8 -1/8 = 5/8
5/8 is left to be divided equally into 10 flowerpots.
5/8 ÷ 10/1
= 5/8 * 1/10
= 5/80
= 1/16

Share and Show – Page No. 173

Question 1.
On Monday, Allie’s bank account balance was – $24. On Tuesday, her account balance was less than it was on Monday. Use absolute value to describe Allie’s balance on Tuesday as a debt.
Type below:
__________

Answer:
On Tuesday, her account balance is less than -$24 means her debt will be bigger than $24 dollars.

Explanation:
On Monday, allies’ bank account balance was -$24.
Balance being negative means he is carrying a debt of $24.
On Tuesday, Allie’s balance account was less than it was on Monday. It means
Her bank account < -$24
So, she must be carrying a debit bigger than $24.
Therefore, on Tuesday, her account balance being less than -$24 means her debt will be greater than $24 dollars.

Question 2.
Matthew scored −36 points in his turn at a video game. In Genevieve’s turn, she scored fewer points than Matthew. Use absolute value to describe Genevieve’s score as a loss.
Type below:
__________

Answer:
Genevieve lost more than 36 points

Explanation:
Matthew scored −36 points in his turn at a video game. In Genevieve’s turn, she scored fewer points than Matthew.
-36 > -40
|-36| < |-40|
36 < 40
Genevieve lost more than 36 points

On Your Own

Question 3.
One of the cats shown in the table is a tabby. The tabby had a decrease in weight of more than 3.3 ounces. Which cat is the tabby?
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 18
Type below:
__________

Answer:
Spot is tabby

Explanation:
|-3.4| = 3.4
So, Spot is tabby

Compare. Write <, >, or =.

Question 4.
−8 _____ |8|

Answer:
−8 < |−8|

Explanation:
|−8| = 8
-8 < 8

Question 5.
13 _____ |13|

Answer:
13 = |−13|

Explanation:
|−13| = 13
13 = 13

Question 6.
|23| _____ |24|

Answer:
|−23| < |−24|

Explanation:
|−23| = 23
|−24| = 24
23 < 24

Question 7.
15 _____ |14|

Answer:
15 > |−14|

Explanation:
|−14| = 14
15 > 14

Question 8.
34 _____ |36|

Answer:
34 < |−36|

Explanation:
|−36| = 36
34 < 36

Question 9.
−5 _____ |6|

Answer:
−5 < |−6|

Explanation:
|−6| = 6
-5 < 6

Question 10.
Write the values in order from least to greatest.
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 19
Type below:
__________

Answer:
1, 2, 3, 6

Explanation:
|-2| = 2
|3| = 3
|-6| = 6
|1| = 1
1 < 2 < 3 < 6

Compare and Contrast – Page No. 174

When you compare and contrast, you look for ways that two or more subjects are alike (compare) and ways they are different (contrast). This helps you to discover information about each subject that you might not have known otherwise. As you read the following passage, think about how the main topics are alike and how they are different.

Trevor mows lawns after school to raise money for a new mountain bike. Last week, it rained every day, and he couldn’t work. While waiting for better weather, he spent some of his savings on lawnmower repairs. As a result, his savings balance changed by −$45. This week, the weather was better, and Trevor returned to work. His savings balance changed by +$45 this week.

Question 11.
The passage has two main parts. Describe them.
Type below:
__________

Answer:
Last week, Trevor couldn’t work, so he spent money to repair the lawnmower!
This week, he goes back to work and earns money again!

Question 12.
Describe the two changes in Trevor’s savings balance
Type below:
__________

Answer:
His savings balance changed by −$45 in one week and his savings balance changed by +$45 in another week.

Question 13.
Reason Quantitatively Compare the two changes in Trevor’s savings balance. How are they alike?
Type below:
__________

Answer:
Each week, Trevor’s balance changed by $45; or his balance is the same distance from 0 each week.

Question 14.
Contrast the two changes in Trevor’s savings balance. How are they different?
Type below:
__________

Answer:
The balances are different because one week the balance had a decrease, while the next week there was an increase in the balance

Compare Absolute Values – Page No. 175

Solve.

Question 1.
Jamie scored −5 points on her turn at a trivia game. In Veronica’s turn, she scored more points than Jamie. Use absolute value to describe Veronica’s score as a loss.
Type below:
__________
Jamie scored −5 points on her turn at a trivia game. In Veronica’s turn, she scored more points than Jamie.

Answer:
In this situation, |-5| represents a loss of 5 points. Veronica lost fewer than 5 points.

Question 2.
The low temperature on Friday was −10°F. The low temperature on Saturday was colder. Use absolute value to describe the temperature on Saturday as a temperature below zero.
Type below:
__________

Answer:
The temperature on Sunday was more than 10 degrees below zero

Explanation:
The low temperature on Friday was −10°F. The low temperature on Saturday was colder. The temperature on Sunday was more than 10 degrees below zero

Question 3.
The table shows changes in the savings accounts of five students. Which student had the greatest increase in money? By how much did the student’s account increase?
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 20
Type below:
__________

Answer:
Carissa; an increase of $15

Compare. Write <, >, or =.

Question 4.
16 _____ |16|

Answer:
−16 < |−16|

Explanation:
|−16| = 16
-16 < 16

Question 5.
20 _____ 20

Answer:
20 = 20

Question 6.
3 _____ |4|

Answer:
3 < |−4|

Explanation:
|−4| = 4
3 < 4

Problem Solving

Question 7.
On Wednesday, Miguel’s bank account balance was −$55. On Thursday, his balance was less than that. Use absolute value to describe Miguel’s balance on Thursday as a debt.
Type below:
__________

Answer:
In this situation, -$55 represents a debt of $55. On Thursday, Miguel had a debt of more than $55.

Explanation:
On Wednesday, Miguel’s bank account balance was −$55. On Thursday, his balance was less than that.
In this situation, -$55 represents a debt of $55. On Thursday, Miguel had a debt of more than $55.

Question 8.
During a game, Naomi lost points. She lost fewer than 3 points. Use an integer to describe her possible score.
Type below:
__________

Answer:
-2, -1

Explanation:
During a game, Naomi lost points. She lost fewer than 3 points.
It may be -2, -1

Question 9.
Give two numbers that fit this description: a number is less than another number but has a greater absolute value. Describe how you determined the numbers.
Type below:
__________

Answer:
Choose a large negative number and a smaller positive number.
Example: Use -14 and 3, -8392 and 274, -1 and 0.5, etc. Even though the negative numbers are technically less, they would have higher absolute values.

Lesson Check – Page No. 176

Question 1.
A temperature of –6° is colder than a temperature of 5°F below zero. Is this statement true or false?
Type below:
__________

Answer:
True

Explanation:
–6° is colder than a temperature of 5°F below zero

Question 2.
Long Beach, California has an elevation of −7 feet. New Orleans, Louisiana is 8 feet below sea level. Which city has a lower elevation?
Type below:
__________

Answer:
New Orleans, Louisiana has a lower elevation

Explanation:
Long Beach, California has an elevation of −7 feet.
New Orleans, Louisiana is 8 feet below sea level. = -8 feet
So, New Orleans, Louisiana has a lower elevation.

Spiral Review

Question 3.
Dawn and Lin took off on skateboards from the same location but traveled in opposite directions. After 20 minutes, Dawn had traveled 6.42 kilometers and Lin had traveled 7.7 kilometers. How far apart were they?
_____ kilometers

Answer:
14.12 kilometers

Explanation:
Distance of Dawn = 6.42 km
Distance from Lin = 7.7 km in the opposite direction.
If they went in opposite directions then they were moving away from each other.
The final distance between the two, d = 6.42 + 7.7 = 14.12 km
After 20 minutes Dawn and Lin were 14.12 km away.

Question 4.
Rico and Josh took off on skateboards going in the same direction. After 20 minutes, Rico had traveled 5.98 kilometers and Josh had gone 8.2 kilometers. How far apart were they?
_____ kilometers

Answer:
2.22 kilometers

Explanation:
Rico and Josh took off on skateboards going in the same direction.
After 20 minutes, Rico had traveled 5.98 kilometers and Josh had gone 8.2 kilometers.
D = 8.2 – 5.98 = 2.22 km
Hence, Rico and Josh were 2.22 km apart from each other.

Question 5.
Etta bought 11.5 yards of fabric selling for $0.90 per yard. What was the total cost?
$ _____

Answer:
$10.35

Explanation:
Multiply 11.5 times 0.90 and get $10.35

Question 6.
Yen calculates the product \(\frac{5}{8} \times \frac{24}{25}\). Before he multiplies, he simplifies all factors. What does the problem look like after he simplifies the factors?
Type below:
__________

Answer:
Yen calculates the product \(\frac{5}{8} \times \frac{24}{25}\).
5/8 = 0.625
24/25 = 0.96
0.625 × 0.96 = 0.6

Share and Show – Page No. 179

Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 21

Question 1.
Write the ordered pair for point J.
Type below:
__________

Answer:
(-1.5, 2.5)

Explanation:
To find the x-coordinate, move 1.5 units to the left.
To find the y-coordinate, move 2.5 units up.
Point J is located at (-1.5, 2.5)

Write the ordered pair for the point.

Question 2.
K
Type below:
__________

Answer:
(1, -1.5)

Explanation:
To find the x-coordinate, move 1 unit to the right.
To find the y-coordinate, move 1.5 units down.
Point K is located at (1, -1.5)

Question 3.
L
Type below:
__________

Answer:
(-2, -1.75)

Explanation:
To find the x-coordinate, move 2 units to the left.
To find y-coordinate, move 1.75 units down.
Point L is located at (-2, -1.75)

Question 4.
M
Type below:
__________

Answer:
(1, 0)

Explanation:
To find the x-coordinate, move 1 unit to the right.
To find y-coordinate, move 0 units.
Point M is located at (1, 0)

Graph and label the point on the coordinate plane.

Question 5.
P(-2.5, 2)
Type below:
__________

Answer:
The x-coordinate is negative. Move 2.5 units to the left.
y-coordinate is positive. Move 2 units up

Question 6.
Q(-2, \(\frac{1}{4}\))
Type below:
__________

Answer:
The x-coordinate is negative. Move 2 units to the left.
y-coordinate is positive. Move 0.25 units up

Question 7.
R(0, 1.5)
Type below:
__________

Answer:
The x-coordinate is positive. Move 0 units.
y-coordinate is positive. Move 1.5 units up

Question 8.
S(-1, \(\frac{-1}{2}\))
Type below:
__________

Answer:
The x-coordinate is negative. Move 1 unit to the left.
y-coordinate is negative. Move 0.5 units down

Question 9.
T( 1\(\frac{1}{2}\), -2 )
Type below:
__________

Answer:
The x-coordinate is positive. Move 1.5 units to the right.
y-coordinate is negative. Move 2 units down

Question 10.
U(0.75, 1.25)
Type below:
__________

Answer:
The x-coordinate is positive. Move 0.75 units to the right.
y-coordinate is positive. Move 1.25 units up

Question 11.
V(-0.5, 0)
Type below:
__________

Answer:
The x-coordinate is negative. Move 0.5 units to the left.
y-coordinate is positive. Move 0 units

Question 12.
W(2, 0)
Type below:
__________

Answer:
The x-coordinate is positive. Move 2 units to the right.
y-coordinate is positive. Move 0 units up

Question 13.
X(0, -2)
Type below:
__________

Answer:
The x-coordinate is positive. Move 0 units.
y-coordinate is negative. Move 2 units down

grade 6 chapter 3 Page no. 175 image 1

On Your Own

Write the ordered pair for the point. Give approximate coordinates when necessary.
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 22

Question 14.
A
Type below:
__________

Answer:
(4, 4)

Explanation:
To find the x-coordinate, move 4 units to the right.
To find y-coordinate, move 4 units up.
Point A is located at (4, 4)

Question 15.
B
Type below:
__________

Answer:
(-4, 3)

Explanation:
To find the x-coordinate, move 4 units to the left.
To find y-coordinate, move 3 units up.
Point B is located at (-4, 3)

Question 16.
C
Type below:
__________

Answer:
(-3, 1)

Explanation:
To find the x-coordinate, move 3 units to the left.
To find y-coordinate, move 1 unit up.
Point C is located at (-3, 1)

Question 17.
D
Type below:
__________

Answer:
(-2, -3)

Explanation:
To find the x-coordinate, move 2 units to the left.
To find y-coordinate, move 3 units down.
Point D is located at (-2, -3)

Question 18.
E
Type below:
__________

Answer:
(5, -3)

Explanation:
To find the x-coordinate, move 5 units to the right.
To find y-coordinate, move 3 units down.
Point E is located at (5, -3)

Question 19.
F
Type below:
__________

Answer:
(2.5, 0)

Explanation:
To find the x-coordinate, move 2.5 units to the right.
To find y-coordinate, move 0 units.
Point F is located at (2.5, 0)

Question 20.
G
Type below:
__________

Answer:
(-4, -5)

Explanation:
To find the x-coordinate, move 4 units to the left.
To find y-coordinate, move 5 units down.
Point G is located at (-4, -5)

Question 21.
H
Type below:
__________

Answer:
(0, 3.5)

Explanation:
To find the x-coordinate, move 0 units.
To find y-coordinate, move 3.5 units up.
Point H is located at (0, 3.5)

Question 22.
J
Type below:
__________

Answer:
(0.5, 0.5)

Explanation:
To find the x-coordinate, move 0.5 units to the right.
To find y-coordinate, move 0.5 units up.
Point J is located at (0.5, 0.5)

Graph and label the point on the coordinate plane.

Question 23.
M(-4, 0)
Type below:
__________

Answer:
The x-coordinate is negative. Move 4 units to the left.
y-coordinate is positive. Move 0 units

Question 24.
N(2, 2)
Type below:
__________

Answer:
The x-coordinate is positive. Move 2 units to the right.
y-coordinate is positive. Move 2 units up

Question 25.
P(-3, 3)
Type below:
__________

Answer:
The x-coordinate is positive. Move 3 units to the left.
y-coordinate is positive. Move 3 units up

Question 26.
Q(0, −2\(\frac{1}{2}\))
Type below:
__________

Answer:
The x-coordinate is positive. Move 0 units.
y-coordinate is negative. Move 2.5 units down

Explanation:

Question 27.
R(0.5, 0.5)
Type below:
__________

Answer:
The x-coordinate is positive. Move 0.5 units to the right.
y-coordinate is positive. Move 0.5 units up

Question 28.
S(-5, \(\frac{1}{2}\))
Type below:
__________

Answer:
The x-coordinate is negative. Move 5 units to the left.
y-coordinate is positive. Move 0.5 units up

Question 29.
T(0, 0)
Type below:
__________

Answer:
It is at the origin. T is at the origin

Question 30.
U(3 \(\frac{1}{2}\), 0)
Type below:
__________

Answer:
The x-coordinate is positive. Move 3.5 units to the right.
y-coordinate is positive. Move 0 units

Question 31.
V(-2, -4)
Type below:
__________

Answer:
The x-coordinate is negative. Move 2 units to the left.
y-coordinate is negative. Move 4 units down

grade 6 chapter 3 Page no. 175 image 2

Question 32.
Look for Structure A point lies to the left of the y-axis and below the x-axis. What can you conclude about the coordinates of the point?
Type below:
__________

Answer:
A point lies to the left of the y-axis. So, the x-coordinate is negative.
A point lies below the x-axis. So, y-coordinate is negative.
Both coordinates points are negative

Problem Solving + Applications – Page No. 180

Many of the streets in downtown Philadelphia can be modeled by a coordinate plane, as shown on the map. Each unit on the map represents one block. Use the map for 33 and 34.
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 23

Question 33.
Anita works at the Historical Society. She leaves the building and walks 3 blocks north to a restaurant. What ordered pair represents the restaurant?
Type below:
__________

Answer:
Anita works at the Historical Society. She leaves the building and walks 3 blocks north to a restaurant.
Historical Society = (2, 4)
As she walks 3 blocks north to a restaurant 4-3 = 1
(2, 1) ordered pair represents the restaurant

Question 34.
Pose a Problem Write and solve a new problem that uses a location on the map.
Type below:
__________

Answer:
Anita is at City Hall. She walked 3 blocks to the East and 2 blocks to the North. What ordered pair represents her present location?
She is at the Fabric Workshop & Museum. The ordered pair is (3, 2)

Question 35.
The points A, B, C, and D on a coordinate plane can be connected to form a rectangle. Point A is located at (2, 0), point B is located at (6, 0), and point C is located at (6, –2.5). Write the ordered pair for point D.
Type below:
__________

Answer:
The point D is at (2, -2.5)

Explanation:
grade 6 chapter 3 Page no. 180 image 1
The points A, B, C, and D on a coordinate plane can be connected to form a rectangle. Point A is located at (2, 0), point B is located at (6, 0), and point C is located at (6, –2.5). The point D is at (2, -2.5)

Question 36.
Identify Relationships Explain how you can tell that the line segment connecting two points is vertical without graphing the points.
Type below:
__________

Answer:
The line segment connecting two points is vertical. By calculating the slope, we can say that the line segment connecting two points is vertical without graphing the points.

Question 37.
For numbers 37a–37d, select True or False for each statement.
37a. Point A (2, –1) is to the right of the y-axis and below the x-axis.
37b. Point B (– 5,2) is to the left of the y-axis and below the x-axis.
37c. Point C (3, 2) is to the right of the y-axis and above the x-axis.
37d. Point D (–2, –1) is to the left of the y-axis and below the x-axis.
37a. __________
37b. __________
37c. __________
37d. __________

Answer:
37a. True
37b. False
37c. True
37d. True

Rational Numbers and the Coordinate Plane – Page No. 181

Write the ordered pair for the point. Give approximate coordinates when necessary.
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 24

Question 1.
A
Type below:
__________

Answer:
(1, 0.5)

Explanation:
To find the x-coordinate, move 1 unit to the right.
To find y-coordinate, move 0.5 units up.
Point A is located at (1, 0.5)

Question 2.
B
Type below:
__________

Answer:
(-0.75, -2.5)

Explanation:
To find the x-coordinate, move 0.75 units to the left.
To find y-coordinate, move 2.5 units down.
Point B is located at (-0.75, -2.5)

Question 3.
C
Type below:
__________

Answer:
(2, -1.5)

Explanation:
To find the x-coordinate, move 2 units to the right.
To find y-coordinate, move 1.5 units down.
Point C is located at (2, -1.5)

Question 4.
D
Type below:
__________

Answer:
(-1.5, 0)

Explanation:
To find the x-coordinate, move 1.5 units to the left.
To find y-coordinate, move 0 units.
Point D is located at (-1.5, 0)

Graph and label the point on the coordinate plane.

Question 5.
G(−\(\frac{1}{2}\), 1 \(\frac{1}{2}\))
Type below:
__________

Answer:
The x-coordinate is negative. Move 0.5 units to the left.
y-coordinate is positive. Move 1.5 units up

Explanation:
-1/2 = -0.5
1 1/2 = 3/2 = 1.5

Question 6.
H(0, 2.50)
Type below:
__________

Answer:
The x-coordinate is positive. Move 0 units.
y-coordinate is positive. Move 2.5 units up

Question 7.
J(−1 \(\frac{1}{2}\), \(\frac{1}{2}\))
Type below:
__________

Answer:
The x-coordinate is negative. Move 1.5 units to the left.
y-coordinate is positive. Move 0.5 units up

Explanation:
-1 1/2 = -3/2 = -1.5
1/2 = 0.5

Question 8.
K(1, 2)
Type below:
__________

Answer:
The x-coordinate is positive. Move 1 unit to the right.
y-coordinate is positive. Move 2 units up

Question 9.
L(−1 \(\frac{1}{2}\), −2 \(\frac{1}{2}\))
Type below:
__________

Answer:
The x-coordinate is negative. Move 1.5 units to the left.
y-coordinate is negative. Move 2.5 units down

Explanation:
-1 1/2 = -3/2 = -1.5
-2 1/2 = -5/2 = -2.5

Question 10.
M(1, -0.5)
Type below:
__________

Answer:
The x-coordinate is positive. Move 1 unit to the up.
y-coordinate is negative. Move 0.5 units down

Question 11.
N(\(\frac{1}{4}\), 1 \(\frac{1}{2}\))
Type below:
__________

Answer:
The x-coordinate is positive. Move 0.25 units to the right.
y-coordinate is positive. Move 1.5 units up

Question 12.
P(1.25, 0)
Type below:
__________

Answer:
The x-coordinate is positive. Move 1.25 units to the right.
y-coordinate is positive. Move 0 units

grade 6 chapter 3 Page no. 180 image 2

Problem Solving

Use the map for 13–15.
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 25

Question 13.
What is the ordered pair for the city hall?
Type below:
__________

Answer:
(-1, 0.5)

Explanation:
To find the x-coordinate, move 1 unit to the left.
To find y-coordinate, move 0.5 units up.
City Hall is located at (-1, 0.5)

Question 14.
The post office is located at (\(\frac{−1}{2}\), 2). Graph and label a point on the map to represent the post office.
Type below:
__________

Answer:
grade 6 chapter 3 Page no. 181 image 1

Explanation:
The x-coordinate is negative. Move 0.5 units to the left.
y-coordinate is positive. Move 2 units up

Question 15.
Describe how to graph the ordered pair (−1, 4.5).
Type below:
__________

Answer:
The x-coordinate is negative. Move 1 unit to the left.
y-coordinate is positive. Move 4.5 units up

Lesson Check – Page No. 182

Question 1.
An artist uses a coordinate plane to create a design. As part of the design, the artist wants to graph the point (−6.5, 2). How should the artist graph this point?
Type below:
__________

Answer:
The Artist should go 6.5 units to the left on the x-axis and then 2 units up on the y-axis giving:
graph {((x + 6.5)^2 + (y – 2)^2 – 0.0125) = 0 [-10, 5, -5, 2.5]}

Question 2.
What are the coordinates of the campground?
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 26
Type below:
__________

Answer:
(-1, -1.5)

Explanation:
The x-coordinate is negative. Move 1 unit to the left.
y-coordinate is negative. Move 1.5 units down

Spiral Review

Question 3.
Four students volunteer at the hospital. Casey volunteers 20.7 hours, Danielle 20 \(\frac{3}{4}\) hours, Javier 18 \(\frac{9}{10}\) hours, and Forrest, 20 \(\frac{18}{25}\) hours. Who volunteered the greatest number of hours?
__________

Answer:
Danielle volunteered the greatest number of hours

Explanation:
Danielle volunteered the most. She did 20.75 hours while Forest had 20.72, Casey had 20.7 and Javier had the least at 18.90 hours.

Question 4.
Directions for making a quilt say to cut fifteen squares with sides that are 3.625 inches long. What is the side length written as a fraction?
_____ \(\frac{□}{□}\)

Answer:
3\(\frac{5}{8}\)

Explanation:
3.625 = 3 0.625
3.625 = 3 0.625(1000)/1000
3.625 = 3 625/1000
3.625 = 3 (625/125) / (1000/125)
3.625 = 3 5/8
The decimal length of the side of the squares (3.625 inches long) witten as a fraction is 3 5/8 inches long.

Question 5.
Cam has a piece of plywood that is 6 \(\frac{7}{8}\) feet wide. He is going to cut shelves from the plywood that are each 1 \(\frac{1}{6}\) feet wide. Which is a good estimate for the number of shelves Cam can make?
Type below:
__________

Answer:
5 shelves

Explanation:
6 7/8= 55/8
6 1/6= 7/6
first, find common denominators
55/8 × 3= 165/24
7/6 × 4= 28/24
165/24 divided by 28/24 is the same as 165/24 time 24/28
so that equals 3960/672 = 5.8928
About 5 shelves

Question 6.
Zach has \(\frac{3}{4}\) hour to play video games. It takes him \(\frac{1}{12}\) hour to set up the system. Each round of his favorite game takes \(\frac{1}{6}\) hour. How many rounds can he play?
_____ rounds

Answer:
4 rounds

Explanation:
Zach has 3/4 hour to play video games. it takes him 1/12 hour to set up the system. Each round of his favorite game takes 1/6 hours.
1) Zach has 3/4 hour to play video games
Convert to minutes
1 hour = 60 minutes
3/4 × 60 = 45 minutes
2) It takes him an hour to set up the system
Convert to minutes
1/12 × 60 = 5 minutes
3) 45 minutes – 5 minutes = 40 minutes
4) Each round of his favorite game takes an hour
Convert to minutes
1/6 × 60 = 10 minutes
5) Divide the time available to play video games by the time each round of his favorite game
40/10 = 4 rounds

Share and Show – Page No. 185

Identify the quadrant where the point is located.

Question 1.
(2, -5)
Type below:
__________

Answer:
Quadrant IV

Explanation:
The x-coordinate is positive. So, the point is 2 units to the right of the origin.
Since the point is to the right of the origin, it must be located in either
Quadrant I or Quadrant IV
The y-coordinate is negative, so the point is 5 units down from the origin.
Since the point is down the origin, it must be located in Quadrant IV.
Check by graphing the point (2, -5) on the coordinate plane.
Quadrant IV.

Question 2.
(4, 1)
Type below:
__________

Answer:
Quadrant I

Explanation:
The x-coordinate is positive. So, the point is 4 units to the right of the origin.
Since the point is to the right of the origin, it must be located in either
Quadrant I or Quadrant IV
y-coordinate is positive, so the point is 1 unit up from the origin.
Since the point is up to the origin, it must be located in Quadrant I.
Check by graphing the point (4, 1) on the coordinate plane.
Quadrant I.

Question 3.
(-6, -2)
Type below:
__________

Answer:
Quadrant III

Explanation:
The x-coordinate is negative. So, the point is 6 units to the left of the origin.
Since the point is to the left of the origin, it must be located in either
Quadrant II or Quadrant III
The y-coordinate is negative, so the point is 2 units down from the origin.
Since the point is down the origin, it must be located in Quadrant III.
Quadrant III.

Question 4.
(-7, 3)
Type below:
__________

Answer:
Quadrant II

Explanation:
The x-coordinate is negative. So, the point is 7 units to the left of the origin.
Since the point is to the left of the origin, it must be located in either
Quadrant II or Quadrant III
The y-coordinate is positive, so the point is 3 units up from the origin.
Since the point is up to the origin, it must be located in Quadrant II.
Quadrant II.

Question 5.
(8, 8)
Type below:
__________

Answer:
Quadrant I

Explanation:
The x-coordinate is positive. So, the point is 8 units to the right of the origin.
Since the point is to the right of the origin, it must be located in either
Quadrant I or Quadrant IV
The y-coordinate is positive, so the point is 8 units up from the origin.
Since the point is up to the origin, it must be located in Quadrant I.
Quadrant I.

Question 6.
(1, -1)
Type below:
__________

Answer:
Quadrant IV

Explanation:
The x-coordinate is positive. So, the point is 1 unit to the right of the origin.
Since the point is to the right of the origin, it must be located in either
Quadrant I or Quadrant IV
The y-coordinate is negative, so the point is 1 unit down from the origin.
Since the point is down to the origin, it must be located in Quadrant IV.
Quadrant IV.

The two points are reflections of each other across the x- or y-axis. Identify the axis.

Question 7.
(-1, 3) and (1, 3)
Type below:
__________

Answer:
y-axis

Explanation:
The given x-axis points are -1 and 1
The y-axis points are 3 and 3
The y-axis points are reflections to each other

Question 8.
(4, 4) and (4, -4)
Type below:
__________

Answer:
x-axis

Explanation:
The given x-axis points are 4 and 4
The y-axis points are 4 and -4
The x-axis points are reflections to each other

Question 9.
(2, -9) and (2, 9)
Type below:
__________

Answer:
x-axis

Explanation:
The given x-axis points are 2 and 2
The y-axis points are -9 and 9
The x-axis points are reflections to each other

Question 10.
(8, 1) and (-8, 1)
Type below:
__________

Answer:
y-axis

Explanation:
The given x-axis points are 8 and -8
The y-axis points are 1 and 1
The y-axis points are reflections to each other

On Your Own

Identify the quadrant where the point is located.

Question 11.
(-8, -9)
Type below:
__________

Answer:
Quadrant III

Explanation:
The x-coordinate is negative. So, the point is 8 units to the left of the origin.
Since the point is to the left of the origin, it must be located in either
Quadrant II or Quadrant III
The y-coordinate is negative, so the point is 9 units down from the origin.
Since the point is down to the origin, it must be located in Quadrant III.
Quadrant III.

Question 12.
(12, 1)
Type below:
__________

Answer:
Quadrant I

Explanation:
The x-coordinate is positive. So, the point is 12 units to the right of the origin.
Since the point is to the right of the origin, it must be located in either
Quadrant I or Quadrant IV
The y-coordinate is positive, so the point is 1 unit up from the origin.
Since the point is up to the origin, it must be located in Quadrant I.
Quadrant I.

Question 13.
(-13, 10)
Type below:
__________

Answer:
Quadrant II

Explanation:
The x-coordinate is negative. So, the point is 13 units to the left of the origin. Since the point is to the left of the origin, it must be located in either
Quadrant II or Quadrant III
The y-coordinate is negative, so the point is 10 units up from the origin.
Since the point is up to the origin, it must be located in Quadrant II.
Quadrant II.

Question 14.
(5, -20)
Type below:
__________

Answer:
Quadrant IV

Explanation:
The x-coordinate is positive. So, the point is 5 units to the right of the origin.
Since the point is to the right of the origin, it must be located in either
Quadrant I or Quadrant IV
The y-coordinate is negative, so the point is 20 units down from the origin.
Since the point is down to the origin, it must be located in Quadrant IV.
Quadrant IV.

The two points are reflections of each other across the x- or y-axis. Identify the axis.

Question 15.
(-9, -10) and (-9, 10)
Type below:
__________

Answer:
x-axis

Explanation:
The given x-axis points are -9 and -9
The y-axis points are -10 and 10
The x-axis points are reflections to each other

Question 16.
(21, -31) and (21, 31)
Type below:
__________

Answer:
x-axis

Explanation:
The given x-axis points are 21 and 21
The y-axis points are -31 and 31
The x-axis points are reflections to each other

Question 17.
(15, -20) and (-15, -20)
Type below:
__________

Answer:
y-axis

Explanation:
The given x-axis points are 15 and -15
The y-axis points are -20 and -20
The y-axis points are reflections to each other

Give the reflection of the point across the given axis.

Question 18.
(−7, −7), y-axis
Type below:
__________

Answer:
(7, -7)

Explanation:
The x-axis point is -7.
So, the reflection of point 7

Question 19.
(−15, 18), x-axis
Type below:
__________

Answer:
(-15, -18)

Explanation:
The y-axis point is 18.
So, the reflection of a point -18

Question 20.
(11, 9), x-axis
Type below:
__________

Answer:
(11, -9)

Explanation:
The y-axis point is 9.
So, the reflection of a point -9

Problem Solving + Applications – Page No. 186

Use the map of Gridville for 21–23.

Question 21.
The library’s location has opposite x- and y-coordinates as City Hall. Across which streets could you reflect City Hall’s location to find the library’s location?
Type below:
__________

Answer:
The library’s location has opposite x- and y-coordinates as City Hall.
City Hall = (2, -3)
The opposite x- and y-coordinates of City Hall = (-2, 3)
So, the library’s location is (-2, 3)

Question 22.
Each unit on the map represents 1 mile. Gregory leaves his house at (−5, 4), cycles 4 miles east, 6 miles south, and 1 mile west. In which quadrant of the city is he now?
Type below:
__________

Answer:
Quadrant III

Explanation:
Gregory leaves his house at (−5, 4)
cycles 4 miles east = -5 + 4 = -1; (-1, 4)
6 miles south = (-1, -1)
1 mile west (-2, -1)
So, he is now in Quadrant III

Question 23.
The bus station has the same x-coordinate as City Hall but the opposite y-coordinate. In which quadrant of the city is the bus station located?
Type below:
__________

Answer:
Quadrant I

Explanation:
The bus station has the same x-coordinate as City Hall but the opposite y-coordinate.
City Hall = (2, -3)
The opposite y-coordinate = 3
Bus station located at (2, 3)
Bus station located at Quadrant I

Question 24.
Describe Relationships Describe the relationship between the locations of the points (2, 5) and (2, −5) on the coordinate plane.
Type below:
__________

Answer:
(2, 5) and (2, −5) have the same x-coordinate.
They have the opposite y-coordinate.

Question 25.
Identify the quadrant where each point is located. Write each point in the correct box.
(−1, 3), (4, −2), (−3, −2), (1, −3), (−1, 2), (3, 4)
Type below:
__________

Answer:
(−1, 3) = Quadrant II
(4, −2) = Quadrant IV
(−3, −2) = Quadrant III
(1, −3) = Quadrant IV
(−1, 2) = Quadrant II
(3, 4) = Quadrant I

Problem Solving + Applications – Page No. 187

Identify the quadrant where the point is located.

Question 1.
(10, -2)
Type below:
__________

Answer:
Quadrant IV

Explanation:
The x-coordinate is positive. So, the point is 10 units to the right of the origin.
Since the point is to the right of the origin, it must be located in either
Quadrant I or Quadrant IV
The y-coordinate is negative, so the point is 2 units down from the origin.
Since the point is down the origin, it must be located in Quadrant IV.
Quadrant IV

Question 2.
(-5, -6)
Type below:
__________

Answer:
Quadrant III

Explanation:
The x-coordinate is negative. So, the point is 5 units to the left of the origin.
Since the point is to the left of the origin, it must be located in either
Quadrant II or Quadrant III
The y-coordinate is negative, so the point is 6 units down from the origin.
Since the point is down the origin, it must be located in Quadrant III.
Quadrant III.

Question 3.
(3, 7)
Type below:
__________

Answer:
Quadrant I

Explanation:
The x-coordinate is positive. So, the point is 3 units to the right of the origin.
Since the point is to the right of the origin, it must be located in either
Quadrant I or Quadrant IV
y-coordinate is positive, so the point is 7 units up from the origin.
Since the point is up to the origin, it must be located in Quadrant I.
Quadrant I

The two points are reflections of each other across the x- or y-axis. Identify the axis.

Question 4.
(5, 3) and (−5, 3)
Type below:
__________

Answer:
y-axis

Explanation:
The given x-axis points are 5 and -5
The y-axis points are 3 and 3
The y-axis points are reflections to each other

Question 5.
(−7, 1) and (−7, −1)
Type below:
__________

Answer:
x-axis

Explanation:
The given x-axis points are -7 and -7
The y-axis points are 1 and -1
The x-axis points are reflections to each other

Question 6.
(−2, 4) and (−2, −4)
Type below:
__________

Answer:
x-axis

Explanation:
The given x-axis points are -2 and -2
The y-axis points are 4 and -4
The x-axis points are reflections to each other

Give the reflection of the point across the given axis.

Question 7.
(−6, −10), y-axis
Type below:
__________

Answer:
(6, -10)

Explanation:
The x-axis point is -6.
So, the reflection of the point 6

Question 8.
(−11, 3), x-axis
Type below:
__________

Answer:
(-11, -3)

Explanation:
The y-axis point is -3.
So, the reflection of a point 3

Question 9.
(8, 2), x-axis
Type below:
__________

Answer:
(8, -2)

Explanation:
The y-axis point is 2.
So, the reflection of a point -2

Problem Solving

Question 10 .
A town’s post office is located at the point (7, 5) on a coordinate plane. In which quadrant is the post office located?
Type below:
__________

Answer:
Quadrant I

Explanation:
A town’s post office is located at the point (7, 5) on a coordinate plane.
The x-coordinate is positive. So, the point is 7 units to the right of the origin.
Since the point is to the right of the origin, it must be located in either
Quadrant I or Quadrant IV
The y-coordinate is positive, so the point is 5 units up from the origin.
Since the point is up the origin, it must be located in Quadrant I.
Quadrant I

Question 11.
The grocery store is located at a point on a coordinate plane with the same y-coordinate as the bank but with the opposite x-coordinate. The grocery store and bank are reflections of each other across which axis?
Type below:
__________

Answer:
y-axis

Explanation:
The grocery store is located at a point on a coordinate plane with the same y-coordinate as the bank but with the opposite x-coordinate.
The grocery store and bank are reflections of each other across the y-axis.

Question 12.
Explain to a new student how a reflection across the y-axis changes the coordinates of the original point.
Type below:
__________

Answer:
The coordinate plane with the same y-coordinate remains same but with the opposite x-coordinate.

Lesson Check – Page No. 188

Question 1.
In which quadrant does the point (−4, 15) lie?
Type below:
__________

Answer:
Quadrant II

Explanation:
The x-coordinate is negative. So, the point is 4 units to the left of the origin.
Since the point is to the left of the origin, it must be located in either
Quadrant II or Quadrant III
The y-coordinate is positive, so the point is 15 units up from the origin.
Since the point is up to the origin, it must be located in Quadrant II.
Quadrant II.

Question 2.
What are the coordinates of the point (10, −4) if it is reflected across the y–axis?
Type below:
__________

Answer:
(-10, -4)

Explanation:
coordinates of the point (-10, −4)
If it is reflected across the y–axis, coordinates of the point will be (-10, -4)

Spiral Review

Question 3.
Small juice bottles come in packages of 6. Yogurt treats come in packages of 10. Paula wants to have the exact same number of each item. What is the least number of bottles of juice and individual yogurt treats she will have? How many packages of each will she need?
Type below:
__________

Answer:
5 packages

Explanation:
Number of packages of small juice bottles = 6
Number of packages of yogurt = 10
For this, we will find the L.C.M. of 6 and 10 =30
So, there will be 5 packages of small juice bottles and 3 packages of yogurt.

Question 4.
Alison saves $29.26 each month. How many months will it take her to save enough money to buy a stereo for $339.12?
_____ month

Answer:
11 months

Explanation:
Round 29 and 339 to 30 and 340.
Divide 340 by 30
The answer should be 11.3 repeatings.
11 months

Question 5.
The library is 1.75 miles directly north of the school. The park is 0.6 miles directly south of the school. How far is the library from the park?
Type below:
__________

Answer:
2.35 miles

Explanation:
The library is 1.75 miles directly north of the school. The park is 0.6 miles directly south of the school.
1.75 + 0.6 would be 2.35 miles, the library to the parking.

Question 6.
Tours of the art museum are offered every \(\frac{1}{3}\) hour starting at 10 A.M. The museum closes at 4:00 P.M. How many tours are offered each day?
_____ tours

Answer:
18 tours

Explanation:
Staring time of tours=10 am
Closing time of tours=4 pm
Duration of tours(10 am to 4 pm)=6 hours
Time for each tour= 1/3 hours
Total number of tours offered in a day= 6 × 3 = 18
Therefore, 18 tours offered each day.

Share and Show – Page No. 191

Find the distance between the pair of points.
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 27

Question 1.
(−3, 1) and (2, 1)
_____ units

Answer:
5 units

Explanation:
The points have the same y-coordinate, so they are located on a horizontal line.
Find the distance between the x-coordinates of the point (-3, 1) and the point (2, 1)
|-3| = 3
3 + 2 = 5

Question 2.
(2, 1) and (2, -4)
_____ units

Answer:
5 units

Explanation:
The points have the same x-coordinate, so they are located on a vertical line.
Find the distance between the y-coordinates of the point (2, 1) and the point (2, -4)
|-4| = 4
1 + 4 = 5

Question 3.
(2, -4) and (4, -4)
_____ units

Answer:
2 units

Explanation:
The points have the same y-coordinate, so they are located on a horizontal line.
Find the distance between the x-coordinates of the point (2, -4) and the point (4, -4)
4 – 2 = 2

Question 4.
(-3, 3) and (-3, 1)
_____ units

Answer:
2 units

Explanation:
The points have the same x-coordinate, so they are located on a vertical line.
Find the distance between the y-coordinates of the point (-3, 3) and the point (-3, 1)
3 – 1 = 2

On Your Own

Practice: Copy and Solve Graph the pair of points. Then find the distance between them.

Question 5.
(0, 5) and (0, -5)
_____ units

Answer:
10 units

Explanation:
The points have the same x-coordinate, so they are located on a vertical line.
Find the distance between the y-coordinates of the point (0, 5) and the point (0, -5)
|-5| = 5
5 + 5 = 10

Question 6.
(1, 1) and (1, -3)
_____ units

Answer:
4 units

Explanation:
The points have the same x-coordinate, so they are located on a vertical line.
Find the distance between the y-coordinates of the point (1, 1) and the point (1, -3)
|-3| = 3
1 + 3 = 4

Question 7.
(-2, -5) and (-2, -1)
_____ units

Answer:
4 units

Explanation:
The points have the same x-coordinate, so they are located on a vertical line.
Find the distance between the y-coordinates of the point (-2, -5) and the point (-2, -1)
|-5| = 5
|-1| = 1
5 – 1 = 4

Question 8.
(-7, 3) and (5, 3)
_____ units

Answer:
12 units

Explanation:
The points have the same y-coordinate, so they are located on a horizontal line.
Find the distance between the x-coordinates of the point (-7, 3) and the point (5, 3)
|-7| = 7
7 + 5 = 12

Question 9.
(3, -6) and (3, -10)
_____ units

Answer:
4 units

Explanation:
The points have the same x-coordinate, so they are located on a vertical line.
Find the distance between the y-coordinates of the point (3, -6) and the point (3, -10)
|-6| = 6
|-10| = 10
10 – 6 = 4

Question 10.
(8, 0) and (8, -8)
_____ units

Answer:
8 units

Explanation:
The points have the same x-coordinate, so they are located on a vertical line.
Find the distance between the y-coordinates of the point (8, 0) and the point (8, -8)
|-8| = 8
0 + 8 = 8

Use Reasoning Algebra Write the coordinates of a point that is the given distance from the given point.

Question 11.
4 units from (3, 5)
Type below:
__________

Answer:
1 or 9

Explanation:
4 units from (3, 5)
(3, 9) or (3, 1)

Question 12.
6 units from (2, 1)
Type below:
__________

Answer:
8 or -4

Explanation:
6 units from (2, 1)
(8, 1) or (-4, 1)

Question 13.
7 units from (−4, −1)
Type below:
__________

Answer:
-8 or 6

Explanation:
7 units from (−4, −1)
(-8, -1) or (-8, 6)

Problem Solving + Applications – Page No. 192

An archaeologist is digging at an ancient city. The map shows the locations of several important finds. Each unit represents 1 kilometer. Use the map for 14–18.

Question 14.
How far is it from the stadium to the statue?
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 28
_____ km

Answer:
8 km

Explanation:
Stadium = (4, 5)
statue = (4, -3)
The points have the same x-coordinate, so they are located on a vertical line.
Find the distance between the y-coordinates of the point (4, 5) and the point (4, -3)
|-3| = 3
5 + 3 = 8

Question 15.
The archaeologist drives 3 km south from the palace. How far is he from the market?
_____ km

Answer:
3 km

Explanation:
The palace is at the origin (0, 0)
So, the answer is 3 km

Question 16.
The archaeologist’s campsite is located at (−9, −3). How far is it from the campsite to the market?
_____ km

Answer:
11 km

Explanation:
the campsite is located at (−9, −3)
the market is located at (-2, -3)
The points have the same y-coordinate, so they are located on a horizontal line.
Find the distance between the x-coordinates of the point (−9, −3) and the point (-2, -3)
|-9| = 9
|-2| = 2
9 + 2 = 11
campsite is 11 km far to the market

Question 17.
The archaeologist rode east on a donkey from the Great Gate, at (−11, 4), to the Royal Road. Then he rode south to the palace. How far did the archaeologist ride?
_____ km

Answer:
15 km

Explanation:
The archaeologist rode east on a donkey from the Great Gate, at (−11, 4), to the Royal Road. Then he rode south to the palace.
First, he needs to move |-11| = 11 km
Then, he needs to move 4 km
4 + 11 = 15 km

Question 18.
Generalize Explain how you could find the distance from the palace to any point on the Imperial Highway.
Type below:
__________

Answer:
The distance varies according to the points on the Imperial Highway

Question 19.
Select the pairs of points that have a distance of 10 between them. Mark all that apply.
(3, −6) and (3, 4)
( −3, 8) and (7, 8)
(4, 5) and (6, 5)
(4, 1) and (4, 11)
Type below:
__________

Answer:
(3, −6) and (3, 4)
( −3, 8) and (7, 8)
(4, 5) and (6, 5)

Explanation:
6 + 4 = 10
3 + 7 = 10
4 + 6 = 10

Distance on the Coordinate Plane – Page No. 193

Find the distance between the pair of points.

Question 1.
(1, 4) and (−3, 4)
_____ units

Answer:
4 units

Explanation:
The points have the same y-coordinate, so they are located on a horizontal line.
Find the distance between the x-coordinates of the point (1, 4) and the point (−3, 4)
|-3| = 3
1 + 3 = 4

Question 2.
(7, −2) and (11, −2)
_____ units

Answer:
3 units

Explanation:
The points have the same y-coordinate, so they are located on a horizontal line.
Find the distance between the x-coordinates of the point (7, −2) and the point (11, −2)
11 – 7 = 3

Question 3.
(6, 4) and (6, −8)
_____ units

Answer:
12 units

Explanation:
The points have the same x-coordinate, so they are located on a vertical line.
Find the distance between the y-coordinates of the point (6, 4) and the point (6, −8)
|-8| = 8
4 + 8 = 12

Question 4.
(8, −10) and (5, −10)
_____ units

Answer:
3 units

Explanation:
The points have the same y-coordinate, so they are located on a horizontal line.
Find the distance between the x-coordinates of the point (8, −10) and the point (5, −10)
8 – 5 = 3

Question 5.
(−2, −6) and (−2, 5)
_____ units

Answer:
11 units

Explanation:
The points have the same x-coordinate, so they are located on a vertical line.
Find the distance between the y-coordinates of the point (−2, −6)and the point (−2, 5)
|-6| = 6
6 + 5 = 11

Question 6.
(−5, 2) and (−5, −4)
_____ units

Answer:
6 units

Explanation:
The points have the same x-coordinate, so they are located on a vertical line.
Find the distance between the y-coordinates of the point (−5, 2) and the point (−5, −4)
|-4| = 4
2 + 4 = 6

Write the coordinates of a point that is the given distance from the given point.

Question 7.
5 units from (−1, −2)
Type below:
__________

Answer:
-6 or 4

Explanation:
5 units from (−1, −2)
(-6, -2) or (4, -2)

Question 8.
8 units from (2, 4)
Type below:
__________

Answer:
12 or -4

Explanation:
8 units from (2, 4)
(2, 12) or (2, -4)

Question 9.
3 units from (−7, −5)
Type below:
__________

Answer:
-2 or -8

Explanation:
3 units from (−7, −5)
(-7, -2) or (-7, -8)

Problem Solving

The map shows the locations of several areas in an amusement park. Each unit represents 1 kilometer.
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 29

Question 10.
How far is the Ferris wheel from the rollercoaster?
_____ km

Answer:
4 km

Explanation:
Ferris wheel = (5, 6)
rollercoaster = (5, 2)
6 – 2 = 4

Question 11.
How far is the water slide from the restrooms?
_____ km

Answer:
7 km

Explanation:
water slide = (-3, -4)
restrooms = (4, -4)
3 + 4 = 7

Question 12.
Graph the points (23, 3), (23, 7), and (4, 3) on a coordinate plane. Explain how to find the distance from (23, 3) to (23, 7) and from (23, 3) and (4, 3).
Type below:
__________

Answer:

Explanation:
(23, 3) to (23, 7)
The points have the same x-coordinate, so they are located on a vertical line.
Find the distance between the y-coordinates of the point (23, 3) and the point (23, 7)
7 – 3 = 4
(23, 3) and (4, 3).
The points have the same y-coordinate, so they are located on a horizontal line.
Find the distance between the x-coordinates of the point (23, 3) and the point (4, 3)
4 – 3 = 1

Lesson Check – Page No. 194

Question 1.
What is the distance between (4, −7) and (−5, −7)?
_____ units

Answer:
9 units

Explanation:
(4, −7) and (−5, −7)
The points have the same y-coordinate, so they are located on a horizontal line.
Find the distance between the x-coordinates of the point (4, −7) and the point (−5, −7)
|-5| = 5
5 + 4 = 9

Question 2.
Point A and point B are 5 units apart. The coordinates of point A are (3, −9). The y–coordinate of point B is −9. What is a possible x–coordinate for point B?
Type below:
__________

Answer:
8 or -2

Explanation:
Point A and point B are 5 units apart. The coordinates of point A are (3, −9). The y–coordinate of point B is −9.
The points have the same y-coordinate, so they are located on a horizontal line.
the distance between the x-coordinates = 5
So, 8 or -2

Spiral Review

Question 3.
An apple is cut into 10 pieces. 0.8 of the apple is eaten. Which fraction, in simplest form, represents the amount of apple that is left?
\(\frac{□}{□}\)

Answer:
\(\frac{1}{5}\)

Explanation:
An apple is cut into 10 pieces. 0.8 of the apple is eaten.
10/10 – 8/10 = 2/10 = 1/5 amount of apple left.

Question 4.
A carton contains soup cans weighing a total of 20 pounds. Each can weighs 1 \(\frac{1}{4}\) pounds. How many cans does the carton contain?
_____ cans

Answer:
16 cans

Explanation:
Divide 20 with 5/4 (=1 1/4)
So, 20 × 4/5 which would be 80/5 = 16 cans

Question 5.
List −1, \(\frac{1}{4}\), and −1 \(\frac{2}{3}\) in order from greatest to least.
Type below:
__________

Answer:
\(\frac{1}{4}\), -1, −1 \(\frac{2}{3}\)

Explanation:
\(\frac{1}{4}\) > -1 > −1 \(\frac{2}{3}\)

Question 6.
The point located at (3, −1) is reflected across the y−axis. What are the coordinates of the reflected point?
Type below:
__________

Answer:
(-3, -1)

Explanation:
The point located at (3, −1) is reflected across the y−axis.
(-3, -1)

Share and Show – Page No. 197

Question 1.
Busby County is rectangular. A map of the county on a coordinate plane shows the vertices of the county at (−5, 8), (8, 8), (8, −10), and (−5, −10). Each unit on the map represents 1 mile. What is the county’s perimeter?
_____ miles

Answer:
62 miles

Explanation:
Busby County is rectangular. A map of the county on a coordinate plane shows the vertices of the county at (−5, 8), (8, 8), (8, −10), and (−5, −10).
The distance of (−5, 8) is 8
The distance of (8, 8) is 8
The distance between -5 to 8 is 5 + 8 = 13
The distance of (8, −10) is 10
The distance of (−5, −10) is 10
The distance between -5 to 8 is 5 + 8 = 13
8 + 8 + 13 + 10 + 10 + 13 = 62

Question 2.
What if the vertices of the county were (−5, 8), (8, 8), (8, −6), and (−5, −6)? What would the perimeter of the county be?
_____ miles

Answer:
54 miles

Explanation:
The distance from – 5 to 8 is 5 + 8 = 13
The distance from – 5 to 8 is 5 + 8 = 13
The distance from 8 to -6 is 8 + 6 = 14
The distance from 8 to -6 is 8 + 6 = 14
13 + 14 + 13 + 14 = 54

Question 3.
On a coordinate map of Melville, a restaurant is located at (−9, −5). A laundry business is located 3 units to the left of the restaurant on the map. What are the map coordinates of the laundry business?
Type below:
__________

Answer:
(-12, -5)

Explanation:
On a coordinate map of Melville, a restaurant is located at (−9, −5).
A laundry business is located 3 units to the left of the restaurant on the map.(-12, -5) is the answer

Question 4.
The library is 4 blocks north and 9 blocks east of the school. The museum is 9 blocks east and 11 blocks south of the school. How far is it from the library to the museum?
_____ blocks

Answer:
15 blocks

Explanation:
the library is 4 blocks north = (0, 4)
9 blocks east = (9, 4)
The museum is 9 blocks east = (9, 0)
11 blocks south = (9, -11)
4 + 11 = 15

Problem Solving + Applications – Page No. 198

Question 5.
Make Sense of Problems Diana left her campsite at (2, 6) on a map of Big Trees Park, hiked to Redwood Grove at (−5, 6), and continued on to Bass Lake at (−5, −3). Each unit on the map represents 1 kilometer. How far did Diana hike?
_____ km

Answer:
16 km

Explanation:
Diana left her campsite at (2, 6) on a map of Big Trees Park, hiked to Redwood Grove at (−5, 6), 2 + 5 = 7
and continued on to Bass Lake at (−5, −3), 6 + 3 = 9
7 + 9 = 16 km

Question 6.
Hector left his house at (−6, 13) on a map of Coleville and walked to the zoo at (−6, 2). From there he walked east to his friend’s house. He walked a total distance of 25 blocks. If each unit on the map represents one block, what are the coordinates of Hector’s friend’s house?
Type below:
__________

Answer:
(19,2) should be the answer. He was -6 above the x-axis. Going east for 25 unit means he walked horizontally keeping the y-axis same

Question 7.
In November, the price of a cell phone was double the price in March. In December, the price was $57, which was $29 less than the price in November. What was the price of the cell phone in March?
$ _____

Answer:
$172

Explanation:
In November, the price of a cell phone was double the price in March. In December, the price was $57, which was $29 less than the price in November.
29 + 57 = 86
86 × 2 = $172

Question 8.
A map of the city holding the Olympics is placed on a coordinate plane. Olympic Stadium is located at the origin of the map. Each unit on the map represents 2 miles.
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 30
Graph the locations of four other Olympic buildings.

Max said the distance between the Aquatics Center and the Olympic Village is greater than the distance between the Media Center and the Basketball Arena. Do you agree with Max? Use words and numbers to support your answer
Type below:
__________

Answer:
Max said is correct
Aquatics Center = (8, 4)
Olympic Village = (-8, 4)
The distance = 8 + 8 = 16
Media Center = (4, -5)
Basketball Arena = (-8, -5)
The distance = 4 + 8 = 12

Problem Solving The Coordinate Plane – Page No. 199

Read each problem and solve.

Question 1.
On a coordinate map of Clifton, an electronics store is located at (6, −7). A convenience store is located 7 units north of the electronics store on the map. What are the map coordinates of the convenience store?
Type below:
__________

Answer:
(6, 0)

Explanation:
On a coordinate map of Clifton, an electronics store is located at (6, −7). A convenience store is located 7 units north of the electronics store on the map.
The map coordinates of the convenience store is (6, 0)

Question 2.
Sonya and Lucas walk from the school to the library. They walk 5 blocks south and 4 blocks west to get to the library. If the school is located at a point (9, −1) on a coordinate map, what are the map coordinates of the library?
Type below:
__________

Answer:
(5, -6)

Explanation:
The school is at (9, −1)
5 blocks South mean that you subtract 5 from the y coordinate:
(9, -1-5) = (9, -6)
4 blocks West means that you subtract 4 from the x coordinate:
(9-4, -6) = (5, -6)
The library is at (5, -6)

Question 3.
On a coordinate map, Sherry’s house is at the point (10, −2) and the mall is at point (−4, −2). If each unit on the map represents one block, what is the distance between Sherry’s house and the mall?
_____ blocks

Answer:
14 blocks

Explanation:
(10,-2)
(-4,-2)
x value- 10-(-4)=14
y value- Since both y values are the same, you don’t do anything.

Question 4.
Arthur left his job at (5, 4) on a coordinate map and walked to his house at (5, −6). Each unit on the map represents 1 block. How far did Arthur walk?
_____ blocks

Answer:
10 blocks

Explanation:
He walked 10 blocks. 4 to -6 is 10. 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6.

Question 5.
A fire station is located 2 units east and 6 units north of a hospital. If the hospital is located at a point (−2, −3) on a coordinate map, what are the coordinates of the fire station?
Type below:
__________

Answer:
(0, 3)

Explanation:
the hospital is located at a point (−2, −3).
A fire station is located 2 units east and 6 units north of a hospital.
(-2 +2, -3+6) = (0,3)

Question 6.
Xavier’s house is located at the point (4, 6). Michael’s house is 10 blocks west and 2 blocks south of Xavier’s house. What are the coordinates of Michael’s house?
Type below:
__________

Answer:
(-6, 4)

Explanation:
the coordinates are -6,4. (x-10,y-2)

Question 7.
Write a problem that can be solved by drawing a diagram on a coordinate plane.
Type below:
__________

Answer:
On a coordinate map, Sherry’s house is at the point (10, −2) and the mall is at point (−4, −2). If each unit on the map represents one block, what is the distance between Sherry’s house and the mall?

Lesson Check – Page No. 200

Question 1.
The points (−4, −4), (−4, 4), (4, 4), and (4, −4) form a square on a coordinate plane. How long is a side length of the square?
_____ units

Answer:
8 units

Explanation:
-4 + 4 = 8 units
side length of the square is 8 units

Question 2.
On a coordinate map, the museum is located at (−5, 7). A park is located 6 units to the right of the museum on the map. What are the coordinates of the park?
Type below:
__________

Answer:
(1, 7)

Explanation:
On a coordinate map, the museum is located at (−5, 7). A park is located 6 units to the right of the museum on the map.
(1,7)

Spiral Review

Question 3.
On a grid Joe’s house is marked at (−5, −3) and Andy’s house is marked at (1, −3). What is the distance, on the grid, between Joe’s house and Andy’s house?
_____ units

Answer:
6 units

Explanation:
On a grid Joe’s house is marked at (−5, −3) and Andy’s house is marked at (1, −3).
|-5| = 5
5 + 0 = 5
0 + 1 = 1
5 + 1 = 6

Question 4.
In the last two years, Mari grew 2 \(\frac{1}{4}\) inches, Kim grew 2.4 inches, and Kate grew 2 \(\frac{1}{8}\) inches. Write the amounts they grew in order from least to greatest.
Type below:
__________

Answer:
2 \(\frac{1}{8}\), 2 \(\frac{1}{4}\), 2.4

Explanation:
In the last two years, Mari grew 2 \(\frac{1}{4}\) inches, Kim grew 2.4 inches, and Kate grew 2 \(\frac{1}{8}\) inches.
2 \(\frac{1}{4}\) = 9/4 = 2.25
2 \(\frac{1}{8}\) = 17/8 = 2.125
2.125, 2.25, 2.4

Question 5.
A jar of jelly that weighs 4.25 ounces costs $2.89. What is the cost of one ounce of jelly?
$ _____

Answer:
$0.68

Explanation:
A jar of jelly that weighs 4.25 ounces costs $2.89.
$2.89/4.25 = $0.68

Question 6.
Jan began with \(\frac{5}{6}\) pound of modeling clay. She used \(\frac{1}{5}\) of the clay to make decorative magnets. She divided the remaining clay into 8 equal portions. What is the weight of the clay in each portion?
\(\frac{□}{□}\) pounds

Answer:
\(\frac{1}{12}\) pounds

Explanation:
Weight of modelling clay is = 5/6 pounds
Part of clay used to make decorative magnets is = 1/5
Remaining part of clay = 1 – 1/5 = 4/5
So, Remaining part of clay is divided into 8 equal parts so, Weight of each clay is given by 4/5 × 5/6 × 1/8 = 1/12 pounds
So, weight of the clay in each portion is 1/12 pounds

Chapter 3 Review/Test – Page No. 201

Question 1.
For numbers 1a–1d, choose Yes or No to indicate whether the situation can be represented by a negative number.
1a. Sherri lost 100 points answering a question wrong. Yes No
1b. The peak of a mountain is 2,000 feet above sea level. Yes No
1c. Yong paid $25 for a parking ticket. Yes No
1d. A puppy gained 3 pounds. Yes No
1a. __________
1b. __________
1c. __________
1d. __________

Answer:
1a. Yes
1b. No
1c. No
1d. No

Question 2.
The low weekday temperatures for a city are shown.
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 31
Part A
Using the information in the table, order the temperatures from lowest to highest.
Type below:
__________

Answer:
-7, -5, -3, 2, 3

Explanation:
Monday = -5
Tuesday = -3
Wednesday = 2
Thursday = -7
Friday = 3
-7, -5, -3, 2, 3

Question 2.
Part B
Explain how to use a vertical number line to determine the order.
Type below:
__________

Answer:
Place the -3, -5, -7, are below the 0. And place 2 and 3 are above the 0.

Page No. 202

Question 3.
For numbers 3a–3e, choose Yes or No to indicate whether the number is between –1 and –2.
3a. \(\frac{-4}{5}\) Yes No
3b. 1 \(\frac{2}{3}\) Yes No
3c. −1.3 Yes No
3d. −1 \(\frac{1}{4}\) Yes No
3e. −2 \(\frac{1}{10}\) Yes No
3a. __________
3b. __________
3c. __________
3d. __________
3e. __________

Answer:
3a. No
3b. No
3c. Yes
3d. Yes
3e. No

Explanation:
3a. \(\frac{-4}{5}\) = -0.8
3b. 1 \(\frac{2}{3}\) = 1.666
3c. -1.3
3d. −1 \(\frac{1}{4}\) = -1.25
3e. −2 \(\frac{1}{10}\) = -21/10 = -2.1

Question 4.
Compare \(\frac{-1}{5}\) and –0.9. Use numbers and words to explain your answer
Type below:
__________

Answer:
\(\frac{-1}{5}\) = -0.2
-0.9
-0.2 and -0.9 both are negative numbers. They lies between 0 and -1

Question 5.
Jeandre said |3| equals |–3|. Is Jeandre correct? Use a number line and words to support your answer.
Type below:
__________

Answer:
grade 6 chapter 3 Page no. 202 image 1

Explanation:
Yes, he is correct and he is referring to the absolute values of number 3 and -3. And by absolute value, this is the distance of the number from the origin zero (0) which is symbolized by two vertical lines, as |3| or |-3| is equal to 3.
The picture shows a number line where green is the origin zero (0). The purple line is the distance between 0 and 3 which is 3. The pink one is the distance of -3 from 0 which is also 3. Therefore, |3| equals |-3|

Question 6.
Write the values in order from least to greatest.
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 32
Type below:
__________

Answer:
|2| |-4| |8| |-12|

Explanation:
|-4| = 4
|2| = 2
|-12| = 12
|8| = 8
2, 4, 8, 12

Question 7.
For numbers 7a–7d, select True or False for each statement.
7a. The x-coordinate of any point on the y-axis is 0. True False
7b. Point D(–2, 1) is to the left of the y-axis and below the x-axis. True False
7c. The point where the axes intersect is the origin. True False
7d. If both the x- and y- coordinates are positive, the point is to the right of the y-axis and below the x-axis. True False
__________
__________
__________
__________

Answer:
7a. True
7b. False
7c. True
7d. False

Page No. 203

Question 8.
Mia’s house is located at point (3, 4) on a coordinate plane. The location of Keisha’s house is the reflection of the location of Mia’s house across the y-axis. In what quadrant is Keisha’s house in?
Type below:
__________

Answer:
quadrant II

Explanation:
Mia’s house is located at point (3, 4) on a coordinate plane. The location of Keisha’s house is the reflection of the location of Mia’s house across the y-axis.
quadrant II is the answer.

Question 9.
Points A(3, 8) and B(–4, 8) are located on a coordinate plane. Graph the pair of points. Then find the distance between them. Use numbers and words to explain your answer.
Type below:
__________

Answer:

Explanation:
Points A(3, 8) and B(–4, 8) are located on a coordinate plane.
3 + 0 = 3
|-4| = 4
4 + 0 = 4
3 + 4 = 7
7 units

Page No. 204

Question 10.
The map shows the location J of Jose’s house and the location F of the football field. Jose is going to go to Tyrell’s house and then the two of them are going to go to the football field for practice.
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 33
Part A
Tyrell’s house is located at point T, the reflection of point J across the y-axis. What are the coordinates of points T, J, and F?
Type below:
__________

Answer:
coordinates of points T (6, 8)
coordinates of points J (-6, 8), and
coordinates of points F(-5, 6)

Question 10.
Part B
If each unit on the map represents 1 block, what was the distance Tyrell traveled to the football field and what was the distance Jose traveled to the football field? Use numbers and words to explain your answer
Type below:
__________

Answer:
If each unit on the map represents 1 block, the distance Jose traveled to the football field
coordinates of points T (6, 8)
coordinates of points J (-6, 8)
|-6| = 6
6 + 6 = 12 units.
the distance Tyrell traveled to the football field
coordinates of points T (6, 8)
coordinates of points F(-5, 6)
6 + 5 = 11 units

Question 11.
For numbers 11a–11d, choose Yes or No to indicate whether the situation could be represented by the integer +3.
11a. A football team gains 3 yards on a play. Yes No
11b. A golfer’s score is 3 over par. Yes No
11c. A student answers a Yes No 3-point question correctly. Yes No
11d. A cat loses 3 pounds. Yes No
11a. __________
11b. __________
11c. __________
11d. __________

Answer:
11a. Yes
11b. Yes
11c. Yes
11d. No

Page No. 205

Question 12.
Jason used a map to record the elevations of five locations.
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 34
Jason wrote the elevations in order from lowest to highest : -3, 5, 8 -18, -20.
Is Jason correct? Use words and numbers to explain why or why not. If Jason is incorrect, what is the correct order?
Type below:
__________

Answer:
Jason is incorrect.
the elevations in order from lowest to highest: -20, -18, -3, 5, 8

Question 13.
For numbers 13a–13d, select True or False for each statement.
13a. \(\frac{1}{5}\) is between 0 and 1. True False
13b. −2 \(\frac{2}{3}\) is between -1 and -2. True False
13c. −3 \(\frac{5}{8}\) is between -3 and -4. True False
13d. 4 \(\frac{3}{4}\) is between 3 and 4. True False
13a. __________
13b. __________
13c. __________
13d. __________

Answer:
13a. True
13b. False
13c. True
13d. False

Question 14.
Choose <, >, or =.
14a. 0.25 ο \(\frac{3}{4}\)
14b. 2 \(\frac{7}{8}\) ο 2.875
14c. \(\frac{1}{3}\) ο 0.325
14d. \(\frac{-3}{4}\) ο \(\frac{-1}{2}\)
0.25 ____ \(\frac{3}{4}\)
2 \(\frac{7}{8}\) _____ 2.875
\(\frac{1}{3}\) _____ 0.325
\(\frac{-3}{4}\) _____ \(\frac{-1}{2}\)

Answer:
0.25 < \(\frac{3}{4}\)
2 \(\frac{7}{8}\) = 2.875
\(\frac{1}{3}\) > 0.325
\(\frac{-3}{4}\) < \(\frac{-1}{2}\)

Explanation:
\(\frac{3}{4}\) = 0.75
0.25 < \(\frac{3}{4}\)
2 \(\frac{7}{8}\) = 23/8 = 2.875
2 \(\frac{7}{8}\) = 2.875
\(\frac{-3}{4}\) = -0.75
\(\frac{-1}{2}\) = -0.5

Page No. 206

Question 15.
Graph 4 and −4 on the number line.
Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 35
Tyler says both 4 and −4 have an absolute value of 4. Is Tyler correct? Use the number line and words to explain why or why not.
Type below:__________

Answer:
Tyler is correct.
|-4| = 4
|4| = 4

Question 16.
Lindsay and Will have online accounts for buying music. Lindsay’s account balance is −$20 and Will’s account balance is −$15. Express each account balance as a debt and explain whose debt is greater.
Type below:
__________

Answer:
Lindsey is 5$ more in dept than Will.
Lindsey= -20$
Will= -15$

Question 17.
Explain how to graph points A(–3, 0), B(0, 0), and C(0, –3) on the coordinate plane. Then, explain how to graph point D, so that ABCD is a square.
Type below:
__________

Answer:
First place the points A(–3, 0), B(0, 0), and C(0, –3) on the coordinate plane.
The length from point A to point B is 3.
A square has equal lengths on each side.
So, to find D, Add 3 units to the left to C or down to A.
D(-3, -3)

Question 18.
Point A(2, –3) is reflected across the x-axis to point B. Point B is reflected across the y-axis to point C. What are the coordinates of point C? Use words and numbers to explain your answer.
Type below:
__________

Answer:
Quadrant III

Explanation:
Point A(2, –3) is reflected across the x-axis to point B. Point B is reflected across the y-axis to point C.
So, Point B is (2,3)
Point C is (-2, 3)
C is in Quadrant III

Conclusion:

We believe that the details provided in the HMH Go Math 6th Grade Answer Key for Chapter 3 Understand Positive and Negative Numbers made you happy. All the explanations are prepared by the math experts as per the latest syllabus. Compare the questions in real-time so that you can understand concepts easily. Stay with us to get the answer keys for all the chapters of grade 6.

Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures

go-math-grade-7-chapter-8-modeling-geometric-figures-answer-key

Students of 7th grade can get a detailed explanation for all the problems in Go Math Answer Key Chapter 8 Modeling Geometric Figures. Redefine yourself by practicing problems from Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures. We have given the pdf to Download HMH Go Math Answer Key of Grade 7 Chapter 8 Modeling Geometric Figures. So, refer to Go Math 7th Grade Answer Key Chapter 8 Modeling Geometric Figures to secure the highest score in exams.

Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures

Get access to Download HMH Go Math Grade 7 Key Chapter 8 Modeling Geometric Figures here. Start preparing for your exams by using the Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures pdf. In this article, you can check the answers to review questions in addition to the exercise and homework questions. So, make use of the below links and learn the problems according to the topics.

Chapter 8 – Modeling Geometric Figures – Lesson: 1

Chapter 8 – Modeling Geometric Figures – Lesson: 2

Chapter 8 – Modeling Geometric Figures – Lesson: 3

Chapter 8 – Modeling Geometric Figures – Lesson: 4

Chapter 8 – Modeling Geometric Figures

Guided Practice – Page No. 240

Question 1.
The scale of a room in a blueprint is 3 in : 5 ft. A wall in the same blueprint is 18 in. Complete the table.
Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 1
a. How long is the actual wall?
Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 2
______ feet

Answer: 30 feet

Explanation:
We complete the table using the direct proportionality
3 in : 5 ft.
A wall in the same blueprint is 18 in. is 30 feet.

Question 1.
b. A window in the room has an actual width of 2.5 feet. Find the width of the window in the blueprint.
______ inches

Answer: 1.5 inches

Explanation:
We determine the number of inches corresponding to 1 foot on the actual window
3 in /5 in.
Multiply and divide by 5
(3 in ÷ 5)/(5 ft ÷ 5) = 0.6/1 ft
Thus 1 foot corresponds to 0.6 inches, so the width of the window in the table is
2.5 × 0.6 = 1.5 inches

Question 2.
The scale in the drawing is 2 in. : 4 ft. What are the length and width of the actual room? Find the area of the actual room.
Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 3
Width: _________ feet
Length: _________ feet
Area: _________ sq ft

Answer:
Width: 28 feet
Length: 14 feet
Area: 392 sq ft

Explanation:
We determine the number of feet corresponding to 1 inch in the drawing
2 in/4 in = (2 in. ÷ 2)/(4 in ÷ 2) = 1/2
Thus 1 inch corresponds to 2 feet on the actual dimensions of the room.
We determine the actual length of the room, labeled 14 inches in the drawing.
14 × 2 = 28 feet
We determine the actual width of the room, labeled 7 inches in the drawing.
7 × = 14 feet
We compute the area of the actual room:
28 × 14 = 392 square feet.

Question 3.
The scale in the drawing is 2 cm: 5 m. What are the length and width of the actual room? Find the area of the actual room.
Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 4
Width: _________ m
Length: _________ m
Area: _________ sq meters

Answer:
Width: 25 m
Length: 15 m
Area: 375 sq meters

Explanation:
We determine the number of meters corresponding to 1 centimeter in the drawing:
2 cm/5 cm = (2 cm ÷ 2)/(5 cm ÷ 2) = 1 cm/ 2.5 m
We determine the actual length of the room, labeled 10 cm in the drawing:
10 × 2.5 = 25 m
We determine the actual width of the room, labeled 6 cm in the drawing:
6 × 2.5 = 15 m
We compute the area of the room:
25 × 15 = 375 square feet.

Question 4.
A scale drawing of a cafeteria is drawn on centimeter grid paper as shown. The scale is 1 cm: 4 m.
a. Redraw the rectangle on centimeter grid paper using a scale of 1 cm:6 m.
Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 5
Type below:
_____________

Answer:
Go Math Grade 7 Chapter 8 Answer Key solution img-1

Question 4.
b. What is the actual length and width of the cafeteria using the original scale? What are the actual dimensions of the cafeteria using the new scale?
Length: _________ m
Width: _________ m

Answer:
In the original scale, the dimensions on the drawing are
l1 = 9 cm
w1 = 6  cm
We determine the actual length using the original scale:
9 × 4 = 36
We determine the actual width using the original scale:
6 × 4 = 24
In the second scale, the dimensions on the drawing are
l2 = 6 cm
w1 = 4 cm
We determine the actual length using the original scale:
6 × 6 = 36
We determine the actual width using the original scale:
4 × 6 = 24
Thus the length is 36m
Width is 24 m

Essential Question Check-In

Question 5.
If you have an accurate, complete scale drawing and the scale, which measurements of the object of the drawing can you find?
Type below:
_____________

Answer:
If we have an accurate, complete scale drawing and scale, we can determine all measurements of the object because they are all proportional with the dimensions on the drawing the ratio being the scale.

Independent Practice – Page No. 241

Question 6.
Art
Marie has a small copy of Rene Magritte’s famous painting, The Schoolmaster. Her copy has dimensions 2 inches by 1.5 inches. The scale of the copy is 1 in.:40 cm.
a. Find the dimensions of the original painting.
Length: _________ cm
Width: _________ cm

Answer:
Length: 80 cm
Width: 60 cm

Explanation:
We are given the data
Scale: 1 in:40 cm
Copy l1 = 2 in.
w1 = 1.5 inches
We determine the length l of the original painting
l = 2 × 40 = 80cm
We determine the width w of the original painting
w = 1.5 × 40 = 60 cm

Question 6.
b. Find the area of the original painting.
_____________ sq cm

Answer: 4800 square cm

Explanation:
We determine the width w of the original painting
A = l.w
A = 80 × 60 = 4,800 square cm

Question 6.
c. Since 1 inch is 2.54 centimeters, find the dimensions of the original painting in inches.
Length: _________ inches
Width: _________ inches

Answer:
We determine the length l of the original painting in inches:
1 in. = 2.54 cm
l = 80/2.54 cm ≈ 31.5 inches
We determine the width w of the original painting in inches:
w = 60/2.54 ≈ 23.6 inches

Question 6.
d. Find the area of the original painting in square inches
_____________ sq inches

Answer: 743.4 square inches

Explanation:
We find the area of the original painting in the square inches:
l × w = 31.5 × 23.6 = 743.4 square inches
Thus the area of the original painting is 743.4 square inches.

Question 7.
A game room has a floor that is 120 feet by 75 feet. A scale drawing of the floor on grid paper uses a scale of 1 unit:5 feet. What are the dimensions of the scale drawing?
Length: _________ units
Width: _________ units

Answer:
Length: 24 units
Width: 15 units

Explanation:
We are given the data:
Scale: 1 unit: 5 feet
Actual dimensions: l = 120 feet, w = 75 feet
We determine the number of units on the drawing corresponding to 1 foot from the actual dimensions.
1 unit/ 5 feet
(1 unit ÷ 5)/(5 feet ÷ 5) = 0.2 units/1 feet
We determine the length of the scale drawing:
120 × 0.2 = 24 units
We determine the width of the scale drawing:
75 × 0.2 = 15 units

Question 8.
Multiple Representations
The length of a table is 6 feet. On a scale drawing, the length is 2 inches. Write three possible scales for the drawing.
Type below:
_____________

Answer:
l = 6 feet
l1 = 2 inches
l = the actual length
l1 = the length on a scale drawing
2 inches:6 ft
1 in:3 ft
2/6×12 = 2/72 = 1/36
1 cm: 36 cm

Question 9.
Analyze Relationships
A scale for a scale drawing is 10 cm:1 mm. Which is larger, the actual object or the scale drawing? Explain.
_____________

Answer:
We are given the scale
10 cm: 1 mm
100 mm: 1 m
This means that the correspondent in actual dimension for 100 mm of drawing is 1mm, so to a greater on the drawing there is a smaller actual distance, therefore the scale drawing is larger.

Question 10.
Architecture
The scale model of a building is 5.4 feet tall.
a. If the original building is 810 meters tall, what was the scale used to make the model?
______ ft. : ______ m

Answer: 1 foot: 150 m

Explanation:
Let’s note:
h1 = the height on the scale model
h = the actual height
We are given the data
h1 = 5.4 feet
h = 810 meters
We determine the scale for the model
h1/h = 5.4 feet/810 m = (5.4 feet ÷ 5.4)/(810 ÷ 5.4)
1 foot/150 m
1 foot: 150 m

Question 10.
b. If the model is made out of tiny bricks each measuring 0.4 inch in height, how many bricks tall is the model?
___________ bricks

Answer: 14 bricks

Explanation:
We determine the scale for the model:
h1/0.4 = 5.4/0.4 = 13.5
The number of bricks: 14

Page No. 242

Question 11.
You have been asked to build a scale model of your school out of toothpicks. Imagine your school is 30 feet tall. Your scale is 1 ft:1.26 cm.
a. If a toothpick is 6.3 cm tall, how many toothpicks tall will your model be?
______ toothpicks

Answer: 6

Explanation:
Given that,
h = 30 feet
1 ft: 1.26 cm
h1 = the height on the scale model
h = the actual height
We determine the height h1 of the model:
h1 = 30 × 1.26 = 37.8 cm
h1/6.3 = 37.8/6.3 = 6
Thus the number of toothpicks = 6

Question 11.
b. Your mother is out of toothpicks, and suggests you use cotton swabs instead. You measure them, and they are 7.6 cm tall. How many cotton swabs tall will your model be?
______ cotton swabs

Answer: 5

Explanation:
We find the number of cotton wabs
h1/7.6 = 37.8/7.6 ≈ 5
Thus the number of cotton wabs = 5

H.O.T.

Focus on Higher Order Thinking

Question 12.
Draw Conclusions
The area of a square floor on a scale drawing is 100 square centimeters, and the scale of the drawing is 1 cm : 2 ft. What is the area of the actual floor? What is the ratio of the area in the drawing to the actual area?
Area = ______ sq. ft.

Answer: 400 sq. ft

Explanation:
A1 = the area of the drawing
A = the area of the actual floor
We are given the data:
A1 = 100 cm²
1 cm: 2 ft
1 cm corresponds to 2 ft
1 cm × 1 cm corresponds to 2 ft × 2 ft
1 cm² corresponds to 4 ft²
A = 100. 4 = 400 ft²
We determine the ratio of the area in the drawing to the actual area:
1 ft = 0.3048 m = 30.48 cm
A1/A = 100/400 × 30.48² ≈ 0.0003

Question 13.
Multiple Representations
Describe how to redraw a scale drawing with a new scale.
Type below:
_____________

Answer:
In order to redraw a scale drawing with a new scale we perform 2 steps:
1. We find how many times the new scale us bigger or smaller than the old one.
2. We multiply this scale factor by the dimensions of the old scale drawing to get a new drawing.

Question 14.
Represent Real-World Problems
Describe how several jobs or professions might use scale drawings at work.
Type below:
_____________

Answer:
Scale drawings are extremely useful in jobs which need to represent bigger areas on smaller devices like
1. Architecture/ constructions
2. medicine
3. agriculture
4. tourism
5. transportation

Guided Practice – Page No. 245

Tell whether each figure creates the conditions to form a unique triangle, more than one triangle, or no triangle.

Question 1.
Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 6
Type below:
_____________

Answer: A unique triangle

Explanation:
We are given two angles and the included side, thus there is a unique triangle as the sides leaving from B and A intersect in a unique point.

Question 2.
Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 7
Type below:
_____________

Answer: No triangle

Explanation:
We are given the three sides of the triangle. We check if the sum of any two sides is greater than the other.
4 + 11 = 15 > 3
11 + 3 = 14 > 4
3 + 4 = 7 is not greater than 11.
Because one inequality is not verified, the triangle doesn’t exist.

Question 3.
Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 8
Type below:
_____________

Answer: A unique triangle

Explanation:
We are given two angles and the included side, thus there is a unique triangle as the sides leaving from B and A intersect in a unique point.

Question 4.
Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 9
Type below:
_____________

Answer: A unique triangle

Explanation:
We are given the three sides of the triangle. We check if the sum of any two sides is greater than the other.
6 + 12 = 18 > 7
12 + 7 = 19 > 6
6 + 7 = 13 > 12
Since all inequalities are verified, there is a unique triangle.

Essential Question Check-In

Question 5.
Describe lengths of three segments that could not be used to form a triangle.
Type below:
_____________

Answer:
Find the lengths of three segments not to be the sides of a triangle, at least one sum of two sides should be smaller than the other side.
Let a, b, c be the lengths of the three segments.
a + b not > a + b + k = c

Independent Practice

Question 6.
On a separate piece of paper, try to draw a triangle with side lengths of 3 centimeters and 6 centimeters, and an included angle of 120°. Determine whether the given segments and angle produce a unique triangle, more than one triangle, or no triangle.
Type below:
_____________

Answer: A unique triangle

Explanation:
∠A = 120°
AB = 6
AC = 3
Go Math Grade 7 Chapter 8 Answer Key solution img-2
We draw the segment AB, the angle A and the segment AC, then we join B and C. The result is an unique triangle.

Question 7.
A landscape architect submitted a design for a triangle-shaped flower garden with side lengths of 21 feet, 37 feet, and 15 feet to a customer. Explain why the architect was not hired to create the flower garden.
Type below:
_____________

Answer:
We are given the sides of a triangle
21 + 37 = 58 > 15
37 + 15 = 52 > 21
15 + 21 = 36 not > 37
We checked the three triangles inequalities
Thus the triangle does not exist, that is the reason why the architect was not hired to create the flower garden.

Page No. 246

Question 8.
Make a Conjecture
The angles in an actual triangle-shaped traffic sign all have measures of 60°. The angles in a scale drawing of the sign all have measures of 60°. Explain how you can use this information to decide whether three given angle measures can be used to form a unique triangle or more than one triangle.
Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 10
Type below:
_____________

Answer: Three given angle measures whose sum is 180° can be used to form an infinity of triangles, having the property that their corresponding sides are proportional.

H.O.T.

Focus on Higher Order Thinking

Question 9.
Communicate Mathematical Ideas
The figure on the left shows a line segment 2 inches long forming a 45° angle with a dashed line whose length is not given. The figure on the right shows a compass set at a width of 1 \(\frac{1}{2}\) inches with its point on the top end of the 2-inch segment. An arc is drawn intersecting the dashed line twice.
Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 11
Explain how you can use this figure to decide whether two sides and an angle not included between them can be used to form a unique triangle, more than one triangle, or no triangle.
Type below:
_____________

Answer:
A trinagle does not exist because one side is shorter than the other two sides. The circle intersects the dashed line only once so that one angles is 45°, so there is only one solution. The circle with the center in B intersects the dashed line twice, thus there are two triangles formed.

Question 10.
Critical Thinking
Two sides of an isosceles triangle have lengths of 6 inches and 15 inches, respectively. Find the length of the third side. Explain your reasoning.
_______ inches

Answer: 15 inches

Explanation:
We are given the two sides of an isosceles triangle
a = 6
b = 15
There are two possibilities the third side is equal to a or b. Lets study both of them
Case 1: a = c = 6, b = 15
a + c = 6 + 6 = 12 not greater than 15 = b
We check the three triangle’s inequalities
a + b = 6 + 15 = 21 > 15 = c
a + c = 6 + 15 = 21 > 15 = b
b + c = 15 + 15 = 30 > 6 = a
Case 2: a = 6, b = c = 15
Thus the third side of the triangle is 15.

Guided Practice – Page No. 249

Describe each cross section.

Question 1.
Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 12
Type below:
_____________

Answer: Triangle/Quadrilateral triangle
The given cross-section in a cube is a triangle/equilateral triangle.

Question 2.
Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 13
Type below:
_____________

Answer: Rectangle
The given cross-section in a cylinder is a rectangle.

Question 3.
Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 14
Type below:
_____________

Answer: Triangle

Explanation:
The given cross-section in the prism is the triangle.

Question 4.
Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 15
Type below:
_____________

Answer: Rainbow shaped curve
The given cross-section in the cone is a rainbow-shaped curve.

Essential Question Check-In

Question 5.
What is the first step in describing what figure results when a given plane intersects a given three-dimensional figure?
Type below:
_____________

Answer:
The first step in describing what figure results when a given plane intersects a given three-dimensional figure is to establish the number of sides the cross-section has.

Independent Practice

Question 6.
Describe different ways in which a plane might intersect the cylinder and the cross section that results.
Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 16
Type below:
_____________

Answer:
The cross-section can be:
1. a circle
2. an ellipse
3. a rectangle

Page No. 250

Question 7.
Make a Conjecture
What cross sections might you see when a plane intersects a cone that you would not see when a plane intersects a pyramid or a prism?
Type below:
_____________

Answer:
The cross-section can be:
1. a circle
2. an ellipse
3. a parabola
4. a hyperbola
5. a triangle

H.O.T.

Focus on Higher Order Thinking

Question 8.
Critical Thinking
The two figures on the left below show that you can form a cross section of a cube that is a pentagon. Think of a plane cutting the cube at an angle in such a way as to slice through five of the cube’s six faces. Draw dotted lines on the third cube to show how to form a cross section that is a hexagon.
Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 17
Type below:
_____________

Answer:
We draw a plane cutting the cube so that the cross-section is a hexagon: for this, we take the middle of 6 adjacent sides:

Question 9.
Analyze Relationships
A sphere has a radius of 12 inches. A horizontal plane passes through the center of the sphere.
a. Describe the cross section formed by the plane and the sphere
Type below:
_____________

Answer: Circle

Explanation:
We are given a sphere and a cross-section passing through the center of the sphere:
The cross section passing through the center of the sphere is a circle having the radius equal to the sphere’s radius.

Question 9.
b. Describe the cross sections formed as the plane intersects the interior of the sphere but moves away from the center.
Type below:
_____________

Answer:  The cross sections formed as a plane intersects the interior of the sphere outside the center are circles.

Question 10.
Communicate Mathematical Ideas
A right rectangular prism is intersected by a horizontal plane and a vertical plane. The cross section formed by the horizontal plane and the prism is a rectangle with dimensions 8 in. and 12 in. The cross section formed by the vertical plane and the prism is a rectangle with dimensions 5 in. and 8 in. Describe the faces of the prism, including their dimensions. Then find its volume.
Type below:
_____________

Answer: 480 cube inches

Explanation:
The horizontal cross section has the dimensions 8×12, while the vertical 5×8.
The prism has the dimensions:
5 inches, 8 inches, 12 inches
We find the volume of the prism:
5 × 8 × 12 = 480 cube inches

Question 11.
Represent Real-World Problems
Describe a real-world situation that could be represented by planes slicing a three-dimensional figure to form cross sections.
Type below:
_____________

Answer:
Examples of real-world situations that can be represented by planes slicing three-dimensional figures to form cross-sections:
– electrical wires
– water/gas pipes
– house design
– geology
– seismology

Guided Practice – Page No. 256

For 1–2, use the figure.
Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 18

Question 1.
Vocabulary
The sum of the measures of ∠UWV and ∠UWZ is 90°, so ∠UWV and ∠UWZ are _____ angles.
Type below:
_____________

Answer: Complementary angles

Explanation:
The sum of ∠UWV and ∠UWZ is 90°, so ∠UWV and ∠UWZ are complementary angles.

Question 2.
Vocabulary
∠UWV and ∠VWX share a vertex and one side. They do not overlap, so ∠UWV and ∠VWX are _____ angles.
Type below:
_____________

Answer: Adjacent angles

Explanation:
∠UWV and ∠VWX share a vertex and one side. They do not overlap, so ∠UWV and ∠VWX are adjacent angles.

For 3–4, use the figure.
Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 19

Question 3.
∠AGB and ∠DGE are _____ angles, so m∠DGE = _____.
Type below:
_____________

Answer: ∠AGB and ∠DGE are vertical angles, so m∠DGE = m∠AGB = 30°

Question 4.
Find the measure of ∠EGF.
_______ °

Answer: 100°

Explanation:
m∠CGD + m∠DGE + m∠EGF = 180°
50° + m∠AGB + m∠EGF = 180°
50° + 30° + 2x = 180°
2x = 180° – 80°
2x = 100°
mm∠EGF = 2x = 100°

Question 5.
Find the value of x and the measure of ∠MNQ.
Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 20
x = _______ °
mMNQ = _______ °

Answer:
∠MNQ + ∠QNP = 90°
3x – 13° + 58° = 90°
3x = 90° + 13° – 58°
3x = 45°
x = 15°
m∠MNQ = 3x – 13°
= 3×15° – 13°
= 45° – 13°
= 32°

Essential Question Check-In

Question 6.
Suppose that you know that ∠T and ∠S are supplementary and that m∠T = 3(m∠S). How can you find m∠T?
Type below:
_____________

Answer:
m∠T + m∠S = 180°
m∠T = 3(m∠S)
m∠S = m∠T/3
Form the second equation we write m∠S in terms of m∠T
m∠T + m∠T/3 = 3 × 180°
3m∠T + m∠T = 3 × 180°
4m∠T = 540°
m∠T = 540°/4
m∠T = 135°

Independent Practice – Page No. 257

For 7–11, use the figure.
Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 21

Question 7.
Name a pair of adjacent angles. Explain why they are adjacent.
Type below:
_____________

Answer:
The pair of adjacent angles are:
∠SUR and ∠RUN (common vertex U and one common side – UR – without overlapping)
∠NUQ and ∠QUP (common vertex U and one common side – UQ – without overlapping)
∠PUT and ∠TUS (common vertex U and one common side – UT – without overlapping)

Question 8.
Name a pair of acute vertical angles.
Type below:
_____________

Answer:
By seeing the above figure we can say that ∠SUR and ∠PUQ are the vertical angles.

Question 9.
Name a pair of supplementary angles.
Type below:
_____________

Answer:
The above figure shows that ∠SUR and ∠RUQ are supplementary angles.

Question 10.
Justify Reasoning
Find m∠QUR. Justify your answer.
_______ °

Answer:
We have to find m∠QUR.
∠SUR and ∠QURare supplementary angles.
m∠SUR + m∠QUR = 180°
m∠QUR + 41° = 180°
m∠QUR = 180° – 41°
m∠QUR = 139°

Question 11.
Draw Conclusions
Which is greater, m∠TUR or m∠RUQ? Explain.
Type below:
_____________

Answer:
m∠QUR = 139°
m∠TUR = m∠TUS + m∠SUR
90° + 41° = 131°
We find m∠TUR
139° > 131°
m∠QUR > m∠TUR

For 12–13, use the figure. A bike path crosses a road as shown. Solve for each indicated angle measure or variable.
Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 22

Question 12.
x = ?
_______ °

Answer: x = 21°

Explanation:
∠KMI and ∠HMG are vertical, thus congruent.
We determine x:
84° = 4x
4x = 84°
x = 84°/4
x = 21°

Question 13.
m∠KMH = ?
_______ °

Answer: 96°

Explanation:
∠KMI and ∠KMH are supplementary.
We determine m∠KMH:
m∠KMH + m∠KMI = 180°
m∠KMH + 84° = 180°
m∠KMH = 180° – 84°
m∠KMH = 96°

For 14–16, use the figure. Solve for each indicated angle measure.
Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 23

Question 14.
m∠CBE = ?
_______ °

Answer: 118°

Explanation:
We determine m∠CBE:
m∠CBE + m∠EBF = 180°
m∠CBE + 62°= 180°
m∠CBE = 180° – 62°
m∠CBE = 118°

Question 15.
m∠ABF = ?
_______ °

Answer: 28°

Explanation:
We determine m∠ABF
m∠ABF + m∠EBF = 90°
m∠ABF + 62° = 90°
m∠ABF = 90° – 62°
m∠ABF = 28°

Question 16.
m∠CBA = ?
_______ °

Answer: 152°

Explanation:
We determine m∠CBA
m∠CBA = m∠DBF = m∠DBE + m∠EBF
90° + 62° = 152°
m∠CBA = 152°

Question 17.
The measure of ∠A is 4° greater than the measure of ∠B. The two angles are complementary. Find the measure of each angle.
mA = __________ °
mB = __________ °

Answer:
mA = 47°
mB = 43°

Explanation:
We are given the data:
m∠A = m∠B + 4°
m∠A + m∠B = 90°
m∠B + 4° + m∠B = 90°
2m∠B = 90° – 4°
2m∠B = 86°
m∠B = 86°/2
m∠B = 43°
m∠A = m∠B + 4°
m∠A = 43° + 4°
m∠A = 47°

Question 18.
The measure of ∠D is 5 times the measure of ∠E. The two angles are supplementary. Find the measure of each angle.
mD = __________ °
mE = __________ °

Answer:
mD = 150°
mE = 30°

Explanation:
We are given the data
m∠D = 5(m∠E)
m∠D + m∠E = 180°
5(m∠E) + m∠E = 180°
6 m∠E = 180°
m∠E = 180°/6
m∠E = 30°
m∠D = 5(m∠E)
m∠D = 5 × 30°
m∠D = 150°

Page No. 258

Question 19.
Astronomy
Astronomers sometimes use angle measures divided into degrees, minutes, and seconds. One degree is equal to 60 minutes, and one minute is equal to 60 seconds. Suppose that ∠J and ∠K are complementary, and that the measure of ∠J is 48 degrees, 26 minutes, 8 seconds. What is the measure of ∠K?
_______ ° _______ ‘ _______ ”

Answer: 41° 33 ‘ 52″

Explanation:
We are given the data
m∠J + m∠K = 90°
m∠J = 48° 26 ‘ 8″
90° – 48° 26 ‘ 8″
89°60’ – 48° 26 ‘ 8″
89°59’60” – 48° 26 ‘ 8″ = 41° 33 ‘ 52″
Thus the measure of ∠K is 41° 33 ‘ 52″

H.O.T.

Focus on Higher Order Thinking

Question 20.
Represent Real-World Problems
The railroad tracks meet the road as shown. The town will allow a parking lot at angle K if the measure of angle K is greater than 38°. Can a parking lot be built at angle K ? Why or why not?
Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 24
_______

Answer:
m∠K = 180° – 50° – 90° = 40°
Since m∠K = 40°> 38°, a parking lot can be built.

Question 21.
Justify Reasoning
Kendra says that she can draw ∠A and ∠B so that m∠A is 119° and ∠A and ∠B are complementary angles. Do you agree or disagree? Explain your reasoning.
_______

Answer:
We are given the data
m∠A = 119°
m∠A + m∠B = 90°
m∠B = 90° – m∠A
= 90° – 119° = -29°
Since m∠B < 0, Kendra is wrong, she cannnot draw the angles.

Question 22.
Draw Conclusions
If two angles are complementary, each angle is called a complement of the other. If two angles are supplementary, each angle is called a supplement of the other.
a. Suppose m∠A = 77°. What is the measure of a complement of a complement of ∠A? Explain.
_______ °

Answer: 77°

Explanation:
90° – (90° – m∠A) = 90° – (90° – 77°)
90° – 77° = 13°
77°

Question 22.
b. What conclusion can you draw about a complement of a complement of an angle? Explain.
Type below:
_____________

Answer:
The complement of a complement of an angle is the angle itself:
90° – (90° – m∠A)
90° – 90° + m∠A

8.1 Similar Shapes and Scale Drawings – Page No. 259

Question 1.
A house blueprint has a scale of 1 in. : 4 ft. The length and width of each room in the actual house are shown in the table. Complete the table by finding the length and width of each room on the blueprint.
Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 25
Type below:
_____________

Answer:
Go-Math-Grade-7-Answer-Key-Chapter-8-Modeling-Geometric-Figures-img-25
Thus for each 4 ft in actual dimension, there is 1 inch in the blueprint.

8.2 Geometric Drawings

Question 2.
Can a triangle be formed with the side lengths of 8 cm, 4 cm, and 12 cm?
______

Answer:
We are given the side lengths
8 + 12 = 20 > 4
4 + 12 = 16 > 8
8 + 4 not > 12
Since one of the inequalities is not verified, the three given side lengths cannot form a triangle.

Question 3.
A triangle has side lengths of 11 cm and 9 cm. Which could be the value of the third side, 20 cm or 15 cm?
______

Answer: 15 cm

Explanation:
We are given the side lengths
11, 9
11 + 9 = 20 not > 20
We check the triangle’s inequalities if we add the third side of 20 cm
Since one of the inequalities is not verified, the three given side lengths cannot form a triangle.
11, 9, 15
11 + 9 = 20 > 15
11 + 15 = 26 > 9
15 + 9 = 24 > 11
We check the triangle’s inequalities are verified, 15 can be the value of the third side.

8.3 Cross Sections

Question 4.
Name one possible cross section of a sphere.
Type below:
_____________

Answer: Circle
One possible cross section of the sphere is a circle.

Question 5.
Name at least two shapes that are cross sections of a cylinder.
Type below:
_____________

Answer: Three possible cross-sections of a cylinder are a circle, an ellipse, and a rectangle.

Essential Question Check-In

Question 5.
How can you model geometry figures to solve real-world problems?
Type below:
_____________

Answer: You can model geometry for making buildings and sky scrapers, also stores.

8.4 Angle Relationships

Question 6.
∠BGC and ∠FGE are _____ angles, so m∠FGE = _____
Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 26
_____ °

Answer: ∠BGC and ∠FGE are vertical angles, so m∠FGE = m∠BGC = 90° – 40° = 50°

Question 7.
Suppose you know that ∠S and ∠Y are complementary, and that m∠S = 2(m∠Y) – 30°. Find m∠Y.
m?Y = _____ °

Answer: 40°

Explanation:
m∠S + m∠Y = 90°
m∠S = 2(m∠Y) – 30°
We replace the expression of m∠S from the second equation into the first we can find m∠Y
2(m∠Y) – 30° + m∠Y = 90°
3m∠Y = 90° + 30°
3m∠Y = 120°
m∠Y = 120°/3
m∠Y = 40°

Selected Response – Page No. 260

Question 1.
Which number can you add to 15 to get a sum of 0?
Options:
a. -10
b. -15
c. 0
d. 15

Answer: -15

Explanation:
The number we add to a number in order to get a sum of zero is its opposite. In or case we should add -15 to 15.
15 + (-15) = 0
Thus the correct answer is option B.

Question 2.
Students are painting the backdrop for the school play. The backdrop is 15 feet wide and 10 feet high. Every 16 inches on the scale drawing represents 5 feet on the backdrop. What is the area of the scale drawing?
Options:
a. 150 in2
b. 6 in2
c. 3096
d. 1536 in2

Answer: 1536 in2

Explanation:
We are given the dimensions l and w of the backdrop and the drawing scale:
l = 15 ft
w = 10 ft
16 in: 5 ft
16 in./5 ft = (16 in. ÷ 5)/(5 ft ÷ 5) = 3.2 in/1 ft
l1 = 15 × 3.2 = 48 inches
w1 = 10 × 32 = 320 inches
l1 × w1 = 48 × 32 = 1536 square inches
Thus the correct answer is option D.

Question 3.
Two sides of a triangle measure 8 cm and 12 cm. Which of the following CANNOT be the measure of the third side?
Options:
a. 4
b. 12
c. 8
d. 16

Answer: 4 cm

Explanation:
We are given two sides of a triangle
a. 4
4 + 8 not > 12
b. 12
12 + 8 > 12
12 + 12 > 8
c. 8
8 + 8 > 12
8 + 12 > 12
d. 16
8 + 12 > 16
8 + 16 > 12
12 + 16 > 8
Thus the only dimension which cannot be the measure of the third side f the triangle is 4 cm.
Thus the correct answer is option A.

Question 4.
A cross section is the intersection of a three-dimensional figure and a _____ .
Options:
a. point
b. plane
c. line
d. set

Answer: Plane

Explanation:
A cross section is the interaction of a three-dimensional figure and a plane.
Thus the correct answer is option B.

For 5–6, use the diagram.
Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures img 27

Question 5.
What is the measure of ∠BFC?
Options:
a. 18
b. 108
c. 72
d. 144

Answer: 108°

Explanation:
∠BFC + ∠BFA = 180°
∠BFC + 72° = 180°
∠BFC = 180° – 72°
∠BFC = 108°
The angles ∠BFC and ∠BFA are supplementary. We determine ∠BFC.
Thus the correct answer is option B.

Question 6.
Which describes the relationship between ∠BFA and ∠CFD?
Options:
a. adjacent angles
b. complementary angles
c. supplementary angles
d. vertical angles

Answer: vertical angles

Explanation:
The angles ∠BFA and ∠CFD are vertical angles because they are opposite angles formed at the intersection of two lines.
Thus the correct answer is option D.

Question 7.
All clothing is being marked down 15%. Which expression represents the new retail price?
Options:
a. 0.85x
b. 1.15x
c. 1.85x
d. 0.15x

Answer: 0.85x

Explanation:
x = initial price
Since the price went down by 15%, the new price will be diminished by 15/100 x
x – 0.15x = 0.85x
Thus the correct answer is option A.

Mini-Tasks

Question 8.
Ira built a model of the Great Pyramid in Egypt for a school project. The Great Pyramid has a square base with sides of length 756 feet. The height of the Great Pyramid is 481 feet. Ira made his model pyramid using a scale of 1 inch : 20 feet.
a. What is the length of each side of the base of Ira’s pyramid?
_____ in

Answer: 37.8 inches
We compute the number of inches corresponding to 1 feet from the actual dimensions:
1 in./20 ft = (1 in. ÷ 20)/(20 ft ÷ 20) = 0.05 in/1 ft.
There are 0.05 inches for 1 feet.
We determine the length of Ira’s  pyramid base:
756 × 0.05 = 37.8 inches

Question 8.
b. What is the area of the base of Ira’s pyramid?
_____ square inches

Answer: 1428.84 square inches

Explanation:
We determine the area of Ira’s pyramid base:
37.8 × 37.8 = 1,428.84 square inches.

Question 8.
c. What is the height of Ira’s pyramid?
_____ in

Answer:
We determine the height of Ira’s pyramid:
481 × 0.05 = 24.05 inches

Question 8.
d. Ira built his model using cross sections that were cut parallel to the base. What shape was each cross section?
Type below:
____________

Answer: The cross sections parallel to the base have the shape of a square.

Final Words:

Hope the solutions provided in Go Math Grade 7 Answer Key Chapter 8 Modeling Geometric Figures is helpful for all the students. Get the answers for all the questions with the simple techniques for all chapters on Go Math Answer 7th grade Key Chapter 8 Modeling Geometric Figures. Stick to our Go Math Answer Key Page to get the latest information about the chapters.

Go Math Grade 4 Answer Key Homework Practice FL Chapter 2 Multiply by 1-Digit Numbers

go-math-grade-4-chapter-2-multiply-by-1-digit-numbers-pages-21-47-answer-key

Hello Kids! Here is Go Math Grade 4 Answer Key Homework Practice FL Chapter 2 Multiply by 1-Digit Numbers in pdf. Without wasting any time just refer to the Ch 2 Answer Key of Go Math Grade 4 and gain proper knowledge about the concept. Go Math Grade 4 Answer Key provided here will increase your Mathematical skills and support parents to understand the concept and educate their children effectively. So, get into these online chapter 2 Multiply by 1-Digit Numbers Go Math 4th Grade Solutions Key & get a good grip on the concepts.

Go Math Grade 4 Answer Key Homework Practice FL Chapter 2 Multiply by 1-Digit Numbers

There are various lessons & concepts included in the Go Math Grade 4 Answer Key Homework Practice FL Chapter 2 Multiply by 1-Digit Numbers such as Multiplication Comparisons, Multiply Tens, Hundreds, and Thousands, Estimate Products, Multiply Using the Distributive Property, and so on. So, move ahead and click on the respective topic to grasp the concept and then solve the sums easily. All these solutions will make you understand the concepts clearly and make you strong on basic fundamentals on your own.

Lesson: 1 – Multiplication Comparisons

Common Core – Multiply by 1-Digit Numbers – Page No. 23
Common Core – Multiply by 1-Digit Numbers – Page No. 24

Lesson: 2 – Comparison Problems

Common Core – Multiply by 1-Digit Numbers – Page No. 25
Common Core – Multiply by 1-Digit Numbers – Page No. 26

Lesson: 3 – Multiply Tens, Hundreds, and Thousands

Common Core – Multiply by 1-Digit Numbers – Page No. 27
Common Core – Multiply by 1-Digit Numbers – Page No. 28

Lesson: 4 – Estimate Products

Common Core – Multiply by 1-Digit Numbers – Page No. 29
Common Core – Multiply by 1-Digit Numbers – Page No. 30

Lesson: 5 – Multiply Using the Distributive Property

Common Core – Multiply by 1-Digit Numbers – Page No. 31
Common Core – Multiply by 1-Digit Numbers – Page No. 32

Lesson: 6 – Multiply Using Expanded Form

Common Core – Multiply by 1-Digit Numbers – Page No. 33
Common Core – Multiply by 1-Digit Numbers – Page No. 34

Lesson: 7 – Multiply Using Partial Products

Common Core – Multiply by 1-Digit Numbers – Page No. 35
Common Core – Multiply by 1-Digit Numbers – Page No. 36

Lesson: 8 – Multiply Using Mental Math

Common Core – Multiply by 1-Digit Numbers – Page No. 37
Common Core – Multiply by 1-Digit Numbers – Page No. 38

Lesson: 9 – Problem Solving Multistep Multiplication Problems

Common Core – Multiply by 1-Digit Numbers – Page No. 39
Common Core – Multiply by 1-Digit Numbers – Page No. 40

Lesson: 10 – Multiply 2-Digit Numbers with Regrouping

Common Core – Multiply by 1-Digit Numbers – Page No. 41
Common Core – Multiply by 1-Digit Numbers – Page No. 42

Lesson: 11 – Multiply 3-Digit and 4-Digit Numbers with Regrouping

Common Core – Multiply by 1-Digit Numbers – Page No. 43
Common Core – Multiply by 1-Digit Numbers – Page No. 44

Lesson: 12 – Solve Multistep Problems Using Equations

Common Core – Multiply by 1-Digit Numbers – Page No. 45
Common Core – Multiply by 1-Digit Numbers – Page No. 46

Lesson: 13 

Common Core – Multiply by 1-Digit Numbers – Page No. 47
Common Core – Multiply by 1-Digit Numbers – Page No. 48

Common Core – Multiply by 1-Digit Numbers – Page No. 23

Multiplication Comparisons

Write a comparison sentence.

Question 1.
6 × 3 = 18
6 times as many as 3 is 18.

Question 2.
63 = 7 × 9
_____ is _____ times as many as _____.

Answer: 63 is 7 times as many as 9.

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Question 3.
5 × 4 = 20
_____ times as many as _____ is _____.

Answer: 5 times as many as 4 is 20.

Explanation:

Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Question 4.
48 = 8 × 6
_____ is _____ times as many as _____.

Answer: 48 is 6 times as many as 8.

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Write an equation.

Question 5.
2 times as many as 8 is 16.
_____ × _____ = _____

Answer: 2 × 8 = 16

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Question 6.
42 is 6 times as many as 7.
_____ = _____ × _____

Answer: 42 = 6 × 7

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Question 7.
3 times as many as 5 is 15.
_____ × _____ = _____

Answer: 3 × 5 = 15

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Question 8.
36 is 9 times as many as 4.
_____ = _____ × _____

Answer: 36 = 9 × 4

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Question 9.
72 is 8 times as many as 9.
_____ = _____ × _____

Answer: 72 = 8 × 9

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Question 10.
5 times as many as 6 is 30.
_____ × _____ = _____

Answer: 5 × 6 = 30

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Problem Solving

Question 11.
Alan is 14 years old. This is twice as old as his brother James is. How old is James?
_____ years old

Answer: 7 years old.

Explanation:
Alan’s age is 14 years old and his brother is James is twice younger than Alan, So James’s age is 14÷2= 7.

Question 12.
There are 27 campers. This is nine times as many as the number of counselors. How many counselors are there?
_____ counselors

Answer: 3 counselors.

Explanation: 27 campers= 9× no.of counselors,
So no.of counselors are 27÷9= 3.

Common Core – Multiply by 1-Digit Numbers – Page No. 24

Lesson Check

Question 1.
Which equation best represents the comparison sentence?
24 is 4 times as many as 6.
Options:
a. 24 × 4 = 6
b. 24 = 4 × 6
c. 24 = 4 + 6
d. 4 + 6 = 24

Answer: 24 = 4 × 6

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers
The correct answer is option b.

Question 2.
Which comparison sentence best represents the equation?
5 × 9 = 45
Options:
a. 5 more than 9 is 45.
b. 9 is 5 times as many as 45.
c. 5 is 9 times as many as 45.
d. 45 is 5 times as many as 9.

Answer: 45 is 5 times as many as 9.

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers
The correct answer is option d.

Spiral Review

Question 3.
Which of the following statements correctly compares the numbers?
Options:
a. 273,915 > 274,951
b. 134,605 < 143,605
c. 529,058 > 530,037
d. 452,731 > 452,819

Answer: 134,605 < 143,605

Explanation:
134,605 is lesser compared to 143,605.
The correct answer is option b.

Question 4.
What is the standard form for
200,000 + 80,000 + 700 + 6?
Options:
a. 2,876
b. 28,706
c. 208,706
d. 280,706

Answer: 280,706

Explanation:
200,000+80,000+700+6= 280,706.
The correct answer is option d.

Question 5.
Sean and Leah are playing a computer game. Sean scored 72,491 points. Leah scored 19,326 points more than Sean. How many points did Leah score?
Options:
a. 53,615
b. 91,717
c. 91,815
d. 91,817

Answer: 91,817

Explanation:
Sean’s score is 72,491 and Leah’s score is 19,326 more than Sean’s score. So Sean score is 72,491+19,326 = 91,817.
The correct answer is option d.

Question 6.
A baseball stadium has 38,496 seats. Rounded to the nearest thousand, how many seats is this?
Options:
a. 38,000
b. 38,500
c. 39,000
d. 40,000

Answer: 38,000

Explanation:
Round off to the nearest thousand is 38,000.
The correct answer is option a.

Common Core – Multiply by 1-Digit Numbers – Page No. 25

Comparison Problems

Draw a model. Write an equation and solve.

Question 1.
Stacey made a necklace using 4 times as many blue beads as red beads. She used a total of 40 beads. How many blue beads did Stacey use?
Go Math Grade 4 Answer Key Homework Practice FL Chapter 2 Multiply by 1-Digit Numbers Common Core - Multiply by 1-Digit Numbers img 1

Question 2.
At the zoo, there were 3 times as many monkeys as lions. Tom counted a total of 24 monkeys and lions. How many monkeys were there?
______ monkeys

Answer: 18 monkeys

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers
Therefore there are 18 monkeys.

Question 3.
Fred’s frog jumped 7 times as far as Al’s frog. The two frogs jumped a total of 56 inches. How far did Fred’s frog jump?
______ inches

Answer: 49 inches

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers
Therefore Fred’s frog jumps 49 inches.

Question 4.
Sheila has 5 times as many markers as Dave. Together, they have 18 markers. How many markers does Sheila have?
______ markers

Answer: 15 markers

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers
Therefore Sheila has 15 markers.

Problem Solving

Question 5.
Rafael counted a total of 40 white cars and yellow cars. There were 9 times as many white cars as yellow cars. How many white cars did Rafael count?
______ white cars

Answer: 36 white cars

Explanation:
Let yellow cars be X, As white cars are 9 times as many as yellow cars, So white cars be 9X. Therefore 9X+X=40, X=4. So no.of white cars are 9×4= 36.
Therefore Rafael count 36 white cars.

Question 6.
Sue scored a total of 35 points in two games. She scored 6 times as many points in the second game as in the first. How many more points did she score in the second game?
______ more points

Answer: 30 more points

Explanation:
Let the first game points are X and second game points be 6X. Sue’s total score is 35 points in two games so 6X+X= 35 then X is 5.
Therefore the second game score is 6 × 5= 30.

Common Core – Multiply by 1-Digit Numbers – Page No. 26

Lesson Check

Question 1.
Sari has 3 times as many pencil erasers as Sam. Together, they have 28 erasers. How many erasers does Sari have?
Options:
a. 7
b. 14
c. 18
d. 21

Answer: 21

Explanation:
Let the X be pencil erasers of Sam and Sari erasers be 3X. As Sari and Sam together have 28 erasers.
So 3X+X= 28. And X is 7. Then Sari has 3×7= 21.
The correct answer is option d.

Question 2.
In Sean’s fish tank, there are 6 times as many goldfish as guppies. There are a total of 21 fish in the tank. How many more goldfish are there than guppies?
Options:
a. 5
b. 12
c. 15
d. 18

Answer: 18

Explanation:

Let Guppies be X and Goldfishes be 6X.
And the total fishes are 21, So X+6X= 21 then X= 3.
So Goldfishes are 6×3= 18.
The correct answer is option d.

Spiral Review

Question 3.
Barbara has 9 stuffed animals. Trish has 3 times as many stuffed animals as Barbara. How many stuffed animals does Trish have?
Options:
a. 3
b. 12
c. 24
d. 27

Answer: 27

Explanation:
Barbara has 9 stuffed animals and Trish has 3 times as Barbara, So 9×3= 27.
The correct answer is option d.

Question 4.
There are 104 students in the fourth grade at Allison’s school. One day, 15 fourth-graders were absent. How many fourth-graders were at school that day?
Options:
a. 89
b. 91
c. 99
d. 119

Answer: 89

Explanation:
Total students in fourth grade are 104, as 15 students were absent 104-15= 89.
The correct answer is option a.

Question 5.
Joshua has 112 rocks. Jose has 98 rocks. Albert has 107 rocks. What is the correct order of the boys from the least to the greatest number of rocks owned?
Options:
a. Jose, Albert, Joshua
b. Jose, Joshua, Albert
c. Albert, Jose, Joshua
d. Joshua, Albert, Jose

Answer: Jose, Albert, Joshua

Explanation:

Given,
Joshua has 112 rocks. Jose has 98 rocks. Albert has 107 rocks.
As 98<107<112. So Jose, Albert, Joshua.
The correct answer is option a.

Question 6.
Alicia has 32 stickers. This is 4 times as many stickers as Benita has. How many stickers does Benita have?
Options:
a. 6
b. 8
c. 9
d. 28

Answer: 8

Explanation:
Given,
Alicia has 32 stickers. This is 4 times as many stickers as Benita has.
Let Benita stickers be S and Alicia has 32 stickers, So 4×S= 32. Therefore Benita stickers are 8.

Common Core – Multiply by 1-Digit Numbers – Page No. 27

Multiply Tens, Hundreds, and Thousands

Find the product.

Question 1.
4 × 7,000 = 28,000
Think: 4 × 7 = 28
So, 4 × 7,000 = 28,000

Question 2.
9 × 60 = ______

Answer: 540

Explanation: 9×6= 54.

Question 3.
8 × 200 = ______

Answer: 1600

Explanation: 8×2=16

Question 4.
5 × 6,000 = ______

Answer: 30,000

Explanation: 5×6=30.

Question 5.
7 × 800 = ______

Answer: 5600

Explanation: 7×8= 56.

Question 6.
8 × 90 = ______

Answer: 720

Explanation: 8×9=72.

Question 7.
6 × 3,000 = ______

Answer: 18,000

Explanation: 6×3= 18.

Question 8.
3 × 8,000 = ______

Answer: 24,000

Explanation: 3×8= 24.

Question 9.
5 × 500 = ______

Answer: 2500

Explanation: 5×5= 25.

Question 10.
9 × 4,000 = ______

Answer: 36,000

Explanation: 9×4= 36.

Question 11.
7 × 7,000 = ______

Answer: 49,000

Explanation: 7×7= 49.

Question 12.
3 × 40 = ______

Answer: 120

Explanation: 3×4= 12.

Question 13.
4 × 5,000 = ______

Answer: 20,000

Explanation: 4×5= 20.

Question 14.
2 × 9,000 = ______

Answer: 18,000

Explanation: 2×9= 18.

Problem Solving

Question 15.
A bank teller has 7 rolls of coins. Each roll has 40 coins. How many coins does the bank teller have?
______ coins

Answer: 280 coins

Explanation:
The bank teller has 7 rolls of coins.
As each roll has 40 coins, So total coins are 7×40= 280
Thus the bank teller has 280 coins.

Question 16.
Theo buys 5 packages of paper. There are 500 sheets of paper in each package. How many sheets of paper does Theo buy?
______ sheets.

Answer: 2,500

Explanation:
Total no.of sheets of papers in each package are 500, And Theo buys 5 packages of papers.
So total sheets of paper Theo bought are 500×5= 2,500.

Common Core – Multiply by 1-Digit Numbers – Page No. 28

Lesson Check

Question 1.
A plane is traveling at a speed of 400 miles per hour. How far will the plane travel in 5 hours?
Options:
a. 200 miles
b. 2,000 miles
c. 20,000 miles
d. 200,000 miles

Answer: 2,000 miles

Explanation:
The speed of the plane is 400 miles per hour.
In 5 hours plane can travel 400×5= 2,000 miles.
Thus the correct answer is option b.

Question 2.
One week, a clothing factory made 2,000 shirts in each of 6 different colors. How many shirts did the factory make in all?
Options:
a. 2,000
b. 12,000
c. 120,000
d. 200,000

Answer: 12,000

Explanation:
The shirts made in one week are 2000 in 6 different colors.
So total shirts made in all are 2000×6= 12,000.
Thus the correct answer is option b.

Spiral Review

Question 3.
Which comparison sentence best represents the equation?
6 × 7 = 42
Options:
a. 7 is 6 times as many as 42.
b. 6 is 7 times as many as 42.
c. 42 is 6 times as many as 7.
d. more than 7 is 42.

Answer: 42 is 6 times as many as 7.

Explanation:
By comparing 42= 6×7 represents the equation.
Thus the correct answer is option c.

Question 4.
The population of Middleton is six thousand, fifty-four people. Which of the following shows this number written in standard form?
Options:
a. 654
b. 6,054
c. 6,504
d. 6,540

Answer: 6,054

Explanation:
The standard form is Six thousand fifty-four is equal to 6,054.
Thus the correct answer is option b.

Question 5.
In an election for mayor, 85,034 people voted for Carl Green and 67,952 people voted for Maria Lewis. By how many votes did Carl Green win the election?
Options:
a. 17,082
b. 17,182
c. 22,922
d. 152,986

Answer: 17,082

Explanation:
Total votes Carl Green has got are 85,034and Maria Lewis got are 67,952. By 85,034-67,952= 17,082 votes Carl Green won the election.
Thus the correct answer is option a.

Question 6.
Meredith picked 4 times as many green peppers as red peppers. If she picked a total of 20 peppers, how many green peppers did she pick?
Options:
a. 4
b. 5
c. 16
d. 24

Answer: 16

Explanation:
Meredith picked 4 times as many green peppers as red peppers.
Let the red peppers be X and green peppers be 4X, And the total she picked is 20 peppers. So X+4X=20
Then X=4. Green peppers she picked are 4×4= 16.
Thus the correct answer is option c.

Common Core – Multiply by 1-Digit Numbers – Page No. 29

Estimate Products

Estimate the product by rounding.

Question 1.
4 × 472
4 × 472

4 × 500 = 2,000

Question 2.
2 × 6,254
Estimate: _______

Answer: 12,000

Explanation:
The nearest rounding off for 6,254 is 6,000.
So 2×6,000= 12,000.

Question 3.
9 × 54
Estimate: _______

Answer: 450

Explanation:
The nearest rounding off for 54 is 50. So 9×50= 450.

Question 4.
5 × 5,503
Estimate: _______

Answer: 30,000

Explanation:
The nearest rounding off for 5,503 is 6,000.
So 5×6,000= 30,000.

Question 5.
3 × 832
Estimate: _______

Answer: 2,400

Explanation:
The nearest rounding off for 832 is 800.
So 3×800= 2,400.

Question 6.
6 × 98
Estimate: _______

Answer: 600

Explanation:
The nearest rounding off for 98 is 100. So 6×100= 600.

Question 7.
8 × 3,250
Estimate: _______

Answer: 24,000

Explanation:
The nearest rounding off for 3,250 is 3,000.
So 8×3,000= 24,000.

Question 8.
7 × 777
Estimate: _______

Answer: 5,600

Explanation:
The nearest rounding off for 777 is 800.
So 7×800= 5,600.

Find two numbers the exact answer is between.

Question 9.
3 × 567
_____ and _____

Answer: 1500 and 1800

Explanation:
The rounding off for 567 is 500 and 600.
So 3×500= 1500 and 3×600= 1800.

Question 10.
6 × 7,381
_____ and _____

Answer: 42,000 and 48,000

Explanation:
The rounding off for 7,381 is 7,000 and 8,000.
So 6×7000= 42,000 and 6×8000= 48,000.

Question 11.
4 × 94
_____ and _____

Answer: 360 and 400

Explanation:
The rounding off for 94 is 90 and 100.
So 4×90= 360 and 4×100= 400.

Question 12.
8 × 684
_____ and _____

Answer: 3600 and 4200

Explanation:
The rounding off for 684 is 600 and 700.
So 6×600= 3600 and 6×700= 4200.

Problem Solving

Question 13.
Isaac drinks 8 glasses of water each day. He says he will drink 2,920 glasses of water in a year that has 365 days. Is the exact answer reasonable? Explain.
_____

Answer: Yes

Explanation:
As the round-off for 365 can be 300 or 400.
So 8×300= 2,400 and 8×400= 3,200.
The estimated answer can be between 2,400 to 3,200.
So the answer is Yes.

Question 14.
Most Americans throw away about 1,365 pounds of trash each year. Is it reasonable to estimate that Americans throw away over 10,000 pounds of trash in 5 years? Explain.
_____

Answer: No

Explanation:
As the round-off for 1,365 can be 1000 or 2000.
So 5×1000= 5,000 and 5×2000= 10,000.
The estimated answer can be between 5,000 to 10,000.

Common Core – Multiply by 1-Digit Numbers – Page No. 30

Lesson Check

Question 1.
A theater has 4,650 seats. If the theater sells all the tickets for each of its 5 shows, about how many tickets will the theater sell in all?
Options:
a. 2,500
b. 10,000
c. 25,000
d. 30,000

Answer: 25,000

Explanation:
A theater has 4,650 seats.
As the nearest round off for 4,650 is 5,000.
So 5,000×5= 25,000.
The correct answer is option c.

Question 2.
Washington Elementary has 4,358 students. Jefferson High School has 3 times as many students as Washington Elementary. About how many students does Jefferson High School have?
Options:
a. 16,000
b. 12,000
c. 10,000
d. 1,200

Answer: 12,000

Explanation:
Given,
Washington Elementary has 4,358 students.
Jefferson High School has 3 times as many students as Washington Elementary.
As the nearest round off for 4,358 is 4,000.
So 4,000×3= 12,000.
The correct answer is option b.

Spiral Review

Question 3.
Diego has 4 times as many autographed baseballs as Melanie has. Diego has 24 autographed baseballs. How many autographed baseballs does Melanie have?
Options:
a. 28
b. 20
c. 8
d. 6

Answer: 6

Explanation:
Let the Melanie baseballs be S.
As Diego has 4 times as many as Melanie and Diego has a total of 24 baseballs.
So 4×S= 24, Then S= 24÷4 which is 6.
The correct answer is option d.

Question 4.
Mr. Turkowski bought 4 boxes of envelopes at the office supply store. Each box has 500 envelopes. How many envelopes did Mr. Turkowski buy?
Options:
a. 200
b. 504
c. 2,000
d. 20,000

Answer: 2,000

Explanation:
Turkowski has 4 boxes of envelopes and each box contains 500 envelopes.
So total envelopes did Turkowski bought are 4×500= 2,000.
The correct answer is option c.

Question 5.
Pennsylvania has a land area of 44,816 square miles. Which of the following shows the land area of Pennsylvania rounded to the nearest hundred?
Options:
a. 44,000 square miles
b. 44,800 square miles
c. 44,900 square miles
d. 45,000 square miles

Answer: 44,800 square miles

Explanation:
As the nearest round off for 44,816 is 44,800.
The correct answer is option b.

Question 6.
The table shows the types of DVDs customers rented from Sunshine Movie Rentals last year.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 2 Multiply by 1-Digit Numbers Common Core - Multiply by 1-Digit Numbers img 2
Options:
How many comedy and action movies were rented in all last year?
a. 13,620
b. 13,000
c. 12,260
d. 10,752

Answer: 12,260

Explanation:
Comedy and action movies that are rented in last year are 6,720+5,540= 12,260.
The correct answer is option c.

Common Core – Multiply by 1-Digit Numbers – Page No. 31

Multiply Using the Distributive Property

Model the product on the grid. Record the product.

Question 1.
4 × 19 = 76
Go Math Grade 4 Answer Key Homework Practice FL Chapter 2 Multiply by 1-Digit Numbers Common Core - Multiply by 1-Digit Numbers img 3
4 × 10 = 40 and 4 × 9 = 36
40 + 36 = 76

Question 2.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 2 Multiply by 1-Digit Numbers Common Core - Multiply by 1-Digit Numbers img 4
5 × 13 = _____

Answer: 65

Explanation:
5×10= 50 and 5×3= 15
50+15= 65.

Find the product.

Question 3.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 2 Multiply by 1-Digit Numbers Common Core - Multiply by 1-Digit Numbers img 5
4 × 14 = _____

Answer: 56

Explanation:
4×10= 40 and 4×4= 16
40+16= 56.

Question 4.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 2 Multiply by 1-Digit Numbers Common Core - Multiply by 1-Digit Numbers img 6
3 × 17 = _____

Answer: 51

Explanation:
3×10=30 and 3×7= 21
30+21= 51

Question 5.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 2 Multiply by 1-Digit Numbers Common Core - Multiply by 1-Digit Numbers img 7
6 × 15 = _____

Answer: 90

Explanation:
6×10= 60 and 6×5= 30
60+30= 90

Problem Solving

Question 6.
Michael arranged his pennies in the following display.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 2 Multiply by 1-Digit Numbers Common Core - Multiply by 1-Digit Numbers img 8
How many pennies does Michael have in all?
_____ pennies

Answer: 91

Explanation: As there are 7 columns and 13 rows, So 13×7= 91.

Question 7.
A farmer has an apple orchard with the trees arranged as shown below.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 2 Multiply by 1-Digit Numbers Common Core - Multiply by 1-Digit Numbers img 9
If the farmer wants to pick one apple from each tree, how many apples will he pick?
_____ apples

Answer: 70 apples

Explanation:
As there are 5 columns and 14 rows, So 5×14= 70.

Common Core – Multiply by 1-Digit Numbers – Page No. 32

Lesson Check

Question 1.
The model shows how Maya planted flowers in her garden.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 2 Multiply by 1-Digit Numbers Common Core - Multiply by 1-Digit Numbers img 10
How many flowers did Maya plant?
Options:
a. 15
b. 18
c. 30
d. 45

Answer: 45

Explanation:
As 3×10= 30 and 3×5= 15
30+15= 45.
The correct answer is option d.

Question 2.
The model below represents the expression 5 × 18.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 2 Multiply by 1-Digit Numbers Common Core - Multiply by 1-Digit Numbers img 11
How many tens will there be in the final product?
Options:
a. 5
b. 6
c. 8
d. 9

Answer: 9

Explanation:
As 5×18 is 90 and 90÷10= 9.
So the answer is 9.
The correct answer is option d.

Spiral Review

Question 3.
Center City has a population of twenty one thousand, seventy people. Which of the following shows the population written in standard form?
Options:
a. 21,007
b. 21,070
c. 21,077
d. 21,700

Answer: 21,070

Explanation:
Center City has a population of twenty one thousand, seventy people.
Twenty-one thousand seventy is equal to 21,070.
The correct answer is option b.

Question 4.
Central School collected 12,516 pounds of newspaper to recycle. Eastland School collected 12,615 pounds of newspapers. How many more pounds of newspaper
did Eastland School collect than Central School?
Options:
a. 99 pounds
b. 101 pounds
c. 199 pounds
d. 1,099 pounds

Answer: 99 pounds

Explanation:
Central school has collected 12,516 pounds and Eastland school collected 12,615 pounds. So 12,615-12,516= 99.
The correct answer is option a.

Question 5.
Allison has 5 times as many baseball cards as football cards. In all, she has 120 baseball and football cards. How many baseball cards does Allison have?
Options:
a. 20
b. 24
c. 96
d. 100

Answer: 100

Explanation:
Let Football cards be X and baseball cards be 5X. So 5X+X= 120 in which X= 20.
As Allison has 5 times as many baseball cards as football cards.
So 5×20= 100.
The correct answer is option d.

Question 6.
A ruby-throated hummingbird beats its wings about 53 times each second. About how many times does a ruby-throated hummingbird beat its wings in 5 seconds?
Options:
a. 25
b. 58
c. 250
d. 300

Answer: 250

Explanation:
As the nearest round-off for 53 is 50, So 50×5= 250.
The correct answer is option c.

Common Core – Multiply by 1-Digit Numbers – Page No. 33

Multiply Using Expanded Form

Record the product. Use expanded form to help.

Question 1.
7 × 14 = 98
7 × 14 = 7 × (10 + 4)
= (7 × 10) + (7 × 4)
= 70 + 28
= 98

Question 2.
8 × 43 = ______

Answer: 344

Explanation:
8×(40+3)
= (8×40)+(8×3)
= 320+24
= 344.

Question 3.
6 × 532 = ______

Answer: 3192

Explanation:
6×(500+30+2)
= (6×500)+(6×30)+(6×2)
= 3000+180+12
= 3,192.

Question 4.
5 × 923 = ______

Answer: 4,615

Explanation:
5×923= 5×(900+20+3)
=(5×900)+(5×20)+(5×3)
=4500+100+15
=4,615.

Question 5.
4 × 2,371 = ______

Answer: 9,484

Explanation:
4×2,371= 4×(2000+300+70+1)
= (4×2,000)+(4×300)+(4×70)+(4×1)
=8000+1200+280+4
=9,484

Question 6.
7 × 1,829 = ______

Answer: 12,803

Explanation:
7×1,829= 7×(1,000+800+20+9)
=(7×1,000)+( 7×800)+( 7×20)+( 7×9)
=7,000+5600+140+63
=12,803

Problem Solving

Question 7.
The fourth-grade students at Riverside School are going on a field trip. There are 68 students on each of the 4 buses. How many students are going on the field trip?
______ students

Answer: 272 students

Explanation:
No. of buses are 4 and on each bus, there are 68 students.
So 68 × 4= 272.
Therefore 272 students are going on the field trip.

Question 8.
There are 5,280 feet in one mile. Hannah likes to walk 5 miles each week for exercise. How many feet does Hannah walk each week?
______ feet

Answer: 26,400 feet

Explanation:
There are 5,280 feet in one mile and Hannah walks 5 miles each week.
So 5,280 5= 26,400.
Hannah walk 26,400 feet each week.

Common Core – Multiply by 1-Digit Numbers – Page No. 34

Lesson Check

Question 1.
Which expression shows how to multiply 7 × 256 by using expanded form and the Distributive Property?
Options:
a. (7 × 2) + (7 × 5) + (7 × 6)
b. (7 × 200) + (7 × 500) + (7 × 600)
c. (7 × 2) + (7 × 50) + (7 × 600)
d. (7 × 200) + (7 × 50) + (7 × 6)

Answer: (7 × 200) + (7 × 50) + (7 × 6)

Explanation:
By Distributive property of multiplication 7×256=(7×200)+(7×50)+(7×6)
The correct answer is option d.

Question 2.
Sue uses the expression (8 × 3,000) + (8 × 200) + (8 × 9) to help solve a multiplication problem. Which is Sue’s multiplication problem?
Options:
a. 8 × 329
b. 8 × 3,029
c. 8 × 3,209
d. 8 × 3,290

Answer: 8 × 3,029

Explanation:
The expression (8×3,000)+(8×200)+(8×9) is written in the Distributive property of multiplication. So 8×3,029.
The correct answer is option b.

Spiral Review

Question 3.
What is another way to write 9 x 200?
Options:
a. 18 ones
b. 18 tens
c. 18 hundreds
d. 18 thousands

Answer: 18 hundreds

Explanation: 9×200= 1800
The correct answer is option c.

Question 4.
What is the value of the digit 4 in 46,000?
Options:
a. 4 ten thousands
b. 4 thousands
c. 4 hundreds
d. 4 tens

Answer: 4 ten thousand

Explanation:
The place value of 4 in 46,000 is 40,000.
The correct answer is option a.

Question 5.
Chris bought 6 packages of napkins for his restaurant. There were 200 napkins in each package. How many napkins did Chris buy?
Options:
a. 120
b. 1,200
c. 12,000
d. 120,000

Answer: 1,200

Explanation:
Total packages are 6 and each package contains 200 napkins.
So 6 × 200=1,200.
The correct answer is option b.

Question 6.
Which of the following lists the numbers in order from least to greatest?
Options:
a. 8,512; 8,251; 8,125
b. 8,251; 8,125; 8,512
c. 8,125; 8,512; 8,251
d. 8,125; 8,251; 8,512

Answer: 8,125; 8,251; 8,512

Explanation:
8,125>8,251>8,512.
The correct answer is option d.

Common Core – Multiply by 1-Digit Numbers – Page No. 35

Multiply Using Partial Products

Estimate. Then record the product.

Question 1.
Estimate: 1,200
2 4 3
×    6
———
1,200
2 4 0
+ 1 8
———
1,458

Question 2.
6 4 0
×    3
———
Estimate: ________
Product: _______

Answer:

Question 3.
$ 1 4 9
×       5
———
Estimate: $ ________
Product: $ _______

Answer:

Question 4.
7 2 1
×   8
———
Estimate: ________
Product: _______

Answer:

Question 5.
2 9 3
×    4
———
Estimate: ________
Product: _______

Answer:

Question 6.
$ 4 1 6
×       6
———
Estimate: $ ________
Product: $ _______

Answer:

Question 7.
9 6 1
×    2
———
Estimate: ________
Product: _______

Answer:

Question 8.
8 3 7
×    9
———
Estimate: ________
Product: _______

Answer:

Question 9.
6 5 2
×    4
———
Estimate: ________
Product: _______

Answer:

Question 10.
3 0 7
×    3
———
Estimate: ________
Product: _______

Answer:

Question 11.
5 4 3
×     7
———
Estimate: ________
Product: _______

Answer:

Question 12.
$ 8 2 2
×       5
———
Estimate: $ ________
Product: $ _______

Answer:

Problem Solving

Question 13.
A maze at a county fair is made from 275 bales of hay. The maze at the state fair is made from 4 times as many bales of hay. How many bales of hay are used for the maze at the state fair?
______ bales

Answer: 1100 bales

Explanation:
No. of country fair bales are 275 and state fair bales are 4 times as many as country fair bales.
So 275 × 4= 1100 bales.

Question 14.
Pedro gets 8 hours of sleep each night. How many hours does Pedro sleep in a year with 365 days?
______ hours

Answer: 2,920 hours

Explanation:
Given,
Pedro sleeps 8 hours each night and 365 days Pedro sleeps 365 × 8= 2,920 hours.

Common Core – Multiply by 1-Digit Numbers – Page No. 36

Lesson Check

Question 1.
A passenger jet flies at an average speed of 548 miles per hour. At that speed, how many miles does the plane travel in 4 hours?
Options:
a. 2,092 miles
b. 2,112 miles
c. 2,192 miles
d. 2,480 miles

Answer: 2,192 miles

Explanation:
The average speed of a passenger jet is 548 miles per hour.
And the plane travels in 4 hours is 548 × 4= 2,192 miles.
The correct answer is option c.

Question 2.
Use the model to find 3 × 157.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 2 Multiply by 1-Digit Numbers Common Core - Multiply by 1-Digit Numbers img 12
Options:
a. 300,171
b. 300,157
c. 471
d. 451

Answer: 471

Explanation:
By distributive property of multiplication 3 x 157= 3 x(100+50+7)
= (3 x100)+(3×50)+(3×7)
= 300+150+21
= 471
The correct answer is option c.

Spiral Review

Question 3.
The school fun fair made $1,768 on games and $978 on food sales. How much money did the fun fair make on games and food sales?
Options
a. $2,636
b. $2,646
c. $2,736
d. $2,746

Answer: $2746

Explanation:
Money made on games is $1,768 and on food, sale is $978.
So total money make on games and food sales are 1768+978= 2746.
The correct answer is option d.

Question 4.
Use the table below.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 2 Multiply by 1-Digit Numbers Common Core - Multiply by 1-Digit Numbers img 13
Which of the following lists the states from least to greatest population?
Options:
a. Alaska, North Dakota, Vermont
b. Vermont, Alaska, North Dakota
c. North Dakota, Vermont, Alaska
d. Vermont, North Dakota, Alaska

Answer: Vermont, North Dakota, Alaska

Explanation:
Vermont has 621,760, North Dakota has 646,844 and Alaska has 698,473.
So Vermont, North Dakota, Alaska.
The correct answer is option d.

Question 5.
A National Park covers 218,375 acres. What is this number written in expanded form?
Options:
a. 200,000 + 10,000 + 8,000 + 300 + 70 + 5
b. 20,000 + 1,000 + 800 + 30 + 75
c. 218 + 375
d. 218 thousand, 375

Answer: 200,000 + 10,000 + 8,000 + 300 + 70 + 5

Explanation:
218,375 is expanded as 200,000 + 10,000 + 8,000 + 300 + 70 + 5
The correct answer is option a.

Question 6.
Last year a business had profits of $8,000. This year its profits are 5 times as great. What are this year’s profits?
Options:
a. $4,000
b. $40,000
c. $44,000
d. $400,000

Answer: $40,000

Explanation:
Last year’s profit of $8,000 and this year 5 times more.
So this year profit is 8000 × 5= 40,000.
The correct answer is option b.

Common Core – Multiply by 1-Digit Numbers – Page No. 37

Multiply Using Mental Math

Find the product. Tell which strategy you used.

Question 1.
6 × 297
Think: 297 = 300 – 3
6 × 297 = 6 × (300 – 3)
= (6 × 300) – (6 × 3)
= 1,800 – 18
= 1,782;
use subtraction

Question 2.
8 × 25 × 23 = _____

Answer: 4,600, Associative property.

Explanation:
8×25×23=(8×25)× 23
=(200) ×23
4,600

Question 3.
8 × 604 = _____

Answer: 4,832, Use Addition.

Explanation:
604= 600+4
8×604= 8×(600+4)
=(8×600)+(8×4)
=4800+32
=4832.

Question 4.
50 × 28 = _____

Answer: 1400, Halving and doubling.

Explanation:
50×28= (25×28)+(50×14)
=700+700
=1400

Question 5.
9 × 199 = _____

Answer: 1,791

Explanation:
By Distributive property 9 × 199= 9 ×(100+90+9)
=(9×100)+(9×90)+(9×9)
=900+810+81
= 1791

Question 6.
20 × 72 × 5 = _____

Answer: 7,200.

Explanation:
The associative property states that the terms in an addition or multiplication problem can be grouped in different ways, and the answer remains the same.
20 × 72 × 5= (20×72) ×5
=1440×5
=7,200.

Question 7.
32 × 25 = _____

Answer: 800

Explanation:
Multiplication.
32×25= 800.

Problem Solving

Question 8.
Section J in an arena has 20 rows. Each row has 15 seats. All tickets cost $18 each. If all the seats are sold, how much money will the arena collect for Section J?
$ _____

Answer: $5400

Explanation:
Total rows in the arena are 20 rows and each row has 15 seats.
So total seats are 20×15= 300 seats.
And each ticket cost is $18, So the total ticket price is 300×15= 5400.

Question 9.
At a high-school gym, the bleachers are divided into 6 equal sections. Each section can seat 395 people. How many people can be seated in the gym?
_____ people

Answer: 2,370 people.

Explanation:
Total sections are 6 and each section contains 395 people.
So the total members can be seated in the gym are 395 × 6= 2,370 people.

Common Core – Multiply by 1-Digit Numbers – Page No. 38

Lesson Check

Question 1.
Pencils come in cartons of 24 boxes. A school bought 50 cartons of pencils for the start of school. Each box of pencils cost $2. How much did the school spend
on pencils?
Options:
a. $240
b. $1,200
c. $2,400
d. $4,800

Answer: $2,400

Explanation:
Given,
Total boxes of pencils are 24 and a school bought 50 cartons of pencils.
So the total no. of boxes are 24×50=1200 and each box of pencils cost $2.
So 1200×2= 2400 school has spent.
Thus the correct answer is option c.

Question 2.
The school also bought 195 packages of markers. There are 6 markers in a package. How many markers did the school buy?
Options:
a. 1,170
b. 1,195
c. 1,200
d. 1,230

Answer: 1,170

Explanation:
The school also bought 195 packages of markers. There are 6 markers in a package.
Multiply the number of packages with the number of markers in the package.
So total markers are 195×6= 1170.
Thus the correct answer is option a.

Spiral Review

Question 3.
Alex has 175 baseball cards. Rodney has 3 times as many baseball cards as Alex. How many fewer cards does Alex have than Rodney?
Options:
a. 700
b. 525
c. 450
d. 350

Answer: 350

Explanation:
Alex has 175 baseball cards and Rodney has 3 times as many as Alex.
So the total no. of cards Rodney has is 175×3= 525. And Alex has 525-175= 350 fewer cards than Rodney.
Thus the correct answer is option d.

Question 4.
A theater seats 1,860 people. The last 6 shows have been sold out. Which is the best estimate of the total number of people attending the last 6 shows?
Options:
a. fewer than 6,000
b. about 6,000
c. fewer than 12,000
d. more than 20,000

Answer: fewer than 12,000

Explanation:
Given,
A theater seats 1,860 people.
The last 6 shows have been sold out.
No. of seats in a theater are 1,860 people and the last 6 shows have been sold out.
So 1,860×6= 11,160 which are fewer than 12,000.
Thus the correct answer is option c.

Question 5.
At one basketball game, there were 1,207 people watching. At the next game, there were 958 people. How many people in all were at the two games?
Options:
a. 2,155
b. 2,165
c. 2,265
d. 10,787

Answer: 2,165

Explanation:
There are 1207 people are watching a basketball game and in the next game, 958 people are there.
So the total no. of people is 1,207+958= 2165.
Thus the correct answer is option b.

Question 6.
Bill bought 4 jigsaw puzzles. Each puzzle has 500 pieces. How many pieces are in all the puzzles altogether?
Options:
a. 200
b. 900
c. 2,000
d. 20,000

Answer: 2,000

Explanation:
Given,
Bill bought 4 jigsaw puzzle and each puzzle has 500 pieces.
So altogether pieces are 500×4= 2000.
Thus the correct answer is option c.

Common Core – Multiply by 1-Digit Numbers – Page No. 39

Problem Solving Multistep Multiplication Problems

Solve each problem.

Question 1.
A community park has 6 tables with a chessboard painted on top. Each board has 8 rows of 8 squares. When a game is set up, 4 rows of 8 squares on each board are covered with chess pieces. If a game is set up on each table, how many total squares are NOT covered by chess pieces?
Go Math Grade 4 Answer Key Homework Practice FL Chapter 2 Multiply by 1-Digit Numbers Common Core - Multiply by 1-Digit Numbers img 14
4 × 8 = 32
32 × 6 = 192 squares

Question 2.
Jonah and his friends go apple picking. Jonah fills 5 baskets. Each basket holds 15 apples. If 4 of Jonah’s friends pick the same amount as Jonah, how many apples do Jonah and his friends pick in all? Draw a diagram to solve the problem.
_____ apples

Answer: 375 apples

Explanation:
As Jonah fills 5 baskets which hold 15 apples, So Jonah picked 15×5= 75 apples.
And 4 of his friends pick the same amount of apples, which means 75×4=300.
So total apples Jonah and his friends picked up are 300+75= 375 apples.

Question 3.
There are 6 rows of 16 chairs set up for the third-grade play. In the first 4 rows, 2 chairs on each end are reserved for teachers. The rest of the chairs are for students. How many chairs are there for students?
_____ chairs

Answer: 80 chairs

Explanation:
As there are 6 rows of 16 chairs which means 16×6= 96 total chairs.
And the first 4 rows 2 chairs on each end are reserved for teachers, which means 4×4= 16 chairs are reserved for teachers.
So 96-16= 80 chairs are left for the students.
Therefore there are 80 chairs for students.

Common Core – Multiply by 1-Digit Numbers – Page No. 40

Lesson Check

Question 1.
At a tree farm, there are 9 rows of 36 spruce trees. In each row, 14 of the spruce trees are blue spruce. How many spruce trees are NOT blue spruce?
Options:
a. 126
b. 198
c. 310
d. 324

Answer: 198

Explanation:
There are 9 rows of 36 spruce trees which means 9×36= 324 spruce trees.
And in that, each row has 14 blue spruce trees which mean 14×9= 126.
So 324-126= 198 spruce trees are not blue.
Thus the correct answer is option b.

Question 2.
Ron is tiling a countertop. He needs to place 54 square tiles in each of 8 rows to cover the counter. He wants to randomly place 8 groups of 4 blue tiles each and have the rest of the tiles be white. How many white tiles will Ron need?
Options:
a. 464
b. 432
c. 400
d. 32

Answer: 400

Explanation:
Ron places 54 square tiles in each of 8 rows which means 54×8=432 tiles.
And he randomly places 8 groups of 4 blue tiles which means 8×4= 32 blue tiles are placed.
So no. of white tiles are 432 – 32= 400.
Thus the correct answer is option c.

Question 3.
Juan reads a book with 368 pages. Savannah reads a book with 172 fewer pages than Juan’s book. How many pages are in the book Savannah reads?
Options:
a. 196
b. 216
c. 296
d. 540

Answer: 196

Explanation:
Given,
Juan reads a book with 368 pages and Savannah reads a book with 172 fewer pages than Juan’s which means 368-172= 196 pages are in Savannah’s read.
Thus the correct answer is option a.

Question 4.
Hailey has bottles that hold 678 pennies each. About how many pennies does she have if she has 6 bottles filled with pennies?
Options:
a. 3,600
b. 3,900
c. 4,200
d. 6,000

Answer: 4,200

Explanation:
Given,
Hailey has bottles that hold 678 pennies each.
Let’s round off 678 to 700 and Hailey has bottles that hold 700 pennies each and if she has 6 bottles filled with pennies which means 700×6= 4200.
Thus the correct answer is option c.

Question 5.
Terrence plants a garden that has 8 rows of flowers, with 28 flowers in each row. How many flowers did Terrence plant?
Options:
a. 1,664
b. 224
c. 164
d. 36

Answer: 224

Explanation:
As the garden has 8 rows of flowers with 28 flowers in each row.
So no. of flowers is 28×8= 224.
Thus the correct answer is option b.

Question 6.
Kevin has 5 fish in his fish tank. Jasmine has 4 times as many fish as Kevin has. How many fish does Jasmine have?
Options:
a. 15
b. 20
c. 25
d. 30

Answer: 20

Explanation:
Given that,
Kevin has 5 fishes and Jasmine has 4 times as many as Kevin which means 5×4= 20 fishes Jasmine has.
Thus the correct answer is option b.

Common Core – Multiply by 1-Digit Numbers – Page No. 41

Multiply 2-Digit Numbers with Regrouping

Estimate. Then record the product.

Question 1.
Estimate: 150
Go Math Grade 4 Answer Key Homework Practice FL Chapter 2 Multiply by 1-Digit Numbers Common Core - Multiply by 1-Digit Numbers img 15

Question 2.
3 2
× 8
———-
Estimate: _________
Product: __________

Answer:
Estimate: 240
Product: 256

Explanation:
The number close to 32 is 30 and 30×8=240.
3 2
× 8
256
Thus the product is 256.

Question 3.
$ 5 5
×   2
———-
Estimate: $ _________
Product: $ __________

Answer:
Estimate: $120
Product: $110

Explanation:
Round off 55 to 60 and 60×2= 120.
$ 5 5
×   2
$110
Thus the product is $110.

Question 4.
6 1
× 8
———-
Estimate: _________
Product: __________

Answer:
Estimate: 480
Product: 488

Explanation:
Round off 61 to 60 and 60×8= 480.
6 1
× 8
488
Thus the product is 488.

Question 5.
3 7
× 9
———-
Estimate: _________
Product: __________

Answer:
Estimate: 360
Product: 333

Explanation:
Round off 37 to 40 and 40×6= 360.
3 7
× 9
333
Thus the product is 333.

Question 6.
$ 1 8
×    7
———-
Estimate: $ _________
Product: $ __________

Answer:
Estimate: $140
Product: $126

Explanation:
Round off 18 to 20 and 20×7= 140.
$ 1 8
×    7
$126
Thus the product is $126.

Question 7.
8 3
× 5
———-
Estimate: _________
Product: __________

Answer:
Estimate: 400
Product: 415

Explanation:
Round off 83 to 80 and 80×5= 400.
8 3
× 5
415
Thus the product is 415.

Question 8.
9 5
× 8
———-
Estimate: _________
Product: __________

Answer:

Estimate: 800
Product: 760

Explanation:
Round off 95 to 100 and 100×8= 800.
9 5
× 8
760
Thus the product is 760.

Question 9.
9 4
× 9
———-
Estimate: _________
Product: __________

Answer:
Estimate: 810
Product: 846

Explanation:
Round off 94 to 90 and 90×9= 810.
9 4
× 9
846
Thus the product is 846.

Question 10.
5 7
× 6
———-
Estimate: _________
Product: __________

Answer:
Estimate: 360
Product: 342

Explanation:
Round off 57 to 60 and 60×6= 360.
5 7
× 6
342
Thus the product is 342.

Question 11.
7 2
× 3
———-
Estimate: _________
Product: __________

Answer:
Estimate: 210
Product: 216

Explanation: Round off 72 to 70 and 70×3= 210.
7 2
× 3
216
Thus the product is 216.

Question 12.
$ 7 9
× 8
———-
Estimate: $ _________
Product: $ __________

Answer:
Estimate: $640
Product: $632

Explanation: Round off 79 to 80 and 80×8= 640.
$ 7 9
× 8
$632
Thus the product is $632.

Problem Solving

Question 13.
Sharon is 54 inches tall. A tree in her backyard is 5 times as tall as she is. The floor of her treehouse is at a height that is twice as tall as she is. What is the difference, in inches, between the top of the tree and the floor of the treehouse?
_______ inches

Answer: 162 inches

Explanation:
Given,
Sharon is 54 inches tall and a tree in her backyard is 5 times as tall as she is which means 54×5= 270.
And her treehouse is twice as tall as she is which means 54×2= 108 inches.
So the difference between the top of the tree and the floor of the treehouse is 270-108= 162 inches.

Question 14.
Mr. Diaz’s class is taking a field trip to the science museum. There are 23 students in the class, and a student admission ticket is $8. How much will the student
tickets cost?
$ _______

Answer: $184

Explanation:
Given,
Mr. Diaz’s class is taking a field trip to the science museum.
There are 23 students in the class, and a student admission ticket is $8.
Total no. of students are 23 and tickets cost is $8, So 23×8= $184.

Common Core – Multiply by 1-Digit Numbers – Page No. 42

Lesson Check

Question 1.
A ferryboat makes four trips to an island each day. The ferry can hold 88 people. If the ferry is full on each trip, how many passengers are carried by the ferry
each day?
Options:
a. 176
b. 322
c. 332
d. 352

Answer: 352

Explanation:
Total trips made by the ferryboat each day are 4 and it can hold 88 people.
So 88×4= 352 passengers are carried by ferryboat each day.
Thus the correct answer is option d.

Question 2.
Julian counted the number of times he drove across the Seven Mile Bridge while vacationing in the Florida Keys. He crossed the bridge 34 times. How many miles in all did Julian drive crossing the bridge?
Options:
a. 328 miles
b. 248 miles
c. 238 miles
d. 218 miles

Answer: 238 miles

Explanation:
Given,
No. of times Julian drive across the bridge is 7 miles and he crossed the bridge 34 times.
So 34×7= 238 miles Julian drive crossing the bridge.
Thus the correct answer is option c.

Spiral Review

Question 3.
Sebastian wrote the population of his city as 300,000 + 40,000 + 60 + 7. Which of the following shows the population of Sebastian’s city written in standard form?
Options:
a. 346,700
b. 340,670
c. 340,607
d. 340,067

Answer: 340,067

Explanation:
300,000+40,000+60+7= 340,067.
Thus the correct answer is option d.

Question 4.
A plane flew 2,190 kilometers from Chicago to Flagstaff. Another plane flew 2,910 kilometers from Chicago to Oakland. How much farther did the plane that flew to Oakland fly than the plane that flew to Flagstaff?
Options:
a. 720 kilometers
b. 820 kilometers
c. 5,000 kilometers
d. 5,100 kilometers

Answer: 720 kilometers

Explanation:
Given,
A plane flew from Chicago to Flagstaff is 2,190 km and another plane flew from Chicago to Oakland is 2,910.
So 2910-2190= 720 km.
Thus the correct answer is option a.

Question 5.
Tori buys 27 packages of miniature racing cars. Each package contains 5 cars. About how many miniature racing cars does Tori buy?
Options:
a. 15
b. 32
c. 100
d. 150

Answer: 150

Explanation:
Given,
Tori buys 27 packages of miniature racing cars.
Each package contains 5 cars.
Let’s round off 27 packages to 30 and each package contains 5 cars, which means 30×5=150.
Thus the correct answer is option d.

Question 6.
Which of the following equations represents the Distributive Property?
Options:
a. 3 × 4 = 4 × 3
b. 9 × 0 = 0
c. 5 × (3 + 4) = (5 × 3) + (5 × 4)
d. 6 × (3 × 2) = (6 × 3) × 2

Answer: 5 × (3 + 4) = (5 × 3) + (5 × 4)

Explanation:
Distributive property means if we multiply a sum by a number is the same as multiplying each addend by the number and adding the products.

Common Core – Multiply by 1-Digit Numbers – Page No. 43

Multiply 3-Digit and 4-Digit Numbers with Regrouping

Estimate. Then find the product.

Question 1.
Estimate: 4,000
Go Math Grade 4 Answer Key Homework Practice FL Chapter 2 Multiply by 1-Digit Numbers Common Core - Multiply by 1-Digit Numbers img 16

Question 2.
5,339
×     6
———-
Estimate: ________
Product: _________

Answer:
Estimate: 30,000
Product: 32,034

Explanation:
Round off 5,339 to 5000 then 5000×6= 30,000.
5,339
×     6
32,034
Thus the product is 32,034.

Question 3.
$ 8 7 9
×       8
———-
Estimate: $ ________
Product: $ _________

Answer:
Estimate: $7,200.
Product: $7,032.

Explanation: Round off 879 to 900 then 900×8= 7,200.
$ 8 7 9
×       8
$7,032
Thus the product is $7,032

Question 4.
3,182
×    5
———-
Estimate: ________
Product: _________

Answer:
Estimate: 15,000
Product: 15,910

Explanation: Round off 3,182 to 3000 then 3000×5= 15,000.
3,182
×    5
15,910
Thus the product is 15,910.

Question 5.
4,616
×     3
———-
Estimate: ________
Product: _________

Answer:
Estimate: 15,000
Product: 13,848

Explanation: Round off 4,616 to 5,000 then 5000×3= 15,000.
4,616
×     3
13,848
Thus the product is 13,848.

Question 6.
2,854
× 9
———-
Estimate: $ ________
Product: $ _________

Answer:
Estimate: 27,000
Product: 25,686

Explanation: Round off 2,854 to 3000 then 3000×9= 27,000.
2,854
×      9
25,686
Thus the product is 25,686.

Question 7.
7,500
× 2
———-
Estimate: ________
Product: _________

Answer:
Estimate: 16,000
Product: 15,000

Explanation: Round off 7,500 to 8000 then 8000×2= 16,000.
7,500
×       2
15,000
Thus the product is 15,000.

Question 8.
9 4 2
×    7
———-
Estimate: ________
Product: _________

Answer:
Estimate: 6,300
Product: 6,594

Explanation: Round off 942 to 900 then 900×7= 6,300.
9 4 2
×    7
6,594
Thus the product is 6,594.

Question 9.
1,752
×     6
———-
Estimate: ________
Product: _________

Answer:
Estimate: 12,000.
Product: 10,512.

Explanation: Round off 1,752 to 2000 then 2000×6= 12,000.
1,752
×     6
10,512
Thus the product is 10,512.

Question 10.
5 5 0
×    9
———-
Estimate: ________
Product: _________

Answer:
Estimate: 5,400
Product: 4,950

Explanation: Round off 550 to 600 then 600×9= 5,400.
5 5 0
×    9
4,950
Thus the product is 4,950.

Question 11.
6,839
×     4
———-
Estimate: ________
Product: _________

Answer:
Estimate: 28,000
Product: 27,356

Explanation: Round off 6,839 to 7000 then 7000×4= 28,000.
6,839
×     4
27,356
Thus the product is 27,356.

Question 12.
$ 9,614
×        3
———-
Estimate: $ ________
Product: $ _________

Answer:
Estimate: 60,000.
Product: 57,684.

Explanation: Round off 9,614 to 10,000 then 10,000×6= 60,000.
$ 9,614
×      3
57,684
Thus the product is 57,684.

Problem Solving

Question 13.
Lafayette County has a population of 7,022 people. Columbia County’s population is 8 times as great as Lafayette County’s population. What is the population of Columbia County?
_____ people

Answer: 56,176 people

Explanation:
Lafayette County has a population of 7,022 people and Columbia County’s population is 8 times Lafayette County which means 7,022×8= 56,176.
Therefore the population of Columbia County is 56,176.

Question 14.
A seafood company sold 9,125 pounds of fish last month. If 6 seafood companies sold the same amount of fish, how much fish did the 6 companies sell last month in all?
_____ pounds

Answer: 54,750 pounds.

Explanation:
As the seafood company sold 9,125 pounds of fishes last month and 6 seafood companies also sold the same amount which means 9,125×6= 54,750 pounds.

Common Core – Multiply by 1-Digit Numbers – Page No. 44

Lesson Check

Question 1.
By recycling 1 ton of paper, 6,953 gallons of water are saved. How many gallons of water are saved by recycling 4 tons of paper?
Options:
a. 24,602 gallons
b. 27,612 gallons
c. 27,812 gallons
d. 28,000 gallons

Answer: 27,812 gallons

Explanation:
Given that,
By recycling 1 ton of paper, 6,953 gallons of water are saved.
So 4 tons of paper can save 6,953×4= 27,812.
The correct answer is option c.

Question 2.
Esteban counted the number of steps it took him to walk to school. He counted 1,138 steps. How many steps does he take walking to and from school each day?
Options:
a. 2,000
b. 2,266
c. 2,276
d. 22,616

Answer: 2,276

Explanation:
Given, Esteban counted the number of steps it took him to walk to school. He counted 1,138 steps.
As Esteban counted 1,138 steps to school and from school, it will be 1,138+1,138=2,276 steps
The correct answer is option c.

Spiral Review

Question 3.
A website has 13,406 people registered. What is the word form of this number?
Options:
a. thirty thousand, four hundred six
b. thirteen thousand, four hundred sixty
c. thirteen thousand, four hundred six
d. thirteen thousand, six hundred six

Answer: thirteen thousand, four hundred six

Explanation:
13,406 in words are thirteen thousand four hundred six.
The correct answer is option c.

Question 4.
In one year, the McAlister family drove their car 15,680 miles. To the nearest thousand, how many miles did they drive their car that year?
Options:
a. 15,000 miles
b. 15,700 miles
c. 16,000 miles
d. 20,000 miles

Answer: 16,000 miles

Explanation: 15,680 nearest thousand is 16,000.
The correct answer is option c.

Question 5.
Connor scored 14,370 points in a game. Amy scored 1,089 fewer points than Connor. How many points did Amy score?
Options:
a. 12,281
b. 13,281
c. 15,359
d. 15,459

Answer: 13,281

Explanation:
Connor scored 14,370 points and Amy scored 1,089 fewer points.
So Amy score is 14,370-1089= 13,281.
The correct answer is option b.

Question 6.
Lea buys 6 model cars that each cost $15. She also buys 4 bottles of paint that each cost $11. How much does Lea spend in all on model cars and paint?
Options:
a. $134
b. $90
c. $44
d. $36

Answer: $134

Explanation: Lea buys 6 model cars that each cost $15.
So the total cost for cars is $15×6= $90.
And 4 bottles of paint that each cost $11.
So the total cost of the paints is $11×4= $44. Then
$90+$44= $134.
The correct answer is option a.

Common Core – Multiply by 1-Digit Numbers – Page No. 45

Solve Multistep Problems Using Equations

Find the value of n.

Question 1.
4 × 27 + 5 × 34 – 94 = n
108 + 5 × 34 – 94 = n
108 + 170 – 94 = n
278 – 94 = n
184 = n

Question 2.
7 × 38 + 3 × 45 – 56 = n
_____ = n

Answer: 345

Explanation:
7 × 38 + 3 × 45 – 56 = n
n = 266 + 135 – 56
n = 401 – 56
n = 345

Question 3.
6 × 21 + 7 × 29 – 83 = n
_____ = n

Answer: 246

Explanation:
6 × 21 + 7 × 29 – 83 = n
n = 126 + 203 – 83
n = 329 – 83
n = 246

Question 4.
9 × 19 + 2 × 57 – 75 = n
_____ = n

Answer: 210

Explanation:
9 × 19 + 2 × 57 – 75 = n
n = 171 + 114 – 75
n = 285 – 75
n = 210.

Question 5.
5 × 62 + 6 × 33 – 68 = n
_____ = n

Answer: 440

Explanation:
5 × 62 + 6 × 33 – 68= n
n = 310 + 198 – 68
n = 508 – 68
n = 440

Question 6.
8 × 19 + 4 × 49 – 39 = n
_____ = n

Answer: 309

Explanation:
8 × 19 + 4 × 49 – 39 = n
n =152 + 196 – 39
n = 348 – 39
n = 309

Problem Solving

Question 7.
A bakery has 4 trays with 16 muffins on each tray. The bakery has 3 trays of cupcakes with 24 cupcakes on each tray. If 15 cupcakes are sold, how many muffins and cupcakes are left?
_____ muffins and cupcakes

Answer: 121 muffins and cupcakes.

Explanation:
Given,
A bakery has 4 trays with 16 muffins on each tray.
The bakery has 3 trays of cupcakes with 24 cupcakes on each tray.
4 × 16 + 3 × 24 – 15 = n
64 + 3 × 24 – 15 = n
64 + 72 – 15 = n
136 – 15 = n
121 = n
Thus 121 muffins and cupcakes are left.

Question 8.
Katy bought 5 packages of stickers with 25 stickers in each package. She also bought 3 boxes of markers with 12 markers in each box. If she receives 8 stickers from a friend, how many stickers and markers does Katy have now?
_____ stickers and markers

Answer: 69 stickers and markers

Explanation:
Given,
Katy bought 5 packages of stickers with 25 stickers in each package.
She also bought 3 boxes of markers with 12 markers in each box.
5 × 25 + 3 × 12 + 8 = n
125 + 3 × 12 + 8 = n
125 + 36 + 8 = n
169 = n
Thus Katy have 69 stickers and markers.

Common Core – Multiply by 1-Digit Numbers – Page No. 46

Lesson Check

Question 1.
What is the value of n?
9 × 23 + 3 × 39 – 28 = n
Options:
a. 240
b. 296
c. 2,310
d. 8,162

Answer: 296

Explanation:
Given the expression,
9 × 23 + 3 × 39 – 28 = n
n = 207 + 117 – 28
n = 324 – 28
n = 296
Thus the correct answer is option b.

Question 2.
Which expression has a value of 199?
Options:
a. 4 × 28 + 6 × 17 – 15
b. 4 × 17 + 6 × 28 – 38
c. 4 × 38 + 6 × 15 – 28
d. 4 × 15 + 6 × 38 – 88

Answer: 4 × 28 + 6 × 17 – 15

Explanation:
Given the expression,
4 × 28 + 6 × 17 – 15 = n
n = 112 + 102 – 15
n = 214 – 15
n = 199.
Thus the correct answer is option a.

Spiral Review

Question 3.
Which expression shows how you can multiply 9 × 475 using expanded form and the Distributive Property?
Options:
a. (9 × 4) + (9 × 7) + (9 × 5)
b. (9 × 4) + (9 × 70) + (9 × 700)
c. (9 × 400) + (9 × 70) + (9 × 5)
d. (9 × 400) + (9 × 700) + (9 × 500)

Answer: (9 × 400) + (9 × 70) + (9 × 5)

Explanation:
Distributive property means if we multiply a sum by a number is the same as multiplying each addend by the number and adding the products.
9 × 475= (9×400)+(9×70)+(9×5)
Thus the correct answer is option c.

Question 4.
Which equation best represents the comparison sentence?
32 is 8 times as many as 4
Options:
a. 32 = 8 × 4
b. 32 × 8 = 4
c. 32 = 8 + 4
d. 8 + 4 = 32

Answer: 32 = 8 × 4

Explanation:
The equation for the sentence 32 is 8 times as many as 4 is 32 = 8 × 4.
Thus the correct answer is option a.

Question 5.
Between which pair of numbers is the exact product of 379 and 8?
Options:
a. between 2,400 and 2,500
b. between 2,400 and 2,800
c. between 2,400 and 3,000
d. between 2,400 and 3,200

Answer: between 2,400 and 3,200

Explanation:
379 × 8 = 3,032
Thus the correct answer is option d.

Question 6.
Which of the following statements shows the halving and doubling strategy to find 28 × 50?
Options:
a. 28 × 50 = 14 × 100
b. 28 × 50 = (14 × 25) × (14 × 25)
c. 28 × 50 = (20 × 50) × (8 × 50)
d. 28 × 50 = 2 × (14 × 25)

Answer: 28 × 50 = 14 × 100

Explanation:
28×50 = 14×100
Thus the correct answer is option a.

Common Core – Multiply by 1-Digit Numbers – Page No. 47

Lesson 2.1

Write a comparison sentence.

Question 1.
27 = 3 × 9
____ is ____ times as many as ____

Answer: 27 is 3 times as many as 9.

Question 2.
7 × 8 = 56
____ times as many as ____ is ____

Answer: 7 times as many as 8 is 56.

Lessons 2.3, 2.5–2.6

Find the product.

Question 3.
2 × 700 = ____

Answer: 1400

Explanation:
2 × 7 = 14
2 × 700 = 1400

Question 4.
6 × 6,000 = ____

Answer: 36000

Explanation:
6 × 6 = 36
6 × 6,000 = 36,000

Question 5.
7 × 13 = ____

Answer: 91

Explanation:
The multiple of 7 and 13 is 91.
7 × 13 = 91

Question 6.
4 × 19 = ____

Answer: 76

Explanation:
The product of 4 and 19 is 76.

Question 7.
5 × 216 = ____

Answer: 1080

Explanation:
The product of 5 and 216 is 1080.

Question 8.
9 × 1,362 = ____

Answer: 12258

Explanation:
The product of 9 and 1,362 is 12,258.

Lessons 2.2, 2.9

Draw a diagram. Write an equation and solve.

Question 9.
Julia saw 5 times as many cars as trucks in a parking lot. If she saw 30 cars and trucks altogether in the parking lot, how many were trucks?
____ trucks

Answer: 5 trucks

Explanation:
Given,
Julia saw 5 times as many cars as trucks in a parking lot.
25 + 5 = 30
25/5 = 5
Thus there are 5 trucks altogether in the parking lot.

Question 10.
Ivan has 6 times as many blue beads as red beads. He has 49 red and blue beads in all. How many blue beads does Ivan have?
____ blue beads

Answer: 42 blue beads

Explanation:
Given that,
Ivan has 6 times as many blue beads as red beads.
He has 49 red and blue beads in all.
Let x be the number of blue beads
y be the number of red beads
We know that,
x + y = 49
x = 49 – y ——> eq. 1
x = 6y ———> eq. 2
Equate equation 1 and 2
49 – y = 6y
6y + y = 49
7y = 49
y = 49/7
y = 7
Now find the value of x
x = 6y
x = 6 × 7 = 42
Therefore the answer is 42 blue beads.

Question 11.
There are 6 rows with 18 chairs in each row. In the center of the chairs, 4 rows of 6 chairs are brown. The rest of the chairs are blue. How many chairs are blue?
____ blue chairs

Answer: 84 blue chairs

Explanation:
Given that,
There are 6 rows with 18 chairs in each row.
In the center of the chairs, 4 rows of 6 chairs are brown. The rest of the chairs are blue.
18 × 6 = 108
4 × 6 = 24
To find the number of chairs that are blue
We have to subtract 24 from 108.
108 – 24 = 84
Thus there are 84 blue chairs.

Common Core – Multiply by 1-Digit Numbers – Page No. 48

Lessons 2.7, 2.10–2.11

Estimate. Then record the product.

Question 1.
3 1 8
×   3
———-
Estimate: _______
Product: _________

Answer:
Estimate: 900
Product: 954

Explanation:
The number close to 318 is 300.
300 × 3 = 900.
The estimated product of 318 and 3 is 900.
3 1 8
×  3
954
The product of 318 and 3 is 954.

Question 2.
$ 5 2 2
×       9
———-
Estimate: _______
Product: _________

Answer:
Estimate: 4500
Product: 4698

Explanation:
The number close to 522 is 500.
500 × 9 = 4500
The estimated product of 522 and 9 is 4500.
$ 5 2 2
×      9
$4698

Question 3.
$ 3 6
×    6
———-
Estimate: _______
Product: _________

Answer:
Estimate: 240
Product: 216

Explanation:
The number close to 36 is 40.
40 × 6 = 240
The estimated product of 40 and 6 is 240.
$ 3 6
×  6
216

Question 4.
5 7
× 8
———-
Estimate: _______
Product: _________

Answer:
Estimate: 480
Product: 456

Explanation:
The number close to 57 is 60.
60 × 8 = 480.
The estimated product of 57 and 8 is 480.
5 7
× 8
456

Question 5.
3,600
×      8
———-
Estimate: _______
Product: _________

Answer:
Estimate: 32,000
Product: 28,800

Explanation:
The number close to 3600 is 4000.
4000 × 8 = 32,000
The estimated product of 3600 and 8 is 32,000.
3,600
×     8
28,800

Question 6.
$ 9,107
× 5
———-
Estimate: _______
Product: _________

Answer:
Estimate: 45,000
Product: 45,535

Explanation:
The number close to 9107 is 9000.
9000 × 5 = 45,000
The estimated product of 9107 and 5 is 45,000.
$ 9,107
×       5
45,535

Lesson 2.8

Find the product. Tell which strategy you used.

Question 7.
(4 × 10) × 10 = ______
Explain:
_________

Answer: 400, Associative property

Explanation:
(4 × 10) × 10 = 4 × 10 × 10
40 × 10 = 400

Question 8.
2 × 898 = ______
Explain:
_________

Answer: 1796, Distributive property

Explanation:
2 × 898 = (2 × 800) + (2 × 90) + (2 × 8)
1600 + 180 + 16 = 1796

Question 9.
______
Explain:
_________

Answer:

Lessons 2.4, 2.12

Question 10.
School pennants cost $18 each. Ms. Lee says she will pay $146 for 7 pennants. Is her answer reasonable? Explain.
______

Answer: No

Explanation:
Given,
School pennants cost $18 each. Ms. Lee says she will pay $146 for 7 pennants.
18 multiplied by 7 is equal to 126 when Ms. Lee is buying the pennants for 146.

Question 11.
Caleb draws 14 dogs on each of 4 posters. He draws 18 cats on each of 6 other posters. If he draws 5 more dogs on each poster with dogs, how many dogs and cats does he draw?
______ dogs and cats

Answer: 184 dogs and cats

Explanation:
Given,
Caleb draws 14 dogs on each of 4 posters. He draws 18 cats on each of 6 other posters.
14 × 4 = 56
18 × 6 = 108
5 × 4 =20
Total = 56 + 108 + 20 = 184
Thus he draw 184 dogs and cats.

Conclusion

Kids have a strong grip on the ch 2 concepts using Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers pdf and secure the highest marks in the exams. Moreover, you can also find other grades Go Math HMH Answer Keys on our site ie., Ccssmathanswers.com

Go Math Grade 8 Answer Key Chapter 6 Functions

go-math-grade-8-chapter-6-functions-answer-key

The solutions of Go Math Grade 8 Answer Key Chapter 6 Functions are provided in the pdf format here. HMH Go Math Grade 8 Answer Key Chapter 6 Functions are presented by the professional math experts in an easy manner and with brief explanations. You can find different ways of solving the problems on this page. So, we suggest the students to refer to Go Math Grade 8 Answer Key Chapter 6 Functions now to begin your practice.

Go Math Grade 8 Chapter 6 Functions Answer Key

Test and improve your knowledge by using Go Math Grade 8 Chapter 6 Functions Solution Key. The Go Math Grade 8 Chapter 6 Functions Answer Key consists of the topics like Identifying and representing functions, describing functions, analyzing graphs, etc. Use HMH Go Math Grade 8 Answer Key for the best practice of maths. After completion of your preparation test yourself by solving the problems given in the model quiz.

Lesson 1: Identifying and Representing Functions 

Lesson 2: Describing Functions

Lesson 3: Comparing Functions 

Lesson 4: Analyzing Graphs

Model Quiz 

Mixed Review 

Guided Practice – Identifying and Representing Functions – Page No. 158

Complete each table. In the row with x as the input, write a rule as an algebraic expression for the output. Then complete the last row of the table using the rule.

Question 1.
Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 1: Identifying and Representing Functions img 1
Type below:
_______________

Answer:
Grade 8 Chapter 6 image 1

Explanation:
Unit Cost of ticket = 40/2 = 20
Total cost = 20x where x is the number of tickets.
x = 20x
10 = 20(100) = 200

Question 2.
Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 1: Identifying and Representing Functions img 2
Type below:
_______________

Answer:
Grade 8 Chapter 6 image 2

Explanation:
Number of pages per minute = 1/2 = 0.5
Total cost = 0.5x where x is the number of minutes.
x = 0.5x
30 = 0.5(30) = 15

Question 3.
Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 1: Identifying and Representing Functions img 3
Type below:
_______________

Answer:
Grade 8 Chapter 6 image 3

Explanation:
Units cost of Muffins = 2.25/1 = 2.25
Total cost = 2.25x where x is the number of muffins
x = 2.25x
12 = 2.25(12) = 27

Determine whether each relationship is a function.

Question 4.
Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 1: Identifying and Representing Functions img 4
_______________

Answer:
Function

Explanation:
Each input is assigned to exactly one output.

Question 5.
Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 1: Identifying and Representing Functions img 5
_______________

Answer:
Not a function

Explanation:
The input value is 4 is paired with two outputs 25 and 35

Question 6.
The graph shows the relationship between the weights of 5 packages and the shipping charge for each package. Is the relationship represented by the graph a function? Explain.
Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 1: Identifying and Representing Functions img 6
_______________

Answer:
Function

Explanation:
Each input is assigned to exactly one output.

Essential Question Check-In

Question 7.
What are four different ways of representing functions? How can you tell if a relationship is a function?
Type below:
_______________

Answer:
The function can be represented by an equation, table, graph, and Venn diagram.
If a relationship is a function, each input is paired with exactly one output.

Independent Practice – Identifying and Representing Functions – Page No. 159

Determine whether each relationship represented by the ordered pairs is a function. Explain.

Question 8.
(2, 2), (3, 1), (5, 7), (8, 0), (9, 1)
_______________

Answer:
Function

Explanation:
Each input value is paired with exactly one output value.

Question 9.
(0, 4), (5, 1), (2, 8), (6, 3), (5, 9)
_______________

Answer:
Not a function

Explanation:
The input value is 5 is paired with two outputs 1 and 9

Question 10.
Draw Conclusions
Joaquin receives $0.40 per pound for 1 to 99 pounds of aluminum cans he recycles. He receives $0.50 per pound if he recycles more than 100 pounds. Is the amount of money Joaquin receives a function of the weight of the cans he recycles? Explain your reasoning.
_______________

Answer:
Yes

Explanation:
The amount of money increases with the weight of the cans. No weight will result in the same amount of money earned.

Question 11.
A biologist tracked the growth of a strain of bacteria, as shown in the graph.
Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 1: Identifying and Representing Functions img 7
a. Explain why the relationship represented by the graph is a function.
Type below:
_______________

Answer:
The relationship is a function as each input has been assigned exactly one output. There is only one number of bacteria for each number of hours.

Question 11.
b. What If?
Suppose there was the same number of bacteria for two consecutive hours. Would the graph still represent a function? Explain.
Type below:
_______________

Answer:
Yes. If the number of bacteria for two consecutive hours is the same, one input will still be paired with one output, hence the relationship is still a function.

Question 12.
Multiple Representations
Give an example of a function in everyday life, and represent it as a graph, a table, and a set of ordered pairs. Describe how you know it is a function.
Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 1: Identifying and Representing Functions img 8
Type below:
_______________

Answer:
The cost of a bouquet of flowers and the number of flowers in the bouquet is a function. The unit cost of flowers = $0.85 and x the number of flowers. Hence, C= 0.85x
Grade 8 Chapter 6 image 4
Grade 8 Chapter 6 image 5
(2, 1.7), (4, 3.4), (6, 5.1), (8, 6.8), (10, 8.5)
Each value of the input is paired with exactly one output.

Identifying and Representing Functions – Page No. 160

The graph shows the relationship between the weights of six wedges of cheese and the price of each wedge.
Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 1: Identifying and Representing Functions img 9

Question 13.
Is the relationship represented by the graph a function? Justify your reasoning. Use the words “input” and “output” in your explanation, and connect them to the context represented by the graph.
_______________

Answer:
Yes, the relationship represented by the graph is a function.
Each input (weight) in the graph is paired with exactly one output(price).

Question 14.
Analyze Relationships
Suppose the weights and prices of additional wedges of cheese were plotted on the graph. Might that change your answer to question 13? Explain your reasoning.
Type below:
_______________

Answer:
No. As the weight of the cheese will increase, the cost of wedges of cheese will increase as well. Hence, for each input (weight), there would be exactly one output (price).

H.O.T.

Focus on Higher Order Thinking

Question 15.
Justify Reasoning
A mapping diagram represents a relationship that contains three different input values and four different output values. Is the relationship a function? Explain your reasoning.
_______________

Answer:
No. Since there are three inputs and four outputs, one of the inputs will have more than one output, hence the relationship cannot be a function.

Question 16.
Communicate Mathematical Ideas
An onion farmer is hiring workers to help harvest the onions. He knows that the number of days it will take to harvest the onions is a function of the number of workers he hires. Explain the use of the word “function” in this context.
Type below:
_______________

Answer:
Number of days = f(number of workers)

Explanation:
We know that the more the number of workers will be involved in the harvesting of onion, the lesser days it will take to complete.
Thus the number of workers becomes the independent variable and the number of days becomes the dependent variable.
Here the word function is used to describe that the number of days is dependent on the number of workers.
Number of days = f(number of workers)

Guided Practice – Describing Functions – Page No. 164

Plot the ordered pairs from the table. Then graph the function represented by the ordered pairs and tell whether the function is linear or nonlinear.

Question 1.
y = 5 − 2x
Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 2: Describing Functions img 10
_______________

Answer:
Grade 8 Chapter 6 image 6
Grade 8 Chapter 6 image 7
Graph of a linear function is a straight line
Linear relationship

Explanation:
Given y = 5 – 2x
y = 5 – 2(-1) = 5 + 2 = 7
y = 5 – 2(1) = 5 – 2 = 3
y = 5 – 2(3) = 5 – 6 = -1
y = 5 – 2(5) = 5 – 10 = -5

Question 2.
y = 2 − x2
Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 2: Describing Functions img 11
_______________

Answer:
y = 2 − x2
Grade 8 Chapter 6 image 8
Graph the ordered pairs. Then draw a line through the points to represent the solution.
Grade 8 Chapter 6 image 9
Graph of a linear function is not a straight line
Non-linear relationship

Explanation:
y = 2 − x2
y = 2 – 4 = -2
y = 2 – 1 = 1
y = 2 – 0 = 2
y = 2 – 1 = 1
y = 2 – 4 = -2

Explain whether each equation is a linear equation.

Question 3.
y = x2 – 1
_______________

Answer:
The equation is not in the form of a linear equation, hence is not a linear equation.

Explanation:
Compare the equation with the general linear equation y = mx + b.
The equation is not in the form of a linear equation, hence is not a linear equation.

Question 4.
y = 1 – x
_______________

Answer:
The equation is in the form of a linear equation, hence is a linear equation.

Explanation:
Compare the equation with the general linear equation y = mx + b.
The equation is in the form of a linear equation, hence is a linear equation.

Essential Question Check-In

Question 5.
Explain how you can use a table of values, an equation, and a graph to determine whether a function represents a proportional relationship.
Type below:
_______________

Answer:
From a table, determine the ratio y/x. If it is constant the relationship is proportional.
From a graph, note if the graph passes through the origin. The graph of a proportional relationship must pass through the origin (0, 0).
From an equation, compare with general linear form of equation, y = mx + b. If b = 0, the relationship is proportional.

Independent Practice – Describing Functions – Page No. 165

Question 6.
State whether the relationship between x and y in y = 4x – 5 is proportional or nonproportional. Then graph the function.
Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 2: Describing Functions img 12
_______________

Answer:
Grade 8 Chapter 6 image 10

Explanation:
First, we compare the equation with the general linear equation y = mx + b. y = 4x – 5 is in the form of y = mx + b, with m = 4 and b = -5. Therefore, the equation is a linear equation. Since b is not equal to 0, the relationship is non-proportional.
Then, we choose several values for the input x. We substitute these values of x in the equation to find the output y.
y = 4x – 5
If x = 0; y = 4(0) – 5 = -5; (0, -5)
If x = 2; y = 4(2) – 5 = 3; (2, 3)
If x = 4; y = 4(4) – 5 = 11; (4, 11)
If x = 6; y = 4(6) – 5 = 19; (6, 19)
We graph the ordered pairs and we draw a line through the points to represent the solutions of the function.

Question 7.
The Fortaleza telescope in Brazil is a radio telescope. Its shape can be approximated with the equation y = 0.013x2. Is the relationship between x and y linear? Is it proportional? Explain.
____________
____________

Answer:
Compare the equation with the general linear equation y = mx + b.
The equation is not in the form of a linear equation, hence it is not a linear equation. Since x is squared, it is not proportional.

Question 8.
Kiley spent $20 on rides and snacks at the state fair. If x is the amount she spent on rides, and y is the amount she spent on snacks, the total amount she spent can be represented by the equation x + y = 20. Is the relationship between x and y linear? Is it proportional? Explain.
____________
____________

Answer:
x + y = 20
Rewriting the equation
y = 20 – x
Compare the equation with the general linear equation y = mx + b.
It is linear
Since b is not equal to 0, the relationship is not proportional.

Question 9.
Represent Real-World Problems
The drill team is buying new uniforms. The table shows y, the total cost in dollars, and x, the number of uniforms purchased.
Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 2: Describing Functions img 13
a. Use the data to draw a graph. Is the relationship between x and y linear? Explain.
____________

Answer:
Grade 8 Chapter 6 image 10
The graph of a linear relationship is a straight line.
x and y are linear.

Question 9.
b. Use your graph to predict the cost of purchasing 12 uniforms.
$ ________

Answer:
$720

Explanation:
Grade 8 Chapter 6 image 10
The cost of 12 uniforms is $720

Question 10.
Marta, a whale calf in an aquarium, is fed a special milk formula. Her handler uses a graph to track the number of gallons of formula y the calf drinks in x hours. Is the relationship between x and y linear? Is it proportional? Explain.
Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 2: Describing Functions img 14
____________
____________

Answer:
The relationship is linear
The relationship is proportional

Explanation:
As the data lies on a straight line, the relationship is linear
As the graph passes through the origin, the relationship is proportional

Describing Functions – Page No. 166

Question 11.
Critique Reasoning
A student claims that the equation y = 7 is not a linear equation because it does not have the form y=mx + b. Do you agree or disagree? Why?
Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 2: Describing Functions img 15
____________

Answer:
Disagree; The equation can be written in the form y = mx + b Where m is 0. The graph of the solutions is a horizontal line.

Question 12.
Make a Prediction
Let x represent the number of hours you read a book and y represent the total number of pages you have read. You have already read 70 pages and can read 30 pages per hour. Write an equation relating x hours and y pages you read. Then predict the total number of pages you will have read after another 3 hours.
_______ pages

Answer:
160 pages

Explanation:
Let x represent the number of hours you read a book and y represents the total number of pages you have read. You have already read 70 pages and can read 30 pages per hour.
m = 30; b = 70 pages
y = 30x + 70
x = 3 hrs
y = 30(3) + 70 = 160

H.O.T.

Focus on Higher Order Thinking

Question 13.
Draw Conclusions
Rebecca draws a graph of a real-world relationship that turns out to be a set of unconnected points. Can the relationship be linear? Can it be proportional? Explain your reasoning.
Type below:
______________

Answer:
The relationship is linear if all the points lie on the same line. If the relationship is linear and passes through the origin, it is proportional.

Question 14.
Communicate Mathematical Ideas
Write a real-world problem involving a proportional relationship. Explain how you know the relationship is proportional.
Type below:
______________

Answer:
The amount of money earned at a car wash is a proportional relationship. When there are 0 cars washed, $0 are earned. The amount of money earned increases by the unit cost of a car wash.

Question 15.
Justify Reasoning
Show that the equation y + 3 = 3(2x + 1) is linear and that it represents a proportional relationship between x and y.
Type below:
______________

Answer:
y + 3 = 3(2x + 1)
y +3 = 6x + 3
y = 6x
As b = 0, it is a Proportional Relationship.

Guided Practice – Comparing Functions – Page No. 170

Doctors have two methods of calculating maximum heart rate. With the first method, maximum heart rate, y, in beats per minute is y = 220 − x, where x is the person’s age. Maximum heart rate with the second method is shown in the table.
Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 3: Comparing Functions img 16

Question 1.
Which method gives the greater maximum heart rate for a 70-year-old?
____________ method

Answer:
Second

Explanation:
y = 220 – x
y = 220 – 70 = 150
Find the slope using two points from the grapgh by
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (20, 194) and (x2, y2) = (30, 187)
Slope m = (y2 -y1)/(x2 – x1) = (187 – 194)/(30 – 20) = -7/10 = -0.7
197 = -0.7(20) + b
y-intercept b = 208
Substituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = -0.7 and b = 208.
y = -0.7x +208
x = 70yrs
y = -0.7(70) + 208 = 159
150 < 159
Second method gives the greater maximum heart rate for a 70 year ols.

Question 2.
Are heart rate and age proportional or nonproportional for each method?
____________

Answer:
For method 1, the relationship is non-propotional.
For method 2, the relationship is non-propotional.

Explanation:
Compare the equation with the general linear equation y = mx + b.
It is linear
Since b is not equal to 0, the relationship is not proportional.

Aisha runs a tutoring business. With Plan 1, students may choose to pay $15 per hour. With Plan 2, they may follow the plan shown on the graph.
Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 3: Comparing Functions img 17

Question 3.
Describe the plan shown on the graph.
Type below:
______________

Answer:
Choose two points on the graph to find the slope.
Find the slope
m = (y2 -y1)/(x2 – x1)
m = (60 – 40)/(4 – 0) = 20/4 = 5
Read the y-intercept from the graph: b = 40
Use your slope and y-intercept values to write an equation in slope-intercept
form.
y = 5x + 40
Plan 2 has an intial cost of $40 and a rate of $5 per hour.

Question 4.
Sketch a graph showing the $15 per hour option.
Type below:
______________

Answer:
Grade 8 Chapter 6 image 11

Question 5.
What does the intersection of the two graphs mean?
Type below:
______________

Answer:
The intersection of the two graphs represents the number of hours for which both plans will cost the same,

Question 6.
Which plan is cheaper for 10 hours of tutoring?
______________

Answer:
Plan 1
y = 15x
x = 10 hrs
y = 15(10) = $150
Plan 2
y = 5x + 40
y = 5(10) + 40 = $90
$150 > $90
Plane 2 is cheaper

Question 7.
Are cost and time proportional or nonproportional for each plan?
Type below:
______________

Answer:
Comparing with the general linear form of equation y = mx + b. Since b = 0, the relationship is proportional
The cost and time are proportional for Plan 1
Comparing with the general linear form of equation y = mx + b. Since b is not equal to 0, the relationship is proportional
The cost and time are not proportional for Plan 2

Essential Question Check-In

Question 8.
When using tables, graphs, and equations to compare functions, why do you find the equations for tables and graphs?
Type below:
______________

Answer:
The tables and graphs represent a part of the solution of the function. By writing the equation, any value can be a substitute to evaluate the function and compared it with the equations.

Independent Practice – Comparing Functions – Page No. 171

The table and graph show the miles driven and gas used for two scooters.
Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 3: Comparing Functions img 18

Question 9.
Which scooter uses fewer gallons of gas when 1350 miles are driven?
______________

Answer:
Scooter B uses fewer gallons of gas when 1350 miles are driven

Explanation:
The equation for Scooter A Slope m = m = (y2 -y1)/(x2 – x1) where (x1, y1) = (150, 2) and (x2, y2) = (300, 4)
Slope m = (y2 -y1)/(x2 – x1) = (4 – 2)/(300 – 150) = 2/150 = 1/75
2 = 1/75(150) + b
y-intercept b = 0
Substituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = 1/75 and b = 0.
y = 1/75x
x = 1350 miles
y = 1/75(1,350)
y = 18gal
The equation for Scooter B Slope m = m = (y2 -y1)/(x2 – x1) where (x1, y1) = (0, 0) and (x2, y2) = (90, 1)
Slope m = (y2 -y1)/(x2 – x1) = (1 – 0)/(90 – 0) = 1/90
2 = 1/90(90) + b
y-intercept b = 0
Substituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = 1/90 and b = 0.
y = 1/90x
x = 1350 miles
y = 1/90(1,350)
y = 15gal
Compare the gallons of gas to drive 1,350 miles
18 > 15
Scooter B uses fewer gallons of gas when 1,350 miles are driven.

Question 10.
Are gas used and miles proportional or nonproportional for each scooter?
______________

Answer:
The gas used and miles are proportional to both scooters.

Explanation:
Compare with general linear form of an equation, y = mx + b. If b = 0, the relationship is proportional.
The gas used and miles are proportional to both scooters.

A cell phone company offers two texting plans to its customers. The monthly cost, y dollars, of one plan is y = 0.10x + 5, where x is the number of texts. The cost of the other plan is shown in the table.
Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 3: Comparing Functions img 19

Question 11.
Which plan is cheaper for under 200 texts?
______________

Answer:
Plane 1 is cheaper

Explanation:
Plan 1
y = 0.10x + 5
Subsitute x = 199
y = 0.10(199) + 5 = $24.90
Find the slope using two points from the graph by m = (y2 -y1)/(x2 – x1) where (x1, y1) = (100, 20), (x2, y2) =(200, 25)
Substitute the value of m and (x1, y1) = (100, 20), (x2, y2) =(200, 25)
Slope m = (y2 -y1)/(x2 – x1) = (25 – 20)/(200 – 100) = 5/100 = 0.05
20 = 0.05(100) + b
y-intercept b = 15
Substituting the value of slope (m) and (x, y) in the slope intercept form to find y intercept (b):
y = 0.05x + 15
x = 199
y = 0.05(199) + 15 = $24.95
Compare the cost for two plans for text < 200
$24.90 < $24.95
Plane 1 is cheaper

Question 12.
The graph of the first plan does not pass through the origin. What does this indicate?
Type below:
______________

Answer:
Plan 1
y = 0.10x + 5
The graph that does not pass through the origin indicates that there is a base price of $5 for the plan.

Question 13.
Brianna wants to buy a digital camera for a photography class. One store offers the camera for $50 down and a payment plan of $20 per month. The payment plan for a second store is described by y = 15x + 80, where y is the total cost in dollars and x is the number of months. Which camera is cheaper when the camera is paid off in 12 months? Explain.
______________

Answer:
For first store, the slope interecept form y = mx + b where m = 20 dollars per month and b = 50 dollar.
y = 20x + 50
x = 12 months
y = 20(12) + 50 = $290
Second store
y = 15x + 80
x = 12 months
y = 15(12) + 80 = $260
Compare the cost of camera if it paid off in 12 months $290 > $260
Camera is cheaper at second store

Comparing Functions – Page No. 172

Question 14.
The French club and soccer team are washing cars to earn money. The amount earned, y dollars, for washing x cars is a linear function. Which group makes the most money per car? Explain.
Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 3: Comparing Functions img 20
______________

Answer:

Explanation:
Find the slope using two points from the grapgh by
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (2, 10) and (x2, y2) = (4, 20)
Slope m = (y2 -y1)/(x2 – x1) = (20 – 10)/(4 – 2) = 10/2 = 5
French Club makes $5 per car.
Find the slope using two points from the grapgh by
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (0, 0) and (x2, y2) = (2, 16)
Slope m = (y2 -y1)/(x2 – x1) = (16 – 0)/(2 – 0) = 16/2 = 8
Soccer Club makes $8 per car.
Compare the money earned for washing one car $5 < $8
Soccer club makes the most money per car

H.O.T.

Focus on Higher Order Thinking

Question 15.
Draw Conclusions
Gym A charges $60 a month plus $5 per visit. The monthly cost at Gym B is represented by y = 5x + 40, where x is the number of visits per month. What conclusion can you draw about the monthly costs of the gyms?
__________ is more expensive

Answer:
Gym A is more expensive

Explanation:
Since the rate per visit is the same, the monthly cost of Gyn A is always more than Gym B.

Question 16.
Justify Reasoning
Why will the value of y for the function y = 5x + 1 always be greater than that for the function y = 4x + 2 when x > 1?
Type below:
______________

Answer:
y1 = 5x + 1 and y2 = 4x + 2 Subtracting y2 from y1
y1 – y2 = 5x + 1 – (4x + 2)
y1 – y2 = x -1
For x>= 1 we get x – 1 >= 0
So y1 – y2 >= 0 or y1 >= y2

Question 17.
Analyze Relationships
The equations of two functions are y = −21x + 9 and y = −24x + 8. Which function is changing more quickly? Explain.
______________

Answer:
y = -21x + 9
y = -24x + 8
y = -24x + 8 is changing more quickly as the absolute value of -24 is greater than the absolute value of -21.

Guided Practice – Analyzing Graphs – Page No. 176

In a lab environment, colonies of bacteria follow a predictable pattern of growth. The graph shows this growth over time.
Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 4: Analyzing Graphs img 21

Question 1.
What is happening to the population during Phase 2?
______________

Answer:
For Phase 2, the graph is increasing quickly. This shows a period of rapid growth.

Question 2.
What is happening to the population during Phase 4?
______________

Answer:
In Phase 4, the graph is decreasing, hence the number of bacterias is decreasing.

The graphs give the speeds of three people who are riding snowmobiles. Tell which graph corresponds to each situation.
Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 4: Analyzing Graphs img 22

Question 3.
Chip begins his ride slowly but then stops to talk with some friends. After a few minutes, he continues his ride, gradually increasing his speed.
______________

Answer:
Graph 2

Explanation:
The slope of the graph is increasing, then it becomes constant and starts increasing again.
Graph 2

Question 4.
Linda steadily increases her speed through most of her ride. Then she slows down as she nears some trees.
______________

Answer:
Graph 3

Explanation:
The slope of the graph is increasing and then decreasing.
Graph 3

Question 5.
Paulo stood at the top of a diving board. He walked to the end of the board, and then dove forward into the water. He plunged down below the surface, then swam straight forward while underwater. Finally, he swam forward and upward to the surface of the water. Draw a graph to represent Paulo’s elevation at different distances from the edge of the pool.
Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 4: Analyzing Graphs img 23
Type below:
______________

Answer:
Grade 8 Chapter 6 image 12

Independent Practice – Analyzing Graphs – Page No. 177

Tell which graph corresponds to each situation below.
Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 4: Analyzing Graphs img 24

Question 6.
Arnold started from home and walked to a friend’s house. He stayed with his friend for a while and then walked to another friend’s house farther from home.
______________

Answer:
Graph 3

Explanation:
The graph increases (as Arnold walks from home to friend’s house), then becomes constant (when he stayed with his friend) and then increases again (when he walk to another friend’s house farther away).
Graph 3

Question 7.
Francisco started from home and walked to the store. After shopping, he walked back home.
______________

Answer:
Graph 1

Explanation:
The graph increases (as Francisco walked from home to store), becomes constant (when he shops), and then decreases (as he walked back home)
Graph 1

Question 8.
Celia walks to the library at a steady pace without stopping.
______________

Answer:
Graph 2

Explanation:
The graph increases at a constant rate (as Celia walks to library without any stops)
Graph 2

Regina rented a motor scooter. The graph shows how far away she is from the rental site after each half hour of riding.
Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 4: Analyzing Graphs img 25

Question 9.
Represent Real-World Problems
Use the graph to describe Regina’s trip. You can start the description like this: “Regina left the rental shop and rode for an hour…”
Type below:
______________

Answer:
Regina left the rental shop and rode for an hour. She rested for half an hour and then started back. After half an hour, she changed her mind and rode for another half an hour. She rest for half an hour. Then she started back and ranched the rental site in 2 hours.

Question 10.
Analyze Relationships
Determine during which half hour Regina covered the greatest distance.
Type below:
______________

Answer:
Regina covered the greatest distance between 0.5 to 1hr of the journey. She covered 12 miles.

Analyzing Graphs – Page No. 178

The data in the table shows the speed of a ride at an amusement park at different times one afternoon.
Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 4: Analyzing Graphs img 26

Question 11.
Sketch a graph that shows the speed of the ride over time.
Type below:
______________

Answer:
Grade 8 Chapter 6 image 13

Question 12.
Between which times is the ride’s speed increasing the fastest?
Type below:
______________

Answer:
The speed is increasing the fastest during the 3: 21 and 3: 22

Question 13.
Between which times is the ride’s speed decreasing the fastest?
Type below:
______________

Answer:
The speed is decreasing the fastest during the 3: 23 and 3: 24

H.O.T.

Focus on Higher Order Thinking
Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 4: Analyzing Graphs img 27

Question 14.
Justify Reasoning
What is happening to the fox population before time t? Explain your reasoning.
Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 4: Analyzing Graphs img 28
Type below:
______________

Answer:
The population decreases and then increases before time t

Question 15.
What If?
Suppose at time t, a conservation organization moves a large group of foxes to the island. Sketch a graph to show how this action might affect the population on the island after time t.
Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 4: Analyzing Graphs img 29
Type below:
______________

Answer:
Grade 8 Chapter 6 image 14

Explanation:
Population is decreasing at first, then it is increasing rapidly.

Question 16.
Make a Prediction
At some point after time t, a forest fire destroys part of the woodland area on the island. Describe how your graph from problem 15 might change.
Type below:
______________

Answer:
The population would dramatically decrease if there was a fire due to lack of food supply and good land.

6.1 Identifying and Representing Functions – Model Quiz – Page No. 179

Determine whether each relationship is a function.

Question 1.
Go Math Grade 8 Answer Key Chapter 6 Functions Model Quiz img 30
__________

Answer:
Not a function

Explanation:
A relationship is a function when each input is paired with exactly one output. The input 5 has more than one output.
Not a function

Question 2.
Go Math Grade 8 Answer Key Chapter 6 Functions Model Quiz img 31
__________

Answer:
Function

Explanation:
A relationship is a function when each input is paired with exactly one output.
Each input is paired with only one output.
Function

Question 3.
(2, 5), (7, 2), (−3, 4), (2, 9), (1, 1)
__________

Answer:
Not a function

Explanation:
A relationship is a function when each input is paired with exactly one output. Input 2 has more than one output.
Not a function

6.2 Describing Functions

Determine whether each situation is linear or nonlinear, and proportional or nonproportional.

Question 4.
Joanna is paid $14 per hour.
__________
__________

Answer:
Linear
Proportional

Explanation:
Writing the situation as an equation, where x is the number of hours.
y = 14x
Compare with general linear equation y = mx + b
Linear
Since b = 0, the relationship is proportional.
Proportional

Question 5.
Alberto started out bench pressing 50 pounds. He then added 5 pounds every week.
__________
__________

Answer:
Linear
Non-proportional

Explanation:
Writing the situation as an equation, where x is the number of hours.
y = 5x + 50
Compare with general linear equation y = mx + b
Linear
Since b is not equal to 0, the relationship is non-proportional.
Non-proportional

6.3 Comparing Functions

Question 6.
Which function is changing more quickly? Explain.
Go Math Grade 8 Answer Key Chapter 6 Functions Model Quiz img 32
__________

Answer:
Function 2 is changing more quickly.

Explanation:
Find the rate of change for function 1
Rate of Change = (20 – 0)/(0 – 5) = -4
Find the rate of change for function 1
Rate of Change = (6.5 – 11)/(3 – 2) = -4.5
Althogh -4.5 < -4, the absolute value of -4.5 s greater than -4.
Function 2 is changing more quickly.

6.4 Analyzing Graphs

Question 7.
Describe a graph that shows Sam running at a constant rate.
Type below:
______________

Answer:
The graph would be a straight line

Explanation:
Since Sam is running at a constant rate, distance covered per unit of time remains the same and the relationship is linear and proportional.
The graph would be a straight line

Essential Question

Question 8.
How can you use functions to solve real-world problems?
Type below:
______________

Answer:
If in the equation the power of x is 1 then it is linear otherwise nonlinear.
In a graph, if the points form a line it is linear if they form a curve it is a nonlinear function.

Selected Response – Mixed Review – Page No. 180

Question 1.
Which table shows a proportional function?
Go Math Grade 8 Answer Key Chapter 6 Functions Mixed Review img 33
Options:
a. A
b. B
c. C
d. D

Answer:
c. C

Explanation:
It contains the ordered pair of the origin (0, 0)
Option C represents a proportional relationship.

Question 2.
What is the slope and y-intercept of the function shown in the table?
Go Math Grade 8 Answer Key Chapter 6 Functions Mixed Review img 34
Options:
a. m = -2; b = -4
b. m = -2; b = 4
c. m = 2; b = 4
d. m = 4; b = 2

Answer:
c. m = 2; b = 4

Explanation:
Find the slope using two points from the grapgh by
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (1, 6) and (x2, y2) = (4, 12)
Slope m = (y2 -y1)/(x2 – x1) = (12 – 6)/(4 – 1) = 6/3 = 2
Substituting the value of the slope m and (x, y) to find the slope-intercept form.
12 = 4(2) + b
y-intercept b = 4

Question 3.
The table below shows some input and output values of a function.
Go Math Grade 8 Answer Key Chapter 6 Functions Mixed Review img 35
What is the missing output value?
Options:
a. 20
b. 21
c. 22
d. 23

Answer:
b. 21

Explanation:
Find the rate of change = (17.5 – 14)/(5 – 4) = 3.5
Since the missing output is corresponding to x = 6 and 3.5 to 17.5 (for x = 5)
Output = 17.5 + 3.5 = 21

Question 4.
Tom walked to school at a steady pace, met his sister, and they walked home at a steady pace. Describe this graph.
Options:
a. V-shaped
b. upside down V-shaped
c. Straight line sloping up
d. Straight line sloping down

Answer:
b. upside-down V-shaped

Explanation:
The graph would increase at a constant rate and would decrease at a constant rate.
The graph would be the upside-down V-shaped

Mini-Task

Question 5.
Linear functions can be used to find the price of a building based on its floor area.Below are two of these functions.
y = 40x + 15,000
Go Math Grade 8 Answer Key Chapter 6 Functions Mixed Review img 36
a. Find and compare the slopes.
Type below:
____________

Answer:
Compare the slopes
The slope for the first function is less than the slope of the second function.
y = 40x + 15000
Compare with slope intercept form y = mx + b where m is the slope m = 40
Second function find the slope using given points by Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (7, 3) and (x2, y2) = (6, 4)
Slope m = (y2 -y1)/(x2 – x1) = (56000 – 32000)/(700 – 400) = 24000/300 = 80
m = 80

Question 5.
b. Find and compare the y-intercepts.
Type below:
____________

Answer:
y = 40x + 15,000
Compare with slope-intercept form y = mx + b where m is the slope b = 15000
The second function find the slope using given points by Slope m and (x, y) in the slope-intercept form to fins y-intercept b
y = mx + b where (x, y) = (700, 56000) and m = 80
56000 = 80(700) + b
b = 0
Compare y intercepts
The y-intercept of the first function is greater than the y-intercept of the second function

Question 5.
c. Describe each function as proportional or nonproportional.
Type below:
____________

Answer:
Comparable to slope interecept form y = mx + b
First function: y = 40x + 15000
Second function: y = 80x
Since b is not equal to 0
First function is non-proportional
Since b = 0
The second function is proportional.

Conclusion:

we wish the detailed prevailed in HMH Go Math 8th Grade Chapter 6 Functions are helpful for you to score the best in the exams. Download our Go Math Grade 8 Solution Key Chapter 6 Functions PDF for free of cost. Keep in touch with us to get the fastest updates about the Go Math Grade 8 Chapter 6 Functions Answer Key. For any queries, you can post your comments in the below comment section.

Go Math Grade 4 Answer Key Homework Practice FL Chapter 4 Divide by 1-Digit Numbers

go-math-grade-4-chapter-4-divide-by-1-digit-numbers-pages-67-93-answer-key

Detailed and Step-by-step explanation of Chapter 5 concepts is provided in this Go Math Grade 4 Answer Key Homework Practice FL Chapter 4 Divide by 1-Digit Numbers. Assure that you should practice with the help of Go math HMH grade 4 chapter 5 solution key and improve mathematical and logical skills. Learning & practicing the fundamentals of math chapter 5 concepts is very important to score more marks in the exams. So, download online Go Math Grade 4 Solution Key Homework Practice FL Chapter 4 Divide by 1-Digit Numbers pdf and overcome all the difficulties in math.

Go Math Grade 4 Answer Key Homework Practice FL Chapter 4 Divide by 1-Digit Numbers

Consistent practice helps students to gain more knowledge and overcome their weak points. So, grab these Concept-wise Chapter 4 Go math Grade 4 Answer Key pdf and practice regularly for securing good scores in the exams. Some of the topics covered in Go Math Solution Key Grade 4 Homework Practice FL Chapter 4 Divide by 1-Digit Numbers are Estimate Quotients Using Multiples, Remainders, Divide Tens, Hundreds, and Thousands, etc. Solve the questions provided at the end of the page and test your subject knowledge.

Lesson: 1 – Estimate Quotients Using Multiples

Lesson: 2 – Remainders

Lesson: 3 – Interpret the Remainder

Lesson: 4 – Divide Tens, Hundreds, and Thousands

Lesson: 5 – Estimate Quotients Using Compatible Numbers

Lesson: 6 – Division and the Distributive Property

Lesson: 7 – Divide Using Repeated Subtraction

Lesson: 8 – Divide Using Partial Quotients

Lesson: 9 – Model Division with Regrouping

Lesson: 10 – Place the First Digit

Lesson: 11 – Divide by 1-Digit Numbers

Lesson: 12 – Problem Solving Multistep Division Problems

Lesson: 13

Common Core – Divide by 1-Digit Numbers – Page No. 69

Estimate Quotients Using Multiples

Find two numbers the quotient is between. Then estimate the quotient.

Question 1.
175 ÷ 6
Think: 6 × 20 = 120 and 6 × 30 = 180. So, 175 ÷ 6 is between 20 and 30. Since 175 is closer to 180 than to 120, the quotient is about 30.
between 20 and 30
about 30

Question 2.
53 ÷ 3
between ____ and ____
about ____

Answer: About 18

Explanation:
17 × 3= 51 and 18 × 3 = 54. 53 is between 51 and 54. 53 ÷ 3 is closest to 17 and 18. So, 53 ÷ 3 is between 17 and 18. So, 53 ÷ 3 will be about 18.

Question 3.
75 ÷ 4
between ____ and ____
about ____

Answer: About 19

Explanation:
18 × 4= 72 and 19 × 4= 76. 75 is between 72 and 76. 75 ÷ 4 is closest to 18 and 19. So, 75÷ 4 is between 18 and 19. So, 75 ÷ 4 will be about 19.

Question 4.
215 ÷ 9
between ____ and ____
about ____

Answer: About 24

Explanation:
23 × 9= 207 and 24 × 9 = 216. 24 is between 207 and 216. 215 ÷ 9 is closest to 23 and 24. So, 215 ÷ 9 is between 23 and 24. So, 215 ÷ 9 will be about 24.

Question 5.
284 ÷ 5
between ____ and ____
about ____

Answer: About 57

Explanation:
56 × 5 = 280 and 57 × 5 = 285. 284 is between 280 and 285. 284 ÷ 5 is closest to 56 and 57. So, 284 ÷ 5 is between 56 and 57. So, 175 ÷ 6 will be about 57.

Question 6.
191 ÷ 3
between ____ and ____
about ____

Answer: About 64

Explanation:
63 × 3 = 189 and 64 × 3 = 192. 191 is between 189 and 192. 191 ÷ 3 is closest to 63 and 64. So, 191 ÷ 3 is between 63 and 64. So, 175 ÷ 6 will be about 64.

Question 7.
100 ÷ 7
between ____ and ____
about ____

Answer: About 14

Explanation:
14 × 7 = 98 and 15 × 7 = 105. 100 is between 98 and 105. 100 ÷ 7 is closest to 14 and 15.
So, 100 ÷ 7 is between 14 and 15. So, 100 ÷ 7 will be about 14.

Question 8.
438 ÷ 7
between ____ and ____
about ____

Answer: About 63

Explanation:
63 × 7 = 441 and 62 × 7 = 434. 438 is between 434 and 441. 438 ÷ 7 is closest to 62 and 63. So, 438 ÷ 7 is between 62 and 63. So, 438 ÷ 7 will be about 63.

Question 9.
103 ÷ 8
between ____ and ____
about ____

Answer: About 13

Explanation:
13 × 8 = 104 and 12 ×8 = 96. 103 is between 96 and 104. 103 ÷ 8 is closest to 12 and 13. So, 103 ÷ 8 is between 12 and 13. So, 103 ÷ 8 will be about 13.

Question 10.
255 ÷ 9
between ____ and ____
about ____

Answer: About 28

Explanation:
28 × 9 = 252 and 29 × 9 = 261. 255 is between 252 and 261. 255 ÷ 9 is closest to 28 and 29.
So, 255 ÷ 9 is between 28 and 29. So, 255 ÷ 9 will be about 28.

Problem Solving

Question 11
Joy collected 287 aluminum cans in 6 hours. About how many cans did she collect per hour?
about ____ cans

Answer: About 48 cans

Explanation:
47 × 6 = 282 and 48 × 6 = 288. 287 is between 282 and 288. 287 ÷ 6 is closest to 47 and 48. So, 287 ÷ 6 is between 47 and 48. So, 287 ÷6 will be about 48.

Question 12.
Paul sold 162 cups of lemonade in 5 hours. About how many cups of lemonade did he sell each hour?
about ____ cups

Answer: About 32 cups of lemonade he sold in each hour

Explanation:
32 × 5 = 160 and 33 × 5 = 165. 162 is between 160 and 165. 162 ÷ 5 is closest to 32 and 33. So, 162 ÷ 5 is between 32 and 33. So, 162 ÷ 5 will be about 32.

Common Core – Divide by 1-Digit Numbers – Page No. 70

Lesson Check

Question 1.
Abby did 121 sit-ups in 8 minutes. Which is the best estimate of the number of sit-ups she did in 1 minute?
Options:
a. about 12
b. about 15
c. about 16
d. about 20

Answer: About 15

Explanation:
15 × 8 = 120 and 16 × 8 = 128. 121 is between 120 and 128. 121 ÷ 8 is closest to 120 and 128. So, 121 ÷ 8 is between 15 and 16.
So, 121 ÷ 8 will be about 15.
Thus the correct answer is option b.

Question 2.
The Garibaldi family drove 400 miles in 7 hours. Which is the best estimate of the number of miles they drove in 1 hour?
Options:
a. about 40 miles
b. about 50 miles
c. about 60 miles
d. about 70 miles

Answer: about 60 miles

Explanation:
Given,
The Garibaldi family drove 400 miles in 7 hours.
57 × 7 = 399 and 58 × 7 = 406.
400 is between 399 and 406. 400 ÷ 7 is closest to 57 and 58.
So, 400 ÷ 7 is between 57 and 58.
So, 400 ÷ 7 will be about 57.
Thus the correct answer is option c.

Spiral Review

Question 3.
Twelve boys collected 16 aluminum cans each. Fifteen girls collected 14 aluminum cans each. How many more cans did the girls collect than the boys?
Options:
a. 8
b. 12
c. 14
d. 18

Answer: 18

Explanation:
Given that,
Twelve boys collected 16 aluminum cans each.
Fifteen girls collected 14 aluminum cans each.
Number of aluminium cans boys had= 12 × 16=192
Number of aluminium cans girls had = 15 × 14=210
Girls collected more cans compared to boys,
Number of more cans collected by girls= 210 – 192=18
Thus the correct answer is option d.

Question 4.
George bought 30 packs of football cards. There were 14 cards in each pack. How many cards did George buy?
Options:
a. 170
b. 320
c. 420
d. 520

Answer: 420

Explanation:
Given,
George bought 30 packs of football cards.
There were 14 cards in each pack.
Number of packs of football cards= 30
Number of cards in each pack= 14
Total number of cards George bought=30×14=420
Thus the correct answer is option c.

Question 5.
Sarah made a necklace using 5 times as many blue beads as white beads. She used a total of 30 beads. How many blue beads did Sarah use?
Options:
a. 5
b. 6
c. 24
d. 25

Answer: 25

Explanation:
Given,
Sarah made a necklace using 5 times as many blue beads as white beads.
She used a total of 30 beads.
Let the number of white beads be x while the number of blue beads are 5x.
Total number of beads in the necklace=30 beads
According to the problem,
5x+x=30
6x=30
x=30/6=5
Therefore the number of blue beads in the necklace are 5x= 5×5=25
Thus the correct answer is option d.

Question 6.
This year, Ms. Webster flew 145,000 miles on business. Last year, she flew 83,125 miles on business. How many more miles did Ms. Webster fly on business this year?
Options:
a. 61,125 miles
b. 61,875 miles
c. 61,985 miles
d. 62,125 miles

Answer: 61,875 miles

Explanation:
Given,
This year, Ms. Webster flew 145,000 miles on business.
Last year, she flew 83,125 miles on business.
Number of miles Ms Webster flew in this year = 145,000 miles
Number of miles Ms Webster flew in the last year = 83,125 miles
Number of more miles travelled by Ms Webster =145,000 – 83,125 = 61,875
Thus the correct answer is option b.

Common Core – Divide by 1-Digit Numbers – Page No. 71

Remainders

Use counters to find the quotient and remainder.

Question 1.
13 ÷ 4
3 r1

Explanation:
Quotient:
A. Use 13 counters to represent the 13 dominoes. Then draw 4 circles to represent the divisor.
B. Share the counters equally among the 4 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 13 ÷ 4
D. Number of circles are equally filled with 4 counters, therefore, the quotient is 3.
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 1
For 13 ÷ 4, the quotient is 3 and the remainder is 1, or 3 r1.

Question 2.
24 ÷ 7
_____ R _____

Answer: 3 r3

Explanation:
Quotient:
A. Use 24 counters to represent the 24 dominoes. Then draw 7 circles to represent the divisor.
B. Share the counters equally among the 7 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 24 ÷ 7
D. Number of circles are equally filled with 3 counters, therefore, the quotient is 3
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 3
For 24 ÷ 7, the quotient is 3 and the remainder is 3, or 3 r3.

Question 3.
39 ÷ 5
_____ R _____

Answer: 7 r4

Explanation:
Quotient:
A. Use 39 counters to represent the 39dominoes. Then draw 5 circles to represent the divisor.
B. Share the counters equally among the 5 groups by placing them in the circles.
C. Number of counters formed in each group = quotient 39 ÷ 5
D. Number of circles are equally filled with 7 counters, therefore, the quotient is 7
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 4
For 39 ÷ 5, the quotient is 7 and the remainder is 4, or 7 r4.

Question 4.
36 ÷ 8
_____ R _____

Answer: 4 r4

Explanation:
Quotient:
A. Use 36 counters to represent the 36 dominoes. Then draw 8 circles to represent the divisor.
B. Share the counters equally among the 8 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 36 ÷ 8
D. Number of circles are equally filled with 4 counters, therefore, the quotient is 4
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 4
For 36 ÷ 8, the quotient is 4 and the remainder is 4, or 4 r4.

Question 5.
6)\(\overline { 27 } \)
_____ R _____

Answer: 4 r3

Explanation:
Quotient:
A. Use 27 counters to represent the 27 dominoes. Then draw 6 circles to represent the divisor.
B. Share the counters equally among the 6 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 27 ÷6
D. Number of circles are equally filled with 4 counters, therefore, the quotient is 4
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 3
For 27 ÷ 6, the quotient is 4 and the remainder is 3, or 4 r3.

Question 6.
25 ÷ 9
_____ R _____

Answer: 2 r7

Explanation:
Quotient:
A. Use 25 counters to represent the 25 dominoes. Then draw 9 circles to represent the divisor.
B. Share the counters equally among the 9 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 25 ÷ 9
D. Number of circles are equally filled with 2 counters, therefore, the quotient is 2
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 7
For 25 ÷ 7, the quotient is 2 and the remainder is 7, or 2 r7.

Question 7.
3)\(\overline { 17 } \)
_____ R _____

Answer: 5 r2

Explanation:
Quotient:
A. Use 17 counters to represent the 17 dominoes. Then draw 3 circles to represent the divisor.
B. Share the counters equally among the 3 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 17 ÷ 3
D. Number of circles are equally filled with 5 counters, therefore, the quotient is 5
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 2
For 17 ÷ 3, the quotient is 5 and the remainder is 2, or 5 r2.

Question 8.
26 ÷ 4
_____ R _____

Answer: 6 r2

Explanation:
Quotient:
A. Use 26 counters to represent the 26 dominoes. Then draw 4 circles to represent the divisor.
B. Share the counters equally among the 4 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 26 ÷ 4
D. Number of circles are equally filled with 6 counters, therefore, the quotient is 6
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 2
For 26 ÷ 4, the quotient is 6 and the remainder is 2, or 6 r2.

Divide. Draw a quick picture to help.

Question 9.
14 ÷ 3
_____ R _____

Answer: Quotient: 4 Remainder: 2

Explanation:
Quotient:
A. Use 14 counters to represent the 14 dominoes. Then draw 3 circles to represent the divisor.
B. Share the counters equally among the 3 groups by placing them in the circles.
C. Number of circles filled= quotient of 14 ÷ 3 = 4
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 2

Question 10.
5)\(\overline { 29 } \)
_____ R _____

Answer: Quotient: 5 Remainder: 4

Explanation:
Quotient:
A. Use 29 counters to represent the 29 dominoes. Then draw 5 circles to represent the divisor.
B. Share the counters equally among the 5 groups by placing them in the circles.
C. Number of circles filled= quotient of 29 ÷ 5 = 5
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 4

Problem Solving

Question 11.
What is the quotient and remainder in the division problem modeled below?
Go Math Grade 4 Answer Key Homework Practice FL Chapter 4 Divide by 1-Digit Numbers Common Core - Divide by 1-Digit Numbers img 1
_____ R _____

Answer: quotient:6 remainder2

Explanation:
Quotient:
A. Use 20 counters to represent the 20 dominoes. Then draw 3 circles to represent the divisor.
B. Share the counters equally among the 3 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 20 ÷ 3
D. Number of circles are equally filled with 6 counters, therefore, the quotient is 6
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 2
For 20 ÷ 3, the quotient is 6 and the remainder is 2, or 6 r2.

Question 12.
Mark drew the following model and said it represented the problem 21 ÷ 4. Is Mark’s model correct? If so, what is the quotient and remainder? If not, what is the correct quotient and remainder?
Go Math Grade 4 Answer Key Homework Practice FL Chapter 4 Divide by 1-Digit Numbers Common Core - Divide by 1-Digit Numbers img 2
_____ : _____ r _____

Answer: 4 r5

Explanation:
Quotient:
A. Use 21 counters to represent the 21 dominoes. Then draw 4 circles to represent the divisor.
B. Share the counters equally among the 4 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 21 ÷ 4
D. Number of circles are equally filled with 4 counters, therefore, the quotient is 4
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 5
For 21 ÷ 4, the quotient is 4 and the remainder is 5, or 4 r5.

Common Core – Divide by 1-Digit Numbers – Page No. 72

Lesson Check

Question 1.
What is the quotient and remainder for 32 ÷ 6?
Options:
a. 4 r3
b. 5 r1
c. 5 r2
d. 6 r1

Answer: 5 r2

Explanation:
Quotient:
A. Use 32 counters to represent the 32 dominoes. Then draw 6 circles to represent the divisor.
B. Share the counters equally among the 5 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 32 ÷ 6
D. Number of circles are equally filled with 5 counters, therefore, the quotient is 5
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 2
For 32 ÷ 6, the quotient is 5 and the remainder is 2, or 5 r2.
Thus the correct answer is option c.

Question 2.
What is the remainder in the division problem modeled below?
Go Math Grade 4 Answer Key Homework Practice FL Chapter 4 Divide by 1-Digit Numbers Common Core - Divide by 1-Digit Numbers img 3
Options:
a. 8
b. 4
c. 3
d. 1

Answer: 3

Explanation:
When a number cannot be divided evenly, the amount left over is called the remainder.
The number of counters that are left = remainder = 3
Thus the correct answer is option c.

Spiral Review

Question 3.
Each kit to build a castle contains 235 parts. How many parts are in 4 of the kits?
Options:
a. 1,020
b. 940
c. 920
d. 840

Answer: 940

Explanation:
Number of parts used to build a castle in each kit=235 parts
Number of kits= 4
Total number of parts in 4 of the kits= 235 x 4=940 parts

Thus the correct answer is option b.

Question 4.
In 2010, the population of Alaska was about 710,200. What is this number written in word form?
Options:
a. seven hundred ten thousand, two
b. seven hundred twelve thousand
c. seventy-one thousand, two
d. seven hundred ten thousand, two hundred

Answer: seven hundred ten thousand, two hundred

Explanation:
The ones and tens place of the number are zeroes, so the next place which is hundreds is considered and the value is 7 so, it can be written as seven hundred and in the thousands period, it can be written as seven hundred ten thousand.
Thus the correct answer is option d.

Question 5.
At the theater, one section of seats has 8 rows with 12 seats in each row. In the center of the first 3 rows are 4 broken seats that cannot be used. How many seats can be used in the section?
Options:
a. 84
b. 88
c. 92
d. 96

Answer: 92

Explanation:
Given,
Number of rows at the theatre = 8
Number of seats in each row= 12
Number of seats broken and that cannot be used to sit= 4
Total number of seats that can be used= 12 × 8 – 4 = 96 – 4 = 92
Thus the correct answer is option c.

Question 6.
What partial products are shown by the model below?
Go Math Grade 4 Answer Key Homework Practice FL Chapter 4 Divide by 1-Digit Numbers Common Core - Divide by 1-Digit Numbers img 4
Options:
a. 300, 24
b. 300, 600, 40, 60
c. 300, 60, 40, 24
d. 300, 180, 40, 24

Answer: 300, 180, 40, 24

Explanation:
The whole rectangle is divided into four small rectangles the areas of these rectangles are:

Area of yellow rectangle= 30 x 10=300
Area of green rectangle= 4 x 10 = 40
Area of pink rectangle= 6 x 30= 180
Area of blue rectangle= 4 x 6= 24
Thus the correct answer is option d.

Common Core – Divide by 1-Digit Numbers – Page No. 73

Interpret the Remainder

Interpret the remainder to solve.

Question 1.
Hakeem has 100 tomato plants. He wants to plant them in rows of 8. How many full rows will he have?
Think: 100 ÷ 8 is 12 with a remainder of 4. The question asks “how many full rows,” so use only the quotient.
12 full rows

Explanation:
Quotient:
A. Use 100 counters to represent the 100 dominoes. Then draw 8 circles to represent the divisor.
B. Share the counters equally among the 8 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 100 ÷ 8
D. Number of circles are equally filled with 12 counters, therefore, the quotient is 12
Therefore, the tomatoes placed in full rows are 12

Question 2.
A teacher has 27 students in her class. She asks the students to form as many groups of 4 as possible. How many students will not be in a group?
______ students

Answer: 3 students will not be in the group

Explanation:
Total number of students in the class= 27
Number of students who make a group=4
Number of groups that can be made =Quotient of 27÷ 4=6
Number of students who do not come under a group= Remainder of 27÷ 4=3

Question 3.
A sporting goods company can ship 6 footballs in each carton. How many cartons are needed to ship 75 footballs?
______ cartons

Answer: 12 full cartons and 0.5 or 1/2 carton to ship all the 75 footballs

Explanation:
Total number of footballs that should be shipped= 75
Number of footballs placed in each carton = 6
Number of cartons required=Quotient of 75÷ 6=12

Since each carton carries 6 balls, half carton contains 3 balls because 6÷3=2, therefore, each half of the carton contains 3 balls.

Question 4.
A carpenter has a board that is 10 feet long. He wants to make 6 table legs that are all the same length. What is the longest each leg can be?
______ foot

Answer: The length of the longest leg = 4 foot-long

Explanation:
According to the question,
Length of the board the carpenter has= 10 foot long
Number of table legs that are to be made = 6
Length of the 6 table legs are equal
then,
Length of each table leg = Quotient of 10 ÷ 6 =1 foot
Length of the longest table leg = Remainder of 10 ÷ 6 = 4 foot.

Question 5.
Allie wants to arrange her flower garden in 8 equal rows. She buys 60 plants. What is the greatest number of plants she can put in each row?
______ plants

Answer: 7

Explanation:
Total number of plants Allie bought = 60
Number of rows = 8
Number of plants in each row= Quotient of 60 ÷ 8 = 7
Thus the greatest number of plants she can put in a row is 7.

Problem Solving

Question 6.
Joanna has 70 beads. She uses 8 beads for each bracelet. She makes as many bracelets as possible. How many beads will Joanna have left over?
______ beads

Answer: 6 beads

Explanation:
Total number of beads Joanna has= 70 beads
Number beads used for each bracelet= 8 beads
Number of bracelets made with these beads= Quotient of 70÷8= 7 bracelets
then,
The number of beads leftover= Remainder of 70÷8= 6 beads

Question 7.
A teacher wants to give 3 markers to each of her 25 students. Markers come in packages of 8. How many packages of markers will the teacher need?
______ packages

Answer: 10 packages

Explanation:
Total number of students= 25
Number of markers each student got= 3
Total number of markers the teacher needs to distribute= 25 x 3= 75
Number of markers in each package= 8
Number of packages the teacher required= Quotient of 75÷8=9
While the remainder = 3
Therefore the total number of packages = 10

Common Core – Divide by 1-Digit Numbers – Page No. 74

Lesson Check

Question 1.
Marcus sorts his 85 baseball cards into stacks of 9 cards each. How many stacks of 9 cards can Marcus make?
Options:
a. 4
b. 8
c. 9
d. 10

Answer: 10

Explanation:
Total number of baseball cards=85
Number of cards in each stack=9
Number of stacks sorted= Quotient of 85÷9=9
While the remainder=4
So the total number of stacks required= 10
Thus the correct answer is option d.

Question 2.
A minivan can hold up to 7 people. How many minivans are needed to take 45 people to a basketball game?
Options:
a. 3
b. 5
c. 6
d. 7

Answer: 7

Explanation:
A minivan can hold up to 7 people.
Total number of people who want to hire the minivan= 45 people
Number of minivans required= Quotient of 45÷7= 6 vans
While the remainder is 3.
Total number of minivans required to take the people to the baseball game= 7 minivans
Thus the correct answer is option d.

Spiral Review

Question 3.
Mrs. Wilkerson cut some oranges into 20 equal pieces to be shared by 6 friends. How many pieces did each person get and how many pieces were left over?
Options:
a. 2 pieces with 4 pieces left over
b. 3 pieces with 2 pieces left over
c. 3 pieces with 4 pieces left over
d. 4 pieces with 2 pieces left over

Answer: 3 pieces with 2 pieces left over

Explanation:
Total number of orange pieces= 20
Number of friends= 6
Number of pieces each friend got= Quotient of 20÷6= 3 pieces
Number of pieces leftover= Remainder of 20÷6= 2 pieces
Thus the correct answer is option b.

Question 4.
A school bought 32 new desks. Each desk cost $24. Which is the best estimate of how much the school spent on the new desks?
Options:
a. $500
b. $750
c. $1,000
d. $1,200

Answer: $750

Explanation:
Total number of desks= 32
Cost of each desk= $24
Total cost spent on the desks= 32 x 24=$768

So the estimated value can be $768.
Thus the correct answer is option b.

Question 5.
Kris has a box of 8 crayons. Sylvia’s box has 6 times as many crayons as Kris’s box. How many crayons are in Sylvia’s box?
Options:
a. 48
b. 42
c. 36
d. 4

Answer: 48

Explanation:
Number of crayons in Kris box=8
Number of crayons in Sylvia’s box= 6 times as many crayons as Kris’s box= 6 x 8=48
Thus the correct answer is option a.

Question 6.
Yesterday, 1,743 people visited the fair. Today, there are 576 more people at the fair than yesterday. How many people are at the fair today?
Options:
a. 1,167
b. 2,219
c. 2,319
d. 2,367

Answer: 2,319

Explanation:
Number of people in the fair yesterday= 1,743
Number of more people at the fair than yesterday= 576
Total number of people in the fair today=2,319

Thus the correct answer is option c.

Common Core – Divide by 1-Digit Numbers – Page No. 75

Divide Tens, Hundreds, and Thousands

Use basic facts and place value to find the quotient.

Question 1.
3,600 ÷ 4 = 900
Think: 3,600 is 36 hundreds.
Use the basic fact 36 ÷ 4 = 9.
So, 36 hundreds ÷ 4 = 9 hundreds, or 900.

Question 2.
240 ÷ 6 = ______

Answer: 40

Explanation:
STEP 1 Identify the basic fact. 24 ÷ 6
STEP 2 Use place value. 240 = 24 tens
STEP 3 Divide. 24 tens ÷ 6 = 4 tens
240 ÷ 6 = 40

Question 3.
5,400 ÷ 9 = ______

Answer: 600

Explanation:
STEP 1 Identify the basic fact. 54 ÷ 9
STEP 2 Use place value. 5,400 = 54 hundreds
STEP 3 Divide. 54 hundreds ÷ 9 = 6 hundreds
5,400 ÷ 9 = 600

Question 4.
300 ÷ 5 = ______

Answer: 60

Explanation:
STEP 1 Identify the basic fact. 30 ÷ 5
STEP 2 Use place value. 300 = 30 tens
STEP 3 Divide. 30 tens ÷ 5 = 60 tens
300 ÷ 5 = 60

Question 5.
4,800 ÷ 6 = ______

Answer: 800

Explanation:
STEP 1 Identify the basic fact. 48 ÷ 6
STEP 2 Use place value. 4,800 = 48 hundreds
STEP 3 Divide. 48 hundreds ÷ 6 = 80 hundreds
4,800 ÷ 6 = 800

Question 6.
420 ÷ 7 = ______

Answer: 60

Explanation:
STEP 1 Identify the basic fact. 42 ÷ 7
STEP 2 Use place value. 420 = 42 tens
STEP 3 Divide. 42 tens ÷ 7 = 60 tens
420 ÷ 7 = 60

Question 7.
150 ÷ 3 = ______

Answer: 50

Explanation:
STEP 1 Identify the basic fact. 15 ÷ 3
STEP 2 Use place value. 150 = 15 tens
STEP 3 Divide. 15 tens ÷ 3 = 5 tens
150 ÷ 3 = 50

Question 8.
6,300 ÷ 7 = ______

Answer: 900

Explanation:
STEP 1 Identify the basic fact. 63 ÷ 7
STEP 2 Use place value. 6,300 = 63 hundreds
STEP 3 Divide. 63 hundreds ÷ 7 = 9 hundreds
6,300 ÷ 7 = 900

Question 9.
1,200 ÷ 4 = ______

Answer: 300

Explanation:
STEP 1 Identify the basic fact. 12 ÷ 4
STEP 2 Use place value. 1,200 = 12 hundreds
STEP 3 Divide. 12 hundreds ÷ 4 = 3 hundreds
1,200 ÷ 4 = 300

Question 10.
360 ÷ 6 = ______

Answer: 60

Explanation:
STEP 1 Identify the basic fact. 36 ÷ 6
STEP 2 Use place value. 360 = 36 tens
STEP 3 Divide. 36 tens ÷ 6 = 6 tens
360 ÷ 6 = 60

Find the quotient.

Question 11.
28 ÷ 4 = ______
280 ÷ 4 = ______
2,800 ÷ 4 = ______

Answer: 7, 70, 700

Explanation:
Quotient:
A. Use 28 counters to represent the 28 dominoes. Then draw 4 circles to represent the divisor.
B. Share the counters equally among the 4 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 28 ÷ 4
D. Number of circles are equally filled with 7 counters, therefore, the quotient is 7

STEP 1 Identify the basic fact. 28 ÷ 4
STEP 2 Use place value. 280 = 28 tens
STEP 3 Divide. 28 tens ÷ 4 = 7 tens
280 ÷ 4 = 70

STEP 1 Identify the basic fact. 28 ÷ 4
STEP 2 Use place value. 2,800 = 28 hundreds
STEP 3 Divide. 28 hundreds ÷ 4 = 7 hundreds
2,800 ÷ 4 = 700

Question 12.
18 ÷ 3 = ______
180 ÷ 3 = ______
1,800 ÷ 3 = ______

Answer: 6, 60, 600

Explanation:
Quotient:
A. Use 18 counters to represent the 18 dominoes. Then draw 3 circles to represent the divisor.
B. Share the counters equally among the 3 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 18 ÷ 3
D. Number of circles are equally filled with 6 counters, therefore, the quotient is 6

STEP 1 Identify the basic fact. 18 ÷ 3
STEP 2 Use place value. 180 = 18 tens
STEP 3 Divide. 18 tens ÷ 3 = 6 tens
180 ÷ 6 = 60

STEP 1 Identify the basic fact. 18 ÷ 3
STEP 2 Use place value. 1,800 = 18 hundreds
STEP 3 Divide. 18 hundreds ÷ 3 = 6 hundreds
1,800 ÷ 3 = 600

Question 13.
45 ÷ 9 = ______
450 ÷ 9 = ______
4,500 ÷ 9 = ______

Answer: 5, 50, 500

Explanation:
Quotient:
A. Use 45 counters to represent the 45 dominoes. Then draw 9 circles to represent the divisor.
B. Share the counters equally among the 9 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 45 ÷ 9
D. Number of circles are equally filled with 5 counters, therefore, the quotient is 5

STEP 1 Identify the basic fact. 45 ÷ 9
STEP 2 Use place value. 450 = 45 tens
STEP 3 Divide. 45 tens ÷ 9 = 5 tens
450 ÷ 9 = 50

STEP 1 Identify the basic fact. 45 ÷ 9
STEP 2 Use place value. 4,500 = 45 hundreds
STEP 3 Divide. 45 hundred ÷ 9 = 5 hundred
4,500 ÷ 9 = 500

Problem Solving

Question 14.
At an assembly, 180 students sit in 9 equal rows. How many students sit in each row?
______ students

Answer: 20

Explanation:
Total number of students= 180
Number of rows= 9
Number of students in each row= 180 ÷ 9 = 20

Question 15.
Hilary can read 560 words in 7 minutes. How many words can Hilary read in 1 minute?
______ words

Answer: 80

Explanation:
Total number of words Hilary can read in 7 minutes = 560
Number of words Hilary can read in 1 minute= 560 ÷ 7= 80
Therefore Hilary can read 80 words in 1 minute.

Question 16.
A company produces 7,200 gallons of bottled water each day. The company puts 8 one-gallon bottles in each carton. How many cartons are needed to hold all the one-gallon bottles produced in one day?
______ cartons

Answer: 900

Explanation:
Total number of gallons bottled in each day= 7,200
Number of gallons bottled in each carton= 8
Number of cartons used= 7,200 ÷ 8= 900

Question 17.
An airplane flew 2,400 miles in 4 hours. If the plane flew the same number of miles each hour, how many miles did it fly in 1 hour?
______ miles

Answer: 600

Explanation:
Total number of miles flew in 4 hours= 2,400
Number of miles flew in 1 hour= 2,400 ÷ 4 = 600

Common Core – Divide by 1-Digit Numbers – Page No. 76

Lesson Check

Question 1.
A baseball player hits a ball 360 feet to the outfield. It takes the ball 4 seconds to travel this distance. How many feet does the ball travel in 1 second?
Options:
a. 9 feet
b. 40 feet
c. 90 feet
d. 900 feet

Answer: 90 feet

Explanation:
The height to which the player hits a ball=360 feet
Height to which the ball travels in 1 second= 360÷4= 90 feet
The correct answer is option c.

Question 2.
Sebastian rides his bike 2,000 meters in 5 minutes. How many meters does he bike in 1 minute?
Options:
a. 4 meters
b. 40 meters
c. 50 meters
d. 400 meters

Answer: 400 meters

Explanation:
Total number of meters travelled in 5 minutes= 2,000
Number of meters travelled in 1 minute= 2,000÷5= 400
The correct answer is option d.

Spiral Review

Question 3.
A full container of juice holds 64 ounces. How many 7-ounce servings of juice are in a full container?
Options:
a. 1
b. 8
c. 9
d. 10

Answer: 9

Explanation:
A full container of juice holds= 63 ounces
Quantity of servings of juice in one glass=7 ounce
The number of servings of the juice are= 63÷7=9
The correct answer is option c.

Question 4.
Paolo pays $244 for 5 identical calculators. Which is the best estimate of how much Paolo pays for one calculator?
Options:
a. $40
b. $50
c. $60
d. $245

Answer: $50

Explanation:
Amount Paolo pays for the identical calculators = $244
Number of identical calculators=5
The best-estimated value of each identical calculator=$244 ÷ 5is approximately $50.
The correct answer is option b.

Question 5.
A football team paid $28 per jersey. They bought 16 jerseys. How much money did the team spend on jerseys?
Options:
a. $44
b. $196
c. $408
d. $448

Answer: $448

Explanation:
Cost of each jersey=$28
Number of jerseys= 16
Total cost of the jerseys= $28 x 16= $448
The correct answer is option d.

Question 6.
Suzanne bought 50 apples at the apple orchard. She bought 4 times as many red apples as green apples. How many more red apples than green apples did Suzanne buy?
Options:
a. 10
b. 25
c. 30
d. 40

Answer: 40

Explanation:
Let the number of green apples be x and the number of red apples be 4x
4x + x = 50
x = 50 ÷ 5= 10
Number of red balls = 4x = 4 x 10 = 40
The correct answer is option d.

Common Core – Divide by 1-Digit Numbers – Page No. 77

Estimate Quotients Using Compatible Numbers

Use compatible numbers to estimate the quotient.

Question 1.
389 ÷ 4
400 ÷ 4 = 100

Question 2.
358 ÷ 3
_____ ÷ 3 = _____

Answer: 120

Explanation:
What number close to358 is easy to divide by 3?
360 is close to 358. What basic fact can you use?
360 ÷ 3
Choose 360 because it is close to 358 and can easily be divided by 3.
36 ÷3 = 12
360 ÷ 3 =120
358 ÷ 3 is about 120

Question 3.
784 ÷ 8
_____ ÷ 8 = _____

Answer: 100

Explanation:
What number close to 784 is easy to divide by 8?
800 is close to 784. What basic fact can you use?
800 ÷ 8
Choose 800 because it is close to 784 and can easily be divided by 8.
80 ÷ 8 = 10
800 ÷ 8 = 100
784 ÷ 8 is about 100.

Question 4.
179 ÷ 9
_____ ÷ 9 = _____

Answer: 20

Explanation:
What number close to 179 is easy to divide by 9?
180 is close to 179. What basic fact can you use?
180 ÷ 9
Choose 180 because it is close to 179 and can easily be divided by 9.
18 ÷ 9 = 2
180 ÷ 9 = 20
179 ÷ 9 is about 20

Question 5.
315 ÷ 8
_____ ÷ 8 = _____

Answer: 40

Explanation:
What number close to 315 is easy to divide by 8?
320 is close to 315. What basic fact can you use?
320 ÷ 8
Choose 320 because it is close to 315 and can easily be divided by 8.
32 ÷ 8 = 4
320 ÷ 8 =40
315 ÷ 8 is about 40.

Question 6.
2,116 ÷ 7
_____ ÷ 7 = _____

Answer: 300

Explanation:
What number close to 2,116 is easy to divide by 7?
2,100 is close to 2,116. What basic fact can you use?
2,100 ÷ 7
Choose 2,100 because it is close to 2,116 and can easily be divided by 7.
21 ÷ 7= 3
2,100 ÷ 7 = 300
2,116 ÷ 7 is about 300

Question 7.
4,156 ÷ 7
_____ ÷ 7 = _____

Answer: 600

Explanation:
What number close to 4,156 is easy to divide by 7?
4,200 is close to 4,156. What basic fact can you use?
4,200 ÷7
Choose 4,200 because it is close to 4,156 and can easily be divided by 7.
42 ÷ 7 = 6
4,200 ÷ 7 = 600
4,156 ÷ 7 is about 600.

Question 8.
474 ÷ 9
_____ ÷ 9 = _____

Answer: 50

Explanation:
What number close to 474 is easy to divide by 9?
450 is close to 474. What basic fact can you use?
450 ÷ 9
Choose 450 because it is close to 474 and can easily be divided by 9.
45 ÷ 9 = 5
450 ÷ 9 = 50
474 ÷ 9 is about 50.

Use compatible numbers to find two estimates that the quotient is between.

Question 9.
1,624 ÷ 3
_____ ÷ 3 = _____
_____ ÷ 3 = _____

Answer: The quotient is between 500 and 600

Explanation:
What number close to 1,624 is easy to divide by 3?
1,500 is close to 1,624. What basic fact can you use?
1,500 ÷ 3
Choose 1,500 because it is close to 1,624 and can easily be divided by 3.
15 ÷ 3 = 5
1,500 ÷ 3 = 500
1,624 ÷ 3 is about 500

What number close to 1,624 is easy to divide by 3?
1,800 is close to 1,624. What basic fact can you use?
1,800 ÷ 3
Choose 1,800 because it is close to 1,624 and can easily be divided by 3.
18 ÷ 3 = 6
1,800 ÷ 3 = 600
1,624 ÷ 3 is about 600

Question 10.
2,593 ÷ 6
_____ ÷ 6 = _____
_____ ÷ 6 = _____

Answer: The quotient is between 400 and 500

Explanation:
What number close to 2,593 is easy to divide by 6?
2,400 is close to 2,593. What basic fact can you use?
2,400 ÷ 6
Choose 2,400 because it is close to 2,593 and can easily be divided by 6.
24 ÷ 6 = 4
2,400 ÷ 6 = 400
2,593 ÷ 6 is about 400

What number close to 2,593 is easy to divide by 6?
3,000 is close to 2,593. What basic fact can you use?
3000 ÷ 6
Choose 3,000 because it is close to 2,593 and can easily be divided by 6.
30 ÷ 6 = 5
3,000 ÷ 6 = 500
2,593 ÷ 6 is about 500

Question 11.
1,045 ÷ 2
_____ ÷ 2 = _____
_____ ÷ 2 = _____

Answer: The quotient is between 520 and 525

Explanation:
What number close to 1,045 is easy to divide by 2?
1,040 is close to 1,045. What basic fact can you use?
1,040 ÷ 2
Choose 1,040 because it is close to 1,045 and can easily be divided by 2.
1,04 ÷ 2 = 52
1,040 ÷ 2 = 520
1,045 ÷ 2 is about 520

What number close to 1,045 is easy to divide by 2?
1,050 is close to 1,045. What basic fact can you use?
1,050 ÷ 2
Choose 1,050 because it is close to 1,045 and can easily be divided by 2.
1,050 ÷ 2 = 525
1,045 ÷ 2 is about 525

Question 12.
1,754 ÷ 9
_____ ÷ 9 = _____
_____ ÷ 9 = _____

Answer: The quotient is between 195 and 200

Explanation:
What number close to 1,754 is easy to divide by 9?
1,755 is close to 1,754. What basic fact can you use?
1,755 ÷ 9
Choose 1,755 because it is close to 1,754 and can easily be divided by 9.
1,755 ÷ 9 = 195
1,754 ÷ 9 is about 195

What number close to 1,754 is easy to divide by 9?
1,800 is close to 1,754. What basic fact can you use?
1,800 ÷ 9
Choose 1,800 because it is close to 1,754 and can easily be divided by 9.
18 ÷ 9 = 2
1,800 ÷ 9 = 200
1,754 ÷ 9 is about 200

Question 13.
2,363 ÷ 8
_____ ÷ 8 = _____
_____ ÷ 8 = _____

Answer: The quotient is between 295 and 300

Explanation:
What number close to 2,363 is easy to divide by 8?
2,360 is close to 2,363. What basic fact can you use?
2,360 ÷ 8
Choose 2,360 because it is close to 2,363 and can easily be divided by 8.
2,360 ÷ 8 = 295
2,363 ÷ 8 is about 295

What number close to 2,363 is easy to divide by 8?
2,400 is close to 2,363. What basic fact can you use?
2,400 ÷ 8
Choose 2,400 because it is close to 2,363 and can easily be divided by 8.
24 ÷ 8 = 3
2,400 ÷ 8= 300
2,363 ÷ 8 is about 300.

Question 14.
1,649 ÷ 5
_____ ÷ 5 = _____
_____ ÷ 5 = _____

Answer: The quotient is between 329 and 330

Explanation:
What number close to 1,649 is easy to divide by 5?
1,645 is close to 1,649. What basic fact can you use?
1,645 ÷ 5
Choose 1,645 because it is close to 1,649 and can easily be divided by 5.
1,645 ÷ 5 = 329
1,649 ÷ 5 is about 329

What number close to 1,650 is easy to divide by 5?
1,650 is close to 1,649. What basic fact can you use?
1,650 ÷ 5
Choose 1,650 because it is close to 1,649 and can easily be divided by 5.
1,650 ÷ 5 = 330
1,649 ÷ 5 is about 330

Question 15.
5,535 ÷ 7
_____ ÷ 7 = _____
_____ ÷ 7 = _____

Answer: The quotient is between 790 and 791

Explanation:
What number close to 5,535 is easy to divide by 7?
5,530 is close to 5,535. What basic fact can you use?
5,530 ÷ 7
Choose 5,530 because it is close to 5,535 and can easily be divided by 7.
553 ÷ 7 = 79
5,530 ÷ 7 = 790
5,535 ÷ 7 is about 790

What number close to 5,535 is easy to divide by 7?
5,537 is close to 5,535. What basic fact can you use?
5,537 ÷ 7
Choose 5,537 because it is close to 5,535 and can easily be divided by 7.
553 ÷ 7 = 79
5,537 ÷ 7 = 791
5,535 ÷ 7 is about 791

Question 16.
3,640 ÷ 6
_____ ÷ 6 = _____
_____ ÷ 6 = _____

Answer: The quotient is between 606 and 607

Explanation:
What number close to 3,640 is easy to divide by 6?
3,636 is close to 3,640. What basic fact can you use?
3,636 ÷ 6
Choose 3,636 because it is close to 3,640 and can easily be divided by 6.
36 ÷ 6 = 6
3,636 ÷ 6 = 606
3,640 ÷ 6 is about 606

What number close to 3,640 is easy to divide by 6?
3,642 is close to 3,640. What basic fact can you use?
3,642 ÷ 6
Choose 3,642 because it is close to 3,640 and can easily be divided by 6.
3,642 ÷ 6 = 607
3,640 ÷ 6 is about 607

Problem Solving

Question 17.
A CD store sold 3,467 CDs in 7 days. About the same number of CDs were sold each day. About how many CDs did the store sell each day?
about _____ CDs

Answer: 495(approx)

Explanation:
Total number of CDs in the store= 3,467
Number of days= 7
Number of CDs sold on one day= 3,467 ÷ 7=495(approx)

Question 18.
Marcus has 731 books. He puts about the same number of books on each of 9 shelves in his a bookcase. About how many books are on each shelf?
about _____ books

Answer: 81 books(approx)

Explanation:
Total number of books Marcus has= 731
Number of shelves= 9
Number of books on each shelf= 731÷9= 81 (approx)

Common Core – Divide by 1-Digit Numbers – Page No. 78

Lesson Check

Question 1.
Jamal is planting seeds for a garden nursery. He plants 9 seeds in each container. If Jamal has 296 seeds to plant, about how many containers will he use?
Options:
a. about 20
b. about 30
c. about 200
d. about 300

Answer: about 30

Explanation:
Total number of seeds Jamal has= 296
Number of seeds placed in each container= 9
Number of containers Jamal used= 296÷9= 32.8=33 (approx)
Therefore, the number of containers used is about 30
The correct answer is option b.

Question 2.
Winona purchased a set of vintage beads. There are 2,140 beads in the set. If she uses the beads to make bracelets that have 7 beads each, about how many bracelets can she make?
Options:
a. about 30
b. about 140
c. about 300
d. about 14,000

Answer: about 300

Explanation:
Total number of beads Winona has= 2,140
Number of beads in each bracelet= 7
Number of bracelets made= 2,140÷7=305.7=306(approx)
Therefore, the number of bracelets made are about 30
The correct answer is option c.

Spiral Review

Question 3.
A train traveled 360 miles in 6 hours. How many miles per hour did the train travel?
Options:
a. 60 miles per hour
b. 66 miles per hour
c. 70 miles per hour
d. 600 miles per hour

Answer: 60 miles per hour

Explanation:
Total number of miles traveled by train= 360
Time taken by the train to cover 360 miles= 6 hours
Number of miles traveled in each hour= 360÷6=60 miles
The correct answer is option a.

Question 4.
An orchard has 12 rows of pear trees. Each row has 15 pear trees. How many pear trees are there in the orchard?
Options:
a. 170
b. 180
c. 185
d. 190

Answer: 180

Explanation:
Number of rows of pear trees in an orchard= 12
Number of pear trees in each row=15
Total number of pear trees in the orchard= 12 x 15=180
The correct answer is option b.

Question 5.
Megan rounded 366,458 to 370,000. To which place did Megan round the number?
Options:
a. hundred thousands
b. ten thousands
c. thousands
d. hundreds

Answer: ten thousands

Explanation:
The given number is 366,458, the ten thousand place digit has 6 which while rounding off should be changed to the next consecutive number and the digits in the other places should be written as zeroes.
The correct answer is option b.

Question 6.
Mr. Jessup, an airline pilot, flies 1,350 miles a day. How many miles will he fly in 8 days?
Options:
a. 1,358 miles
b. 8,400 miles
c. 10,800 miles
d. 13,508 miles

Answer: 10,800 miles

Explanation:
Number of miles flew by Mr.Jessup in one day= 1,350 miles
Number of days=8
Total number of miles flew by Mr.Jessup in 8 days= 1,350 x 8= 10,800 miles.
The correct answer is option c.

Common Core – Divide by 1-Digit Numbers – Page No. 79

Division and the Distributive Property

Find the quotient.

Question 1.
54 ÷ 3 = ( 30 ÷ 3) + ( 24 ÷ 3)
= 10 + 8
= 18
Go Math Grade 4 Answer Key Homework Practice FL Chapter 4 Divide by 1-Digit Numbers Common Core - Divide by 1-Digit Numbers img 5

Question 2.
81 ÷ 3 = ______

Answer: 27

Explanation:
81 ÷ 3
STEP1 Find the nearest estimates of the number 81
STEP2 We can break the number 81 into 21 + 60
STEP3 We must divide the two parts of the number (dividend) with the divisor.
STEP4 (60 ÷ 3) + (21 ÷ 3)
STEP5 Add quotients of the above 20 +7= 27

Question 3.
232 ÷ 4 = ______

Answer: 58

Explanation:
232 ÷ 4
STEP1 Find the nearest estimates of the number 232
STEP2 We can break the number 232 into 200 + 32
STEP3 We must divide the two parts of the number (dividend) with the divisor.
STEP4 (200 ÷ 4) + (32 ÷ 4)
STEP5 Add quotients of the above 50 +8= 58

Question 4.
305 ÷ 5 = ______

Answer: 61

Explanation:
305 ÷ 5
STEP1 Find the nearest estimates of the number 305
STEP2 We can break the number 305 into 300 + 5
STEP3 We must divide the two parts of the number (dividend) with the divisor.
STEP4 (300 ÷ 5) + (5 ÷ 5)
STEP5 Add quotients of the above 60 +1= 61

Question 5.
246 ÷ 6 = ______

Answer: 41

Explanation:
246 ÷ 6
STEP1 Find the nearest estimates of the number 246
STEP2 We can break the number 246 into 240 + 6
STEP3 We must divide the two parts of the number (dividend) with the divisor.
STEP4 (240 ÷ 6) + (6 ÷ 6)
STEP5 Add quotients of the above 40 +1= 41

Question 6.
69 ÷ 3 = ______

Answer: 23

Explanation:
69 ÷ 3
STEP1 Find the nearest estimates of the number 69
STEP2 We can break the number 69 into 60 + 9
STEP3 We must divide the two parts of the number (dividend) with the divisor.
STEP4 (60 ÷ 3) + (9 ÷ 3)
STEP5 Add quotients of the above 20 +3= 23

Question 7.
477 ÷ 9 = ______

Answer: 53

Explanation:
477 ÷ 9
STEP1 Find the nearest estimates of the number 477
STEP2 We can break the number 477 into 450 + 27
STEP3 We must divide the two parts of the number (dividend) with the divisor.
STEP4 (450 ÷ 9) + (27 ÷ 9)
STEP5 Add quotients of the above 50 +3= 53

Question 8.
224 ÷ 7 = ______

Answer: 32

Explanation:
224 ÷ 7
STEP1 Find the nearest estimates of the number 224
STEP2 We can break the number 224 into 210 + 14
STEP3 We must divide the two parts of the number (dividend) with the divisor.
STEP4 (210 ÷ 7) + (14 ÷ 7)
STEP5 Add quotients of the above 30 +2= 32

Question 9.
72 ÷ 4 = ______

Answer: 18

Explanation:
72 ÷ 4
STEP1 Find the nearest estimates of the number 72
STEP2 We can break the number 72 into 40 + 32
STEP3 We must divide the two parts of the number (dividend) with the divisor.
STEP4 (40 ÷ 4) + (32 ÷ 4)
STEP5 Add quotients of the above 10 +8= 18

Question 10.
315 ÷ 3 = ______

Answer: 105

Explanation:
315 ÷ 3
STEP1 Find the nearest estimates of the number 315
STEP2 We can break the number 315 into 300 + 15
STEP3 We must divide the two parts of the number (dividend) with the divisor.
STEP4 (300 ÷ 3) + (15 ÷3)
STEP5 Add quotients of the above 100 +5= 105

Problem Solving

Question 11.
Cecily picked 219 apples. She divided the apples equally into 3 baskets. How many apples are in each basket?
______ apples

Answer: 73 apples

Explanation:
The total number of apples Cecily picked= 219 apples
Number of parts into which she wanted to divide the apples= 3
Number of apples in each part = Quotient of 147 ÷ 7
STEP1 Find the nearest estimates of the number 219
STEP2 We can break the number 219 into 210 + 9
STEP3 We must divide the two parts of the number (dividend) with the divisor.
STEP4 (210 ÷ 3) + (9 ÷ 3)
STEP5 Add quotients of the above 70 +3= 73

Question 12.
Jordan has 260 basketball cards. He divides them into 4 equal groups. How many cards are in each group?
______ cards

Answer: 65 cards

Explanation:
The total number of basketball cards Jordan has= 260 basketball cards
Number of parts into which he wanted to divide the cards= 4
Number of apples in each part = Quotient of 260 ÷ 4
STEP1 Find the nearest estimates of the number 260
STEP2 We can break the number 260 into 240 + 20
STEP3 We must divide the two parts of the number (dividend) with the divisor.
STEP4 (240 ÷ 4) + (20 ÷ 4)
STEP5 Add quotients of the above 60 +5= 65

Question 13.
The Wilsons drove 324 miles in 6 hours. If they drove the same number of miles each hour, how many miles did they drive in 1 hour?
______ miles

Answer: 54 miles

Explanation:
The total number of miles drove by Wilson= 324 miles
Number of hours he drove = 6
Number of miles drove in each hour = Quotient of 324 ÷ 6
STEP1 Find the nearest estimates of the number 324
STEP2 We can break the number 324 into 300 + 24
STEP3 We must divide the two parts of the number (dividend) with the divisor.
STEP4 (300 ÷ 6) + (24 ÷ 6)
STEP5 Add quotients of the above 50 +4= 54

Question 14.
Phil has 189 stamps to put into his stamp album. He puts the same number of stamps on each of 9 pages. How many stamps does Phil put on each page?
______ stamps

Answer: 21 stamps

Explanation:
The total number of stamps Phil has= 189 stamps
Number of pages= 9
Number of stamps put on each page = Quotient of 189 ÷ 9
STEP1 Find the nearest estimates of the number 189
STEP2 We can break the number 189 into 180 + 9
STEP3 We must divide the two parts of the number (dividend) with the divisor.
STEP4 (180 ÷ 9) + (9 ÷ 9)
STEP5 Add quotients of the above 20 +1= 21

Common Core – Divide by 1-Digit Numbers – Page No. 80

Lesson Check

Question 1.
A landscaping company planted 176 trees in 8 equal rows in the new park. How many trees did the company plant in each row?
Options:
a. 18
b. 20
c. 22
d. 24

Answer: 22

Explanation:
The total number of trees in the landscaping= 176 trees
Number of rows= 8
Number of trees in each row = Quotient of 176 ÷ 8
STEP1 Find the nearest estimates of the number 176
STEP2 We can break the number 176 into 160 + 16
STEP3 We must divide the two parts of the number (dividend) with the divisor.
STEP4 (160 ÷ 8) + (16 ÷ 8)
STEP5 Add quotients of the above 20 +2= 22

Question 2.
Arnold can do 65 pushups in 5 minutes. How many pushups can he do in 1 minute?
Options:
a. 11
b. 13
c. 15
d. 17

Answer: 13

Explanation:
The total number of pushups done by Arnold = 65
Number of minutes spent on pushups= 5
Number of pushups done in each minute = Quotient of 65 ÷ 5
STEP1 Find the nearest estimates of the number 65
STEP2 We can break the number 65 into 60 + 5
STEP3 We must divide the two parts of the number (dividend) with the divisor.
STEP4 (60 ÷ 5) + (5 ÷ 5)
STEP5 Add quotients of the above 12 +1= 13

Spiral Review

Question 3.
Last Saturday, there were 1,486 people at the Cineplex. There were about the same number of people in each of the 6 theaters. Which is the best estimate of the number of people in each theater?
Options:
a. between 20 and 30
b. between 80 and 90
c. between 100 and 200
d. between 200 and 300

Answer: between 200 and 300

Explanation:
Total number of people at the Cineplex= 1,486 people
Number of theatres = 6
Number of people at each theatre= estimate of the number of people 1,486 ÷ 6

What number close to 1,486 is easy to divide by 6?
1,488 is close to 1,486. What basic fact can you use?
1,488 ÷ 6
Choose 1,488 because it is close to 1,486 and can easily be divided by 6.
1,488 ÷ 6 = 248
1,486 ÷ 6 is about 248

What number close to 1,486 is easy to divide by 6?
1,482 is close to 1,486 . What basic fact can you use?
1,482 ÷ 6
Choose 1,482 because it is close to 1,486 and can easily be divided by 6.
1,482 ÷ 6 = 247
1,486 ÷ 6 is about 247

Question 4.
Nancy walked 50 minutes each day for 4 days last week. Gillian walked 35 minutes each day for 6 days last week. Which statement is true?
Options:
a. Gillian walked 10 minutes more than Nancy.
b. Gillian walked 20 minutes more than Nancy.
c. Nancy walked 10 minutes more than Gillian.
d. Nancy walked 15 minutes more than Gillian.

Answer: Nancy walked 15 minutes more than Gillian.

Explanation:
Time walked by Nancy= 50 minutes
Time walked by Gillian= 35 minutes
Nancy walked more time compared to Gillian
50-35=15 minutes
Therefore, Nancy walked 15 minutes more than Gillian.

Question 5.
Three boys share 28 toy cars equally. Which best describes how the cars are shared?
Options:
a. Each gets 3 cars with 1 left over.
b. Each gets 8 cars with 2 left over.
c. Each gets 9 cars with 1 left over.
d. Each gets 10 cars with 2 left over.

Answer: Each gets 9 cars with 1 left over.

Explanation:
Total number of toys three boys have= 28
Number of toys each boy got= 28 ÷3=9.33
Therefore we can say that each gets 9 cars with 1 leftover.

Question 6.
An airplane flies at a speed of 474 miles per hour. How many miles does the plane fly in 5 hours?
Options:
a. 2,070 miles
b. 2,140 miles
c. 2,370 miles
d. 2,730 miles

Answer: 2,370 miles

Explanation:
Number of miles flew by airplane in one hour= 474
Number of hours the airplane flew= 5 hours
Total number of miles flew in 5 hours= 474 x 5= 2,370 miles

Common Core – Divide by 1-Digit Numbers – Page No. 81

Divide Using Repeated Subtraction

Use repeated subtraction to divide.

Question 1.
42 ÷ 3 = 14
3)\(\overline { 42 } \)
-30 ← 10 × 3 | 10
——-
12
-12 ← 4 × 3 | +4
——-             ———
0                     14

Question 2.
72 ÷ 4 = ______

Answer: 18

Explanation:
A. Begin with 72 counters. Subtract 4 counters.
B. Subtract 4 counters from 72 and repeat the processes until the remainder cannot be subtracted from the divisor.
C. Record the number of counters left and the number of times you subtracted.
D. The number of times you subtracted is the quotient is 18

Question 3.
93 ÷ 3 = ______

Answer: 31

Explanation:
A. Begin with 93 counters. Subtract 3 counters.
B. Subtract 3 counters from 93 and repeat the processes until the remainder cannot be subtracted from the divisor.
C. Record the number of counters left and the number of times you subtracted.
D. The number of times you subtracted is the quotient is 31

Question 4.
35 ÷ 4 = ______ r ______

Answer: 8r3

Explanation:
Quotient:
A. Use 35 counters to represent the 35 dominoes. Then draw 4 circles to represent the divisor.
B. Share the counters equally among the 4 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 35 ÷ 4
D. Number of circles are equally filled with 4 counters, therefore, the quotient is 8
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 3
For 35 ÷ 4, the quotient is 8 and the remainder is 3, or 8 r3.

Question 5.
93 ÷ 10 = ______ r ______

Answer: 9r3

Explanation:
Quotient:
A. Use 93 counters to represent the 93 dominoes. Then draw 10 circles to represent the divisor.
B. Share the counters equally among the 10 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 93 ÷ 10
D. Number of circles are equally filled with 10 counters, therefore, the quotient is 9
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 3
For 93 ÷ 10, the quotient is 9 and the remainder is 3, or 9 r3.

Question 6.
86 ÷ 9 = ______ r ______

Answer: 9r5

Explanation:
Quotient:
A. Use 86 counters to represent the 86 dominoes. Then draw 9 circles to represent the divisor.
B. Share the counters equally among the 9 groups by placing them in the circles.
C. Number of counters formed in each group = quotient of 86 ÷ 9
D. Number of circles are equally filled with 9 counters, therefore, the quotient is 9
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 5
For 86 ÷ 9, the quotient is 9 and the remainder is 5, or 9 r5.

Draw a number line to divide.

Question 7.
70 ÷ 5 = ______

Answer: 14

Explanation:
A. Draw a number line with 5 as each interval.
B. Draw up to 70 and count the intervals, it gives the quotient.
C. The quotient is 14

Problem Solving

Question 8.
Gretchen has 48 small shells. She uses 2 shells to make one pair of earrings. How many pairs of earrings can she make?
______ pairs

Answer: 24 pairs

Explanation:
Total number of small shells= 48
Number of shells used to make one pair of earrings = 2
Number of pair of earrings made = 48 ÷ 2 =24

Question 9.
James wants to purchase a telescope for $54. If he saves $3 per week, in how many weeks will he have saved enough to purchase the telescope?
______ weeks

Answer: $18

Explanation:
Cost of the telescope=$54
Amount saved each week = $3
Number of weeks he has to save the money to purchase the telescope = $54 ÷ $3 = $18

Common Core – Divide by 1-Digit Numbers – Page No. 82

Lesson Check

Question 1.
Randall collects postcards that his friends send him when they travel. He can put 6 cards on one scrapbook page. How many pages does Randall need to fit 42 postcards?
Options:
a. 3
b. 4
c. 6
d. 7

Answer: 7

Explanation:
Total number of postcards Randall has = 42 postcards
Number of postcards on one scrapbook page = 6 cards
Number of pages needed to fit the postcards = 42 ÷ 6=7
The correct answer is option d.

Question 2.
Ari stocks shelves at a grocery store. He puts 35 cans of juice on each shelf. The shelf has 4 equal rows and another row with only 3 cans. How many cans are in each of the equal rows?
Options:
a. 6
b. 7
c. 8
d. 9

Answer: 8

Explanation:
Total number of cans of juice on each shelf = 35
Number of rows = 4
Number of cans on the other shelf = 3
Number of cans placed on the first shelf = 35 – 3 = 32
Number of juice cans in the first row = 32 ÷ 4 = 8 cans
The correct answer is option c.

Spiral Review

Question 3.
Fiona sorted her CDs into separate bins. She placed 4 CDs in each bin. If she has 160 CDs, how many bins did she fill?
Options:
a. 4
b. 16
c. 40
d. 156

Answer: 40

Explanation:
Total number of CD’s in Fiona has = 160 CD’s
Number of CD’s placed in each bin = 4
Number of bins required to place the CD’s = 160 ÷ 4 = 40
The correct answer is option c.

Question 4.
Eamon is arranging 39 books on 3 shelves. If he puts the same number of books on each shelf, how many books will there be on each shelf?
Options:
a. 11
b. 12
c. 13
d. 14

Answer: 13

Explanation:
Total number of books Eamon has = 39 books
Number of shelves = 3
Number of books in each shelf = 39 ÷ 3 = 13
The correct answer is option c.

Question 5.
A newborn boa constrictor measures 18 inches long. An adult boa constrictor measures 9 times the length of the newborn plus 2 inches. How long is the adult?
Options:
a. 142 inches
b. 162 inches
c. 164 inches
d. 172 inches

Answer: 164 inches

Explanation:
Length of newborn boa constrictor = 18 inches
Length of an adult boa constrictor = 9 x Length of newborn boa constrictor = 9 x 18 = 162
Total length of an adult boa constrictor = 162 + 2 = 164 inches
The correct answer is option c.

Question 6.
Madison has 6 rolls of coins. Each roll has 20 coins. How many coins does Madison have in all?
Options:
a. 110
b. 120
c. 125
d. 130

Answer: 120

Explanation:
Number of rolls of coins = 6
Number of coins in each roll = 20
Total number of coins Madison has = 20 x 6 = 120
The correct answer is option b.

Common Core – Divide by 1-Digit Numbers – Page No. 83

Divide Using Partial Quotients

Divide. Use partial quotients.

Question 1.
8)\(\overline { 184 } \)
-80 ← 10 × 8 10
——-
104
-80 ← 10 × 8 +10
-24
-24 ← 3 × 8  +3
——-              ———
0                      23

Question 2.
6)\(\overline { 258 } \)
______

Answer: 43

Explanation:
STEP 1
Start by subtracting a greater multiple, such as 40 times the divisor.
Continue subtracting until the remaining number is less than the multiple, 6.
STEP 2
Subtract smaller multiples, such as 3 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient.
So, there are 40 x 6 = 240 : 258 – 240 = 18
3 x 6 = 18 : 18 – 18 = 0
Therefore the quotient is 43 ( 40 + 3)

Question 3.
5)\(\overline { 630 } \)
______

Answer: 126

Explanation:
STEP 1
Start by subtracting a greater multiple, such as 100 times the divisor.
Continue subtracting until the remaining number is less than the multiple, 5.
STEP 2
Subtract smaller multiples, such as 20 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient.
So, there are 100 x 5 = 500 : 630 – 500 = 130
5 x 20 = 100 : 130 – 100 = 30 : 5 x 6 = 30 : 30 – 30 = 0
Therefore the quotient is 126 ( 100 + 20 + 6)

Divide. Use rectangular models to record the partial quotients.

Question 4.
246 ÷ 3 = ____

Answer: 82

Explanation:
STEP 1
Start by subtracting a greater multiple, such as 80 times the divisor.
Continue subtracting until the remaining number is less than the multiple, 3.
STEP 2
Subtract smaller multiples, such as 80 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient.
So, there are 80 x 3 = 240 : 246 – 240 = 6
3 x 2 = 6 : 6 – 6 = 0
Therefore the quotient is 82 ( 80 + 2)
The rectangle models are given below :

Question 5.
126 ÷ 2 = ____

Answer: 63

Explanation:
STEP 1
Start by subtracting a greater multiple, such as 60 times the divisor.
Continue subtracting until the remaining number is less than the multiple,2.
STEP 2
Subtract smaller multiples, such as 60 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient.
So, there are 60 x 2 = 120 : 126 – 120 = 6
2 x 3 = 6 : 6 – 6 = 0
Therefore the quotient is 63 ( 60 +3)
The rectangle models are given below :

Question 6.
605 ÷ 5 = ____

Answer: 121

Explanation:
STEP 1
Start by subtracting a greater multiple, such as 100 times the divisor.
Continue subtracting until the remaining number is less than the multiple, 5.
STEP 2
Subtract smaller multiples, such as 20 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient.
So, there are 100 x 5 = 500 : 605 – 500 = 105
5 x 20 = 100 : 105 – 100 = 5 : 5 x 1 = 5 : 5 – 5 = 0
Therefore the quotient is 121 ( 100 + 20 + 1)
The rectangle models are given below :

Divide. Use either way to record the partial quotients.

Question 7.
492 ÷ 3 = ____

Answer: 164

Explanation:
STEP 1
Start by subtracting a greater multiple, such as 100 times the divisor.
Continue subtracting until the remaining number is less than the multiple, 3.
STEP 2
Subtract smaller multiples, such as 50 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient.
So, there are 100 x 3 = 300 : 492 – 300 = 192
50 x 3 = 150 : 192 – 150 = 42 : 3 x 14 = 42 : 42 – 42 = 0
Therefore the quotient is 164 ( 100 + 50 + 14)

Question 8.
224 ÷ 7 = ____

Answer: 32

Explanation:
STEP 1
Start by subtracting a greater multiple, such as 30 times the divisor.
Continue subtracting until the remaining number is less than the multiple, 7.
STEP 2
Subtract smaller multiples, such as 30 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient.
So, there are 30 x 7 = 210 : 224 – 210 = 14
7 x 2 = 14 : 14 – 14 = 0
Therefore the quotient is 32 ( 30 + 2)

Question 9.
692 ÷ 4 = ____

Answer: 173

Explanation:
STEP 1
Start by subtracting a greater multiple, such as 100 times the divisor.
Continue subtracting until the remaining number is less than the multiple, 4.
STEP 2
Subtract smaller multiples, such as 100 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient.
So, there are 100 x 4 = 400 : 692 – 400 = 392
4 x 50 = 200 : 392 – 200 = 192 : 4 x 48 = 192 : 192 – 192 = 0
Therefore the quotient is 198 ( 100 + 50 + 48)

Problem Solving

Question 10.
Allison took 112 photos on vacation. She wants to put them in a photo album that holds 4 photos on each page. How many pages can she fill?
____ pages

Answer: 28 pages

Explanation:
STEP 1
Start by subtracting a greater multiple, such as 20 times the divisor.
Continue subtracting until the remaining number is less than the multiple, 4.
STEP 2
Subtract smaller multiples, such as 20 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient.
So, there are 20 x 4 = 80 : 112 – 80 = 32
4 x 8 = 32 : 32 – 32 = 0
Therefore the quotient is 28 ( 20 + 8)

Question 11.
Hector saved $726 in 6 months. He saved the same amount each month. How much did Hector save each month?
$ ____

Answer: $121

Explanation:
STEP 1
Start by subtracting a greater multiple, such as 100 times the divisor.
Continue subtracting until the remaining number is less than the multiple, 6.
STEP 2
Subtract smaller multiples, such as 100 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient.
So, there are 100 x 6 = 600 : 726 – 600 = 126
6 x 20 = 120 : 126 – 120 = 6 : 6 x 1 = 6 : 6 – 6 = 0
Therefore the quotient is 121 ( 100 + 20 +1)

Common Core – Divide by 1-Digit Numbers – Page No. 84

Lesson Check

Question 1.
Annaka used partial quotients to divide 145 ÷ 5. Which shows a possible sum of partial quotients?
Options:
a. 50 + 50 + 45
b. 100 + 40 + 5
c. 10 + 10 + 9
d. 10 + 4 + 5

Answer: 10 + 10 + 9

Explanation:
STEP 1
Start by subtracting a greater multiple, such as 100 times the divisor.
Continue subtracting until the remaining number is less than the multiple, 4.
STEP 2
Subtract smaller multiples, such as 10 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient.
So, there are 10 x 5 = 50 : 145 – 50 = 95
5 x 10 = 50 : 95 – 50 = 45 : 5 x 9 = 45 : 45 – 45 = 0
Therefore the quotient is 29 ( 10 + 10 +9)

Question 2.
Mel used partial quotients to find the quotient 378 ÷ 3. Which might show the partial quotients that Mel found?
Options:
a. 100, 10, 10, 9
b. 100, 10, 10, 6
c. 100, 30, 30, 6
d. 300, 70, 8

Answer: 100, 10, 10, 6

Explanation:
STEP 1
Start by subtracting a greater multiple, such as 100 times the divisor.
Continue subtracting until the remaining number is less than the multiple, 3.
STEP 2
Subtract smaller multiples, such as 10 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient.
So, there are 100 x 3 = 300 : 378 – 300 = 78
10 x 3 =30 : 78 – 30 = 48 : 3 x 16 = 48 : 48 – 48 = 0
Therefore the quotient is 126 ( 100 + 10 +10 + 6)

Spiral Review

Question 3.
What are the partial products of 42 × 5?
Options:
a. 9 and 7
b. 20 and 10
c. 200 and 7
d. 200 and 10

Answer: 200 and 10

Explanation:
STEP1
42 x 5
Start by multiplying the digit five with the units digit 2 = 5 x 2 =10
Multiply the digit 5 with 4 in the tens place = 4 x 5 = 20
Since 4 is in the tens place when we multiply 4 and 5 we must place it in the hundreds place by assuming the units digit to be zero.
Therefore, the partial product of 42 x 5 = 200

Question 4.
Mr. Watson buys 4 gallons of paint that cost $34 per gallon. How much does Mr. Watson spend on paint?
Options:
a. $38
b. $126
c. $136
d. $1,216

Answer: $136

Explanation:
Cost of each gallon of paint = $34
Number of gallons = 4
The total cost of the gallons = $ 34 x 4 = $136

Question 5.
Use the area model to find the product 28 × 32.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 4 Divide by 1-Digit Numbers Common Core - Divide by 1-Digit Numbers img 6
Options:
a. 840
b. 856
c. 880
d. 896

Answer: 896

Explanation:
The whole rectangle is divided into four small rectangles the areas of these rectangles are:

Area of yellow rectangle= 30 x 20=600
Area of green rectangle= 2 x 20 = 40
Area of pink rectangle= 8 x 30= 240
Area of blue rectangle= 2 x 8= 16
Product of 32 and 28 = Area of yellow rectangle + Area of green rectangle + Area of pink rectangle + Area of the blue rectangle = 600+40+240+16 = 896

Question 6.
An adult male lion eats about 108 pounds of meat per week. About how much meat does an adult male lion eat in one day?
Options:
a. about 14 pounds
b. about 15 pounds
c. about 16 pounds
d. about 17 pounds

Answer: about 15 pounds

Explanation:
Mass of meat an adult lion eats in one week = 108
Number of days in a week = 7
Mass of meat ate by the lion in one day = 108 ÷ 7 = 15.4 pounds = about 15 pounds

Common Core – Divide by 1-Digit Numbers – Page No. 85

Model Division with Regrouping

Divide. Use base-ten blocks.

Question 1.
63 ÷ 4 = 15 r3
Go Math Grade 4 Answer Key Homework Practice FL Chapter 4 Divide by 1-Digit Numbers Common Core - Divide by 1-Digit Numbers img 7

Explanation:
A. draw 4 circles to represent the divisor. Then use base-ten blocks to model 63. Show 63 as 6 tens and 3 ones.
B. Share the tens equally among the 4 groups.
C. If there are any tens left, regroup them as ones. Share the ones equally among the 4 groups.
D. There are 1 ten(s) and 5 one(s) in each group. So, the quotient is 15.
E. After grouping, there are 3 blocks that weren’t grouped. So, the remainder is 3

Question 2.
83 ÷ 3
_____ R _____

Answer: 27 r 2

Explanation:
A. Draw 3 circles to represent the divisor. Then use base-ten blocks to model 83. Show 83 as 8 tens and 3 ones.
B. Share the tens equally among the 3 groups.
C. If there are any tens left, regroup them as ones. Share the ones equally among the 3 groups.
D. There are 2 ten(s) and 7 one(s) in each group. So, the quotient is 27.
E. After grouping, there are 2 blocks that weren’t grouped. So, the remainder is 2

Divide. Draw quick pictures. Record the steps.

Question 3.
85 ÷ 5
_____

Answer: 17

Explanation:
A. Draw 5 circles to represent the divisor. Then use base-ten blocks to model 85. Show 85 as 8 tens and 5 ones.
B. Share the tens equally among the 5 groups.
C. If there are any tens left, regroup them as ones. Share the ones equally among the 5 groups.
D. There are 1 ten(s) and 7 one(s) in each group. So, the quotient is 17.

Question 4.
97 ÷ 4
_____ R _____

Answer: 24 r 1

Explanation:
A. Draw 4 circles to represent the divisor. Then use base-ten blocks to model 97. Show 97 as 9 tens and 7 ones.
B. Share the tens equally among the 4 groups.
C. If there are any tens left, regroup them as ones. Share the ones equally among the 4 groups.
D. There are 2 ten(s) and 4 one(s) in each group. So, the quotient is 24.
E. After grouping, there is 1 block that wasn’t grouped. So, the remainder is 1.

Problem Solving

Question 5.
Tamara sold 92 cold drinks during her 2-hour shift at a festival food stand. If she sold the same number of drinks each hour, how many cold drinks did she sell each hour?
_____ cold drinks

Answer: 46 cold drinks

Explanation:
Total number of cold drinks Tamara sold = 92
The time in which she sold the drinks = 2 hours
Number of drinks she sold in each hour = 92 ÷ 2 = 46

Question 6.
In 3 days Donald earned $42 running errands. He earned the same amount each day. How much did Donald earn from running errands each day?
$ _____

Answer: $14

Explanation:
Total amount earned by Donald = $42
Number of days = 3
Amount earned on each day = $42 ÷ 3 = $14

Common Core – Divide by 1-Digit Numbers – Page No. 86

Lesson Check

Question 1.
Gail bought 80 buttons to put on the shirts she makes. She uses 5 buttons for each shirt. How many shirts can Gail make with the buttons she bought?
Options:
a. 14
b. 16
c. 17
d. 18

Answer: 16

Explanation:
Total number of buttons = 80
Number of buttons used for each shirt = 5
Number of shirts she can make = 80 ÷ 5 =16
The correct answer is option b.

Question 2.
Marty counted how many breaths he took in 3 minutes. In that time, he took 51 breaths. He took the same number of breaths each minute. How many breaths did Marty take in one minute?
Options:
a. 15
b. 16
c. 17
d. 19

Answer: 17

Explanation:
Total number of breaths Marty counted = 51
Time in which the breath was counted = 3 minutes
Number of breaths in one minute = 51 ÷ 3 = 17
The correct answer is option c.

Spiral Review

Question 3.
Kate is solving brain teasers. She solved 6 brain teasers in 72 minutes. How long did she spend on each brain teaser?
Options:
a. 12 minutes
b. 14 minutes
c. 18 minutes
d. 22 minutes

Answer: 12 minutes

Explanation:
Number of brain teasers solved = 6
Number of minutes spent on brain teasers = 72 minutes
Number of minutes spent on each problem = 72 ÷ 6 =12 minutes
The correct answer is option a.

Question 4.
Jenny works at a package delivery store. She puts mailing stickers on packages. Each package needs 5 stickers. How many stickers will Jenny use if she is mailing 105 packages?
Options:
a. 725
b. 625
c. 525
d. 21

Answer: 525

Explanation:
Number of packages = 105
Number of stickers on each package = 5
Total number of stickers on the packages = 105 x 5 = 525
The correct answer is option c.

Question 5.
The Puzzle Company packs standardized puzzles into boxes that hold 8 puzzles. How many boxes would it take to pack up 192 standard-sized puzzles?
Options:
a. 12
b. 16
c. 22
d. 24

Answer: 24

Explanation:
Total number of puzzles = 192
Number of puzzles in each box = 8
Number of boxes used = 192 ÷ 8 = 24 boxes
The correct answer is option d.

Question 6.
Mt. Whitney in California is 14,494 feet tall. Mt. McKinley in Alaska is 5,826 feet taller than Mt. Whitney. How tall is Mt. McKinley?
Options:
a. 21,310 feet
b. 20,320 feet
c. 20,230 feet
d. 19,310 feet

Answer: 20,320 feet

Explanation:
Height of Mt. Whitney in California = 14,494 feet
The height of Mt. McKinley in Alaska is 5,826 feet taller than Mt. Whitney.
Therefore the height of Mt. McKinley in Alaska = 14,494 feet + 5,826 feet = 20,320 feet
The correct answer is option b.

Common Core – Divide by 1-Digit Numbers – Page No. 87

Place the First Digit

Divide.

Question 1.
62
3)\(\overline { 186 } \)
-18
——–
06
-6
——–
0

Explanation:
STEP 1 Use place value to place the first digit. Look at the hundreds in 186. 180 hundred can be shared among 3 groups
without regrouping.
Now there is 18 tens and 6 ones to share among 3 groups.
The first digit of the quotient will be in the tens place.
STEP 2 Divide the tens.
Divide. 180 ÷ 3
Multiply. 3 × 60 = 180
Subtract. 186 − 180 = 6 ones
STEP 3 Divide the ones.
Now there are 6 ones to share among 3 groups.
Divide. 6 ones ÷ 3
Multiply. 2×3 ones
Subtract. 6 ones − 2 ones =0 one
So, the quotient is 62 (60 + 2) and the remainder is 0

Question 2.
4)\(\overline { 298 } \)
_____ R _____

Answer:
STEP 1 Use place value to place the first digit. Look at the hundreds in 298. 280 hundred can be shared among 4 groups
without regrouping.
Now there are 28 tens and 18 ones to share among 4 groups.
The first digit of the quotient will be in the hundreds place.
STEP 2 Divide the tens.
Divide. 280 ÷ 4
Multiply. 4 × 70 = 280
Subtract. 280 − 280 = 0 ones
STEP 3 Divide the ones.
Now there are 18 ones to share among 4 groups.
Divide. 18 ones ÷ 4
Multiply. 4×4 ones
Subtract. 18 ones − 16 ones = 2 ones
So, the quotient is 74 (70 + 4) and the remainder is 2.

Question 3.
3)\(\overline { 461 } \)
_____ R _____

Answer: 153

Explanation:
STEP 1 Use place value to place the first digit. Look at the hundreds in 461. 450 hundred can be shared among 3 groups
without regrouping.
Now there is 45 tens and 11 ones to share among 3 groups.
The first digit of the quotient will be in the hundreds place.
STEP 2 Divide the tens.
Divide. 450 ÷ 3
Multiply. 3 × 150 = 450
Subtract. 450 − 450 = 0 ones
STEP 3 Divide the ones.
Now there are 11 ones to share among 3 groups.
Divide. 11 ones ÷ 3
Multiply. 3×3 ones
Subtract. 11 ones − 9 ones = 2 ones
So, the quotient is 153 (150 + 3) and the remainder is 2

Question 4.
9)\(\overline { 315 } \)
_____ R _____

Answer: 35

Explanation:
STEP 1 Use place value to place the first digit. Look at the hundreds in 315. 310 hundred can be shared among 9 groups
without regrouping.
Now there is 31 tens and 5 ones to share among 9 groups.
The first digit of the quotient will be in the hundreds place.
STEP 2 Divide the tens.
Divide.310 ÷ 9
Multiply. 9 × 30 = 270
Subtract. 310 − 270 = 40 ones
STEP 3 Divide the ones.
Now there are 40 + 5 = 45 ones to share among 9 groups.
Divide. 45 ones ÷ 9
Multiply. 5×9 ones
Subtract. 45 ones − 45 ones = 0 ones
So, the quotient is 35 (30 + 5) and the remainder is 0

Question 5.
2)\(\overline { 766 } \)
_____ R _____

Answer: 383

Explanation:
STEP 1 Use place value to place the first digit. Look at the hundreds in 766. 760 hundred can be shared among 2 groups
without regrouping.
Now there is 76 tens and 6 ones to share among 2 groups.
The first digit of the quotient will be in the hundreds place.
STEP 2 Divide the tens.
Divide. 760 ÷ 2
Multiply. 2 × 380 = 760
Subtract. 760 − 760 = 0 ones
STEP 3 Divide the ones.
Now there are 6 ones to share among 2 groups.
Divide. 6 ones ÷ 2
Multiply. 2×3 ones
Subtract. 6 ones − 6 ones = 0 ones
So, the quotient is 383 (380 + 3) and the remainder is 0

Question 6.
4)\(\overline { 604 } \)
_____ R _____

Answer: 151

Explanation:
STEP 1 Use place value to place the first digit. Look at the hundreds in 604. 600 hundred can be shared among 4 groups
without regrouping.
Now there is 60 tens and 4 ones to share among 4 groups.
The first digit of the quotient will be in the hundreds place.
STEP 2 Divide the tens.
Divide. 600 ÷ 4
Multiply. 4 × 150 = 600
Subtract. 600 − 600 = 0 ones
STEP 3 Divide the ones.
Now there are 4 ones to share among 4 groups.
Divide. 4 ones ÷ 4
Multiply. 4×1 ones
Subtract. 4 ones − 4 ones = 0 ones
So, the quotient is 151 (150 + 1) and the remainder is 0

Question 7.
6)\(\overline { 796 } \)
_____ R _____

Answer: 132

Explanation:
STEP 1 Use place value to place the first digit. Look at the hundreds in 796. 790 hundred can be shared among 6 groups
without regrouping.
Now there is 79 tens and 6 ones to share among 6 groups.
The first digit of the quotient will be in the hundreds place.
STEP 2 Divide the tens.
Divide. 790 ÷ 6
Multiply. 6 × 131 = 786
Subtract. 790 − 786 = 4 ones
STEP 3 Divide the ones.
Now there are 4 + 6 = 10 ones to share among 6 groups.
Divide. 10 ones ÷ 6
Multiply. 6×1 ones
Subtract. 10 ones − 6 ones = 4 ones
So, the quotient is 132 (131 + 1) and the remainder is 4.

Question 8.
5)\(\overline { 449 } \)
_____ R _____

Answer: 89

Explanation:
STEP 1 Use place value to place the first digit. Look at the hundreds in 449. 440 hundred can be shared among 5 groups
without regrouping.
Now there is 44 tens and 9 ones to share among 5 groups.
The first digit of the quotient will be in the hundreds place.
STEP 2 Divide the tens.
Divide. 440 ÷ 5
Multiply. 5 × 88 = 440
Subtract. 440 − 440 = 0 ones
STEP 3 Divide the ones.
Now there are 9 ones to share among 5 groups.
Divide. 9 ones ÷ 5
Multiply. 5×1 ones
Subtract. 9 ones − 5 ones = 4 ones
So, the quotient is 89 (88 + 1) and the remainder is 4

Question 9.
6)\(\overline { 756 } \)
_____ R _____

Answer: 126

Explanation:
STEP 1 Use place value to place the first digit. Look at the hundreds in 756. 750 hundred can be shared among 6 groups
without regrouping.
Now there is 75 tens and 6 ones to share among 6 groups.
The first digit of the quotient will be in the hundreds place.
STEP 2 Divide the tens.
Divide. 750 ÷ 6
Multiply. 6 × 125 = 750
Subtract. 750 − 750 = 0 ones
STEP 3 Divide the ones.
Now there are 6 ones to share among 6 groups.
Divide. 6 ones ÷ 6
Multiply. 6×1 ones
Subtract. 6 ones − 6 ones = 0 ones
So, the quotient is 126 (125 + 1) and the remainder is 0

Question 10.
7)\(\overline { 521 } \)
_____ R _____

Answer: 74

Explanation:
STEP 1 Use place value to place the first digit. Look at the hundreds in 521. 520 hundred can be shared among 7 groups
without regrouping.
Now there is 52 tens and 1 one to share among 7 groups.
The first digit of the quotient will be in the hundreds place.
STEP 2 Divide the tens.
Divide. 520 ÷ 7
Multiply. 7 × 74 = 518
Subtract. 520 − 518 = 2 ones
STEP 3 Divide the ones.
Now there are 2 + 1 = 3 ones to share among 7 groups.
Divide. 3 ones ÷ 7 (not possible)
So, the quotient is 74 and the remainder is 3

Question 11.
5)\(\overline { 675 } \)
_____ R _____

Answer: 135

Explanation:
STEP 1 Use place value to place the first digit. Look at the hundreds in 675. 670 hundred can be shared among 5 groups
without regrouping.
Now there is 67 tens and 5 ones to share among 5 groups.
The first digit of the quotient will be in the hundreds place.
STEP 2 Divide the tens.
Divide. 670 ÷ 5
Multiply. 5 × 134 = 670
Subtract. 670 − 670 = 0 ones
STEP 3 Divide the ones.
Now there are 5 ones to share among 5 groups.
Divide. 5 ones ÷ 5
Multiply. 5×1 ones
Subtract. 5 ones − 5 ones = 0 ones
So, the quotient is 135 (134 + 1) and the remainder is 0.

Question 12.
8)\(\overline { 933 } \)
_____ R _____

Answer: 116

Explanation:
STEP 1 Use place value to place the first digit. Look at the hundreds in 933. 930 hundred can be shared among 8 groups
without regrouping.
Now there is 93 tens and 3 ones to share among 8 groups.
The first digit of the quotient will be in the hundreds place.
STEP 2 Divide the tens.
Divide. 930 ÷ 8
Multiply. 8 × 116 = 928
Subtract. 930 − 928 = 2 ones
STEP 3 Divide the ones.
Now there are 2 + 3 = 5 ones to share among 8 groups.
Divide. 5 ones ÷ 8 (not possible)
So, the quotient is 116 (100 + 3) and the remainder is 5.

Problem Solving

Question 13.
There are 132 projects in the science fair. If 8 projects can fit in a row, how many full rows of projects can be made? How many projects are in the row that is not full?
_____ full rows
_____ projects in the non-full row

Answer: 16 full rows and 4 projects in the non-full row

Explanation:
Total number of projects = 132
Number of projects placed in full row = 8
Number of rows having full projects =Quotient of 132 ÷ 8 = 16
Number of projects in the non-full row = Remainder of 132 ÷ 8 = 4

Question 14.
There are 798 calories in six 10-ounce bottles of apple juice. How many calories are there in one 10-ounce bottle of apple juice?
_____ R _____ calories in one 10-ounce bottles of juice

Answer: 133 calories

Explanation:
Number of calories in 6 bottles of apple juice = 798
Number of calories in each bottle = 798 ÷6 = 133 calories

Common Core – Divide by 1-Digit Numbers – Page No. 88

Lesson Check

Question 1.
To divide 572 ÷ 4, Stanley estimated to place the first digit of the quotient. In which place is the first digit of the quotient?
Options:
a. ones
b. tens
c. hundreds
d. thousands

Answer: hundreds

Explanation:
The quotient of 572÷ 4 is 143
STEP 1 Use place value to place the first digit. Look at the hundreds in 572. 560 hundred can be shared among 4 groups
without regrouping.
Now there is 1 ten to share among 4 groups.
The first digit of the quotient will be in the hundreds place.

Question 2.
Onetta biked 325 miles in 5 days. If she biked the same number of miles each day, how far did she bike each day?
Options:
a. 1,625 miles
b. 320 miles
c. 65 miles
d. 61 miles

Answer: 65 miles

Explanation:
Total number of miles biked = 325 miles
Number of days biked = 5
Number of miles biked on each day = Quotient of 325 ÷ 5 = 65

Spiral Review

Question 3.
Mort makes beaded necklaces that he sells for $32 each. About how much will Mort make if he sells 36 necklaces at the local art fair?
Options:
a. $120
b. $900
c. $1,200
d. $1,600

Answer: $1,200

Explanation:
Cost of each beaded necklace = $32
Number of necklaces = 36
The total cost of the necklaces = $32 x 36 = $1,200 (approx)

Question 4.
Which is the best estimate of 54 × 68?
Options:
a. 4,200
b. 3,500
c. 3,000
d. 350

Answer: 3,500

Explanation:

Taking the terms nearest to the 54 x 68 as 54 x 65 = 3510 = 3500 (approx)

Question 5.
Ms. Eisner pays $888 for 6 nights in a hotel. How much does Ms. Eisner pay per night?
Options:
a. $5,328
b. $882
c. $148
d. $114

Answer: $148

Explanation:
Total pays of Ms Eisner in a hotel = $888
Number of nights = 6
Amount Ms Eisner pay per night = $888 ÷ 6 = $148

Question 6.
Which division problem does the model show?
Go Math Grade 4 Answer Key Homework Practice FL Chapter 4 Divide by 1-Digit Numbers Common Core - Divide by 1-Digit Numbers img 8
Options:
a. 42 ÷ 3
b. 44 ÷3
c. 51 ÷ 3
d. 54 ÷ 3

Answer: 54 ÷ 3

Explanation:
Number of counters in each model = 18
Number of models = 3
Total number of counters = 18 x 3 = 54
Therefore the model displays = 54 ÷ 3

Common Core – Divide by 1-Digit Numbers – Page No. 89

Divide by 1-Digit Numbers

Divide and check.

Question 1.
318
\(\overline { 2)636 } \) 318
-6     × 2
———  ———
03 636
-2
———
16
-16
———
0

Question 2.
4)\(\overline { 631 } \)
_____ R _____

Answer:
STEP 1 Use place value to place the first digit. The first digit of the quotient will be in the hundreds place.
STEP 2 Divide the hundreds.
STEP 3 Divide the tens.
STEP 4 Divide the ones.

Question 3.
8)\(\overline { 906 } \)
_____ R _____

Answer:
STEP 1 Use place value to place the first digit. The first digit of the quotient will be in the hundreds place.
STEP 2 Divide the hundreds.
STEP 3 Divide the tens.
STEP 4 Divide the ones.

Question 4.
6)\(\overline { 6,739 } \)
_____ R _____

Answer:
STEP 1 Use place value to place the first digit. Look at the thousands in 6,739. 6 thousand can be shared among 6 groups without regrouping. The first digit of the quotient will be in the thousands place.
STEP 2 Divide the thousands.
STEP 3 Divide the hundreds.
STEP 4 Divide the tens.
STEP 5 Divide the ones.

Question 5.
4)\(\overline { 2,328 } \)
_____ R _____

Answer:
STEP 1 Use place value to place the first digit. Look at the thousands in 2,328. 2 thousand can be shared among 4 groups without regrouping. The first digit of the quotient will be in the thousands place.
STEP 2 Divide the thousands.
STEP 3 Divide the hundreds.
STEP 4 Divide the tens.
STEP 5 Divide the ones.

Question 6.
5)\(\overline { 7,549 } \)
_____ R _____

Answer:
STEP 1 Use place value to place the first digit. Look at the thousands in 7,549. 7 thousand can be shared among 5 groups without regrouping. The first digit of the quotient will be in the thousands place.
STEP 2 Divide the thousands.
STEP 3 Divide the hundreds.
STEP 4 Divide the tens.
STEP 5 Divide the ones.

Problem Solving

Use the table for 7 and 8.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 4 Divide by 1-Digit Numbers Common Core - Divide by 1-Digit Numbers img 9

Question 7.
The Briggs rented a car for 5 weeks. What was the cost of their rental car per week?
$ _____

Answer: $197

Explanation:
Cost of the car of Briggs = $985
Number of weeks = 5
Cost of rent per week = $985 ÷ 5 =$ 197

Question 8.
The Lees rented a car for 4 weeks. The Santos rented a car for 2 weeks. Whose weekly rental cost was lower? Explain.
The rental cost of _________

Answer: Weekly rental cost was lower for Lees compared to Santos

Explanation:
Cost of the car of Lees = $632
Number of weeks = 4
Cost of rent per week = $632 ÷ 4 =$ 158

Cost of the car of Santos = $328
Number of weeks = 2
Cost of rent per week = $328 ÷ 2 =$ 164
Therefore weekly rental cost was lower for Lees compared to Santos.

Common Core – Divide by 1-Digit Numbers – Page No. 90

Lesson Check

Question 1.
Which expression can be used to check
the quotient 646 ÷ 3?
Options:
a. (251 × 3) + 1
b. (215 × 3) + 2
c. (215 × 3) + 1
d. 646 × 3

Answer: (215 × 3) + 1

Explanation:
Multiply 215 x 3 = 645
Then add 1 to 645
Then the dividend is 645 + 1 = 646
Thus the correct answer is option c.

Question 2.
There are 8 volunteers at the telethon. The goal for the evening is to raise $952. If each volunteer raises the same amount, what is the minimum amount each needs to raise to meet the goal?
Options:
a. $7,616
b. $944
c. $119
d. $106

Answer: $7,616

Explanation:
Number of volunteers = 8
Amount raised by each volunteer = $952
Total amount raised = $952 x 8 = $7,616

Thus the correct answer is option a.

Spiral Review

Question 3.
Which product is shown by the model?
Go Math Grade 4 Answer Key Homework Practice FL Chapter 4 Divide by 1-Digit Numbers Common Core - Divide by 1-Digit Numbers img 10
Options:
a. 5 × 15 = 75
b. 5 × 16 = 80
c. 5 × 17 = 75
d. 5 × 17 = 85

Answer: 5 × 17 = 85

Explanation:
By counting the number of counters we can give the expression.
Number of counters in one row = 17
Number of rows = 5
Therefore the expression = 5 × 17 = 85
Thus the correct answer is option d.

Question 4.
The computer lab at a high school ordered 26 packages of CDs. There were 50 CDs in each package. How many CDs did the computer lab order?
Options:
a. 1,330
b. 1,300
c. 1,030
d. 130

Answer: 1,300

Explanation:
Number of packages = 26
Number of CDs in each pack = 50
Total number of CDs the computer lab ordered = 26 x 50 = 1,300
Thus the correct answer is option b.

Question 5.
Which of the following division problems has a quotient with the first digit in the hundreds place?
Options:
a. 892 ÷ 9
b. 644 ÷ 8
c. 429 ÷ 5
d. 306 ÷ 2

Answer: 306 ÷ 2

Explanation:
Use place value to place the first digit. Look at the hundreds in 306. 300 hundred can be shared among 2 groups
without regrouping.
Now there is 30 tens and 6 ones to share among 2 groups.
The first digit of the quotient will be in the hundreds place.
Thus the correct answer is option d.

Question 6.
Sharon has 64 ounces of juice. She is going to use the juice to fill as many 6-ounce glasses as possible. She will drink the leftover juice. How much juice will Sharon drink?
Options:
a. 4 ounces
b. 6 ounces
c. 10 ounces
d. 12 ounces

Answer: 4 ounces

Explanation:
The total quantity of juice = 64 ounces
Quantity of juice she filled = 6 ounces
Quantity of juice she drank = Remainder of 64 ÷ 6 = 4

Thus the correct answer is option a.

Common Core – Divide by 1-Digit Numbers – Page No. 91

Problem Solving Multistep Division Problems

Solve. Draw a diagram to help you.

Question 1.
There are 3 trays of eggs. Each tray holds 30 eggs. How many people can be served if each person eats 2 eggs?
Go Math Grade 4 Answer Key Homework Practice FL Chapter 4 Divide by 1-Digit Numbers Common Core - Divide by 1-Digit Numbers img 11
Think: What do I need to find? How can I draw a diagram to help?
45 people can be served

Question 2.
There are 8 pencils in a package. How many packages will be needed for 28 children if each child gets 4 pencils?
______ packages

Answer: 14 packages

Explanation:
Number of pencils in each package = 8

Number of children = 28

Number of pencils each child needs = 4
Total number of pencils = 28 x 4 =112
Number of packages = 112 ÷ 8 = 14

Question 3.
There are 3 boxes of tangerines. Each box has 93 tangerines. The tangerines will be divided equally among 9 classrooms. How many tangerines will each classroom get?
______ tangerines

Answer: 31

Explanation:
Number of boxes = 3
Number of tangerines in each box = 93
Total number of tangerines = 93 x 3 = 279

Number of classrooms = 9
Number of tangerines in each classroom = 279 ÷ 9 = 31

Question 4.
Misty has 84 photos from her vacation and 48 photos from a class outing. She wants to put all the photos in an album with 4 photos on each page. How many pages does she need?
______ pages

Answer: 33 pages

Explanation:
Number of photos from her vacation = 84

Number of photos from her class outing = 48

Total number of photos = 84 + 48 = 132
Number of photos in each page = 4
Number of pages required = 132 ÷ 4 = 33

Common Core – Divide by 1-Digit Numbers – Page No. 93

Lessons 4.1, 4.5

Estimate the quotient.

Question 1.
67 ÷ 4
about ______

Answer: About 17

Explanation:
The number close to 67 is 70.
Divide 70 by 4 is 17.5
Thus the estimated quotient of 67 ÷ 4 is 17.

Question 2.
72 ÷ 5
about ______

Answer: About 14

Explanation:
The number close to 72 is 70.
Divide 70 by 5 is 14.
Thus the estimated quotient of 72 ÷ 5 is 14.

Question 3.

213 ÷ 3
about ______

Answer: About 70

Explanation:
The number close to 213 is 210.
Divide 210 by 3 is 70.
Thus the estimated quotient of 213 ÷ 3 is 70.

Question 4.
484 ÷ 6
about ______

Answer: About 80

Explanation:
The number close to 484 is 480.
Divide 480 by 6 is 80.
Thus the estimated quotient of 484 ÷ 6 is 80.

Question 5.
446 ÷ 7
about ______

Answer: About 60

Explanation:
The number close to 446 is 440.
Divide 440 by 7 is 60.
Thus the estimated quotient of 446 ÷ 7 is 60.

Question 6.
1,246 ÷ 4
about ______

Answer: About 300

Explanation:
The number close to 1246 is 1200.
Divide 1200 by 4 is 300.
Thus the estimated quotient of 1,246 ÷ 4 is 300.

Question 7.
708 ÷ 9
about ______

Answer: About 80

Explanation:
The number close to 708 is 700.
Divide 700 by 9 is 80 (approx).
Thus the estimated quotient of 708 ÷ 9 is 80.

Question 8.
2,657 ÷ 3
about ______

Answer: About 900

Explanation:
The number close to 2,657 is 2700.
Divide 2700 by 3 is 900.
Thus the estimated quotient of 2,657 ÷ 3 is 900.

Lesson 4.2

Use counters or quick pictures to find the quotient and remainder.

Question 9.
44 ÷ 5
______ R ______

Answer: 8R4

Explanation:
Quotient:
A. Use 44 counters to represent the 44 dominoes. Then draw 5 circles to represent the divisor.
B. Share the counters equally among the 5 groups by placing them in the circles.
C. Number of groups of counters formed = quotient of 44 ÷ 5
D. Number of circles equally filled is8, therefore, the quotient is 8.
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 4
For 44 ÷ 5, the quotient is 8 and the remainder is 4, or 8R4.

Question 10.
8)\(\overline { 21 } \)
______ R ______

Answer: 2R5

Explanation:
Quotient:
A. Use 21 counters to represent the 21 dominoes. Then draw 8 circles to represent the divisor.
B. Share the counters equally among the 8 groups by placing them in the circles.
C. Number of groups of counters formed = quotient of 21 ÷ 8
D. Number of circles equally filled is 2, therefore, the quotient is 2.
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 5
For 21 ÷ 8, the quotient is 2 and the remainder is 5, or 2R5.

Question 11.
4)\(\overline { 75 } \)
______ R ______

Answer: 18R3

Explanation:
Quotient:
A. Use 75 counters to represent the 75 dominoes. Then draw 4 circles to represent the divisor.
B. Share the counters equally among the 4 groups by placing them in the circles.
C. Number of groups of counters formed = quotient of 75 ÷ 4
D. Number of circles equally filled is 18, therefore, the quotient is 18.
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 3
For 21 ÷ 8, the quotient is 18 and the remainder is 3, or 18R3.

Question 12.
76 ÷ 6
______ R ______

Answer: 12R4

Explanation:
Quotient:
A. Use 76 counters to represent the 76 dominoes. Then draw 6 circles to represent the divisor.
B. Share the counters equally among the 6 groups by placing them in the circles.
C. Number of groups of counters formed = quotient of 76 ÷ 6
D. Number of circles equally filled is 12, therefore, the quotient is 12.
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 4
For 76 ÷ 6, the quotient is 12 and the remainder is 4, or 12R4.

Lesson 4.3

Interpret the remainder to solve.

Question 13.
Kelly divides 29 markers equally among 7 friends. If Kelly keeps the leftover markers, how many markers will she keep?
______ marker(s)

Answer: 1 marker

Explanation:
Given,
Kelly divides 29 markers equally among 7 friends.
1 because 4 markers for each friend (4 × 7) would be 28 and the last one would be leftover because it’s not enough for everyone.

Question 14.
Dave has a board that is 29 inches long. He cuts the board into 4 equal pieces. How long will each piece be?
______ inches

Answer: 7 inches

Explanation:
Dave has a board that is 29 inches long and want to cut it into 4 pieces.
You are asked the length of each piece.
To solve the question, you need to divide the total length of the board by the number of pieces Dave wants to make.
Then, the length of each piece would be: 29 inches/4= 7.25 inches

Question 15.
Eight students can ride in each van. How many vans are needed for 29 students?
______ vans

Answer: 4 vans

Explanation:
Given,
Eight students can ride in each van.
29/8 = 3.625 = 4(approx)
Therefore 4 vans are needed for 29 students.

Question 16.
Mac has 40 ounces of juice. He pours 6 ounces in each glass. How many glasses can he fill?
______ glasses

Answer: 6 glasses

Explanation:
Given,
Mac has 40 ounces of juice. He pours 6 ounces in each glass.
Divide 40 by 6
40/6 = 6.66 ≈ 6
Thus Mac can fill 6 glasses.

Lesson 4.4

Use basic facts and place value to find the quotient.

Question 17.
120 ÷ 4 = ______

Answer: 30

Explanation:
STEP 1 Identify the basic fact. 120 ÷ 4
STEP 2 Use place value. 120 = 12 tens
STEP 3 Divide. 12 tens ÷ 4 = 3 tens
120 ÷ 4 = 30

Question 18.
280 ÷ 7 = ______

Answer: 40

Explanation:
STEP 1 Identify the basic fact. 280 ÷ 7
STEP 2 Use place value. 280 = 28 tens
STEP 3 Divide. 28 tens ÷ 7 = 4 tens
280 ÷ 7 = 40

Question 19.
3,000 ÷ 5 = ______

Answer: 600

Explanation:
STEP 1 Identify the basic fact. 3000 ÷ 5
STEP 2 Use place value. 3000 = 300 tens
STEP 3 Divide. 300 tens ÷ 5 = 60 tens
3,000 ÷ 5 = 60 tens

Question 20.
4,800 ÷ 6 = ______

Answer: 800

Explanation:
STEP 1 Identify the basic fact. 4,800 ÷ 6
STEP 2 Use place value. 4800 = 480 tens
STEP 3 Divide. 480 tens ÷ 6 = 80 tens
4,800 ÷ 6 = 800

Question 21.
5,600 ÷ 8 = ______

Answer: 700

Explanation:
STEP 1 Identify the basic fact. 5,600 ÷ 8
STEP 2 Use place value. 5600 = 560 tens
STEP 3 Divide. 560 tens ÷ 8 = 70 tens
5,600 ÷ 8 = 700

Question 22.
6,300 ÷ 9 = ______

Answer: 700

Explanation:
STEP 1 Identify the basic fact. 6,300 ÷ 9
STEP 2 Use place value. 6300 = 630 tens
STEP 3 Divide. 630 tens ÷ 9 = 70 tens
6,300 ÷ 9 = 700

Common Core – Divide by 1-Digit Numbers – Page No. 94

Lessons 4.6–4.7

Choose a method and divide.

Question 1.
68 ÷ 4 = ______

Answer: 17

Explanation:
The number close to 68 is 70.
Divide 70 by 4 is 17 (approx).
Thus the estimated quotient of 68 ÷ 4 is 17.

Question 2.
48 ÷ 3 = ______

Answer: 16

Explanation:
The number close to 48 is 50.
Divide 50 by 3 is 16  (approx).
Thus the estimated quotient of 48 ÷ 3 is 16.

Question 3.
108 ÷ 9 = ______

Answer: 12

Explanation:
The number close to 108 is 100.
Divide 100 by 9 is 12 (approx).
Thus the estimated quotient of 108 ÷ 9 is 12.

Question 4.
74 ÷ 2 = ______

Answer: 37

Explanation:
The number close to 74 is 70.
Divide 70 by 2 is 37 (approx).
Thus the estimated quotient of 74 ÷ 2 is 37.

Question 5.
122 ÷ 5 = ______ R ______

Answer: 24R2

Explanation:
Quotient:
A. Use 122 counters to represent the 122 dominoes. Then draw 5 circles to represent the divisor.
B. Share the counters equally among the 5 groups by placing them in the circles.
C. Number of groups of counters formed = quotient of 122 ÷ 5
D. Number of circles equally filled are 24, therefore, the quotient is 24.
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 2
For 122 ÷ 5, the quotient is 24 and the remainder is 2, or 24R2.

Question 6.
165 ÷ 6 = ______ R ______

Answer: 27R3

Explanation:
Quotient:
A. Use 165 counters to represent the 165 dominoes. Then draw 6 circles to represent the divisor.
B. Share the counters equally among the 6 groups by placing them in the circles.
C. Number of groups of counters formed = quotient of 165 ÷ 6.
D. Number of circles equally filled are 27, therefore, the quotient is 27.
Remainder:
The number of counters left over is the remainder. The number of counters leftover= 3
For 165 ÷ 6, the quotient is 27 and the remainder is 3, or 27R3.

Lessons 4.8–4.9

Divide.

Question 7.
4)\(\overline { 848 } \)
______

Answer: 212

Go Math Grade 4 Chapter 4 Answer Key

Question 8.
7)\(\overline { 287 } \)
______

Answer: 41

Go Math Grade 4 Answer Key Homework Practice FL Chapter 4 Divide by 1-Digit Numbers img-2

Question 9.
5)\(\overline { 405 } \)
______

Answer: 81
Go Math Grade 4 Answer Key Homework Practice FL Chapter 4 Divide by 1-Digit Numbers img-3

Question 10.
3)\(\overline { 696 } \)
______

Answer: 232
Go Math Grade 4 Answer Key Homework Practice FL Chapter 4 Divide by 1-Digit Numbers img-4

Question 11.
96 ÷ 6 = ______

Answer: 16
Go Math Grade 4 Answer Key Homework Practice FL Chapter 4 Divide by 1-Digit Numbers img-5

Question 12.
76 ÷ 5 = ______ R ______

Answer: 15R1
Go Math Grade 4 Answer Key Homework Practice FL Chapter 4 Divide by 1-Digit Numbers img-6

Question 13.
58 ÷ 4 = ______ R ______

Answer: 14R2
Go Math Grade 4 Answer Key Homework Practice FL Chapter 4 Divide by 1-Digit Numbers img-7

Question 14.
85 ÷ 2 = ______ R ______

Answer: 42R1
Go Math Grade 4 Answer Key Homework Practice FL Chapter 4 Divide by 1-Digit Numbers img-8

Lessons 4.10–4.11

Divide and check.

Question 15.
4)\(\overline { 896 } \)
______

Answer: 224

Explanation:
224
× 4
896

Question 16.
5)\(\overline { 833 } \)
______ R ______

Answer: 166r3

Explanation:
166
× 5
830
+ 3
833

Question 17.
6)\(\overline { 527 } \)
______ R ______

Answer: 87r5

Explanation:
87
×6
522
+ 5
527

Question 18.
3)\(\overline { 935 } \)
______ R ______

Answer: 311r2

Explanation:
311
× 3
933
+ 2
935

Question 19.
3)\(\overline { 1,976 } \)
______ R ______

Answer: 658R2

Explanation:
658
× 3
1974
+    2
1976

Question 20.
6)\(\overline { 1,042 } \)
______ R ______

Answer: 173r4

Explanation:
173
×   6
1038
+   4
1042

Lesson 4.12

Solve. Draw a diagram to help you.

Question 21.
Ellis has 2 dozen white baseballs and 4 dozen yellow baseballs. He needs to divide them into cartons that hold 6 each. How many cartons can he fill?
______ cartons

Answer: 6 cartons

Explanation:
Given,
Ellis has 2 dozen white baseballs and 4 dozen yellow baseballs.
He needs to divide them into cartons that hold 6 each.
6 2 Dozens and 4 Dozens are 12+24 = 36/6 = 6
Therefore he can fill 6 cartons.

Question 22.
A family of 2 adults and 3 children went out to dinner. The total bill was $42. Each child’s dinner cost $4. How much did each adult’s dinner cost?
$ ______

Answer: $15

Explanation:
Each child’s dinner – $4
3 child’s dinner – $4 x 3 = $12
$42 – 12 = $30
$30 divided by 2 = $15
Thus each adult’s dinner cost is $15.

Conclusion:

Find more questions for practice from here, Go Math Grade 4 Answer Key Chapter 4 Divide by 1-Digit Numbers and develop your mathematical skills. Drop your queries and feedback by posting the comment below and we’ll update if anything requires as well as we’ll answer your doubts Asap.

Go Math Grade 4 Answer Key Homework FL Chapter 5 Factors, Multiples, and Patterns Review/Test

go-math-grade-4-chapter-5-factors-multiples-and-patterns-review-test-answer-key

Go Math Grade 4 Answer Key Homework FL Chapter 5 Factors, Multiples, and Patterns Review/Test includes all the topics of chapter 5. In Practice Test, Chapter Test, Cumulative Practice, etc., we have compiled detailed Solutions for all the Questions. So, check out the 4th Grade Go math Answer Key Homework FL Chapter 5 Factors, Multiples, and Patterns Review/Test & cross-check your knowledge & math skills.

Go Math Grade 4 Answer Key Homework FL Chapter 5 Factors, Multiples, and Patterns Review/Test

Improve your subject Skills with the help of Go Math Grade 4 Answer Key Homework FL Review/Test and score better grades in your exams. Also, you can take help from the 4th Grade Go Math Ch 5 Review/Test Solution Key for effective preparation and better practice sessions. Moreover, it let students know where they went wrong and clear their doubts. Hence, this guide is so helpful for 4th standard students to score high in exams.

Chapter 5: Review/Test

Review/Test – Page No. 219

Choose the best term from the box.
Go Math Grade 4 Answer Key Homework FL Chapter 5 Factors, Multiples, and Patterns Review Test img 1

Question 1.
The product of two numbers is a _______________ of both numbers.

Answer:
The product of two numbers is a multiple of both numbers.

Question 2.
A _______________ has exactly two factors.

Answer:
A prime has exactly two factors.

Question 3.
A number is always a multiple of its ____________ .

Answer:
A number is always a multiple of its multiple.

List all the factor pairs in the table.

Question 4.
Go Math Grade 4 Answer Key Homework FL Chapter 5 Factors, Multiples, and Patterns Review Test img 2

Answer:
Factors of 48 are 1,2,3,4,6.

Explanation:
1×48= 48    1,48.
2×24= 48    2,24.
3×16= 48     3,16.
4×12= 48     4,12.
6×8= 48       6,8

Question 5.
Go Math Grade 4 Answer Key Homework FL Chapter 5 Factors, Multiples, and Patterns Review Test img 3

Answer:
Factors of 81 are 1,3,9.

Explanation:
1×81= 81     1,81
3×27= 81     3,27
9×9= 81       9,9

Is the number a multiple of 9? Write yes or no.

Question 6.
3 _____

Answer: No

Explanation:
The number 3 is a factor of 9 but not a multiple of 9.

Question 7.
39 _____

Answer: No

Explanation:
The number 39 is not a multiple of 39.

Question 8.
45 _____

Answer: Yes

Explanation:
9×5= 45, so the number 45 is a multiple of 9.

Question 9.
93 _____

Answer: No.

Explanation:
The number 93 is not a multiple of 9.

Tell whether the number is prime or composite.

Question 10.
65 _________

Answer: Composite number.

Explanation:
As the number 65 factors are 1,5,13,65. So the number 65 is a composite number as it has more than two factors.

Question 11.
37 _________

Answer: Prime number.

Explanation:
The number 37 has only two factors 1 and 37, so the number is a prime number.

Question 12.
77 _________

Answer: Composite number.

Explanation:
The factors of 77 are 1,7,11 and 77, so the number 77 is a composite number.

Use the rule to write the first twelve terms in the pattern.
Describe another pattern in the numbers.

Question 13.
Rule: Add 10, subtract 5.

Answer:
1,6,11,16,21,26,31,36,41,46,51,56.

Explanation:
1
(1+10)-5= 11-5= 6
(6+10)-5= 16-5= 11
(11+10)-5= 21-5= 16
(16+10)-5= 26-5= 21
(21+10)-5= 31-5= 26
(26+10)-5= 36-5= 31
(31+10)-5= 41-5= 36
(36+10)-5= 46-5= 41
(41+10)-5= 51-5= 46
(46+10)-5= 56-5= 51
(51+10)-5= 61-5= 56.

Review/Test – Page No. 220

Question 14.
Erica knits 18 squares on Monday. She knits 7 more squares each day for the rest of the week. How many squares does Erica have on Friday?
Options:
a. 36
b. 46
c. 54
d. 90

Answer: b

Explanation:
As Erica knits 18 squares on Monday and she knits 7 more squares each day for the rest of the week, so on Friday Erica have 18+7+7+7+7= 46.

Question 15.
James works in a flower shop. He will put 36 tulips in vases for a wedding. He must use the same number of tulips in each vase. How many tulips could be in each vase?
Options:
a. 1, 2, 8
b. 2, 4, 8
c. 2, 4, 9
d. 6, 12, 16

Answer: c

Explanation:
As James put 36 tulips in vases for a wedding and he must use the same number of tulips in each vase, so we must find the factors of 36 to find how many tulips could be in each vase. So the factors of 36 are 1,2,3,4,6,9,12,18,36. So
2 tulips in 18 vases each
4 tulips in 9 vases each
9 tulips in 4 vases each.

Question 16.
What multiple of 7 is a factor of 7?
Options:
a. 0
b. 1
c. 7
d. 14

Answer: c

Explanation:
The number 7 is multiple and a factor of 7.

Question 17.
Hot dogs come in packages of 6. Hot dog buns come in packages of 8. Antonio will buy the same number of hot dogs as hot dog buns. How many hot dogs could he buy?
Options:
a. 6
b. 8
c. 18
d. 24

Answer: 24.

Explanation:
As hot dogs come in packages of 6, and hot dog buns come in packages of 8. So to find how many hot dogs could Antonio bought we must find the multiples of 6 and 8. So multiples of 6 and 8 are
Multiples of 6 are 6, 12, 18, 24, 30
Multiples of 8 are 8, 16, 24, 32, 40.
So Antonio bought 24 hot dogs.

Question 18.
Sean has 54 flower bulbs. He planted all the bulbs in rows. Each row has the same number of bulbs. How many bulbs could be in each row?
Options:
a. 6
b. 8
c. 12
d. 26

Answer: a

Explanation:
As Sean has 54 flower bulbs and planted all the bulbs in rows and each row has the same number of bulbs, so we will find the factors of 54. And the factors of 54 are 1,2,3,6,9,18,27, and 54. So Sean will plant 6 bulbs in each row.

Review/Test – Page No. 221

Question 19.
An ice-cream truck visits Julio’s street every 3 days and Lara’s street every 4 days. The truck visits both streets on April 12. When will the truck visit both streets next?
Options:
a. April 15
b. April 16
c. April 19
d. April 24

Answer: d

Explanation:
As an ice-cream truck visits Julio’s street every 3 days and Lara’s street every 4 days, and the truck visits both streets on April 12, so the next visit will be on April 24. By finding the multiples of 3 and 4 we will get the answer.
Multiples of 3 are 3,6,9,12,15,18,21,24
Multiples of 6 are 6,12,18,24.

Question 20.
The factors of a number include 2, 3, 4, 6, 8, 12, 16, 32, and 48. Which could be the number?
Options:
a. 32
b. 64
c. 96
d. 98

Answer: 96

Explanation:
As the number 96 is divisible by all the given numbers.

Question 21.
Ms. Booth has 16 red buttons and 24 blue buttons. She is making finger puppets. Each puppet has the same number of blue buttons and red buttons. How many puppets can she make if she uses all of the buttons?
Options:
a. 1, 2, 4, or 8
b. 1, 2, 4, 8, or 16
c. 1, 2, 4, 8, or 24
d. 1, 2, 4, 8, 16, or 24

Answer: a

Explanation:
As Ms. Booth has 16 red buttons and 24 blue buttons and she is making finger puppets and each puppet has the same number of blue buttons and red buttons, so to find how many puppets can she make if she uses all of the buttons we will find the factors of 16 and 24
so the factors of 16 are 1,2,4,8,16
Factors of 24 are 1,2,3,4,6,8,12,24.
So the common factors in both 16 and 24 are 1,2,4,8,16.

Review/Test – Page No. 222

Question 22.
I am a number between 60 and 100. My ones digit is two less than my tens digit. I am a prime number. What number am I?
Explain.
_____

Answer: 97.

Explanation:
Let’s name the digit:
X be one’s digit and y be tens digit
we know that X=Y-2. Now, Y can be 6,7,8,9 the number is between 60 and 100
As the possibilities with x=y-2, the numbers would be 64,75,86,97.
And 64 and 86 are even, so they can’t be prime. 75 is a composite number as there are more than two factors. So the remaining number is 97.

Question 23.
The number of pieces on display at an art museum is shown in the table.
Go Math Grade 4 Answer Key Homework FL Chapter 5 Factors, Multiples, and Patterns Review Test img 4
A. The museum’s show for July features 30 oil paintings by different artists. All artists show the same number of paintings and each artist shows more than 1 painting. How many artists could be featured in the show?

Answer:
15 artists with 2 paintings per artist.
10 artists with 3 paintings per artist.
6 artists with 5 paintings per artist.
5 artists with 6 paintings per artist.
3 artists with 10 paintings per artist.
2 artists with 15 paintings per artist.

Explanation:
As the museum’s show for July features 30 oil paintings by different artists and all artists show the same number of paintings and each artist shows more than 1 painting, so the number of artists are
15 artists with 2 paintings per artist.
10 artists with 3 paintings per artist.
6 artists with 5 paintings per artist.
5 artists with 6 paintings per artist.
3 artists with 10 paintings per artist.
2 artists with 15 paintings per artist.

Question 23.
B. The museum wants to display all the art pieces in rows. Each row has the same number of pieces and the same type of pieces. How many pieces could be in each row?

Answer: 3

Explanation:
Given that 30 oil paintings, 24 photographs, and 21 sketches that a museum wants a display. The arrangement of all these art pieces must be in rows such that each row has the same number and same type of art piece displayed. And the greatest common factor of 30,24,21 is 3. So 3 pieces could be in each row.

Question 23.
C. The museum alternates between adding 3 new pieces one month and retiring one piece the following month. If the museum starts with 75 pieces and the pattern continues, write the numbers in the pattern for the next 8 months. Describe other patterns in the numbers.

Answer: 78, 77, 80, 79, 82, 81, 84, 83.

Explanation:
As the museum alternates between adding 3 new pieces one month and retiring one piece the following month and if the museum starts with 75 pieces and the pattern continues, so the numbers are 78, 77, 80, 79, 82, 81, 84, 83. Here the pattern is every other number differs by 2 and the numbers alternate between even and odd.

Conclusion:

Students are recommended to use this Go Math Grade 4 Answer Key Homework FL Chapter 5 Factors, Multiples, and Patterns Review/Test and identify their lag areas and cover them properly. If you have any doubts leave a comment below and we will sort it out very soon. Also, visit our site for more questions to practice from Go Math Grade 4 Answer Key Homework practice FL Chapter 5 and enhance your problem-solving skills.

Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers

go-math-grade-4-chapter-8-multiply-fractions-by-whole-numbers-answer-key

Download Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers pdf for free of cost. Check out the 4th Grade HMH Go Math chapter 8 questions during your preparation and know the topics clearly. Solving the Chapter Test, Practice Test covered questions will help students to score more marks in the exams. Also, they can match the answers with the help of the Go Math Grade 4 Answer Key Chapter 8. Grade 4 Go Math Answer Key Chapter 8 Multiply Fractions by Whole Numbers provided Step by Step Solutions helps you to master the concepts and become a pro in the subject.

Go Math Grade 4 Chapter 8 Multiply Fractions by Whole Numbers Answer Key

The topics of Chapter 8 Multiply Fractions by Whole Numbers having different kinds of methods to solve the questions in no time. Concepts and their step-wise answers are provided in our HMH Go Math Grade 4 Ch 8 Answer Key. So, 4th Grade ch 8 will be easy to solve for those students who practice the sums from Go Math Grade 4 Solutions Key Ch 8 Multiply Fractions by Whole Number.

Lesson 1: Multiples of Unit Fractions

Lesson 2: Multiples of Fractions

Mid-Chapter Checkpoint

Lesson 3: Multiply a Fraction by a Whole Number Using Models

Lesson 4: Multiply a Fraction or Mixed Number by a Whole Number

Lesson 5: Problem Solving • Comparison Problems with Fractions

Review/Test

Common Core – New – Page No. 459

Multiples of Unit Fractions

Write the fraction as a product of a whole number and a unit fraction.

Question 1.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers Common Core - New img 1

Answer:
5 x 1/6

Explanation:
Given that 5/6 or 5 sixth-size parts.
Each sixth-size part of the given fraction can be shown by the unit fraction 1/6.
You can use unit fractions to show 5/6
5/6 = 5 x 1/6.

Question 2.
\(\frac{7}{8}\) =
Type below:
__________

Answer:
7 x 1/8

Explanation:
Given that 7/8 or 7 eighth-size parts.
Each eighth-size part of the given fraction can be shown by the unit fraction 1/8.
You can use unit fractions to show 7/8
7/8 = 7 x 1/8.

Question 3.
\(\frac{5}{3}\) =
Type below:
__________

Answer:
5 x 1/3

Explanation:
Given that 5/3 or 5 third-size parts.
Each third-size part of the given fraction can be shown by the unit fraction 1/3.
You can use unit fractions to show 5/6
5/3 = 5 x 1/3.

Question 4.
\(\frac{9}{10}\) =
Type below:
__________

Answer:
9 x 1/10

Explanation:
Given that 9/10 or 9 tenth-size parts.
Each tenth-size part of the given fraction can be shown by the unit fraction 1/10.
You can use unit fractions to show 9/10
9/10 = 9 x 1/10.

Question 5.
\(\frac{3}{4}\) =
Type below:
__________

Answer:
3 x 1/4

Explanation:
Given that 3/4 or 3 fourth-size parts.
Each fourth-size part of the given fraction can be shown by the unit fraction 1/4.
You can use unit fractions to show 5/6
3/4 = 3 x 1/4.

Question 6.
\(\frac{11}{12}\) =
Type below:
__________

Answer:
11 x 1/12

Explanation:
Given that 11/12 or 11 twelve-size parts.
Each twelve-size part of the given fraction can be shown by the unit fraction 1/12.
You can use unit fractions to show 5/6
11/12 = 11 x 1/12.

Question 7.
\(\frac{4}{6}\) =
Type below:
__________

Answer:
4 x 1/6

Explanation:
Given that 4/6 or 4 sixth-size parts.
Each sixth-size part of the given fraction can be shown by the unit fraction 1/6.
You can use unit fractions to show 4/6
4/6 = 4 x 1/6.

Question 8.
\(\frac{8}{20}\) =
Type below:
__________

Answer:
8 x 1/20

Explanation:
Given that 8/20 or 8 twenty-size parts.
Each twenty-size part of the given fraction can be shown by the unit fraction 1/20.
You can use unit fractions to show 8/20
8/20 = 8 x 1/20.

Question 9.
\(\frac{13}{100}\) =
Type below:
__________

Answer:
13 x 1/100

Explanation:
Given that 13/100 or 13 hundred-size parts.
Each hundred-size part of the given fraction can be shown by the unit fraction 1/100.
You can use unit fractions to show 13/100
13/100 = 13 x 1/100.

List the next four multiples of the unit fraction.

Question 10.
\(\frac{1}{5}\) ,
Type below:
__________

Answer:
2/5, 3/5, 4/5, 5/5

Explanation:
Grade 4 Chapter 8 Multiply Fractions Image 2
2/5, 3/5, 4/5, 5/5

Question 11.
\(\frac{1}{8}\) ,
Type below:
__________

Answer:
2/8, 3/8, 4/8, 5/8

Explanation:
Grade 4 Chapter 8 Multiply Fractions Image 3
2/8, 3/8, 4/8, 5/8

Problem Solving

Question 12.
So far, Monica has read \(\frac{5}{6}\) of a book. She has read the same number of pages each day for 5 days. What fraction of the book does Monica read each day?
\(\frac{□}{□}\) of the book

Answer:
1/6 of the book

Explanation:
Monica has read 5/6 of a book. She has read the same number of pages each day for 5 days.
For 1 day, she read one page. In total, she read 5 pages in 5 days. So, Monica read 1/6 of a book each day.

Question 13.
Nicholas buys \(\frac{3}{8}\) pound of cheese. He puts the same amount of cheese on 3 sandwiches. How much cheese does Nicholas put on each sandwich?
\(\frac{□}{□}\) pound of cheese

Answer:
1/8 pound of cheese

Explanation:
Nicholas buys 3/8 pound of cheese. He bought 3 sandwiches. Then, he applied 3/8 pound of cheese on 3 sandwiches. So, 3 x 1/8 cheese he put on 3 sandwiches. So, for one sandwich he put 1/8 pound of cheese.

Common Core – New – Page No. 460

Lesson Check

Question 1.
Selena walks from home to school each morning and back home each afternoon. Altogether, she walks \(\frac{2}{3}\) mile each day. How far does Selena live from school?
Options:
a. \(\frac{1}{3}\) mile
b. \(\frac{2}{3}\) mile
c. 1 \(\frac{1}{3}\) mile
d. 2 miles

Answer:
a. \(\frac{1}{3}\) mile

Explanation:
Selena walks from home to school each morning and back home each afternoon. Altogether, she walks 2/3 miles each day. The distance between home and school will remain the same. So, 2/3 x 1/2 = 1/3 mile far Selena live from the school.

Question 2.
Will uses \(\frac{3}{4}\) cup of olive oil to make 3 batches of salad dressing. How much oil does Will use for one batch of salad dressing?
Options:
a. \(\frac{1}{4}\) cup
b. \(\frac{1}{3}\) cup
c. 2 \(\frac{1}{3}\) cups
d. 3 cups

Answer:
1/8 pound of cheesa. \(\frac{1}{4}\) cup

Explanation:
Will uses 34 cups of olive oil to make 3 batches of salad dressing. To know the one batch of salad dressing, we need to take one part of salad dressing = 1/3. So, 3/4 x 1/3 = 1/4 cup of olive oil will use for one batch of salad dressing.

Spiral Review

Question 3.
Liza bought \(\frac{5}{8}\) pound of trail mix. She gives \(\frac{2}{8}\) pound of trail mix to Michael. How much trail mix does Liza have left?
Options:
a. \(\frac{1}{8}\) pound
b. \(\frac{2}{8}\) pound
c. \(\frac{3}{8}\) pound
d. \(\frac{4}{8}\) pound

Answer:
c. \(\frac{3}{8}\) pound

Explanation:
Liza bought 58 pound of trail mix. She gives 28 pound of trail mix to Michael.
So, Liza have left 5/8 – 2/8 = 3/8 trail mix.

Question 4.
Leigh has a piece of rope that is 6 \(\frac{2}{3}\) feet long. How do you write 6 \(\frac{2}{3}\) as a fraction greater than 1?
Options:
a. \(\frac{11}{3}\)
b. \(\frac{15}{3}\)
c. \(\frac{20}{3}\)
d. \(\frac{62}{3}\)

Answer:
c. \(\frac{20}{3}\)

Explanation:
Multiply the denominator with the whole number. i.e Multiply 3 with 6 in the given example, 6 (2/3).
3 x 6 =18.
Add 18 + 2 =20.
Keep the Denominator the same i.e. 3.
The obtained fraction is 20/3.

Question 5.
Randy’s house number is a composite number. Which of the following could be Randy’s house number?
Options:
a. 29
b. 39
c. 59
d. 79

Answer:
b. 39

Explanation:
The composite numbers can be defined as the whole numbers that have more than two factors. Whole numbers that are not prime are composite numbers because they are divisible by more than two numbers. 39 is the composite number. 39 is divide by 13 and 3.

Question 6.
Mindy buys 12 cupcakes. Nine of the cupcakes have chocolate frosting and the rest have vanilla frosting. What fraction of the cupcakes have vanilla frosting?
Options:
a. \(\frac{1}{4}\)
b. \(\frac{1}{3}\)
c. \(\frac{2}{3}\)
d. \(\frac{3}{4}\)

Answer:
a. \(\frac{1}{4}\)

Explanation:
Mindy buys 12 cupcakes.
Nine of the cupcakes have chocolate frosting = 9/12.
The rest have vanilla frosting. So, there are 3 cups remained = 3/12 = 1/4.
1/4 cupcakes have vanilla frosting.

Page No. 463

Question 1.
Write three multiples of \(\frac{3}{8}\).
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 2
1 × \(\frac{3}{8}\) = \(\frac{■}{8}\)
2 × \(\frac{3}{8}\) = \(\frac{■}{8}\)
3 × \(\frac{3}{8}\) = \(\frac{■}{8}\)
Multiples of \(\frac{3}{8}\) are ____ , ____ , and ____ .
Type below:
__________

Answer:
3/8, 6/8, 9/8, 12/8.

Explanation:
1 x 3/8 = 3/8.
2 x 3/8 = 6/8.
3 x 3/8 = 9/8.
4 x 3/8 = 12/8.
Multiples of 3/8 are 3/8, 6/8, 9/8, 12/8.

List the next four multiples of the fraction.

Question 2.
\(\frac{3}{6}\) ,
Type below:
__________

Answer:
6/6, 9/6, 12/6, 20/6

Explanation:
1 x 3/6 = 3/6.
2 x 3/6 = 6/6.
3 x 3/6 = 9/6.
4 x 3/6 = 12/6.
5 x 4/6 = 20/6.
Next four multiples of 3/6 are 6/6, 9/6, 12/6, 20/6.

Question 3.
\(\frac{2}{10}\) ,
Type below:
__________

Answer:
4/10, 6/10, 8/10, 10/10

Explanation:
1 x 2/10 = 2/10.
2 x 2/10 = 4/10.
3 x 2/10 = 6/10.
4 x 2/10 = 8/10.
5 x 2/10 = 10/10.
The next four multiples of 2/10 are 4/10, 6/10, 8/10, 10/10.

Write the product as the product of a whole number and a unit fraction.

Question 4.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 3
3 × \(\frac{3}{4}\) =
Type below:
__________

Answer:
9/4 = 9 x 1/4

Explanation:
1 group of 3/4 = 3/4
2 groups of 3/4 = 6/4
3 groups of 3/4 = 9/4
3 x 3/4 = 9/4.

Question 5.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 4
2 × \(\frac{4}{6}\) =
Type below:
__________

Answer:
8/6 = 8 x 1/6

Explanation:
1 group of 4/6 = 4/6
2 groups of 4/6 = 8/6
2 x 4/6 = 8/6 = 8 x 1/6.

List the next four multiples of the fraction.

Question 6.
\(\frac{4}{5}\) ,
Type below:
__________

Answer:
8/5, 12/5, 16/5, 20/5

Explanation:
1 x 4/5 = 4/5.
2 x 4/5 = 8/5.
3 x 4/5 = 12/5.
4 x 4/5 = 16/5.
5 x 4/5 = 20/5.
The next four multiples of 4/5 are 8/5, 12/5, 16/5, 20/5.

Question 7.
\(\frac{2}{4}\) ,
Type below:
__________

Answer:
4/4, 6/4, 8/4, 10/4

Explanation:
1 x 2/4 = 2/4.
2 x 2/4 = 4/4.
3 x 2/4 = 6/4.
4 x 2/4 = 8/4.
5 x 2/4 = 10/4.
The next four multiples of 2/4 are 4/4, 6/4, 8/4, 10/4.

Write the product as the product of a whole number and a unit fraction.

Question 8.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 5
4 × \(\frac{2}{8}\) =
Type below:
__________

Answer:
8/8 = 8 x 1/8

Explanation:
1 group of 2/8 = 2/8
2 groups of 2/8 = 4/8
3 groups of 2/8 = 6/8
4 groups of 2/8 = 8/8
4 x 2/8 = 8/8 = 8 x 1/8.

Question 9.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 6
3 × \(\frac{3}{5}\) =
Type below:
__________

Answer:
9/5 = 9 x 1/5

Explanation:
1 group of 3/5 = 3/5
2 groups of 3/5 = 6/5
3 groups of 3/5 = 9/5
3 x 3/5 = 9/5 = 9 x 1/5.

Question 10.
Use Repeated Reasoning Are \(\frac{6}{10}\) and \(\frac{6}{30}\) multiples of \(\frac{3}{10}\)?
Explain.
Type below:
__________

Answer:
3/30

Explanation:
Use Repeated Reasoning Are 6/10 and 6/30 multiples of 3/10 and 3/30.

Question 11.
Which is greater, 4 × \(\frac{2}{7}\) or 3 × \(\frac{3}{7}\)? Explain.
4 × \(\frac{2}{7}\) _____ 3 × \(\frac{3}{7}\)

Answer:
4 × \(\frac{2}{7}\) __<___ 3 × \(\frac{3}{7}\)

Explanation:
8/7 < 9/7
So, 4 x 2/7 < 3 x 3/7

Page No. 464

Question 12.
Josh is watering his plants. He gives each of 2 plants \(\frac{3}{5}\) pint of water. His watering can holds \(\frac{1}{5}\) pint. How many times will he fill his watering can to water both plants?
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 7
a. What do you need to find?
Type below:
__________

Answer:
We need to find how many times Josh needs to fill his watering can to water both plants.

Question 12.
b. What information do you need to use?
Type below:
__________

Answer:
Use the Number of plants = 2.
He gives each plant a 3/5 pint of water.
His watering can hold 1/5 pint.

Question 12.
c. How can drawing a model help you solve the problem?
Type below:
__________

Answer:
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 6

Question 12.
d. Show the steps you use to solve the problem.
Type below:
__________

Answer:
If Josh gives each plant 3/5 pint, then that’s a total of 6/5 pint.
6/5 = 6 x 1/5.

Question 12.
e. Complete the sentence. Josh will fill his watering can ____ times.
____ times

Answer:
Josh will fill his watering can 6 times.

Question 13.
Alma is making 3 batches of tortillas. She adds \(\frac{3}{4}\) cup of water to each batch. The measuring cup holds \(\frac{1}{4}\) cup. How many times must Alma measure \(\frac{1}{4}\) cup of water to have enough for the tortillas? Shade the model to show your answer.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 8
Alma must measure \(\frac{1}{4}\) cup ______ times.
____ times

Answer:
12 times

Explanation:
Alma is making 3 batches of tortillas. She adds a 3/4 cup of water to each batch. The measuring cup holds 1/4 cup.
Alma must measure 1/4 cup 12 times.

Common Core – New – Page No. 465

Multiples of Fractions

List the next four multiples of the fraction.

Question 1.
\(\frac{3}{5}\) ,
Type below:
__________

Answer:
6/5, 9/5, 12/5, 20/5

Explanation:
1 x 3/5 = 3/5.
2 x 3/5 = 6/5.
3 x 3/5 = 9/5.
4 x 3/5 = 12/5.
5 x 4/5 = 20/5.
The next four multiples of 3/5 are 6/5, 9/5, 12/5, 20/5.

Question 2.
\(\frac{2}{6}\) ,
Type below:
__________

Answer:
4/6, 6/6, 8/6, 10/6

Explanation:
1 x 2/6 = 2/6.
2 x 2/6 = 4/6.
3 x 2/6 = 6/6.
4 x 2/6 = 8/6.
5 x 2/6 = 10/6.
The next four multiples of 2/6 are 4/6, 6/6, 8/6, 10/6.

Question 3.
\(\frac{4}{8}\) ,
Type below:
__________

Answer:
8/8, 12/8, 16/8, 20/8

Explanation:
1 x 4/8 = 4/8.
2 x 4/8 = 8/8.
3 x 4/8 = 12/8.
4 x 4/8 = 16/8.
5 x 4/8 = 20/8.
The next four multiples of 4/8 are 8/8, 12/8, 16/8, 20/8.

Question 4.
\(\frac{5}{10}\) ,
Type below:
__________

Answer:
10/10, 15/10, 20/10, 25/10

Explanation:
1 x 5/10 = 5/10.
2 x 5/10 = 10/10.
3 x 5/10 = 15/10.
4 x 5/10 = 20/10.
5 x 5/10 = 25/10.
The next four multiples of 5/10 are 10/10, 15/10, 20/10, 25/10.

Write the product as the product of a whole number and a unit fraction.

Question 5.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers Common Core - New img 9
2 × \(\frac{4}{5}\) =
Type below:
__________

Answer:
8/5 = 8 x 1/5

Explanation:
1 group of 4/5 = 4/5
2 groups of 4/5 = 8/5
2 x 4/5 = 8/5 = 8 x 1/5.

Question 6.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers Common Core - New img 10
5 × \(\frac{2}{3}\) =
Type below:
__________

Answer:
10/3 = 10 x 1/3

Explanation:
1 group of 2/3 = 2/3
2 group of 2/3 = 4/3
3 group of 2/3 = 6/3
4 group of 2/3 = 8/3
5 group of 2/3 = 10/3
5 x 2/3 = 10/3 = 10 x 1/3.

Problem Solving

Question 7.
Jessica is making 2 loaves of banana bread. She needs \(\frac{3}{4}\) cup of sugar for each loaf. Her measuring cup can only hold \(\frac{1}{4}\) cup of sugar. How many times will Jessica need to fill the measuring cup in order to get enough sugar for both loaves of bread?
_____ times

Answer:
6 times

Explanation:
Jessica is making 2 loaves of banana bread. She needs a 3/4 cup of sugar for each loaf.
For 2 loaves, she needs 2 x 3/4 = 6/4 cups of sugar.
Her measuring cup can only hold 1/4 cup of sugar. So, to get the 3/4 cup of sugar, she needs to fill the cup 3 times. 1/4 + 1/4 + 1/4 = 3/4.
So, to fill 2 loaves, she needs to fill cup 3 x 2 = 6 times.

Question 8.
A group of four students is performing an experiment with salt. Each student must add \(\frac{3}{8}\) teaspoon of salt to a solution. The group only has a \(\frac{1}{8}\) teaspoon measuring spoon. How many times will the group need to fill the measuring spoon in order to perform the experiment?
_____ times

Answer:
12 times

Explanation:
A group of four students is performing an experiment with salt. Each student must add a 3/8 teaspoon of salt to a solution. 4 x 3/8 = 12/8 teaspoon of salt required to finish the experiment.
If they have 1/8 teaspoon measuring spoon, 12 x 1/8.
So, the group needs to fill the measuring spoon 12 times in order to perform the experiment.

Common Core – New – Page No. 466

Lesson Check

Question 1.
Eloise made a list of some multiples of \(\frac{5}{8}\). Which of the following lists could be Eloise’s list?
Options:
a. \(\frac{5}{8}, \frac{10}{16}, \frac{15}{24}, \frac{20}{32}, \frac{25}{40}\)
b. \(\frac{5}{8}, \frac{10}{8}, \frac{15}{8}, \frac{20}{8}, \frac{25}{8}\)
c. \(\frac{5}{8}, \frac{6}{8}, \frac{7}{8}, \frac{8}{8}, \frac{9}{8}\)
d. \(\frac{1}{8}, \frac{2}{8}, \frac{3}{8}, \frac{4}{8}, \frac{5}{8}\)

Answer:
b. \(\frac{5}{8}, \frac{10}{8}, \frac{15}{8}, \frac{20}{8}, \frac{25}{8}\)

Explanation:
1 x 5/8 = 5/8.
2 x 5/8 = 10/8.
3 x 5/8 = 15/8.
4 x 5/8 = 20/8.
5 x 5/8 = 25/8.
The next four multiples of 5/8 are 10/8, 15/8, 20/8, 25/8.

Question 2.
David is filling five \(\frac{3}{4}\) quart bottles with a sports drink. His measuring cup only holds \(\frac{1}{4}\) quart. How many times will David need to fill the measuring cup in order to fill the 5 bottles?
Options:
a. 5
b. 10
c. 15
d. 20

Answer:
c. 15

Explanation:
David is filling five 3/4 quart bottles with a sports drink = 5 x 3/4 = 15/4.
His measuring cup only holds 1/4 quart.
So, 15 x 1/4. David needs to fill the measuring cup 15 times in order to fill the 5 bottles.

Spiral Review

Question 3.
Ira has 128 stamps in his stamp album. He has the same number of stamps on each of the 8 pages. How many stamps are on each page?
Options:
a. 12
b. 14
c. 16
d. 18

Answer:
c. 16

Explanation:
Ira has 128 stamps in his stamp album. He has the same number of stamps on each of the 8 pages.
128/8 = 16 stamps on each page.

Question 4.
Ryan is saving up for a bike that costs $198. So far, he has saved $15 per week for the last 12 weeks. How much more money does Ryan need in order to be able to buy the bike?
Options:
a. $ 8
b. $ 18
c. $ 48
d. $ 180

Answer:
b. $ 18

Explanation:
Ryan is saving up for a bike that costs $198.
So far, he has saved $15 per week for the last 12 weeks = $15 x 12 = $180.
$198 – $180 = $18 need in order to buy the bike.

Question 5.
Tina buys 3 \(\frac{7}{8}\) yards of material at the fabric store. She uses it to make a skirt. Afterward, she has 1 \(\frac{3}{8}\) yards of the fabric leftover. How many yards of material did Tina use?
Options:
a. 1 \(\frac{4}{8}\)
b. 2 \(\frac{1}{8}\)
c. 2 \(\frac{4}{8}\)
d. 5 \(\frac{2}{8}\)

Answer:
c. 2 \(\frac{4}{8}\)

Explanation:
Tina buys 3 7/8 yards of material at the fabric store. She uses it to make a skirt. Afterward, she has 1 3/8 yards of the fabric leftover.
3 -1 = 2; 7/8 – 3/8 = 4/8. So, answer is 2 4/8.

Question 6.
Which list shows the fractions in order from least to greatest?
Options:
a. \(\frac{2}{3}, \frac{3}{4}, \frac{7}{12}\)
b. \(\frac{7}{12}, \frac{3}{4}, \frac{2}{3}\)
c. \(\frac{3}{4}, \frac{2}{3}, \frac{7}{12}\)
d. \(\frac{7}{12}, \frac{2}{3}, \frac{3}{4}\)

Answer:
d. \(\frac{7}{12}, \frac{2}{3}, \frac{3}{4}\)

Explanation:
2/3 = 0.666
3/4 = 0.75
7/12 = 0.5833
7/12, 2/3, 3/4

Page No. 467

Choose the best term from the box.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 11

Question 1.
A __________ of a number is the product of the number and a counting number.
__________

Answer:
Multiple

Question 2.
A _________ always has a numerator of 1.
_________

Answer:
Unit Fraction

List the next four multiples of the unit fraction.

Question 3.
\(\frac{1}{2}\) ,
Type below:
_________

Answer:
2/2, 3/2, 4/2, 5/2

Explanation:
1 x 1/2 = 1/2.
2 x 1/2 = 2/2.
3 x 1/2 = 3/2.
4 x 1/2 = 4/2.
5 x 1/2 = 5/2.
The next four multiples of 1/2 are 2/2, 3/2, 4/2, 5/2.

Question 4.
\(\frac{1}{5}\) ,
Type below:
_________

Answer:
2/5, 3/5, 4/5, 5/5

Explanation:
1 x 1/5 = 1/5.
2 x 1/5 = 2/5.
3 x 1/5 = 3/5.
4 x 1/5 = 4/5.
5 x 1/5 = 5/5.
The next four multiples of 1/5 are 2/5, 3/5, 4/5, 5/5.

Write the fraction as a product of a whole number and a unit fraction.

Question 5.
\(\frac{4}{10}\) = _____ × \(\frac{1}{10}\)

Answer:
4

Explanation:
4/10 = 4 x 1/10

Question 6.
\(\frac{8}{12}\) = _____ × \(\frac{1}{12}\)

Answer:
8

Explanation:
8/12 = 8 x 1/12

Question 7.
\(\frac{3}{4}\) = _____ × \(\frac{1}{4}\)

Answer:
3

Explanation:
3/4 = 3 x 1/4

List the next four multiples of the fraction.

Question 8.
\(\frac{2}{5}\) ,
Type below:
_________

Answer:
4/5, 6/5, 8/5, 10/5

Explanation:
1 x 2/5 = 1/5.
2 x 2/5 = 4/5.
3 x 2/5 = 6/5.
4 x 2/5 = 8/5.
5 x 2/5 = 10/5.
The next four multiples of 1/5 are 4/5, 6/5, 8/5, 10/5.

Question 9.
\(\frac{5}{6}\) ,
Type below:
_________

Answer:
10/6, 15/6, 20/6, 25/6

Explanation:
1 x 5/6 = 5/6.
2 x 5/6 = 10/6.
3 x 5/6 = 15/6.
4 x 5/6 = 20/6.
5 x 5/6 = 25/6.
The next four multiples of 5/6 are 10/6, 15/6, 20/6, 25/6.

Write the product as the product of a whole number and a unit fraction.

Question 10.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 12
4 × \(\frac{2}{6}\) =
Type below:
_________

Answer:
8/6 = 8 x 1/6

Explanation:
1 group of 2/6 = 2/6
2 groups of 2/6 = 4/6
3 groups of 2/6 = 6/6
4 groups of 2/6 = 8/6
4 x 2/6 = 8/6 = 8 x 1/6.

Question 11.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 13
3 × \(\frac{3}{8}\) =
Type below:
_________

Answer:
9/8 = 9 x 1/8

Explanation:
1 group of 3/8 = 3/8
2 groups of 3/8 = 6/8
3 groups of 3/8 = 9/8
3 x 3/8 = 9/8 = 9 x 1/8.

Page No. 468

Question 12.
Pedro cut a sheet of poster board into 10 equal parts. His brother used some of the poster board and now \(\frac{8}{10}\) is left. Pedro wants to make a sign from each remaining part of the poster board. How many signs can he make?
______ signs

Answer:
8 signs

Explanation:
Pedro cut a sheet of poster board into 10 equal parts.
His brother uses some of the poster board and now an 8/10 is left.
So, the remaining part of the b\poster board is 8/10 parts.
Pedro can use 8/ 10 parts of the board to make signs.
So, he can make 8 signs.

Question 13.
Ella is making 3 batches of banana milkshakes. She needs \(\frac{3}{4}\) gallon of milk for each batch. Her measuring cup holds \(\frac{1}{4}\) gallon. How many times will she need to fill the measuring cup to make all 3 batches of milkshakes?
______ times

Answer:
9 times

Explanation:
Ella is making 3 batches of banana milkshakes. She needs 3/4 gallon of milk for each batch. So, she needs 3 x 3/4 = 9/4 cups for 3 batches of banana milkshakes. Her measuring cup holds 1/4 gallon.
9/4 = 9 x 1/4.
So, Ella needs to fill the measuring cup 9 times to make all 3 batches of milkshakes.

Question 14.
Darren cut a lemon pie into 8 equal slices. His friends ate some of the pie and now \(\frac{5}{8}\) is left. Darren wants to put each slice of the leftover pie on its own plate. What part of the pie will he put on each plate?
\(\frac{□}{□}\) of the pie on each plate.

Answer:
5/8 of the pie on each plate

Explanation:
Darren cut a lemon pie into 8 equal slices. His friends ate some of the pie and now 5/8 is left. So, 5 pie slices leftover.
Darren can put 5/8 parts of the pie on each plate.

Question 15.
Beth is putting liquid fertilizer on the plants in 4 flowerpots. Her measuring spoon holds \(\frac{1}{8}\) teaspoon. The directions say to put \(\frac{5}{8}\) teaspoon of fertilizer in each pot. How many times will Beth need to fill the measuring spoon to fertilize the plants in the 4 pots?
______ times

Answer:
20 times

Explanation:
Beth is putting liquid fertilizer on the plants in 4 flowerpots. Her measuring spoon holds 1/8 teaspoon.
The directions say to put 5/8 teaspoon of fertilizer in each pot. So, 4 x 5/8 = 20/8.
20/8 = 20 x 1/8. Beth needs to fill the measuring spoon 20 times to fertilize the plants in the 4 pots.

Page No. 471

Question 1.
Find the product of 3 × \(\frac{5}{8}\).
1 group of \(\frac{5}{8}\) = \(\frac{□}{8}\)
2 groups of \(\frac{5}{8}\) = \(\frac{□}{8}\)
3 groups of \(\frac{5}{8}\) = \(\frac{□}{8}\)
3 × \(\frac{5}{8}\) = \(\frac{□}{□}\)

Answer:
15/8

Explanation:
1 group of 5/8 = 2/8
2 groups of 5/8 = 4/8
3 groups of 5/8 = 6/8
3 x 5/8 = 15/8.

Multiply.

Question 2.
2 × \(\frac{4}{5}\) = \(\frac{□}{□}\)

Answer:
8/5

Explanation:
1 group of 4/5 = 4/5
2 groups of 4/5 = 8/5
2 x 4/5 = 8/5.

Question 3.
4 × \(\frac{2}{3}\) = \(\frac{□}{□}\)

Answer:
8/3

Explanation:
1 group of 2/3 = 2/3
2 groups of 2/3 = 4/3
3 groups of 2/3 = 6/3
4 groups of 2/3 = 8/3
4 x 2/3 = 8/3

Question 4.
5 × \(\frac{3}{10}\) = \(\frac{□}{□}\)

Answer:
15/10

Explanation:
1 group of 3/10 = 3/10
2 groups of 3/10 = 6/10
3 groups of 3/10 = 9/10
4 groups of 3/10 = 12/10
5 groups of 3/10 = 15/10
5 x 3/10 = 15/10

Question 5.
4 × \(\frac{5}{6}\) = \(\frac{□}{□}\)

Answer:
20/6

Explanation:
1 group of 5/6 = 5/6
2 groups of 5/6 = 10/6
3 groups of 5/6 = 15/6
4 groups of 5/6 = 20/6
4 x 5/6 = 20/6

Multiply.

Question 6.
2 × \(\frac{7}{12}\) = \(\frac{□}{□}\)

Answer:
7/6

Explanation:
1 group of 7/12 = 7/12
2 groups of 7/12 = 14/12
2 x 7/12 = 14/12 = 7/6

Question 7.
6 × \(\frac{3}{8}\) = \(\frac{□}{□}\)

Answer:
9/4

Explanation:
1 group of 3/8 = 3/8
2 groups of 3/8 = 6/8
3 groups of 3/8 = 9/8
4 groups of 3/8 = 12/8
5 groups of 3/8 = 15/8
6 groups of 3/8 = 18/8
6 x 3/8 = 18/8 = 9/4

Question 8.
5 × \(\frac{2}{4}\) = \(\frac{□}{□}\)

Answer:
5/2

Explanation:
1 group of 2/4 = 2/4
2 groups of 2/4 = 4/4
3 groups of 2/4 = 6/4
4 groups of 2/4 = 8/4
5 groups of 2/4 = 10/4
5 x 2/4 = 10/4 = 5/2

Question 9.
3 × \(\frac{4}{6}\) = \(\frac{□}{□}\)

Answer:
2

Explanation:
1 group of 4/6 = 4/6
2 groups of 4/6 = 8/6
3 groups of 4/6 = 12/6
3 x 4/6 = 12/6 = 2

Question 10.
2 × \(\frac{5}{10}\) = \(\frac{□}{□}\)

Answer:
2

Explanation:
1 group of 5/10 = 5/10
2 groups of 5/10 = 10/10
2 x 10/10 = 2 x 1 = 2

Question 11.
4 × \(\frac{2}{8}\) = \(\frac{□}{□}\)

Answer:
1

Explanation:
1 group of 2/8 = 2/8
2 groups of 2/8 = 4/8
3 groups of 2/8 = 6/8
4 groups of 2/8 = 8/8
4 x 2/8 = 8/8 = 1

Look for a Pattern Algebra Write the unknown number.

Question 12.
□ × \(\frac{2}{3}\) = \(\frac{12}{3}\)
□ = ____

Answer:
6

Explanation:
Let the unknown number is s.
s x 2/3 = 12/3
s = 12/3 x 3/2 = 6.

Question 13.
5 × \(\frac{□}{4}\) = \(\frac{10}{4}\)
□ = ____

Answer:
2

Explanation:
Let the unknown number is s.
5 x s/4 = 10/4
5/4 x s = 10/4
s = 10/4 x 4/5 =2.

Question 14.
2 × \(\frac{7}{□}\) = \(\frac{14}{8}\)
□ = ____

Answer:
8

Explanation:
Let the unknown number is s.
2 x 7/s = 14/8
14/s = 14/8
s x 14/8 = 14
s = 14 x 8/14
s = 8.

Page No. 472

Question 15.
Lisa makes clothes for pets. She needs \(\frac{5}{6}\) yard of fabric to make 1 dog coat. How much fabric does she need to make 3 dog coats?
a. What do you need to find?
Type below:
_________

Answer:
The number of fabric yards required for 3 dog coats

Question 15.
b. What information do you need?
Type below:
_________

Answer:
How much she needs of fabric for 1 dog coat can helps to find for 3 dog coats.

Question 15.
c. Show the steps you use to solve the problem.
Type below:
_________

Answer:
Lisa makes clothes for pets. She needs a 5/6 yard of fabric to make 1 dog coat.
For 3 dogs = 5/6 x 3 =5/2

Question 15.
d. Complete the sentence.
Lisa needs _____ yards of fabric to make 3 dog coats.
\(\frac{□}{□}\)

Answer:
Lisa needs a 5/2 yard of fabric to make 3 dog coats.

Question 16.
Manuel’s small dog eats \(\frac{2}{4}\) bag of dog food in 1 month. His large dog eats \(\frac{3}{4}\) bag of dog food in 1 month. How many bags do both dogs eat in 6 months?
\(\frac{□}{□}\) bags

Answer:
2 bags

Explanation:
Manuel’s small dog eats a 2/4 bag of dog food in 1 month. His large dog eats a 3/4 bag of dog food in 1 month.
In total 2/4 + 3/4 = 5/4 bag of dog food eat in 1 month.
So, for 6 months = 6 x 5/4 = 30/4 = 15/2.
So, 2 bags need for 6 months.

Question 17.
Select the correct product for the equation.
9 × \(\frac{2}{12}\) = □
3 × \(\frac{6}{7}\) = □
6 × \(\frac{4}{7}\) = □
8 × \(\frac{3}{12}\) = □
Type below:
_________

Answer:
8 × \(\frac{3}{12}\) = 2

Explanation:
9 × \(\frac{2}{12}\) = 3/2
3 × \(\frac{6}{7}\) = 18/7
6 × \(\frac{4}{7}\) = 24/7
8 × \(\frac{3}{12}\) = 2

Common Core – New – Page No. 473

Multiply a Fraction by a Whole Number Using Models

Multiply.

Question 1.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers Common Core - New img 14

Answer:
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers Common Core - New img 14

Question 2.
3 × \(\frac{2}{5}\) = \(\frac{□}{□}\)

Answer:
Grade 4 Chapter 8 Image 1 473
3 x 2/5 = 6/5

Question 3.
7 × \(\frac{3}{10}\) = \(\frac{□}{□}\)

Answer:
Grade 4 Chapter 8 Image 2 473
7 x 3/10 = 21/10

Question 4.
3 × \(\frac{5}{12}\) = \(\frac{□}{□}\)

Answer:
Grade 4 Chapter 8 Image 3 473
3 x 5/12 = 15/12

Question 5.
6 × \(\frac{3}{4}\) = \(\frac{□}{□}\)

Answer:
Grade 4 Chapter 8 Image 4 473
6 x 3/4 = 18/4

Question 6.
4 × \(\frac{2}{8}\) = \(\frac{□}{□}\)

Answer:
Grade 4 Chapter 8 Image 5 473
4 x 2/8 = 8/8

Question 7.
5 × \(\frac{2}{3}\) = \(\frac{□}{□}\)

Answer:
Grade 4 Chapter 8 Image 6 473
5 x 2/3 = 10/3

Question 8.
2 × \(\frac{7}{8}\) = \(\frac{□}{□}\)

Answer:
Grade 4 Chapter 8 Image 7 473
2 x 7/8 = 14/8

Question 9.
6 × \(\frac{4}{5}\) = \(\frac{□}{□}\)

Answer:
Grade 4 Chapter 8 Image 8 473
6 x 4/5 = 28/5

Problem Solving

Question 10.
Matthew walks \(\frac{5}{8}\) mile to the bus stop each morning. How far will he walk in 5 days?
\(\frac{□}{□}\)

Answer:
25/8 miles

Explanation:
Matthew walks 5/8 mile to the bus stop each morning.
In 5 days, 5 x 5/8 = 25/8 miles.

Question 11.
Emily uses \(\frac{2}{3}\) cup of milk to make one batch of muffins. How many cups of milk will Emily use if she makes 3 batches of muffins?
\(\frac{□}{□}\)

Answer:
6/3 cups of milk

Explanation:
Emily uses a 2/3 cup of milk to make one batch of muffins.
Emily use 3 x 2/3 = 6/3 cups of milk to make 3 batches of muffins

Common Core – New – Page No. 474

Lesson Check

Question 1.
Aleta’s puppy gained \(\frac{3}{8}\) pound each week for 4 weeks. Altogether, how much weight did the puppy gain during the 4 weeks?
Options:
a. \(\frac{8}{12}\) pound
b. 1 \(\frac{2}{8}\) pounds
c. \(\frac{12}{8}\) pounds
d. 4 \(\frac{3}{8}\) pounds

Answer:
6/3 cups of milk

Explanation:
Aleta’s puppy gained 3/8 pound each week.
It gained 4 x 3/8 = 12/8 pounds in 4 weeks.

Question 2.
Pedro mixes \(\frac{3}{4}\) teaspoon of plant food into each gallon of water. How many teaspoons of plant food should Pedro mix into 5 gallons of water?
Options:
a. \(\frac{3}{20}\) teaspoon
b. \(\frac{4}{15}\) teaspoon
c. \(\frac{8}{4}\) teaspoons
d. \(\frac{15}{4}\) teaspoons

Answer:
d. \(\frac{15}{4}\) teaspoons

Explanation:
If Pedro mixes 3/4 teaspoon of plant food into each gallon of water, then 5 x 3/4 = 15/4 teaspoon of plant food mix into 5 gallons of water.

Spiral Review

Question 3.
Ivana has \(\frac{3}{4}\) pound of hamburger meat. She makes 3 hamburger patties. Each patty weighs the same amount. How much does each hamburger patty weigh?
Options:
a. \(\frac{1}{4}\) pound
b. \(\frac{1}{3}\) pound
c. 2 \(\frac{1}{4}\) pounds
d. 3 pounds

Answer:
a. \(\frac{1}{4}\) pound

Explanation:
Ivana has 3/4 pound of hamburger meat. She makes 3 hamburger patties.
Each patty weighs the same amount. So, each hamburger patty weight 1/4 pound.

Question 4.
Which of the following expressions is NOT equal to \(\frac{7}{10}\)?
Options:
a. \(\frac{5}{10}+\frac{1}{10}+\frac{1}{10}\)
b. \(\frac{2}{10}+\frac{2}{10}+\frac{3}{10}\)
c. \(\frac{3}{10}+\frac{3}{10}+\frac{2}{10}\)
d. \(\frac{4}{10}+\frac{2}{10}+\frac{1}{10}\)

Answer:
c. \(\frac{3}{10}+\frac{3}{10}+\frac{2}{10}\)

Explanation:
a. \(\frac{5}{10}+\frac{1}{10}+\frac{1}{10}\) = 7/10
b. \(\frac{2}{10}+\frac{2}{10}+\frac{3}{10}\) = 7/10
c. \(\frac{3}{10}+\frac{3}{10}+\frac{2}{10}\) = 8/10
d. \(\frac{4}{10}+\frac{2}{10}+\frac{1}{10}\) = 7/10

Question 5.
Lance wants to find the total length of 3 boards. He uses the expression 3 \(\frac{1}{2}\) + (2 + 4 \(\frac{1}{2}\)). How can Lance rewrite the expression using both the Associative and Commutative Properties of Addition?
Options:
a. 5 + 4 \(\frac{1}{2}\)
b. (3 \(\frac{1}{2}\) + 2) + 4 \(\frac{1}{2}\)
c. 2 + (3 \(\frac{1}{2}\) + 4 \(\frac{1}{2}\))
d. 3 \(\frac{1}{2}\) + (4 \(\frac{1}{2}\) + 2)

Answer:
She can write as (3 \(\frac{1}{2}\) + 2) + 4 \(\frac{1}{2}\)

Question 6.
Which of the following statements is true?
Options:
a. \(\frac{5}{8}>\frac{9}{10}\)
b. \(\frac{5}{12}>\frac{1}{3}\)
c. \(\frac{3}{6}>\frac{4}{5}\)
d. \(\frac{1}{2}>\frac{3}{4}\)

Answer:
6/3 cups of milk

Explanation:
0.625 > 0.9
0.416 > 0.333
0.5 > 0.8
0.5 > 0.75

Page No. 477

Question 1.
2 × 3 \(\frac{2}{3}\) = □
_____ \(\frac{□}{□}\)

Answer:
7\(\frac{1}{3}\)

Explanation:
3 \(\frac{2}{3}\) = 11/3
2 x 11/3 = 22/3
22/3 = 7 and remainder 1. So, 22/3 = 7 (1/3)

Multiply. Write the product as a mixed number.

Question 2.
6 × \(\frac{2}{5}\) = _____ \(\frac{□}{□}\)

Answer:
2\(\frac{2}{5}\)

Explanation:
6 × \(\frac{2}{5}\) = 12/5. 12/5 = 2 and remainder . So, 12/5 = 2 2/5

Question 3.
3 × 2 \(\frac{3}{4}\) = _____ \(\frac{□}{□}\)

Answer:
8\(\frac{1}{4}\)

Explanation:
2 \(\frac{3}{4}\) = 11/4
3 x 11/4 = 33/4. 33/4 = 8 and remainder 1. So, 33/4 = 8 1/4

Question 4.
4 × 1 \(\frac{5}{6}\) = _____ \(\frac{□}{□}\)

Answer:
7 \(\frac{2}{6}\)

Explanation:
1 \(\frac{5}{6}\) = 11/6
4 x 11/6 = 44/6. 44/6 = 7 and remainder 2. So, 44/6 = 7 2/6

Question 5.
4 × \(\frac{5}{8}\) = _____ \(\frac{□}{□}\)

Answer:
2\(\frac{1}{2}\)

Explanation:
4 × \(\frac{5}{8}\) = 5/2. 5/2 = 2 and remainder 1. So, 5/2 = 2 1/2

Question 6.
6 × \(\frac{5}{12}\) = _____ \(\frac{□}{□}\)

Answer:
2\(\frac{1}{2}\)

Explanation:
6 × \(\frac{5}{12}\) = 5/2. 5/2 = 2 and remainder 1. So, 5/2 = 2 1/2

Question 7.
3 × 3 \(\frac{1}{2}\) = _____ \(\frac{□}{□}\)

Answer:
10 \(\frac{1}{2}\)

Explanation:
3 \(\frac{1}{2}\) = 7/2
3 x 7/2 = 21/2. 21/2 = 10 and remainder 1. So, 21/2 = 10 1/2

Question 8.
2 × 2 \(\frac{2}{3}\) = _____ \(\frac{□}{□}\)

Answer:
5\(\frac{1}{3}\)

Explanation:
2 \(\frac{2}{3}\) = 8/3
2 x 8/3 = 16/3. 16/3 = 5 and remainder 1. So, 16/3 = 5 1/3

Question 9.
5 × 1 \(\frac{2}{4}\) = _____ \(\frac{□}{□}\)

Answer:
7 \(\frac{1}{2}\)

Explanation:
1 \(\frac{2}{4}\) = 6/4
5 x 6/4 = 30/4 = 15/2. 15/2 = 7 and remainder 1. So, 15/2 = 7 1/2

Question 10.
4 × 2 \(\frac{2}{5}\) = _____ \(\frac{□}{□}\)

Answer:
9\(\frac{3}{5}\)

Explanation:
2 \(\frac{2}{5}\) = 12/5
4 x 12/5 = 48/5. 48/5 = 9 and remainder 3. So, 48/5 = 9 3/5

Look for a Pattern Algebra Write the unknown number.

Question 11.
□ × 2 \(\frac{1}{3}\) = 9 \(\frac{1}{3}\)
□ = ______

Answer:
4

Explanation:
2 \(\frac{1}{3}\) = 7/3
9 \(\frac{1}{3}\) = 28/3
Let the unknown numer s.
s x 7/3 = 28/3
s = 4

Question 12.
3 × 2 \(\frac{2}{□}\) = 7 \(\frac{2}{4}\)
□ = ______

Answer:
4

Explanation:
7 \(\frac{2}{4}\) = 30/4
Let the unknown number s. If s is 4, 3 × 2 \(\frac{2}{4}\) = 3 x 10/4 = 30/4.
So, the unknown number is 4.

Question 13.
3 × □ \(\frac{3}{8}\) = 4 \(\frac{1}{8}\)
□ = ______

Answer:
1

Explanation:
4 \(\frac{1}{8}\) = 33/8
Let the unknown number is s. If s is 1, 3 × 1 \(\frac{3}{8}\) = 3 x 11/8 = 33/8.

Question 14.
Describe two different ways to write \(\frac{7}{3}\) as a mixed number.
Type below:
_________

Answer:
One is 2\(\frac{1}{3}\)
Another one is 2 + 1/3

Explanation:
7/3 = 2 and the remainder is 1. So, 2 1/3 is one mixed fraction.
Seond method is 3/3 + 3/3 + 1/3 = 2 + 1/3.

Page No. 478

Use the recipe for 15–18.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 15

Question 15.
Otis plans to make 3 batches of sidewalk chalk. How much plaster of Paris does he need?
______ \(\frac{□}{□}\) cups plaster of Paris

Answer:
4\(\frac{1}{2}\) cups plaster of Paris

Explanation:
1\(\frac{1}{2}\) = 3/2 + 3/2 + 3/2 = 9/2
9/2 = 4, the remainder is 1. So, 4 1/2 cups plaster of Paris need for 3 batches of sidewalk chalk.

Question 16.
What’s the Question? The answer is \(\frac{32}{3}\).
Type below:
_________

Answer:
How many tablespoons of powdered paint are needed for 4 batches of chalk?

Question 17.
Patty has 2 cups of warm water. Is that enough water to make 4 batches of sidewalk chalk? Explain how you know without finding the exact product.
______

Answer:
No. 4 x 1/2 = 2 and also 3/4 is greater than 1/2. So, 4 x 3/4 is greater than 2.

Question 18.
Rita makes sidewalk chalk 2 days a week. Each of those days, she spends 1 \(\frac{1}{4}\) hours making the chalk. How much time does Rita spend making sidewalk chalk in 3 weeks?
______ \(\frac{□}{□}\) hours

Answer:
7\(\frac{1}{2}\) hours

Explanation:
Rita makes sidewalk chalk 2 days a week. Each of those days, she spends 1 1/4 hours making the chalk.
1 week = 2 x 5/4 = 10/4 = 5/2.
3 weeks = 3 x 5/2 = 15/2 = 7 1/2.

Question 19.
Oliver has music lessons Monday, Wednesday, and Friday. Each lesson is \(\frac{3}{4}\) of an hour. Oliver says he will have lessons for 3 \(\frac{1}{2}\) hours this week. Without multiplying, explain how you know Oliver is incorrect.
Type below:
__________

Answer:
3/4 is less than 1, and 1 × 3 = 3. So 3/4 × 3 will also be less than 3.
Oliver’s answer, 3 1/2 is greater than 3, so it is incorrect.

Common Core – New – Page No. 479

Multiply a Fraction or Mixed Number by a Whole Number.

Multiply. Write the product as a mixed number.

Question 1.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers Common Core - New img 16

Answer:
1\(\frac{5}{10}\)

Explanation:
5 x 3/10 = 15/10 = 1 and remainder is 5. So, the mixed fraction is 1 5/10

Question 2.
3 × \(\frac{3}{5}\) =
______ \(\frac{□}{□}\)

Answer:
1\(\frac{4}{5}\)

Explanation:
3 x 3/5 = 9/5 = 1 and remainder is 4. So, the mixed fraction is 1 4/5

Question 3.
5 × \(\frac{3}{4}\) =
______ \(\frac{□}{□}\)

Answer:
3\(\frac{3}{4}\)

Explanation:
15/4 = 3 and remainder is 3. So, the mixed fraction is 3 3/4

Question 4.
4 × 1 \(\frac{1}{5}\) =
______ \(\frac{□}{□}\)

Answer:
4\(\frac{4}{5}\)

Explanation:
1 \(\frac{1}{5}\) = 6/5.
4 x 6/5 = 24/5 = 4 and the remainder is 4. So, the mixed fraction is 4 4/5

Question 5.
2 × 2 \(\frac{1}{3}\) =
______ \(\frac{□}{□}\)

Answer:
4\(\frac{2}{3}\)

Explanation:
2 \(\frac{1}{3}\) = 7/3.
2 x 7/3 = 14/3.
14/3 = 4 and the remainder is 2. So, the mixed fraction is 4 2/3

Question 6.
5 × 1 \(\frac{1}{6}\) =
______ \(\frac{□}{□}\)

Answer:
5\(\frac{5}{6}\)

Explanation:
1 \(\frac{1}{6}\) = 7/6
5 x 7/6 = 35/6.
35/6 = 5 and the remainder is 5. So, the mixed fraction is 5 5/6

Question 7.
2 × 2 \(\frac{7}{8}\) =
______ \(\frac{□}{□}\)

Answer:
6\(\frac{1}{1}\)

Explanation:
2 \(\frac{7}{8}\) = 23/8
2 x 23/8 = 46/8 = 6 1/1

Question 8.
7 × 1 \(\frac{3}{4}\) =
______ \(\frac{□}{□}\)

Answer:
9\(\frac{3}{4}\)

Explanation:
1 \(\frac{3}{4}\) = 7/4
7 x 7/4 = 39/4
39/4 = 9 and the remainder is 3. So, the mixed fraction is 9 3/4

Question 9.
8 × 1 \(\frac{3}{5}\) =
______ \(\frac{□}{□}\)

Answer:
12\(\frac{4}{5}\)

Explanation:
1 \(\frac{3}{5}\) = 8/5
8 x 8/5 = 64/5
64/5 = 12 and the remainder is 4. So, the mixed fraction is 12 4/5

Problem Solving

Question 10.
Brielle exercises for \(\frac{3}{4}\) hour each day for 6 days in a row. Altogether, how many hours does she exercise during the 6 days?
______ \(\frac{□}{□}\)

Answer:
4\(\frac{2}{4}\)

Explanation:
6 x 3/4 = 18/4 = 4 and the remainder is 2. So, the mixed fraction is 4 2/4.

Question 11.
A recipe for quinoa calls for 2 \(\frac{2}{3}\) cups of milk. Conner wants to make 4 batches of quinoa. How much milk does he need?
______ \(\frac{□}{□}\)

Answer:
10\(\frac{2}{3}\)

Explanation:
quinoa calls for 8/3 cups of milk. Conner wants to make 4 batches of quinoa.
So, 4 x 8/3 = 32/3 = 10 and the remainder is 2. So, the mixed fraction is 10 2/3

Common Core – New – Page No. 480

Lesson Check

Question 1.
A mother is 1 \(\frac{3}{4}\) times as tall as her son. Her son is 3 feet tall. How tall is the mother?
Options:
a. 4 \(\frac{3}{4}\) feet
b. 5 \(\frac{1}{4}\) feet
c. 5 \(\frac{1}{2}\) feet
d. 5 \(\frac{3}{4}\) feet

Answer:
b. 5 \(\frac{1}{4}\) feet

Explanation:
A mother is 1 3/4 times as tall as her son. Her son is 3 feet tall.
So, 3 x 7/4 = 21/4 = 5 and the remainder is 1. The mixed fraction is 5 1/4 feet.

Question 2.
The cheerleaders are making a banner that is 8 feet wide. The length of the banner is 1 \(\frac{1}{3}\) times the width of the banner. How long is the banner?
Options:
a. 8 \(\frac{1}{3}\) feet
b. 8 \(\frac{3}{8}\) feet
c. 10 \(\frac{1}{3}\) feet
d. 10 \(\frac{2}{3}\) feet

Answer:
d. 10 \(\frac{2}{3}\) feet

Explanation:
The cheerleaders are making a banner that is 8 feet wide. he length of the banner is 1 1/3 times the width of the banner.
So, 8 x 4/3 = 32/3 =10 and the remainder is 2. The mixed fraction is 10 2/3 feet.

Spiral Review

Question 3.
Karleigh walks \(\frac{5}{8}\) mile to school every day. How far does she walk to school in 5 days?
Options:
a. \(\frac{5}{40}\) mile
b. \(\frac{25}{40}\) mile
c. \(\frac{10}{8}\) miles
d. \(\frac{25}{8}\) miles

Answer:
d. \(\frac{25}{8}\) miles

Explanation:
5 x 5/8 = 25/8.

Question 4.
Which number is a multiple of \(\frac{4}{5}\)?
Options:
a. \(\frac{8}{10}\)
b. \(\frac{12}{15}\)
c. \(\frac{16}{20}\)
d. \(\frac{12}{5}\)

Answer:
d. \(\frac{12}{5}\)

Explanation:
The multiple of \(\frac{4}{5}\) has the denominator 5. So, \(\frac{12}{5}\) is the correct answer.

Question 5.
Jo cut a key lime pie into 8 equal-size slices. The next day, \(\frac{7}{8}\) of the pie is left. Jo puts each slice on its own plate. How many plates does she need?
Options:
a. 5
b. 6
c. 7
d. 8

Answer:
c. 7

Explanation:
Jo cut a key lime pie into 8 equal-size slices. The next day, \(\frac{7}{8}\) of the pie is left. Jo puts each slice on its own plate. She needs 7 plates.

Question 6.
Over the weekend, Ed spent 1 \(\frac{1}{4}\) hours doing his math homework and 1 \(\frac{3}{4}\) hours doing his science project. Altogether, how much time did Ed spend doing homework over the weekend?
Options:
a. 3 hours
b. 2 \(\frac{3}{4}\) hours
c. 2 \(\frac{1}{2}\) hours
d. 2 hours

Answer:
a. 3 hours

Explanation:
5/4 + 7/4 = 12/4 = 3 hours

Page No. 483

Question 1.
Komodo dragons are the heaviest lizards on Earth. A baby Komodo dragon is 1 \(\frac{1}{4}\) feet long when it hatches. Its mother is 6 times as long. How long is the mother?
First, draw a bar model to show the problem.
Type below:
_________

Answer:
Grade 4 Chapter 8 Image 1 483

Question 1.
Then, write the equation you need to solve.
Type below:
_________

Answer:
A baby Komodo dragon is 5/4 feet.
Her mother is 6 x 5/4 = 30/4 feet long.

Question 1.
Finally, find the length of the mother Komodo dragon.
The mother Komodo dragon is _____ feet long.
______ \(\frac{□}{□}\)

Answer:
7\(\frac{2}{4}\)

Explanation:
30/4 = 7 and the remainder is 2. The mixed fraction is 7 2/4 feet.

Question 2.
What if a male Komodo dragon is 7 times as long as the baby Komodo dragon? How long is the male? How much longer is the male than the mother?
______ \(\frac{□}{□}\) feet long
______ \(\frac{□}{□}\) feet longer

Answer:
35/4 feet long
5/4 feet longer

Explanation:
If a male Komodo dragon is 7 times as long as the baby Komodo dragon, then 7 x 5/4 = 35/4.
35/4 – 30/4 = 5/4 feet male Komodo dragon is grater than female Komodo dragon.

Question 3.
The smallest hummingbird is the Bee hummingbird. It has a mass of about 1 \(\frac{1}{2}\) grams. A Rufous hummingbird’s mass is 3 times the mass of the Bee hummingbird. What is the mass of a Rufous hummingbird?
______ \(\frac{□}{□}\) grams

Answer:
9/2 grams

Explanation:

The smallest hummingbird is the Bee hummingbird. It has a mass of about 1 \(\frac{1}{2}\) grams. A Rufous hummingbird’s mass is 3 times the mass of the Bee hummingbird.
3 x 3/2 = 9/2 grams.

Question 4.
Sloane needs \(\frac{3}{4}\) hour to drive to her grandmother’s house. It takes her 5 times as long to drive to her cousin’s house. How long does it take to drive to her cousin’s house?
______ \(\frac{□}{□}\) hours

Answer:
\(\frac{15}{4}\) hours

Explanation:
5 x 3/4 = 15/4
To drive to her cousin’s house, it takes 15/4 hours.

Page No. 484

Use the table for 5 and 6.

Payton has a variety of flowers in her garden. The table shows the average heights of the flowers.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 17

tulip = 5/4 = 1.25
daisy = 5/2 = 2.5
tiger lily = 10/3 = 3.33
sunflower = 31/4 = 7.75

Question 5.
Make Sense of Problems What is the difference between the height of the tallest flower and the height of the shortest flower in Payton’s garden?
______ \(\frac{□}{□}\) feet

Answer:
6\(\frac{2}{4}\) feet

Explanation:
tallest flower = sunflower
shortest flower = tulip
Difference between the tallest flower and shortest flower = 31/4 – 5/4 = 26/4 =6 and the remainder is 2. So, the mixed fraction is 6 2/4 feet.

Question 6.
Payton says her average sunflower is 7 times the height of her average tulip. Do you agree or disagree with her statement? Explain your reasoning.
Type below:
_________

Answer:
I will disagree with her statement. Tulip = 5/4. 7 x 5/4 = 35/4. 31/4 is smaller than 35/4. Som the statement is not correct.

Question 7.
Miguel ran 1 \(\frac{3}{10}\) miles on Monday. On Friday, Miguel ran 3 times as far as he did on Monday. How much farther did Miguel run on Friday than he did on Monday?
______ \(\frac{□}{□}\) miles

Answer:
3\(\frac{9}{10}\) miles

Explanation:
Miguel ran 13/10 miles on Monday.
On Friday, 3 x 13/10 = 39/10 miles = 3 and the remainder is 9. the mixed fraction is 3 9/10 miles

Question 8.
The table shows the lengths of different types of turtles at a zoo.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 18
For numbers 8a–8d, select True or False for each statement.
a. Daisy is 4 times as long as Tuck.
i. True
ii. False

Answer:
ii. False

Explanation:
Tuck = 7/6
Lolly = 35/6
Daisy = 7/2
7/6 x 4 = 28/6.
So, the statement is false.

Question 8.
b. Lolly is 5 times as long as Tuck.
i. True
ii. False

Answer:
i. True

Explanation:
5 x 7/6 = 35/6.
So, the statement is true.

Question 8.
c. Daisy is 3 times as long as Tuck.
i. True
ii. False

Answer:
i. True

Explanation:
3 x 7/6 = 21/6 = 7/2
So, the statement is true.

Question 8.
d. Lolly is 2 times as long as Daisy.
i. True
ii. False

Answer:
ii. False

Explanation:
2 x 7/2 = 7.
So, the statement is false.

Common Core – New – Page No. 485

Problem Solving Comparison

Problems with Fractions

Read each problem and solve.

Question 1.
A shrub is 1 \(\frac{2}{3}\) feet tall. A small tree is 3 times as tall as the shrub. How tall is the tree?
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers Common Core - New img 19

Answer:
5 feet

Explanation:
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers Common Core - New img 19

Question 2.
You run 1 \(\frac{3}{4}\) miles each day. Your friend runs 4 times as far as you do. How far does your friend run each day?
__________ miles

Answer:
7 miles

Explanation:
4 x 7/4 = 7 miles each day

Question 3.
At the grocery store, Ayla buys 1 \(\frac{1}{3}\) pounds of ground turkey. Tasha buys 2 times as much ground turkey as Ayla. How much ground turkey does Tasha buy?
______ \(\frac{□}{□}\) pounds

Answer:
2\(\frac{2}{3}\) pounds

Explanation:
2 x 4/3 = 8/3 = 2 and the remainder is 2. The mixed fraction is 2 2/3 pounds

Question 4.
When Nathan’s mother drives him to school, it takes \(\frac{1}{5}\) hour. When Nathan walks to school, it takes him 4 times as long to get to school. How long does it take Nathan to walk to school?
\(\frac{□}{□}\) hours

Answer:
\(\frac{4}{5}\) hours

Explanation:
4 x 1/5 = 4/5 hour

Common Core – New – Page No. 486

Lesson Check

Question 1.
A Wilson’s Storm Petrel is a small bird with a wingspan of 1 \(\frac{1}{3}\) feet. A California Condor is a larger bird with a wingspan almost 7 times as wide as the wingspan of the petrel. About how wide is the wingspan of the California Condor?
Options:
a. \(\frac{4}{21}\) foot
b. 2 \(\frac{1}{3}\) feet
c. 7 \(\frac{1}{3}\) feet
d. 9 \(\frac{1}{3}\) feet

Answer:
d. 9 \(\frac{1}{3}\) feet

Explanation:
1 1/3 = 4/3.
7 x 4/3 = 28/3 feet = 9 and the remainder is 1. The mixed fraction is 9 1/3

Question 2.
The walking distance from the Empire State Building in New York City to Times Square is about \(\frac{9}{10}\) mile. The walking distance from the Empire State Building to Sue’s hotel is about 8 times as far. About how far is Sue’s hotel from the Empire State Building?
Options:
a. \(\frac{9}{80}\) mile
b. \(\frac{72}{80}\) mile
c. 1 \(\frac{7}{10}\) miles
d. 7 \(\frac{2}{10}\) miles

Answer:
d. 7 \(\frac{2}{10}\) miles

Explanation:
8 x 9/10 mile = 72/10 mile = 7 and the remainder is 2. The mixed fraction is 7 2/10 miles.

Spiral Review

Question 3.
Which of the following expressions is NOT equal to 3 × 2 \(\frac{1}{4}\)?
Options:
a. 3 × \(\frac{9}{4}\)
b. (3 × 2) + (3 × \(\frac{1}{4}\))
c. 6 \(\frac{3}{4}\)
d. 3 × 2 + \(\frac{1}{4}\)

Answer:
d. 3 × 2 + \(\frac{1}{4}\)

Explanation:
3 × 2 \(\frac{1}{4}\) = 3 x 9/4 = 27/4
a. 3 × \(\frac{9}{4}\) = 27/4
b. (3 × 2) + (3 × \(\frac{1}{4}\)) = 6 + 3/4 = 27/4
c. 6 \(\frac{3}{4}\) = 27/4
d. 3 × 2 + \(\frac{1}{4}\) = 6 + 1/4 = 25/4

Question 4.
At a bake sale, Ron sells \(\frac{7}{8}\) of an apple pie and \(\frac{5}{8}\) of a cherry pie. Altogether, how much pie does he sell at the bake sale?
Options:
a. \(\frac{2}{8}\)
b. \(\frac{12}{16}\)
c. \(\frac{12}{8}\)
d. \(\frac{35}{8}\)

Answer:
c. \(\frac{12}{8}\)

Explanation:
7/8 + 5/8 = 12/8
The bake sale 12/8 pie.

Question 5.
On a ruler, which measurement is between \(\frac{3}{16}\) inch and \(\frac{7}{8}\) inch?
Options:
a. \(\frac{1}{16}\) inch
b. \(\frac{1}{8}\) inch
c. \(\frac{11}{16}\) inch
d. \(\frac{15}{16}\) inch

Answer:
c. \(\frac{11}{16}\) inch

Question 6.
Which of the following numbers is composite?
Options:
a. 4
b. 3
c. 2
d. 1

Answer:
a. 4

Explanation:
4 has more than 2 factors.

Page No. 487

Question 1.
What are the next four multiples of \(\frac{1}{8}\)?
Type below:
_________

Answer:
2/8, 3/8, 4/8, 5/8

Explanation:
1 x 1/8 = 1/8.
2 x 1/8 = 2/8.
3 x 1/8 = 3/8.
4 x 1/8 = 4/8.
5 x 1/8 = 5/8.
Next four multiples of 1/8 are 2/8, 3/8, 4/8, 5/8.

Question 2.
Marta is making 3 servings of fruit salad. She adds \(\frac{3}{8}\) cup blueberries for each serving. Her measuring cup holds \(\frac{1}{8}\) cup. How many times must Marta measure \(\frac{1}{8}\) cup of blueberries to have enough for the fruit salad? Shade the models to show your answer.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 20
Marta must measure \(\frac{1}{8}\) _________ cup times.
_________

Answer:
Grade 4 Chapter 8 Image 1 487

Marta must measure \(\frac{1}{8}\) 9 cup times.

Question 3.
Mickey exercises \(\frac{3}{4}\) hour every day. How many hours does he exercise in 8 days?
_____ hours

Answer:
6 hours

Explanation:
8 x 3/4 = 24/4 = 6

Page No. 488

Question 4.
Molly is baking for the Moms and Muffins event at her school. She will bake 4 batches of banana muffins. She needs 1 \(\frac{3}{4}\) cups of bananas for each batch of muffins.
Part A
Molly completed the multiplication below and said she needed 8 cups of bananas for 4 batches of muffins. What is Molly’s error?
\(4 \times 1 \frac{3}{4}=4 \times \frac{8}{4}=\times \frac{32}{4}=8\)
Type below:
_________

Answer:
4 x 1 3/4 = 4 x 8/4 = 8
Molly did not write the mixed number, 1 3/4 as a fraction correctly. 1 3/4 is not equal to 8/4.

Question 4.
Part B
What is the correct number of cups Molly needs for 4 batches of muffins? Explain how you found your answer.
_____ cups

Answer:
7 cups

Explanation:
She will bake 4 batches of banana muffins. She needs 7/4 cups of bananas for each batch of muffins.
So, if she prepares 4 batches of muffins = 4 x 7/4 = 7 cups of banana.

Question 5.
Which fraction is a multiple of \(\frac{1}{9}\)? Mark all that apply.
Options:
a. \(\frac{3}{9}\)
b. \(\frac{9}{12}\)
c. \(\frac{2}{9}\)
d. \(\frac{4}{9}\)
e. \(\frac{9}{10}\)
f. \(\frac{9}{9}\)

Answer:
a. \(\frac{3}{9}\)
c. \(\frac{2}{9}\)
d. \(\frac{4}{9}\)
f. \(\frac{9}{9}\)

Explanation:
The multiples of \(\frac{1}{9}\) have the denominator of 9.

Question 6.
Mimi recorded a soccer game that lasted 1 \(\frac{2}{3}\) hours. She watched it 3 times over the weekend to study the plays. How many hours did Mimi spend watching the soccer game? Show your work.
_____ hours

Answer:
5 hours

Explanation:
3 x 1 2/3 = 3 x 5/3 = 5 hours.

Question 7.
Theo is comparing shark lengths. He learned that a horn shark is 2 \(\frac{3}{4}\) feet long. A blue shark is 4 times as long. Complete the model. Then find the length of a blue shark.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 21
A blue shark is ____ feet long.
_____

Answer:
Grade 4 Chapter 8 Image 2 487
4 x 11/4 = 11.
A blue shark is 11 feet long.

Page No. 489

Question 8.
Joel made a number line showing the multiples of \(\frac{3}{5}\).
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 22
The product 2 × \(\frac{3}{5}\) is shown by the fraction _________ on the number line.
\(\frac{□}{□}\)

Answer:
The product 2 × \(\frac{3}{5}\) is shown by the fraction \(\frac{6}{5}\) on the number line.

Question 9.
Bobby has baseball practice Monday, Wednesday, and Friday. Each practice is 2 \(\frac{1}{2}\) hours. Bobby says he will have practice for 4 hours this week.
Part A
Without multiplying, explain how you know Bobby is incorrect.
Type below:
_________

Answer:
Bobby needs to find 3 × 2 1/2. If he estimates 3 × 2 hours, then he finds the practice is at least 6 hours. 6 is greater than 4, so Bobby’s answer is incorrect.

Question 9.
Part B
How long will Bobby have baseball practice this week? Write your answer as a mixed number. Show your work.
______ \(\frac{□}{□}\) hours

Answer:
7\(\frac{1}{2}\) hours

Explanation:
3 x 2 1/2 = 3 x 5/2 = 15/2 = 7 1/2

Question 10.
Look at the number line. Write the missing fractions.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 23
Type below:
_________

Answer:
9/6, 10/6, 11/6, 12/6

Question 11.
Ana’s dachshund weighed 5 \(\frac{5}{8}\) pounds when it was born. By age 4, the dog weighed 6 times as much. Fill each box with a number or symbol from the list to show how to find the weight of Ana’s dog at age 4. Not all numbers and symbols may be used.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 24
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 25
Type below:
_________

Answer:
Grade 4 Chapter 8 Image 1 489

Page No. 490

Question 12.
Asta made a fraction number line to help her find 3 × \(\frac{4}{5}\).
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 26
Select a way to write 3 × \(\frac{4}{5}\) as the product of a whole number and a unit fraction.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 27
Type below:
_________

Answer:
Grade 4 Chapter 8 Image 1 490
12 × \(\frac{1}{5}\)

Explanation:
3 x 4/5 = 12/5 = 12 x 1/5.

Question 13.
Yusif wanted to give \(\frac{1}{3}\) of his total toy car collection to 2 of his friends. How many of his toy cars will he give away?
\(\frac{□}{□}\)

Answer:
\(\frac{2}{3}\)

Explanation:
Yusif wanted to give \(\frac{1}{3}\) of his total toy car collection to 2 of his friends. He has three toy cars in total. He has given 2 cars out of 3 cars. So, the answer is \(\frac{2}{3}\).

Question 14.
Select the correct product for the equation.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 28
4 × \(\frac{5}{8}\) = □ 4 × \(\frac{4}{8}\) = □
Type below:
_________

Answer:
4 × \(\frac{5}{8}\) = \(\frac{20}{8}\)
4 × \(\frac{4}{8}\) = \(\frac{16}{8}\)

Page No. 491

Question 15.
The lengths of different types of snakes at a zoo are shown in the table.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 29
For numbers 15a–15d, select True or False for the statement.
a. Bobby is 4 times as long as Kenny.
i. True
ii. False

Answer:
ii. False

Explanation:
Kenny = 3/2
Bobby = 9/2
Puck = 15/2
4 x 3/2 =6
So, the statement is false.

Question 15.
b. Bobby is 3 times as long as Kenny.
i. True
ii. False

Answer:
i. True

Explanation:
3 x 3/2 = 9/2
So, the statement is true.

Question 15.
c. Puck is 5 times as long as Kenny.
i. True
ii. False

Answer:
i. True

Explanation:
5 x 3/2 = 15/2
So, the statement is true.

Question 15.
d. Puck is 2 times as long as Bobby.
i. True
ii. False

Answer:
ii. False

Explanation:
2 x 9/2 = 9
So, the statement is false.

Question 16.
Hank used 3 \(\frac{1}{2}\) bags of seed to plant grass in his front yard. He used 3 times as much seed to plant grass in his back yard. How much seed did Hank need for the backyard?
_____ \(\frac{□}{□}\)

Answer:
10\(\frac{1}{2}\)

Explanation:
3 x 7/2 = 21/2 = 10 and the remainder is 1. The answer is 10 1/2.

Question 17.
Jess made a big kettle of rice and beans. He used 1 \(\frac{1}{2}\) cups of beans. He used 4 times as much rice.
Part A
Draw a model to show the problem.
Type below:
_________

Answer:
Grade 4 Chapter 8 Image 1 491

Question 17.
Part B
Use your model to write an equation. Then solve the equation to find the amount of rice Jess needs.
Type below:
_________

Answer:
6 cups

Explanation:
Rice = 4 x 3/2 = 12/2 = 6.
Jess needs 6 cups of rice.

Page No. 492

Question 18.
Mrs. Burnham is making modeling clay for her class. She needs \(\frac{2}{3}\) cup of warm water for each batch.
Part A
Mrs. Burnham has a 1-cup measure that has no other markings. Can she make 6 batches of modeling clay using only the 1-cup measure? Describe two ways you can find the answer.
Type below:
_________

Answer:
Yes. She needs 6 x 2/3 cups of water. 6 x 2/3 = 12/3 = 4 cups.
So, she can use the 1-cup measure 4 times to make 6 batches.

Question 18.
Part B
The modeling clay recipe also calls for \(\frac{1}{2}\) cup of cornstarch. Nikki says Mrs. Burnham will also need 4 cups of cornstarch. Do you agree or disagree? Explain.
Type below:
_________

Answer:
Disagree; 6 x 1/2 = 3 cups of cornstrach.
She doesn’t need 4 cups of cornstarch.

Question 19.
Donna buys some fabric to make place mats. She needs \(\frac{1}{5}\) yard of each type of fabric. She has 9 different types of fabrics to make her design. Use the following equation. Write the number in the box to make the statement true.
\(\frac{9}{5}\) = ______ × \(\frac{1}{5}\)

Answer:
9

Question 20.
Mr. Tuyen uses \(\frac{5}{8}\) of a tank of gas each week to drive to and from his job. How many tanks of gas does Mr. Tuyen use in 5 weeks? Write your answer two different ways.
Mr. Tuyen uses __________ or _________ tanks of gas.
Type below:
_________

Answer:
Mr. Tuyen uses 25/8 or 3\(\frac{1}{8}\) tanks of gas

Explanation:
5 x 5/8 = 25/8 = 3 and the remainder is 1. So, the mixed fraction is 3 1/8.

Question 21.
Rico is making 4 batches of salsa. Each batch needs \(\frac{2}{3}\) cup of corn. He only has a \(\frac{1}{3}\)– cup measure. How many times must Rico measure \(\frac{1}{3}\) cup of corn to have enough for all of the salsa?
______ times

Answer:
8 times

Explanation:
Rico is making 4 batches of salsa. Each batch needs \(\frac{2}{3}\) cup of corn. He only has a \(\frac{1}{3}\)– cup measure.
So, he needs 2x 1/3 cups for one batch. For 4 batches of salsa, 4 x 2 = 8 cups of corn required.

Page No. 497

Question 1.
Write five tenths as a fraction and as a decimal.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 30
Fraction: __________ Decimal: __________
Type below:
_________

Answer:
Grade 4 Chapter 8 Image 1 497
5/10 = 0.5

Write the fraction or mixed number and the decimal shown by the model.

Question 2.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 31
Type below:
_________

Answer:
3\(\frac{2}{10}\)
three and two-tenths

Question 3.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 32
Type below:
_________

Answer:
\(\frac{8}{10}\)
Grade 4 Chapter 8 Image 2 497

Write the fraction or mixed number and the decimal shown by the model.

Question 4.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 33
Type below:
_________

Answer:
4/10 = 0.4

Explanation:
4 boxes are shaded out of 10 boxes. So, the fraction is 4/10.

Question 5.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 34
Type below:
_________

Answer:
1\(\frac{2}{10}\)

Question 6.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 35
Type below:
_________

Answer:
2\(\frac{9}{10}\)

Question 7.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 36
Type below:
_________
Answer:
3\(\frac{4}{10}\)

Practice: Copy and Solve Write the fraction or mixed number as a decimal.

Question 8.
5 \(\frac{9}{10}\) = _____

Answer:
\(\frac{59}{10}\)

Explanation:
Multiply 10 x 5 = 50.
Add 50 + 9 = 59.
The fraction is 59/10

Question 9.
\(\frac{1}{10}\) = _____

Answer:
0.1

Question 10.
\(\frac{7}{10}\) = _____

Answer:
0.7

Question 11.
8 \(\frac{9}{10}\) = _____

Answer:
\(\frac{89}{10}\)

Explanation:
Multiply 10 x 8 = 80.
Add 80 + 9 = 89.
The fraction is 89/10

Question 12.
\(\frac{6}{10}\) = _____

Answer:
0.6

Question 13.
6 \(\frac{3}{10}\) = _____

Answer:
\(\frac{63}{10}\)

Explanation:
Multiply 10 x 6 = 60.
Add 60 + 3 = 63.
The fraction is 63/10

Question 14.
\(\frac{5}{10}\) = _____

Answer:
0.5

Question 15.
9 \(\frac{7}{10}\) = _____

Answer:
\(\frac{97}{10}\)

Explanation:
Multiply 10 x 9 = 90.
Add 90 +7 = 97.
The fraction is 97/10

Page No. 498

Use the table for 16−19.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 37
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 38

Question 16.
What part of the rocks listed in the table are igneous? Write your answer as a decimal.
_____

Answer:
0.5

Question 17.
Sedimentary rocks make up what part of Ramon’s collection? Write your answer as a fraction and in word form.
Type below:
_________

Answer:
3/10 and three-tenths

Question 18.
What part of the rocks listed in the table are metamorphic? Write your answer as a fraction and as a decimal.
Type below:
_________

Answer:
2/10 or 0.2

Question 19.
Communicate Niki wrote the following sentence in her report: “Metamorphic rocks make up 2.0 of Ramon’s rock collection.” Describe her error.
Type below:
_________

Answer:
Metamorphic rocks make up 2.0 of Ramon’s rock collection. But from the given table, it is clearly mentioned that the answer is 0.2. So, she made a mistake to make up Ramon’s rock collection.

Question 20.
Josh paid for three books with two $20 bills. He received $1 in change. Each book was the same price. How much did each book cost?
$ _____ each book

Answer:
$19/3 for each book.

Explanation:
Josh paid for three books with two $20 bills. He received $1 in change. So, he paid $19 for three books. As the each book has same price, the answer is $19/3 for each book.

Question 21.
Select a number shown by the model. Mark all that apply.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 39
Type below:
_________

Answer:
1\(\frac{7}{10}\)
1.7

Conclusion:

We understand the knowledge shed regarding Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers PDF has benefited you more. If you have any queries you can examine your knowledge using the Grade 4 Chapter 8 Answer Key Homework Practice FL. Visit our site to ask for details about the Go Math Solution Key of different grades.

Go Math Grade 3 Answer Key Chapter 9 Compare Fractions Extra Practice

go-math-grade-3-chapter-9-compare-fractions-extra-practice-answer-key

Access the Answer Key for Go Math Grade 3 Chapter 9 Compare Fractions Extra Practice and use them as a quick reference. Get the Homework Help Go Math Grade 3 Answer Key Chapter 9 Compare Fractions Extra Practice and test your preparation standard. We provide the Step by Step Solution for all the Problems in 3rd Grade Go Math Ch 9 Extra Practice for better understanding.

Grade 3 Go Math Answer Key Chapter 9 Compare Fractions Extra Practice

Before you begin your preparation make sure to check out the topics list in 3rd Grade Go Math Ch 9 Answer Key Compare Fractions. You have different methods for solving the Comparing Fractions. Avail the quick links and get to know the concepts better. Practice the Problems in 3rd Grade Go Math Ch 9 on your own and verify the solutions in the Go Math Answer Key Grade 3 Chapter 9 Compare Fractions.

Common Core – Page No. 189000

Lesson 9.1

Solve. Show your work.

Question 1.
Nick finished \(\frac{4}{8}\) of his homework before dinner. Ed finished \(\frac{7}{8}\) of his homework before dinner. Who finished the greater part of his homework?
Go Math Grade 3 Answer Key Chapter 9 Compare Fractions Extra Practice Common Core img 1
_____

Answer: Ed

Explanation:

Compare the fractions \(\frac{4}{8}\) and \(\frac{7}{8}\)
The denominator of both the fractions is the same. So, compare the numerators.
The numerator with the greatest number will be the greatest fraction.
7 is greater than 4.
\(\frac{7}{8}\) > \(\frac{4}{8}\)
Therefore Ed finished the greater part of his homework.

Question 2.
Rafael walked \(\frac{2}{3}\) mile and then rode his scooter \(\frac{2}{6}\) mile. Which distance is farther?
Go Math Grade 3 Answer Key Chapter 9 Compare Fractions Extra Practice Common Core img 2
\(\frac{□} {□}\) mile is farther

Answer: \(\frac{2}{3}\)

Explanation:

Rafael walked \(\frac{2}{3}\) mile and then rode his scooter \(\frac{2}{6}\) mile.
The numerator of both the fractions is the same but the denominators are different.
The fraction is smaller if the denominator is greater.
Thus \(\frac{2}{3}\) > \(\frac{2}{6}\)
\(\frac{2}{3}\) mile is farther.

Lessons 9.2–9.3

Compare. Write <, >, or =.

Question 3.
\(\frac{2}{6}\) _____ \(\frac{3}{6}\)

Answer: \(\frac{2}{6}\) < \(\frac{3}{6}\)

Explanation:

Compare the fractions \(\frac{2}{6}\) and \(\frac{3}{6}\)
The denominators are the same and the numerators are different.
So compare the numerators of two fractions.
2 is less than 3.
So, \(\frac{2}{6}\) < \(\frac{3}{6}\)

Question 4.
\(\frac{6}{8}\) _____ \(\frac{1}{8}\)

Answer: \(\frac{6}{8}\) > \(\frac{1}{8}\)

Explanation:

Compare \(\frac{6}{8}\) and \(\frac{1}{8}\)
The denominators are the same and the numerators are different.
6 is greater than 1.
\(\frac{6}{8}\) > \(\frac{1}{8}\)

Question 5.
\(\frac{3}{8}\) _____ \(\frac{3}{4}\)

Answer: \(\frac{3}{8}\) < \(\frac{3}{4}\)

Explanation:

Compare the fractions \(\frac{3}{8}\) and \(\frac{3}{4}\)
The numerators are the same and denominators are different.
Compare the denominators of two fractions.
The fraction with lesser number will be the greatest.
\(\frac{3}{8}\) < \(\frac{3}{4}\)

Question 6.
\(\frac{1}{6}\) _____ \(\frac{1}{8}\)

Answer: \(\frac{1}{6}\) > \(\frac{1}{8}\)

Explanation:

The numerator of both the fractions is the same.
The denominator with the greatest number will be the smallest fraction.
So, \(\frac{1}{6}\) > \(\frac{1}{8}\)

Question 7.
\(\frac{2}{3}\) _____ \(\frac{2}{6}\)

Answer: \(\frac{2}{3}\) > \(\frac{2}{6}\)

Explanation:

The numerator of both the fractions is the same.
The denominator with the greatest number will be the smallest fraction.
\(\frac{2}{3}\) > \(\frac{2}{6}\)

Question 8.
\(\frac{1}{8}\) _____ \(\frac{3}{8}\)

Answer: \(\frac{1}{8}\) < \(\frac{3}{8}\)

Explanation:

The denominator of both the fractions is the same.
So, compare the numerators. The fraction with the small number will be the smallest fraction.
\(\frac{1}{8}\) < \(\frac{3}{8}\)

Lesson 9.4

Compare. Write <, >, or = . Write the strategy you used.

Question 9.
\(\frac{2}{8}\) _____ \(\frac{2}{3}\)

Answer: \(\frac{2}{8}\) < \(\frac{2}{3}\)

Explanation:

The numerator of both the fractions is the same.
Compare the denominators.
The denominator with the greatest number will be the smallest fraction.
\(\frac{2}{8}\) < \(\frac{2}{3}\)

Question 10.
\(\frac{5}{6}\) _____ \(\frac{1}{6}\)

Answer: \(\frac{5}{6}\) > \(\frac{1}{6}\)

Explanation:

The denominator of both the fractions is the same.
The fraction with the small number will be the smallest fraction.
5 is greater than 1.
\(\frac{5}{6}\) > \(\frac{1}{6}\)

Question 11.
\(\frac{7}{8}\) _____ \(\frac{3}{4}\)

Answer: \(\frac{7}{8}\) > \(\frac{3}{4}\)

Explanation:

Compare \(\frac{7}{8}\) and \(\frac{3}{4}\)
Make the denominators equal to compare the fractions.
\(\frac{3}{4}\) × \(\frac{8}{8}\) = \(\frac{24}{32}\)
\(\frac{7}{8}\) × \(\frac{4}{4}\) = \(\frac{28}{32}\)
\(\frac{28}{32}\) > \(\frac{24}{32}\)
\(\frac{7}{8}\) > \(\frac{3}{4}\)

Common Core – Page No. 190000

Lesson 9.5

Write the fractions in order from greatest to least.

Question 1.
\(\frac{1}{2}, \frac{1}{4}, \frac{1}{3}\)
Type below:
__________

Answer: \(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}\)

Explanation:

The numerator of the three fractions is the same.
So, the order from greatest to least is \(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}\)

Question 2.
\(\frac{4}{6}, \frac{1}{6}, \frac{2}{6}\)
Type below:
__________

Answer: \(\frac{4}{6}, \frac{2}{6}, \frac{1}{6}\)

Explanation:

The denominator of the three fractions is the same.
Compare the numerator of the fraction.
4 > 2 > 1
\(\frac{4}{6}, \frac{2}{6}, \frac{1}{6}\)

Question 3.
\(\frac{3}{6}, \frac{3}{4}, \frac{3}{8}\)
Type below:
__________

Answer: \(\frac{3}{4}, \frac{3}{6}, \frac{3}{8}\)

Explanation:

The numerator of the three fractions is the same.
So, the order is \(\frac{3}{4}, \frac{3}{6}, \frac{3}{8}\)

Question 4.
\(\frac{6}{8}, \frac{3}{8}, \frac{5}{8}\)
Type below:
__________

Answer: \(\frac{6}{8}, \frac{5}{8}, \frac{3}{8}\)

Explanation:

The denominator of the three fractions is the same.
Compare the numerator and write the order from greatest to least fraction.
\(\frac{6}{8}, \frac{5}{8}, \frac{3}{8}\)

Lessons 9.6–9.7

Shade the model. Then divide the pieces to find the equivalent fraction.

Question 5.
Go Math Grade 3 Answer Key Chapter 9 Compare Fractions Extra Practice Common Core img 3
\(\frac{1}{4}=\frac{■}{8}\)
\(\frac{1}{4}\) = \(\frac{□} {□}\)

Answer: \(\frac{1}{4}\) = \(\frac{2} {8}\)

Explanation:

Go Math Chapter 9 Key Grade 3 Extra Practice Solution image_1

\(\frac{1}{4}\) = \(\frac{2} {8}\)

Question 6.
Go Math Grade 3 Answer Key Chapter 9 Compare Fractions Extra Practice Common Core img 4
\(\frac{2}{3}=\frac{■}{6}\)
\(\frac{2}{3}\) = \(\frac{□} {□}\)

Answer: \(\frac{2}{3}\) = \(\frac{4} {6}\)

Explanation:

Chapter 9 Go Math Grade 3 Answer Key Extra Practice solution image_2

\(\frac{2}{3}\) = \(\frac{4} {6}\)

Use the number line to find the equivalent fraction.

Question 7.
Go Math Grade 3 Answer Key Chapter 9 Compare Fractions Extra Practice Common Core img 5
\(\frac{1}{2}=\frac{■}{8}\)
\(\frac{1}{2}\) = \(\frac{□} {□}\)

Answer: \(\frac{1}{2}\) = \(\frac{4} {8}\)

Explanation:

Go math answer key grade 3 compare fractions extra practice solution image_5

Question 8.
Go Math Grade 3 Answer Key Chapter 9 Compare Fractions Extra Practice Common Core img 6
\(\frac{2}{2}=\frac{■}{6}\)
\(\frac{2}{2}\) = \(\frac{□} {□}\)

Answer: \(\frac{2}{2}\) = \(\frac{6} {6}\)

Explanation:

Go Math Chapter 9 Grade 3 Answer Key Extra Practice solution image_5

Each shape is 1 whole. Shade the model to find the equivalent fraction.

Question 9.
Go Math Grade 3 Answer Key Chapter 9 Compare Fractions Extra Practice Common Core img 7
\(\frac{3}{4}=\frac{■}{8}\)
\(\frac{3}{4}\) = \(\frac{□} {□}\)

Answer: \(\frac{3}{4}\) = \(\frac{6} {8}\)

Explanation:

Go Math Answer Key Grade 3 Compare Fractions Extra Practice solution image_4

\(\frac{3}{4}\) = \(\frac{6} {8}\)

Question 10.
Go Math Grade 3 Answer Key Chapter 9 Compare Fractions Extra Practice Common Core img 8
\(\frac{1}{2}=\frac{■}{6}\)
\(\frac{1}{2}\) = \(\frac{□} {□}\)

Answer: \(\frac{1}{2}\) = \(\frac{3} {6}\)

Explanation:

HMH Go Math key Grade 3 Compare Fractions Extra Practice solution image_3

\(\frac{1}{2}\) = \(\frac{3} {6}\)

Conclusion

Learn the fundamentals right from the young age and become pro in the subject. To help you understand the concepts better we even drew pictures. Utilize Go Math Grade 3 Answer Key Chapter 9 Extra Practice and score better grades in the exams. To Clear all your queries check out Go Math Grade 3 Answer Key Chapter 9 Compare Fractions PDF.

Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume

go-math-grade-5-chapter-11-geometry-and-volume-answer-key

Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume comes with Crystal Clear Solutions and makes it easy for you to grasp the topics in it. Get Acquainted with the Geometry and Volume of Rectangular Prisms in the later sections. We provide Go Math Grade 5 Answer Key by Subject experts and explained them clearly so that students will no longer feel the concepts of Geometry and Volume difficult anymore.

Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume

Anyone who wishes to know the Procedure on How to find the Geometry and Volume of different shapes can get them using the 5th Grade Go Math Answer Key for Ch 11 Geometry and Volume. You can access the Topics of 5th Grade Go Math Answer Key Chapter 11 through the direct links available out there. The Topics Covered in the Geometry and Volume Chapter include polygons, quadrilaterals, triangles, understand volume, estimate volume, the volume of the rectangular prism, etc.

Lesson 1: Polygons

Lesson 2: Triangles

Lesson 3: Quadrilaterals

Lesson 4: Properties of Two-Dimensional Figures

Mid-Chapter Checkpoint

Lesson 5: Unit Cubes and Solid Figures

Lesson 6: Understand Volume

Lesson 7: Estimate Volume

Lesson 8: Volume of Rectangular Prisms

Lesson 9: Algebra Apply Volume Formulas

Lesson 10: Problem Solving Compare Volumes

Lesson 11: Find Volume of Composed Figures

Chapter Review/Test

Share and Show – Lesson 1: Polygons – Page No. 639

Question 1.
Name the polygon. Then use the markings on the figure to tell whether it is a regular polygon or not a regular polygon.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 1: Polygons img 1
a. Name the polygon.
__________

Answer: Triangle

Explanation:
A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. It is named by the number of sides and angles it has. The above figure consists of three sides. So, the name of the polygon is a triangle.

Question 1.
b. Are all the sides and all the angles congruent?
_____

Answer: Yes

Explanation:
When line segments have the same length or when angles have the same measure, they are congruent. All sides are equal in the above figure.
Thus the above figure is congruent.

Question 1.
c. Is the polygon a regular polygon?
_____

Answer: Yes

Explanation:
In a regular polygon, all sides are congruent and all angles are congruent.
The above figure has the same sides and same angles. Thus the above figure is a regular polygon.

Name each polygon. Then tell whether it is a regular polygon or not a regular polygon.

Question 2.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 1: Polygons img 2
Name: __________
Type: __________

Answer:
i. Hexagon
ii. Regular

Explanation:
A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. It is named by the number of sides and angles it has. The above figure consists of 6 sides. So, the name of the polygon is Hexagon.
In a regular polygon, all sides are congruent and all angles are congruent. The above figure has the same sides and same angles. Thus the above figure is a regular polygon.

Question 3.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 1: Polygons img 3
Name: __________
Type: __________

Answer:
i. Quadrilateral
ii. Not regular

Explanation:
A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. It is named by the number of sides and angles it has. The above figure consists of 4 sides. So, the name of the polygon is Quadrilateral.
The above figure doesn’t have the same sides thus the above figure is not a regular polygon.

Question 4.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 1: Polygons img 4
Name: __________
Type: __________

Answer:
i. Octagon
ii. Regular

Explanation:
A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. It is named by the number of sides and angles it has. The above figure consists of 8 sides. So, the name of the polygon is Octagon.
In a regular polygon, all sides are congruent and all angles are congruent. The above figure has the same sides and same angles. Thus the above Octagon is a regular polygon.

Name each polygon. Then tell whether it is a regular polygon or not a regular polygon.

Question 5.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 1: Polygons img 5
Name: __________
Type: __________

Answer:
i. Quadrilateral
ii. Regular

Explanation:
A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. It is named by the number of sides and angles it has. The above figure consists of 4 sides. So, the name of the polygon is Quadrilateral.
In a regular polygon, all sides are congruent and all angles are congruent. The above figure has the same sides and same angles. Thus the above Quadrilateral is a regular polygon.

Question 6.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 1: Polygons img 6
Name: __________
Type: __________

Answer:
i. Triangle
ii. Not regular

Explanation:
A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. It is named by the number of sides and angles it has. The above figure consists of three sides. So, the name of the polygon is a triangle.
The above figure doesn’t have the same sides thus the above figure is not a regular polygon.

Question 7.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 1: Polygons img 7
Name: __________
Type: __________

Answer:
i. Heptagon
ii. Regular

Explanation:
A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. It is named by the number of sides and angles it has. The above figure consists of 7 sides. So, the name of the polygon is Heptagon.
In a regular polygon, all sides are congruent and all angles are congruent. The above figure has the same sides and same angles. Thus the above Heptagon is a regular polygon.

Question 8.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 1: Polygons img 8
Name: __________
Type: __________

Answer:
i. Hexagon
ii. Not regular

Explanation:
A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. It is named by the number of sides and angles it has. The above figure consists of six sides. So, the name of the polygon is a Hexagon.
The above figure doesn’t have the same sides and angles thus the above figure is not a regular polygon.

Question 9.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 1: Polygons img 9
Name: __________
Type: __________

Answer:
i. Pentagon
ii. Not regular

Explanation:
A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. It is named by the number of sides and angles it has. The above figure consists of five sides. So, the name of the polygon is a Pentagon.
The above figure doesn’t have the same sides and angles thus the above figure is not a regular polygon.

Question 10.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 1: Polygons img 10
Name: __________
Type: __________

Answer:
i. Pentagon
ii. Regular

Explanation:
A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. It is named by the number of sides and angles it has. The above figure consists of five sides. So, the name of the polygon is a Pentagon.
In a regular polygon, all sides are congruent and all angles are congruent. The above figure has the same sides and same angles. Thus the above Pentagon is a regular polygon.

Problem Solving – Lesson 1: Polygons – Page No. 640

For 11–12, use the Castel del Monte floor plan at the right.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 1: Polygons img 11

Question 11.
Which polygons in the floor plan have four equal sides and four congruent angles? How many of these polygons are there?
polygon: __________
The number of polygons: __________

Answer:
polygon: Quadrilateral
The number of polygons: 8

Explanation:
By seeing the above figure we can say that there are eight Quadrilaterals in the octagon. And the number of polygons is 8.

Question 12.
Is there a quadrilateral in the floor plan that is not a regular polygon? Name the quadrilateral and tell how many of the quadrilaterals are in the floor plan.
Name of quadrilateral: __________
The number of quadrilaterals: __________

Answer:
Name of quadrilateral: Trapezoid
The number of quadrilaterals: 8

Explanation:
The name of the Quadrilateral for the above figure is Trapezoid. There is 8 number of quadrilaterals in the floor plan.

Question 13.
Sketch eight points. Then connect the points to draw a closed plane figure.
What kind of polygon did you draw?
__________

Answer: Octagon

Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 1: Polygons img 4

Question 14.
Look at the angles for all regular polygons. As the number of sides increases, do the measures of the angles increase or decrease? What pattern do you see?
angles measures __________

Answer: Increase

Explanation:
As the number of sides increases, the measures of the angles increase.
we know that
The measure of the interior angle in a regular polygon is equal to
x = (n-2)/n(180°)
where
n is the number of sides of the regular polygon.
x is the measure of the interior angle in a regular polygon.

Question 15.
Test Prep Which of the following is a regular hexagon?
Options:
a. Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 1: Polygons img 12
b. Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 1: Polygons img 13
c. Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 1: Polygons img 14
d. Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 1: Polygons img 15

Answer: Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 1: Polygons img 14

Share and Show – Lesson 2: Triangles – Page No. 645

Classify each triangle. Write isosceles, scalene, or equilateral.

Then write acute, obtuse, or right.

Question 1.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 2: Triangles img 16
△ __________
∠ __________

Answer:
△ – Scalene
∠ – Acute

Explanation:
The 3 sides of the triangle are unequal. If three sides of the triangle are different it is known as Scalene. The angles are less than 90° thus the angle is known as an acute angle.

Question 2.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 2: Triangles img 17
△ __________
∠ __________

Answer:
△ – Equilateral
∠ – Acute

Explanation:
The 3 sides of the triangle are equal. If three sides of the triangle are equal it is known as the equilateral triangle. The angles are less than 90° thus the angle is known as an acute angle.

Question 3.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 2: Triangles img 18
△ __________
∠ __________

Answer:

△ – Isosceles
∠ – Acute

Explanation:
The 2 sides of the triangle are equal and the third side is not equal. If two sides of the triangle are different it is known as Isosceles.
The angles are less than 90° thus the angle is known as an acute angle.

On Your Own

Classify each triangle. Write isosceles, scalene, or equilateral.

Then write acute, obtuse, or right.

Question 4.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 2: Triangles img 19
△ __________
∠ __________

Answer:
△ – Scalene
∠ – Right

Explanation:
The 3 sides of the triangle are unequal. If three sides of the triangle are different it is known as Scalene. One of the angle is 90° thus the angle is known as a right angle.

Question 5.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 2: Triangles img 20
△ __________
∠ __________

Answer:
△ – Isosceles
∠ – Acute

Explanation:
The 2 sides of the triangle are equal and the third side is not equal. If two sides of the triangle are different it is known as Isosceles.
The angles are less than 90° thus the angle is known as an acute angle.

Question 6.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 2: Triangles img 21
△ __________
∠ __________

Answer:
△ – Scalene
∠ – Obtuse

Explanation:
The 3 sides of the triangle are unequal. If three sides of the triangle are different it is known as Scalene. The angles are more than 90° thus the angle is known as an obtuse angle.

A triangle has sides with the lengths and angle measures given.

Classify each triangle. Write isosceles, scalene, or equilateral.

Then write acute, obtuse, or right.

Question 7.
sides: 3.5 cm, 6.2 cm, 3.5 cm
angles: 27°, 126°, 27°
△ __________
∠ __________

Answer:
△ – Isosceles
∠ – Obtuse

Explanation:
The 2 sides of the triangle are equal and the third side is not equal. If two sides of the triangle are different it is known as Isosceles. One of the angle is more than 90° thus the angle is known as an obtuse angle.

Question 8.
sides: 2 in., 5 in., 3.8 in.
angles: 43°, 116°, 21°
△ __________
∠ __________

Answer:
△ – Scalene
∠ – Obtuse

Explanation:
The 3 sides of the triangle are unequal. If three sides of the triangle are different it is known as Scalene. One of the angle is more than 90° thus the angle is known as an obtuse angle.

Question 9.
Circle the figure that does not belong.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 2: Triangles img 22
Type below:
__________

Answer:
Go-Math-Grade-5-Answer-Key-Chapter-11-Geometry-and-Volume-img-22

Problem Solving – Lesson 2: Triangles – Page No. 646

Question 10.
Draw 2 equilateral triangles that are congruent and share a side. What polygon is formed? Is it a regular polygon?
What polygon is formed? __________
Is it a regular polygon? __________

Answer:
The name for the polygon is Quadrilateral.
In a regular polygon, all sides are congruent and all angles are congruent.

Question 11.
What’s the Error? Shannon said that a triangle with exactly 2 congruent sides and an obtuse angle is an equilateral obtuse triangle. Describe her error.
Type below:
__________

Answer: All angles of an equilateral triangle are acute. You cannot have an obtuse angle in an equilateral angle. And all of the angles must be congruent.

Question 12.
Test Prep Which kind of triangle has exactly 2 congruent sides?
Options:
a. isosceles
b. equilateral
c. scalene
d. right

Answer: isosceles

Explanation:
An isosceles triangle, therefore, has both two equal sides and two equal angles.
Thus the correct answer is option A.

Connect to Science
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 2: Triangles img 23

Classify the triangles in the structures below. Write isosceles, scalene, or equilateral. Then write acute, obtuse, or right.

Question 13.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 2: Triangles img 24
△ __________
∠ __________

Answer:
△ – Equilateral triangle
∠ – Acute

Explanation:
From the figure, we can see an equilateral triangle. In an equilateral triangle, all sides will be less than 90°. So it is an acute angle.

Question 14.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 2: Triangles img 25
△ __________
∠ __________

Answer:
△ – Scalene triangle
∠ – Right

Explanation:
In the above figure, we can see a right-angle triangle. The three sides of the above triangle is different. So, it is known as the scalene triangle.

Share and Show – Lesson 3: Quadrilaterals – Page No. 651

Question 1.
Use quadrilateral ABCD to answer each question. Complete the sentence.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 3: Quadrilaterals img 26
a. Measure the sides. Are any of the sides congruent?
Mark any congruent sides.
_____

Answer: Yes

Explanation:
The above figure consists of same sides. Thus the above Quadrilateral is congruent.

Question 1.
b. How many right angles, if any, does the quadrilateral have?
_____

Answer: 0

The above figure doesn’t have any straight line. Thus the above figure has 0 right angles.

Question 1.
c. How many pairs of parallel sides, if any, does the quadrilateral have?
_____ pairs

Answer: 2

Explanation:
The above has two parallel sides. Yes, the Quadrilateral has the parallel sides.

Question 1.
So, quadrilateral ABCD is a ______________ .
_________

Answer: Parallelogram

Explanation:
A parallelogram is a special trapezoid with opposite sides are equal.

Classify the quadrilateral in as many ways as possible.

Write quadrilateral, parallelogram, rectangle, rhombus, square, or trapezoid.

Question 2.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 3: Quadrilaterals img 27
1. _________
2. _________
3. _________

Answer:
The possible ways of Quadrilateral are:
1. Rectangle
2. Parallelogram
3. Quadrilateral

Question 3.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 3: Quadrilaterals img 28
1. _________
2. _________

Answer:
The possible ways of Quadrilateral are:
1. Quadrilateral
2. Trapezoid

On Your Own

Classify the quadrilateral in as many ways as possible.

Write quadrilateral, parallelogram, rectangle, rhombus, square, or trapezoid.

Question 4.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 3: Quadrilaterals img 29
1. _________
2. _________
3. _________
4. _________
5. _________

Answer:
The possible ways of Quadrilateral for the above figure are:
1. Square
2. Quadrilateral
3. Parallelogram
4. Rectangle
5. Rhombus

Question 5.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 3: Quadrilaterals img 30
1. _________
2. _________

Answer:
The possible ways of Quadrilateral for the above figure are:
1. Trapezoid
2. Parallelogram

Question 6.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 3: Quadrilaterals img 31
1. _________
2. _________
3. _________

Answer:
The possible ways of Quadrilateral for the above figure are:
1. Rhombus
2. Parallelogram
3. Square

Question 7.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 3: Quadrilaterals img 32
1. _________
2. _________

Answer:
The possible ways of Quadrilateral for the above figure are:
1. Rectangle
2. Parallelogram

Problem Solving – Lesson 3: Quadrilaterals – Page No. 652

Solve the problems.

Question 8.
A quadrilateral has exactly 2 congruent sides. Which quadrilateral types could it be? Which quadrilaterals could it not be?
Type below:
_________

Answer: A rectangle has 2 congruent sides.

Explanation:
The type of quadrilateral that has two congruent sides is a rectangle.

Question 9.
What’s the Error? A quadrilateral has exactly 3 congruent sides. Davis claims that the figure must be a rectangle. Why is his claim incorrect? Use a diagram to explain your answer.
Type below:
_________

Answer: Daviss’s claim is incorrect because a rectangle does not have three congruent sides.

Question 10.
The opposite corners of a quadrilateral are right angles. The quadrilateral is not a rhombus. What kind of quadrilateral is this figure? Explain how you know.
Type below:
_________

Answer:

It depends, is it just one set of opposite angles that are right angles? Then it could be just a quadrilateral, or it could be a kite, or it could be a rectangle. Because a Quadrilateral is the least restrictive, the best answer is. “It is a quadrilateral”.
Or is it both sets of opposite angles are right angles? Then it can only be a “rectangle, that is not a square”.
Go Math Grade 5 Answer Key Chapter 11 solution img-1

Question 11.
I am a figure with four sides. I can be placed in the following categories: quadrilateral, parallelogram, rectangle, rhombus, and square. Draw me. Explain why I fit into each category.
Type below:
_________

Answer: Square
Go Math 5th Grade Solution Key Chapter 11 img-2

Question 12.
Test Prep A quadrilateral has exactly 1 pair of parallel sides and no congruent sides. What type of quadrilateral is it?
Options:
a. rectangle
b. rhombus
c. parallelogram
d. trapezoid

Answer: Trapezoid

Explanation:
A quadrilateral with one pair of parallel sides is a trapezoid.
Thus the correct answer is option D.

Share and Show – Lesson 4: Properties of Two-Dimensional Figures – Page No. 455

Question 1.
Erica thinks that triangle X Y Z, below, has two congruent sides, but she does not have a ruler to measure the sides. Are two sides congruent?
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 4: Properties of Two-Dimensional Figures img 33
First, trace the triangle and cut out the tracing.
Type below:
_________

Answer:
Go-Math-Grade-5-Answer-Key-Chapter-11-Geometry-and-Volume-img-22 (1)

Question 1.
Then, fold the triangle to match each pair of sides to determine if at least two of the sides are congruent. As you test the sides, record or draw the results for each pair to make sure that you have checked all pairs of sides. Possible drawings are shown.
Type below:
_________

Question 1.
Finally, answer the question.
______

Answer: Yes

Question 2.
What if Erica also wants to show, without using a protractor, that the triangle has one right angle and two acute angles? Explain how she can show this.

Answer:
The sum of three angles = 180
If one of the angles is 90 then the other two angles will be acute angles.

Question 3.
December, January, and February were the coldest months in Kristen’s town last year. February was the warmest of these months. December was not the coldest. What is the order of these months from coldest to warmest?
Coldest: _________
_________
Warmest: _________
_________

Answer:
Coldest: January
December
Warmest: February

Explanation:
January and December are the coldest months of the year depending on the direction of the wind. February is the warmest month among these months.

Question 4.
Jan enters a 20-foot by 30-foot rectangular room. The long sides face north and south. Jan enters the exact center of the south side and walks 10 feet north. Then she walks 8 feet east. How far is she from the east side of the room?
______ ft

Answer: 7 feet

Explanation:
Given that,
Jan enters a 20-foot by 30-foot rectangular room.
The long sides face north and south.
Jan enters the exact center of the south side and walks 10 feet north.
Then she walks 8 feet east.
Jan is 7 feet from the east wall in the room.

On Your Own – Lesson 4: Properties of Two-Dimensional Figures – Page No. 456

Question 5.
Max drew a grid to divide a piece of paper into 18 congruent squares, as shown. What is the least number of lines Max can draw to divide the grid into 6 congruent rectangles?
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 4: Properties of Two-Dimensional Figures img 34
______ lines

Answer: 3 lines

Explanation:
From the above figure, we can see that there are 18 congruent squares.
To find the least number of lines Max can draw we have to divide number of squares by number of congruent rectangles
18 ÷ 6 = 3
Thus the least number of lines that Max can Draw is 3 lines.

Question 6.
Of the 95 fifth and sixth graders going on a field trip, there are 27 more fifth-graders than sixth graders. How many fifth graders are going on the field trip?
5th graders = ______

Answer: 61

Explanation:
Since we are not told how many 6th graders are going on the trip let’s use a variable, the letter x.
Now let’s understand the problem in the “math” language.
x= the number of 6th graders.
X+27= the number of 5th graders since there are 27 more fifth-graders than sixth graders.
x+x+27 = 95
2x+27=95
-27 -27
2x+ 0 =68
2x=68
divide by 2 on both sides.
x = 34
Now, remember how x+27 = the number of 5th graders going on the trip?
Since we know that x=34, substitute the x as 34+27 which = 61 fifth graders going on the trip.

Use the map to solve 7–8.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 4: Properties of Two-Dimensional Figures img 35

Question 7.
Sam’s paper route begins and ends at the corner of Redwood Avenue and Oak Street. His route is made up of 4 streets, and he makes no 90° turns. What kind of polygon do the streets of Sam’s paper route form? Name the streets in Sam’s route.
_________

Answer: Parallelogram

Explanation:
Given that, Sam’s paper route begins and ends at the corner of Redwood Avenue and Oak Street. His route is made up of 4 streets, and he makes no 90° turns.
By following the route map we can say that the polygon is a parallelogram.

Question 8.
Sam’s paper route includes all 32 houses on two pairs of parallel streets. If each street has the same number of houses, how many houses are on each street?
Name the parallel streets.
______ houses on each street

Answer: 8

Explanation:
Given,
Sam’s paper route includes all 32 houses on two pairs of parallel streets.
If each street has same number of houses we have to divide 32 by 4
32 ÷ 4 = 8
Thus there are 8 houses on each street.

Question 8.
Test Prep Which figure below is a quadrilateral that has opposite sides that are congruent and parallel?
Options:
a. Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 4: Properties of Two-Dimensional Figures img 36
b. Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 4: Properties of Two-Dimensional Figures img 37
c. Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 4: Properties of Two-Dimensional Figures img 38
d. Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 4: Properties of Two-Dimensional Figures img 39

Answer: Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 4: Properties of Two-Dimensional Figures img 37

Explanation:
Square is a type of quadrilateral that has opposite sides that are congruent and parallel.
Thus the correct answer is option B.

Share and Show – Lesson 4: Properties of Two-Dimensional Figures – Page No. 656

Classify the solid figure. Write prism, pyramid, cone, cylinder, or sphere.

Question 1.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 4: Three-Dimensional Figures img 40
_________

Answer: Triangular prism

Explanation:
A triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides. A right triangular prism has rectangular sides, otherwise, it is oblique.

Question 2.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 4: Three-Dimensional Figures img 41
_________

Answer: Sphere

Explanation:
A sphere has no bases and 1 curved surface.

Question 3.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 4: Three-Dimensional Figures img 42
_________

Answer: Hexagonal Base Pyramid

Explanation:
A pyramid that has a hexagonal base, that is, base with six sides and 6 triangular lateral faces, then it is a hexagonal pyramid.

Question 4.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 4: Three-Dimensional Figures img 43
_________

Answer: Pentagonal prism

Explanation:
A pentagonal prism is a prism that has two pentagonal bases like top and bottom and five rectangular sides. It is a type of heptahedron with 7 faces, 10 vertices, and 15 edges.

Question 5.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 4: Three-Dimensional Figures img 44
_________

Answer: Pentagonal Base Pyramid

Explanation:
In geometry, a pentagonal pyramid is a pyramid with a pentagonal base upon which are erected five triangular faces that meet at a point.

Question 6.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 4: Three-Dimensional Figures img 45
_________

Answer: Cylinder

Explanation:
A cylinder has 2 congruent circular bases and 1 curved surface.

On Your Own

Classify the solid figure. Write prism, pyramid, cone, cylinder, or sphere.

Question 7.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 4: Three-Dimensional Figures img 46
_________

Answer: Rectangular prism

Explanation:
A rectangular prism is a polyhedron with two congruent and parallel bases. It is also a cuboid. It has six faces, and all the faces are in a rectangle shape and have twelve edges. Because of its cross-section along the length, it is said to be a prism.

Question 8.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 4: Three-Dimensional Figures img 47
_________

Answer: Cylinder

Explanation:
A cylinder has 2 congruent circular bases and 1 curved surface.

Question 9.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 4: Three-Dimensional Figures img 48
_________

Answer: Cone

Explanation:
A cone has 1 circular base and 1 curved surface.

Question 10.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 4: Three-Dimensional Figures img 49
_________

Answer: Triangle base pyramid

Explanation:
A triangle-based pyramid has four triangular sides. The base can be any shape or size of the triangle but usually, it is an equilateral triangle. This means the three sides of the pyramid are the same size as each other and the pyramid looks the same if you rotate it.

Question 11.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 4: Three-Dimensional Figures img 50
_________

Answer: Rectangular prism

Explanation:
A rectangular prism is a polyhedron with two congruent and parallel bases. It is also a cuboid. It has six faces, and all the faces are in a rectangle shape and have twelve edges. Because of its cross-section along the length, it is said to be a prism.

Question 12.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 4: Three-Dimensional Figures img 51
_________

Answer: Triangular prism

Explanation:
A prism’s base shape is used to name the solid figure. The base shape of this prism is a triangle. The prism is a triangular prism.

Question 13.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 4: Three-Dimensional Figures img 52
_________

Answer: Hexagonal Prism

Explanation:
In geometry, the hexagonal prism is a prism with a hexagonal base. This polyhedron has 8 faces, 18 edges, and 12 vertices. Since it has 8 faces, it is an octahedron. However, the term octahedron is primarily used to refer to the regular octahedron, which has eight triangular faces.

Question 14.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 4: Three-Dimensional Figures img 53
_________

Answer: Square Pyramid

Explanation:
In geometry, a square pyramid is a pyramid having a square base. If the apex is perpendicularly above the center of the square, it is a right square pyramid and has symmetry. If all edges are equal, it is an equilateral square pyramid.

Question 15.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 4: Three-Dimensional Figures img 54
_________

Answer: Octogonal Prism

Explanation:
In geometry, the octagonal prism is the sixth in an infinite set of prisms, formed by square sides and two regular octagon caps. If faces are all regular, it is a semiregular polyhedron.

Problem Solving – Lesson 4: Properties of Two-Dimensional Figures – Page No. 657

Question 16.
Mario is making a sculpture out of stone. He starts by carving a base with five sides. He then carves five triangular lateral faces that all meet at a point at the top. What three-dimensional figure does Mario make?
_________

Answer: Pentagonal Pyramid

Explanation:
Given,
Mario is making a sculpture out of stone.
He starts by carving a base with five sides.
He then carves five triangular lateral faces that all meet at a point at the top.
The polygon which has 5 sides is a pentagon.
The three-dimensional figure which meets at the same point is the pyramid.
The 3-dimensional figure that Mario makes is Pentagonal Pyramid
So, the answer to the above question is Pentagonal Pyramid.

Question 17.
What is another name for a cube? Explain your reasoning.
Type below:
_________

Answer: The cube can also be called a regular hexahedron. It is one of the five regular polyhedrons, which are also sometimes referred to as the Platonic solids.

Connect to Reading

Example Read the description. Underline the details you need to identify the solid figure that will name the correct building.

This building is one of the most identifiable structures in its city’s skyline. It has a square foundation and 28 floors. The building has four triangular exterior faces that meet at a point at the top of the structure.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 4: Three-Dimensional Figures img 55
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 4: Three-Dimensional Figures img 56
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 4: Three-Dimensional Figures img 57

Identify the solid figure and name the correct building.

Question 18.
Solve the problem in the Example.
Solid figure: _________
Building: _________

Answer:
i. Pyramid
ii. Luxor Hotel-Las Vegas-Nevada

Explanation:
The 3rd figure is in the form of a pyramid. The name of the pyramid-shaped building is Luxor Hotel-Las Vegas-Nevada.

Question 19.
This building was completed in 1902. It has a triangular foundation and a triangular roof that are the same size and shape. The three sides of the building are rectangles.
Solid figure: _________
Building: _________

Answer:
i. prism
ii. Flatiron Building-New York City-New York

Explanation:
The triangle-shaped figure is in the form of a prism. The name of the triangular prism building is Flatiron Building-New York, City-New York.

Mid-Chapter Review – Vocabulary – Page No. 661

Choose the best term from the box.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Mid-Chapter Review img 58

Question 1.
A closed plane figure with all sides congruent and all angles congruent is called a ________ .
_________

Answer: Regular Polygon

Question 2.
Line segments that have the same length or angles that have the same measure are __________ .
_________

Answer: Congruent

Concepts and Skills

Name each polygon. Then tell whether it is a regular polygon or not a regular polygon.

Question 3.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Mid-Chapter Review img 59
Name: _________
Type: _________

Answer:
i. Hexagon
ii. Regular Polygon

Question 4.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Mid-Chapter Review img 60
Name: _________
Type: _________

Answer:
i. Triangle
ii. Non-Regular

Question 5.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Mid-Chapter Review img 61
Name: _________
Type: _________

Answer:
i. Pentagon
ii. Not Regular

Classify each triangle. Write isosceles, scalene, or equilateral.

Then write acute, obtuse, or right.

Question 6.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Mid-Chapter Review img 62
△ _________
∠ _________

Answer:
i. Equilateral
ii. Acute

Question 7.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Mid-Chapter Review img 63
△ _________
∠ _________

Answer:
i. Isosceles
ii. Right

Question 8.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Mid-Chapter Review img 64
△ _________
∠ _________

Answer:
i. Isosceles
ii. Obtuse

Classify the quadrilateral in as many ways as possible. Write quadrilateral, parallelogram, rectangle, rhombus, square, or trapezoid.

Question 9.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Mid-Chapter Review img 65
1. _________
2. _________

Answer:
1. Quadrilateral
2. Trapezoid

Question 10.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Mid-Chapter Review img 66
1. _________
2. _________
3. _________

Answer:
1. Quadrilateral
2. Parallelogram
3. Rectangle

Question 11.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Mid-Chapter Review img 67
1. _________
2. _________
3. _________
4. _________
5. _________

Answer:
1. Quadrilateral
2. Parallelogram
3. Rhombus
4. Rectangle
5. Square

Mid-Chapter Review – Page No. 662

Fill in the bubble completely to show your answer.

Question 12.
What type of triangle is shown below?
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Mid-Chapter Review img 68
Options:
a. right isosceles
b. right scalene
c. equilateral
d. obtuse scalene

Answer: right isosceles

Explanation:
The above figure is a right angle and the two sides of the triangle are equal. The above figure is a right isosceles.
Thus the correct answer is option A.

Question 13.
Classify the quadrilateral in as many ways as possible.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Mid-Chapter Review img 69
Options:
a. quadrilateral, parallelogram, rhombus
b. quadrilateral, parallelogram, rhombus, trapezoid
c. quadrilateral, parallelogram, rhombus, rectangle, trapezoid, square
d. quadrilateral, parallelogram, rhombus, rectangle, square

Answer: quadrilateral, parallelogram, rhombus, rectangle, square

Question 14.
Classify the following figure.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Mid-Chapter Review img 70
Options:
a. cone
b. cube
c. rectangular prism
d. rectangular pyramid

Answer: rectangular prism

Explanation:
The 3-dimensional figure of the above rectangle is a rectangular prism.
Thus the correct answer is option C.

Share and Show – Lesson 5: Unit Cubes and Solid Figures – Page No. 665

Count the number of cubes used to build each solid figure.

Question 1.
The rectangular prism is made up of _____ unit cubes.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 5: Unit Cubes and Solid Figures img 71
______

Answer: 3

Explanation:
By seeing the above figure we can say that the rectangular prism has 3 unit cubes.

Question 2.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 5: Unit Cubes and Solid Figures img 72
______ unit cubes

Answer: 15

Explanation:
The above figure shows that there are 5 congruent squares of 3 lines.
5 × 3 = 15 unit cubes

Question 3.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 5: Unit Cubes and Solid Figures img 73
______ unit cubes

Answer: 12

Explanation:
The above figure shows that there are 4 congruent squares of 3 lines.
4 × 3 = 12 unit cubes

Question 4.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 5: Unit Cubes and Solid Figures img 74
______ unit cubes

Answer: 12

Explanation:
The above figure shows that there are 6 congruent squares of 2 lines.
6 × 2 = 12

Question 5.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 5: Unit Cubes and Solid Figures img 75
______ unit cubes

Answer: 5

Explanation:
By seeing the above figure we can say that there are 5 unit cubes.

Question 6.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 5: Unit Cubes and Solid Figures img 76
______ unit cubes

Answer: 6

Explanation:
There are 6 congruent squares in the above figure.

Question 7.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 5: Unit Cubes and Solid Figures img 77
______ unit cubes

Answer: 7

Explanation:
The figure shows that there are 7 unit cubes.

Question 8.
How are the rectangular prisms in Exercises 3–4 related? Can you show a different rectangular prism with the same relationship? Explain.
Type below:
_________

Answer:
Go Math Grade 5 key Chapter 11 solution img-3
A rectangular prism is a polyhedron with two congruent and parallel bases. It is also a cuboid. It has six faces, and all the faces are in a rectangle shape and have twelve edges. Because of its cross-section along the length, it is said to be a prism.

Compare the number of unit cubes in each solid figure. Use < , > or =.

Question 9.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 5: Unit Cubes and Solid Figures img 78 ______ Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 5: Unit Cubes and Solid Figures img 79

Answer: Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 5: Unit Cubes and Solid Figures img 78 = Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 5: Unit Cubes and Solid Figures img 79

Explanation:
There are 5 cubes in the first figure and there are 5 cubes in the second figure.
Thus the figures Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 5: Unit Cubes and Solid Figures img 78 is equal to Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 5: Unit Cubes and Solid Figures img 79

Question 10.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 5: Unit Cubes and Solid Figures img 80 ______ Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 5: Unit Cubes and Solid Figures img 81

Answer: Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 5: Unit Cubes and Solid Figures img 80 < Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 5: Unit Cubes and Solid Figures img 81

Explanation:
There are 4 cubes in the first figure and there are 5 cubes in the second figure.
4 is less than 5
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 5: Unit Cubes and Solid Figures img 80 is less than Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 5: Unit Cubes and Solid Figures img 81

Lesson 5: Unit Cubes and Solid Figures – Page No. 666

Use the information to answer the questions.

The Cube Houses of Rotterdam, Netherlands
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 5: Unit Cubes and Solid Figures img 82

The Nakagin Capsule Tower, Tokyo, Japan
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 5: Unit Cubes and Solid Figures img 83

Question 11.
There are 38 Cube Houses. Each house could hold 1,000 unit cubes that are 1 meter by 1 meter by 1 meter. Describe the dimensions of a cube house using unit cubes. Remember that the edges of a cube are all the same length.
Each dimension = ______ meters

Answer: 10 meters

Explanation:
So each house can hold 1000 cubes that are 1 meter in length.
The house is also shaped like a cube, so you need to cube-root 1000.
The cube-root of 1000 is 10. So the cube house has a length, width, and height of 10 meters.
V = lbh
V = 10 m × 10 m × 10 m = 1000 cu. meter
Thus Each dimension is 10 meters.

Question 12.
The Nakagin Capsule Tower has 140 modules and is 14 stories high. If all of the modules were divided evenly among the number of stories, how many modules would be on each floor? How many different rectangular prisms could be made from that number?
Type below:
_________

Answer: 10 modules on each floor

Explanation:
The Nakagin Capsule Tower has 140 modules and is 14 stories high.
Divide 140 modules by 14
140 ÷ 14 = 10
Thus 10 modules would be on each floor.
The factors of 10 are 1, 2, 5.
1 × 10 = 10
2 × 5 = 10
Thus 2 different rectangular prisms can be made from 10 unit cubes.

Share and Show – Lesson 6: Understand Volume – Page No. 671

Use the unit given. Find the volume.

Question 1.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 6: Understand Volume img 84
Each cube = 1 cu cm
Volume = ______ cu ______

Answer: 48 cu. cm

Explanation:
Given that,
L = 4cm
B = 4cm
H = 3 cm
We know that,
The volume of the cuboid is lbh
V = 4 cm × 4 cm × 3 cm = 48 cubic cm
Thus the volume for the above cube is 48 cubic cm.

Question 2.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 6: Understand Volume img 85
Each cube = 1 cu in.
Volume = ______ cu ______

Answer: 24 cu. in.

Explanation:
Given that,
L = 3 in
B = 2 in
H = 4 in.
We know that,
The volume of the cuboid is lb
V = 3 in × 2 in × 4 in = 24 cubic inches
Therefore the volume for the above cube is 24 cubic inches.

Question 3.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 6: Understand Volume img 86
Each cube = 1 cu ft
Volume = ______ cu ______

Answer: 36 cu. ft

Explanation:
Given that,
L = 6 ft
B = 2 ft
H = 3 ft
We know that,
The volume of the cuboid is lbh
V = 6 ft × 2 ft × 3 ft = 36 cubic feet
V = 36 cu. ft
Therefore the volume for the above figure is 36 cu. ft

Question 4.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 6: Understand Volume img 87
Each cube = 1 cu in.
Volume = ______ cu ______

Answer: 60 cu. in

Given that,
L = 5 in.
B = 4 in.
H = 3 in.
We know that,
The volume of the cuboid is lbh
V = 5 in × 4 in × 3 in = 60 cubic inches
Thus the volume for the above figure is 60 cu. in.

Compare the volumes. Write < , >, or =.

Question 5.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 6: Understand Volume img 88 ______ Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 6: Understand Volume img 89

Answer: Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 6: Understand Volume img 88Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 6: Understand Volume img 89

Explanation:
Figure 1:
L = 4 cm
B = 4 cm
H = 2 cm
V = 4 × 4 × 2 = 32 cu. cm
Figure 2:
L = 4 in
B = 4 in
H = 2 in
V = 4 × 4 × 2 = 32 cu. in
32 cu. cm is less than 32 cu. in
Thus Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 6: Understand Volume img 88Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 6: Understand Volume img 89

Question 6.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 6: Understand Volume img 90 ______ Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 6: Understand Volume img 91

Answer: Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 6: Understand Volume img 90 > Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 6: Understand Volume img 91

Explanation:
Let us find the volume for both the figures,
Figure 1:
L = 9 ft
B = 4 ft
H = 3 ft
Volume of the cuboid = lbh
V = 9 × 4 × 3 = 108 cu. ft
Figure 2:
L = 8 ft
B = 5 ft
H = 2 ft
Volume of the cuboid = lbh
V = 8 ft × 5 ft × 3 ft = 120 cu. ft
By seeing the volume for both the figures we can say that 120 cu. ft is greater than 108 cu. ft
Thus, Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 6: Understand Volume img 90 > Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 6: Understand Volume img 91

Problem Solving – Lesson 6: Understand Volume – Page No. 672

Question 7.
What’s the Error? Jerry says that a cube with edges that measure 10 centimeters has a volume that is twice as much as a cube with sides that measure 5 centimeters. Explain and correct Jerry’s error.
Type below:
__________

Answer:
Let v1 equal the 10 cm sided cube’s volume.
Let v2 equal the 5 cm sided cube’s volume.
v1 = 10 × 10 10 = 1000 cu. cm
v2 = 5 × 5 × 5 = 125 cu. cm
To find the relationship between the two volumes, divide the first volume by the second.
r = v1 ÷ v2
r = 1000 ÷ 125 = 8
The volume differ by a factor of 8.
Thus the volume differs by a factor of 8, not by a factor of 2.

Question 8.
Pattie built a rectangular prism with cubes. The base of her prism has 12 centimeter cubes. If the prism was built with 108 centimeter cubes, how many layers does her prism have? What is the height of her prism?
layers: ______ the height of the prism: ______ cm

Answer: 9 layers, the height of the prism is 9 cm

Explanation:
Given:
Pattie built a rectangular prism with cubes.
The base of her prism has 12-centimeter cubes.
The prism was built with 108 cm cubes.
To find the layers divide the number of cubes by base of the prism
That means 108 ÷ 12
108/12 = 9
Thus the prism has 9 layers.
Now we have to find the base of the prism
108 = b × h
12 × h = 108
h = 108/12 = 9
Therefore the height of the prism = 9 cm

Question 9.
A packing company makes boxes with edges each measuring 3 feet. What is the volume of the boxes? If 10 boxes are put in a larger, rectangular shipping container and completely fill it with no gaps or overlaps, what is the volume of the shipping container?
volume of the boxes: __________ cu ft
volume of the shipping container = __________ cu ft

Answer:
the volume of the boxes: 27 cu ft
the volume of the shipping container = 27 cu ft

Explanation:
A packing company makes boxes with edges each measuring 3 feet.
Volume of the cube = lbh
V = 3 × 3 × 3 = 27 cubic feet
Thus the volume of the boxes is 27 feet.
The volume of the boxes for 10 boxes is 27 × 10 = 270 cubic feet
Therefore the volume of the shipping container is 27 cu ft

Question 10.
Test Prep Find the volume of the rectangular prism.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 6: Understand Volume img 92
Each cube = 1 cu cm
Options:
a. 25 cubic feet
b. 25 cubic meters
c. 75 cubic meters
d. 75 cubic centimeters

Answer: 75 cubic centimeters

Explanation:
L = 5 cm
B = 3 cm
H = 5 cm
Volume of the rectangular prism is lbh
V = 5 cm × 3 cm × 5 cm = 75 cubic centimeter
V = 75 cu. cm
Thus the correct answer is option D.

Share and Show – Lesson 7: Estimate Volume – Page No. 677

Estimate the volume.

Question 1.
Each tissue box has a volume of 125 cubic inches.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 7: Estimate Volume img 93
There are _______ tissue boxes in the larger box.
The estimated volume of the box holding the tissue
boxes is ______ × 125 = _____ cu in.
_____ tissue boxes _____ cu in.

Answer:
Given that the volume of each box is 125 cubic inches.
By seeing the above figure we can say that there are 9 boxes in the larger box.
Thus there are 9 tissue boxes in the larger box.
Now to find the volume of the tissue boxes.
We have to multiply the number of boxes with the volume of the box
V = 125 × 9 = 1125 cubic inches.
Therefore The estimated volume of the box holding the tissue boxes is 1125 cubic inches.

Question 2.
Volume of chalk box: 16 cu in.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 7: Estimate Volume img 94
Volume of large box: ______________ .
_____ cu in.

Answer:
Given that, the volume of the chalk box is 16 cubic inches.
From the figure, we can see that there are 24 boxes.
The volume of the large box is 24 × 16 = 384 cubic inches.
Therefore the estimated volume of the large box is 384 cu in.

Question 3.
Volume of small jewelry box: 30 cu cm
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 7: Estimate Volume img 95
Volume of large box: __________
_____ cu cm

Answer:
Given, the volume of the small jewelry box is 30 cu cm
There are 10 small jewelry boxes.
V = 30 × 10 = 300 cu. cm
Thus the estimated volume of large box is 300 cu. cm

On Your Own

Estimate the volume.

Question 4.
Volume of book: 80 cu in.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 7: Estimate Volume img 96
Volume of large box: __________
_____ cu in.

Answer:
Given that, the volume of the book is 80 cu. in
There are 12 books in the figure.
Multiply the number of books with the volume of each book
= 12 × 80 = 960 cu. inches
Thus the estimated volume of large books is 960 cu in.

Question 5.
Volume of spaghetti box: 750 cu cm
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 7: Estimate Volume img 97
Volume of large box: ________
_____ cu cm

Answer:
Volume of spaghetti box is 750 cu. cm
Volume = 2 × 5 × 4 = 40
Number of boxes = 40
Now multiply 40 with 750 cu. cm to find the volume of large box
V = 40 × 750 cu. cm
V = 30000 cubic cm
Therefore the estimated Volume of large box is 30000 cubic cm

Question 6.
Volume of cereal box: 324 cu in.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 7: Estimate Volume img 98
Volume of large box: __________
cu in.

Answer:
Given, Volume of a cereal box is 324 cu. in
Number of boxes is 2 × 3 × 3 = 18
The volume of large box is 18 × 324 cu. in
V = 18 × 324 cu. in = 5832 cubic inches
Thus the estimated Volume of large box is 5832 cubic inches.

Question 7.
Volume of pencil box: 4,500 cu cm
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 7: Estimate Volume img 99
Volume of large box: ________
_____ cu cm

Answer:
Volume of pencil box is 4500 cu cm
Number of pencil boxes = 2 × 5 = 10
The volume of large box is 4500 × 10 = 45000 cu cm
Thus the estimated volume of large box is 45000 cu cm

Problem Solving – Lesson 7: Estimate Volume – Page No. 678

Sense or Nonsense?

Question 8.
Marcelle estimated the volume of the two boxes below, using one of his books. His book has a volume of 48 cubic inches. Box 1 holds about 7 layers of books, and Box 2 holds about 14 layers of books. Marcelle says that the volume of either box is about the same.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 7: Estimate Volume img 100
Does Marcelle’s statement make sense or is it nonsense?
Explain your answer.
Type below:
_________

Answer:
Calculate the books in box 1
V = lbh
V1 = 2 × 4 × 7 = 56 books
Calculate the volume of books in box 2
V = lbh
V2 = 1 × 4 × 14 = 56 books
So, both boxes hold the same number of books.
Thus Marcelle’s statement make sense.

Share and Show – Lesson 8: Volume of Rectangular Prisms – Page No. 683

Find the volume.

Question 1.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 8: Volume of Rectangular Prisms img 101
The length of the rectangular prism is ______.
The width is ______. So, the area of the base is ______.
The height is ______. So, the volume of the prism is ______.
Type below:
_________

Answer: 120 cu. in

Explanation:
From the figure, we can say that the length of the rectangular prism is 4 in
The width of the rectangular prism is 5 in
The height of the rectangular prism is 6 in.
The volume of the rectangular prism is l × w × h
V = 4 in × 6 in × 5 in = 120 cu. in
So, the volume of the prism is 120 cu. in

Question 2.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 8: Volume of Rectangular Prisms img 102
Volume: ______ cu cm

Answer: 18

Explanation:
From the figure, we can say that the length of the rectangular prism is 2 cm
The width of the rectangular prism is 3 cm
The height of the rectangular prism is 3 cm
The volume of the rectangular prism is l × w × h
V = 2 cm × 3 cm × 3 cm = 18 cu. cm
Thus the volume of the rectangular prism is 18 cu. cm

Question 3.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 8: Volume of Rectangular Prisms img 103
Volume: ______ cu in.

Answer: 12

Explanation:
From the figure, we can say that the length of the rectangular prism is 2 in.
The width of the rectangular prism is 6 in.
The height of the rectangular prism is 1 in.
The volume of the rectangular prism is l × w × h
V = 2 in × 6 in × 1 in
V = 12 Cu in.
Thus the volume of the rectangular prism is 12 Cu in.

On Your Own

Find the volume.

Question 4.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 8: Volume of Rectangular Prisms img 104
Volume: ______ cu mm

Answer: 24

Explanation:
From the figure, we can say that the length of the rectangular prism is 1 mm
The width of the rectangular prism is 8 mm
The height of the rectangular prism is 3 mm
The volume of the rectangular prism is l × w × h
V = 1 mm × 8 mm × 3 mm
V = 24 Cu. mm
Thus the volume of the rectangular prism is 24 Cu. mm

Question 5.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 8: Volume of Rectangular Prisms img 105
Volume: ______ cu cm

Answer: 160

Explanation:
From the figure, we can say that the length of the rectangular prism is 10 cm
The width of the rectangular prism is 4 cm
The height of the rectangular prism is 4 cm
The volume of the rectangular prism is l × w × h
V = 10 cm × 4 cm × 4 cm = 160 Cu. cm
Thus the volume of the rectangular prism is 160 Cu. cm

Question 6.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 8: Volume of Rectangular Prisms img 106
Volume: ______ cu ft

Answer: 150

Explanation:
From the figure, we can say that the length of the rectangular prism is 5 ft
The width of the rectangular prism is 6 ft
The height of the rectangular prism is 5 ft
The volume of the rectangular prism is l × w × h
V = 5 ft × 6 ft × 5 ft
V = 150 Cu. ft
Thus the volume of the rectangular prism is 150 Cu. ft

Question 7.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 8: Volume of Rectangular Prisms img 107
Volume: ______ cu in.

Answer: 196

Explanation:
From the figure, we can say that the length of the rectangular prism is 7 in.
The width of the rectangular prism is 7 in.
The height of the rectangular prism is 4 in.
The volume of the rectangular prism is l × w × h
V = 7 in × 7 in × 4 in = 196 Cu. in
Thus the volume of the rectangular prism is 196 Cu. in

UNLOCK the Problem – Lesson 8: Volume of Rectangular Prisms – Page No. 684

Question 8.
Rich is building a travel crate for his dog, Thomas, a beagle mix who is about 30 inches long, 12 inches wide, and 24 inches tall. For Thomas to travel safely, his crate needs to be a rectangular prism that is about 12 inches greater than his length and width, and 6 inches greater than his height. What is the volume of the travel crate that Rich should build?
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 8: Volume of Rectangular Prisms img 108
a. What do you need to find to solve the problem?
Type below:
_________

Answer: We need to find the volume of the travel crate that Rich should build.

Question 8.
b. How can you use Thomas’s size to help you solve the problem?
Type below:
_________

Answer: Thomas’s size helps to find the length, width and height of the dog crate.

Question 8.
c. What steps can you use to find the size of Thomas’s crate?
Type below:
_________

Answer:
Rich is building a travel crate for his dog, Thomas, a beagle mix who is about 30 inches long, 12 inches wide, and 24 inches tall.
For Thomas to travel safely, his crate needs to be a rectangular prism that is about 12 inches greater than his length and width, and 6 inches greater than his height.
Length of the dog crate is 30 in + 12 in = 42 inches
Width of the dog crate is 12 inches more than width of Thomas crate = 12 in + 12 in = 24 inches
Height of the dog crate is 24 in + 6 in = 30 inches
V = 42 in × 24 in × 30 in
V = 30,240 cu in

Question 8.
d. Fill in the blanks for the dimensions of the dog crate.
length: _____
width: _____
height: _____
area of base: _____
Type below:
_________

Answer:
Crate length = 30 + 12 = 42 in
Crate width = 12 + 12 = 24 in
Crate height = 24 + 6 = 30 in
Area of base = l × w
A = 42 in × 24 in = 1008 sq in.

Question 8.
e. Find the volume of the crate by multiplying the base area and the height.
______ × ______ = ______
So, Rich should build a travel crate for Thomas that has a volume of ______ .
Type below:
_________

Answer:
Area of base = l × w
A = 42 in × 24 in = 1008 sq in.
Height = 30 in
V = 1008 sq in × 30 in = 30240 cu. in
So, Rich should build a travel crate for Thomas that has a volume of 30240 cu. in

Question 9.
What is the volume of the rectangular prism at the right?
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 8: Volume of Rectangular Prisms img 109
Options:
a. 35 in.3
b. 125 in.3
c. 155 in.3
d. 175 in.3

Answer: 175 in.3

Explanation:
Length = 5 in
Width = 7 in
Height = 5 in
Volume of the rectangular prism is l × w × h
V = 5 in × 7 in × 5 in
V = 175 in.3
The volume of the rectangular prism is 175 in.3
Therefore the correct answer is option D.

Share and Show – Lesson 9: Algebra Apply Volume Formulas – Page No. 689

Find the volume.

Question 1.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 9: Algebra Apply Volume Formulas img 110
V =____ cu ft

Answer: 40

Explanation:
length = 2 ft
width = 4 ft
height = 5 ft
Volume of the rectangular prism is l × w × h
V = 2 ft × 4 ft × 5 ft
V = 40 cu ft
Volume of the rectangular prism is 40 cu. ft

Question 2.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 9: Algebra Apply Volume Formulas img 111
V =____ cu cm

Answer: 144

Explanation:
length = 4 cm
width = 4 cm
height = 9 cm
Volume of the rectangular prism is l × w × h
V = 4 cm × 4 cm × 9 cm
V = 144 cu cm
Volume of the rectangular prism is 144 cu cm

On Your Own

Find the volume.

Question 3.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 9: Algebra Apply Volume Formulas img 112
V =____ cu in.

Answer: 216

Explanation:
length = 6 in
width = 6 in
height = 6 in
Volume of the prism is l × w × h
V = 6 in × 6 in × 6 in
V = 216 cu. in
Thus the Volume of the prism is 216 cu. in.

Question 4.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 9: Algebra Apply Volume Formulas img 113
V =____ cu ft

Answer: 192

Explanation:
length = 12 ft
width = 4 ft
height = 4 ft
Volume of the rectangular prism is l × w × h
V = 12 ft × 4 ft × 4 ft
V = 192 cu ft
Therefore, the Volume of the rectangular prism is 192 cu ft.

Question 5.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 9: Algebra Apply Volume Formulas img 114
V =____ cu cm

Answer: 240

Explanation:
length = 10 cm
width = 6 cm
height = 4 cm
Volume of the rectangular prism is l × w × h
V = 10 cm × 6 cm × 4 cm
V = 240 Cu. cm
Therefore, the Volume of the rectangular prism is 240 Cu. cm.

Question 6.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 9: Algebra Apply Volume Formulas img 115
V =____ cu in.

Answer: 1008

Explanation:
length = 14 in.
width = 6 in.
height = 12 in.
Volume of the rectangular prism is l × w × h
V = 14 in × 6 in × 12 in
V = 1008 cu. in
Thus the Volume of the rectangular prism is 1008 cu. in

Question 7.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 9: Algebra Apply Volume Formulas img 116
V =420 cu ft
■ = ____ ft

Answer: 10

Explanation:
length = 7 ft
width = 6 ft
height = ■ ft
Volume of the rectangular prism is l × w × h
420 cu ft = 7 ft × 6 ft × ■
■ × 42 sq ft = 420 cu ft
■ = 420 cu ft ÷ 42 sq ft
■ = 10 ft

Question 8.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 9: Algebra Apply Volume Formulas img 117
V =900 cu cm
■ = ____ cm

Answer: 10

Explanation:
length = 6 cm
width = 15 cm
height = ■ cm
Volume of the rectangular prism is l × w × h
V = 900 cu cm
900 cu cm = 6 cm × 15 cm × ■ cm
900 cu cm = 90 sq cm × ■ cm
■ cm = 900 cu cm ÷ 90 sq cm
■ cm = 10 cm

Problem Solving – Lesson 9: Algebra Apply Volume Formulas – Page No. 690

Question 9.
The Jade Restaurant has a large aquarium on display in its lobby. The base of the aquarium is 5 feet by 2 feet. The height of the aquarium is 4 feet. How many cubic feet of water are needed to completely fill the aquarium?
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 9: Algebra Apply Volume Formulas img 118
V =____ cu ft of water

Answer: 40 cu ft of water

Explanation:
The Jade Restaurant has a large aquarium on display in its lobby.
The base of the aquarium is 5 feet by 2 feet.
The height of the aquarium is 4 feet.
Volume = b × w × h
V = 5 feet × 2 feet× 4 feet
V = 40 Cu. ft
Therefore, the volume of the aquarium is 40 cu ft of water.

Question 10.
The Pearl Restaurant put a larger aquarium in its lobby. The base of their aquarium is 6 feet by 3 feet, and the height is 4 feet. How many more cubic feet of water does the Pearl Restaurant’s aquarium hold than the Jade Restaurant’s aquarium?
____ cu ft

Answer: 32 cu ft

Explanation:
The Pearl Restaurant put a larger aquarium in its lobby.
The base of their aquarium is 6 feet by 3 feet, and the height is 4 feet.
Volume = b × w × h
V = 6 feet × 3 feet × 4 feet = 72 cu. feet
Thus the Volume of Pearl Restaurant’s aquarium is 72 cu. feet
The volume of the Jade Restaurant’s aquarium is 40 cu ft of water
V = Vp – Vj
V = 72 – 40 = 32 cu feet

Question 11.
Eddie measured his aquarium using a small fish food box. The box has a base area of 6 inches and a height of 4 inches. Eddie found that the volume of his aquarium is 3,456 cubic inches. How many boxes of fish food could fit in the aquarium? Explain your answer.
____ boxes

Answer: 144 boxes

Explanation:
Volume = b × h
V = 6 in × 4 in = 24 cu in
To find out how many boxes will fit, divide the aquarium volume by the food box volume.
numfit = Vaq/Vbox
numfit = 3456/24 = 144
144 fish food boxes fir inside the aquarium.

Question 12.
Describe the difference between area and volume.
Type below:
_________

Answer: The surface area is the sum of the areas of all the faces of the solid figure. It is measured in square units. Volume is the number of cubic units that make up a solid figure.

Question 13.
Test Prep Adam stores his favorite CDs in a box like the one at the right. What is the volume of the box?
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 9: Algebra Apply Volume Formulas img 119
Options:
a. 150 cubic centimeters
b. 750 cubic centimeters
c. 1,050 cubic centimeters
d. 1,150 cubic centimeters

Answer: 1,050 cubic centimeters

Explanation:
L = 15 cm
W = 10 cm
H = 7 cm
V = lwh
V = 15 cm × 10 cm × 7 cm = 1050 cubic centimeters
Thus the correct answer is option C.

Share and Show – Lesson 10: Problem Solving Compare Volumes – Page No. 695

Question 1.
Mr. Price makes cakes for special occasions. His most popular-sized cakes have a volume of 360 cubic inches. The cakes have a height, or thickness, of 3 inches, and have different whole number lengths and widths. No cakes have a length or width of 1 or 2 inches. How many different cakes, each with a different-size base, have a volume of 360 cubic inches?
First, think about what the problem is asking you to solve, and the information that you are given.
Next, make a table using the information from problem.
Finally, use the table to solve the problem.
Type below:
_________

Answer: There are total of 8 different possible combination of length and width

Explanation:
Volume = 360 cubic inches
Height = 3 inches
Volume = l x w x h
360 = l x w x 3
l x w = 120
The factors of 120 are,
1 x 120,
2x 60,
3 x 40,
4 x 30,
5 x 24,
6 x 20,
8 x 15,
10 x 12

Question 2.
What if the 360 cubic-inch cakes are 4 inches thick and any whole number length and width are possible? How many different cakes could be made? Suppose that the cost of a cake that size is $25, plus $1.99 for every 4 cubic inches of cake. How much would the cake cost?
Type below:
_________

Answer:
Since the store have a volume of 360 cu in and a height of 4 in.
We need to find the number of different stones which have a base of 90 sq in.
V = b × h
B = 360 cu in/4 in
B = 90 sq in.
Consider the factors of 90.
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Make a table with the base, height and volume for each pair of factors
Height = 4 in
1 × 90 × 4 = 360 cu in
2 × 45 × 4 = 360 cu in
3 × 30 × 4 = 360 cu in
5 × 18 × 4 = 360 cu in
6 × 15 × 4 = 360 cu in
9 × 10 × 4 = 360 cu in
6 different sized paving stones.
Remember that each store has a volume of 360 cu in.
Divide by 4 to find how many 4 cu in per stone
Concrete = $0.18 × (360/4)
= $0.18 × 90 = $18.70
The cost of the stone plus the concrete
cost = $2.50 + concrete
Cost = $2.50 + $16.20 = $18.70

Question 3.
One company makes inflatable swimming pools that come in four sizes of rectangular prisms. The length of each pool is twice the width and twice the depth. The depth of the pools are each a whole number from 2 to 5 feet. If the pools are filled all the way to the top, what is the volume of each pool?
Type below:
_________

Answer:
If the depth of the pool is 2 feet
then the length of the pool is twice the width and twice the depth
That means 2 feet × 2 × 2 = 8 feet
Width is twice the depth
W = 2 feet × 2 = 4 feet
The volume of the rectangular swimming pool is l × w × h
V = 8 ft × 4 feet × 2 ft
V = 64 cu ft
If the depth of the pool is 3 feet
then the length of the pool is twice the width and twice the depth
That means 3 feet × 2 × 2 = 12 feet
Width is twice the depth
W = 3 feet × 2 = 6 feet
The volume of the rectangular swimming pool is l × w × h
V = 12 ft × 6 feet × 2 ft
V = 144 cu ft
If the depth of the pool is 4 feet
then the length of the pool is twice the width and twice the depth
That means 4 feet × 2 × 2 = 16 feet
Width is twice the depth
W = 4 feet × 2 = 8 feet
The volume of the rectangular swimming pool is l × w × h
V = 16 ft × 8 feet × 2 ft
V = 256 cu ft
If the depth of the pool is 5 feet
then the length of the pool is twice the width and twice the depth
That means 5 feet × 2 × 2 = 20 feet
Width is twice the depth
W = 5 feet × 2 = 10 feet
The volume of the rectangular swimming pool is l × w × h
V = 20 ft × 10 feet × 2 ft
V = 400 cu ft

On Your Own – Lesson 10: Problem Solving Compare Volumes – Page No. 696

Question 4.
Ray wants to buy the larger of two aquariums. One aquarium has a base that is 20 inches by 20 inches and a height that is 18 inches. The other aquarium has a base that is 40 inches by 12 inches and a height that is 12 inches. Which aquarium has a greater volume? By how much?
Type below:
_________

Answer: 1440 cu. in

Explanation:
Volume = l × w × h
Volume of Aquarium 1 = 20 in × 20 in × 18 in
V = 7200 cu. in
Volume = l × w × h
Volume of Aquarium 2 is 40 in × 12 in × 12 in
V for A2 = 5760 cu in
A1 > A2
A1 has a greater volume.
Subtract A2 from A1
A1 – A2 = 7200 cu in – 5760 cu in
= 1440 cu in
The volume of Aquarium 1 is 1440 cu in more than Volume of Aquarium 2.

Question 5.
Ken owns 13 CDs. His brother Keith has 7 more CDs than he does. Their brother, George, has more CDs than either of the younger brothers. Together, the three brothers have 58 CDs. How many CDs does George have?
______ CDs

Answer: 25 CDs

Explanation:
Given that,
Ken owns 13 CDs.
His brother Keith has 7 more CDs than he does.
Their brother, George, has more CDs than either of the younger brothers.
Together, the three brothers have 58 CDs.
Keith has 7 more CDs than Ken
That means he has 7 + 13 = 20 CDs
Now subtract Ken’s CDs, Keith CDs from the total number of CDs.
= 58 – 20 – 13 = 25 CDs.
Thus George has 25 CDs.

Question 6.
Kathy has ribbons that have lengths of 7 inches, 10 inches, and 12 inches. Explain how she can use these ribbons to measure a length of 15 inches.
Type below:
_________

Answer: She could take the 10-inch ribbon and then use 5 inches from the 7-inch ribbon

Question 7.
A park has a rectangular playground area that has a length of 66 feet and a width of 42 feet. The park department has 75 yards of fencing material. Is there enough fencing material to enclose the playground area? Explain.
______

Answer: Yes

Explanation:
A park has a rectangular playground area that has a length of 66 feet and a width of 42 feet.
The park department has 75 yards of fencing material.
Area of the rectangular playground = l × w
A = 66 feet × 42 feet
A = 2772 sq. ft
Perimeter of the rectangular playground = 2l + 2w
P = 2 × 66 + 2 × 42
P = 216 ft
Now convert from feet to yard
We know that 1 yard = 3 feet
216 ft = 1/3 × 216 = 72 yard
72 yard is less than 75 yard
Thus the park department has enough fencing material.

Question 8.
Test Prep John is making a chest that will have a volume of 1,200 cubic inches. The length is 20 inches and the width is 12 inches. How many inches tall will his chest be?
Options:
a. 4 in.
b. 5 in.
c. 6 in.
d. 7 in.

Answer: 5 in

Explanation:
John is making a chest that will have a volume of 1,200 cubic inches.
The length is 20 inches and the width is 12 inches.
Volume = l × w × h
1200 cu in = 20 in × 12 in × h
240 sq in × h = 1200 cu in
h = 1200 cu in ÷ 240 sq in
h = 5 in
Thus John’s chest will be 5 inches tall.
The correct answer is option B.

Share and Show – Lesson 11: Find Volume of Composed Figures – Page No. 701

Find the volume of the composite figure.

Question 1.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 11: Find Volume of Composed Figures img 120
V = ______ cu in.

Answer: 88 cu in.

Explanation:
Split the figure into 2 parts
Volume of figure 1:
b = 2 in
h = 3 in
w = 4 in
V = 2 in × 4 in × 3 in
V = 24 cu. in
Volume of figure 2:
b = 8 in
w = 4 in
h = 2 in
V = 8 in × 4 in × 2 in
V = 64 in
Volume of the composite figure = 24 cu in + 64 cu. in = 88 cu. in

Question 2.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 11: Find Volume of Composed Figures img 121
V = ______ cu cm

Answer: 48 cu cm

Explanation:
Split the figure into 2 parts
Volume of figure 1:
b = 3 cm
h = 1 cm
w = 2 cm
V = 3 cm × 2 cm × 1 cm
V = 6 cu. cm
Volume of figure 2:
b = 7 cm
w = 6 cm
h = 1 cm
V = 7 cm × 6 cm × 1 cm
V = 42 cu. cm
Volume of the composite figure = 42 cu. cm + 6 cu. cm = 48 cu cm

On Your Own

Find the volume of the composite figure.

Question 3.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 11: Find Volume of Composed Figures img 122
V = ______ cu ft

Answer: 52 cu ft

Explanation:
Split the figure into 2 parts
Volume of figure 1:
b = 6 ft
h = 2 ft
w = 3 ft
V = 6 ft × 3 ft × 2 ft
V = 36 cu. ft
Volume of figure 2:
b = 4 ft
w = 2 ft
h = 2 ft
V = 4 ft × 2 ft × 2 ft
V = 16 cu. ft
Volume of the composite figure = 36 cu. ft + 16 cu. ft = 52 cu ft

Question 4.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 11: Find Volume of Composed Figures img 123
V = ______ cu cm

Answer: 108 cu. cm

Explanation:
Split the figure into 2 parts
Volume of figure 1:
b = 3 cm
w = 8 cm
h = 2 cm
V = 3 cm × 8 cm × 2 cm
V = 48 cu cm
Volume of figure 2:
b = 10 cm
w = 3 cm
h = 2 cm
V = 10 cm × 3 cm × 2 cm
V = 60 cu cm
Volume of the composite figure = 48 cu cm + 60 cu cm = 108 cu. cm

Question 5.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 11: Find Volume of Composed Figures img 124
V = ______ cu in.

Answer: 204 cu. in

Explanation:
Split the figure into 2 parts
Volume of figure 1:
b = 3 in
h = 5 in
w = 4 in
V = 3 in × 4 in × 5 in
V = 60 cu. in
Volume of figure 2:
b = 12 in
w = 4 in
h = 3 in
V = 12 in × 4 in × 3 in
V = 144 cu. in
Volume of the composite figure = 60 cu in + 144 cu. in = 204 cu. in

Question 6.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 11: Find Volume of Composed Figures img 125
V = ______ cu ft

Answer: 96 cu ft

Explanation:
Split the figure into 3 parts.
Figure 1:
V1 = 9 ft × 4 ft × 2 ft
V1 = 72 cu. ft
Figure 2:
V2 = 3 ft × 4 ft × 2 ft
V2 = 24 cu. ft
V = V1 + V2
V = 72 cu. ft + 24 cu. ft = 96 cu. ft
Thus the volume of the composite figure is 96 cu. ft

Question 7.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 11: Find Volume of Composed Figures img 126
V = ______ cu ft

Answer: 300 cu. ft

Explanation:
Go-Math-Grade-5-Answer-Key-Chapter-11-Geometry-and-Volume-img-126
Split the figure into 3 parts.
Figure 1:
V1 = 5 ft × 4 ft × 4 ft
V1 = 80 cu. ft
Figure 2:
V2 = 6 ft × 5 ft × 6 ft
V2 = 180 cu ft
Figure 3:
V3 = 4 ft × 5 ft × 2 ft
V3 = 40 cu. ft
V = V1 + V2 + V3
V = 80 cu. ft + 180 cu ft + 40 cu ft = 300 cu. ft

Question 8.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 11: Find Volume of Composed Figures img 127
V = ______ cu cm

Answer: 102 cu cm

Explanation:
Go-Math-Grade-5-Answer-Key-Chapter-11-Geometry-and-Volume-img-127
Figure 1:
V1 = 10 cm × 3 cm × 2 cm = 60 cu cm
V1 = 60 cu. cm
Figure 2:
V2= 2 cm × 3 cm × 4 cm
V2 = 24 cu. cm
Figure 3:
V3 = 2 cm × 3 cm × 3 cm
V3 = 18 cu. cm
V = V1 + V2 + V3
V = 60 cu. cm + 24 cu. cm + 18 cu. cm = 102 cu. cm

Problem Solving – Lesson 11: Find Volume of Composed Figures – Page No. 702

Use the composite figure at the right for 9–11.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 11: Find Volume of Composed Figures img 128

Question 9.
As part of a wood-working project, Jordan made the figure at the right out of wooden building blocks. How much space does the figure he made take up?
______ cu in.

Answer: 784 cu. in

Explanation:
Split the figure into 2 parts
Figure 1:
V1 = 14 in × 4 in × 5 in
V1 = 280 cu. in
Figure 2:
V2 = 12 in × 14 in × 3 in
V2 = 504 cu. in
V = V1 + V2
V = 280 cu. in + 504 cu. in
V = 784 cu. in

Question 10.
What are the dimensions of the two rectangular prisms you used to find the volume of the figure? What other rectangular prisms could you have used?
Type below:
________

Answer:
Dimensions for figure 1:
Base = 14 in
Width = 4 in
Height = 5 in
Dimensions for figure 2:
Base = 12 in
Width = 14 in
Height = 3 in

Question 11.
If the volume is found using subtraction, what is the volume of the empty space that is subtracted? Explain.
______ cu in.

Answer: 560 cu. in

Explanation:
B = 8 in
H = 5 in
W = 14 in
V = 8 in × 14 in × 5 in
V = 560 cu. in
Thus the volume of the empty space is 560 cu. in

Question 12.
Explain how you can find the volume of composite figures that are made by combining rectangular prisms.
Type below:
________

Answer:

Split the figure into 2 parts
Figure 1:
V1 = 14 in × 4 in × 5 in
V1 = 280 cu. in
Figure 2:
V2 = 12 in × 14 in × 3 in
V2 = 504 cu. in
V = V1 + V2
V = 280 cu. in + 504 cu. in
V = 784 cu. in

Question 13.
Test Prep What is the volume of the composite figure?
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Lesson 11: Find Volume of Composed Figures img 129
Options:
a. 126 cubic centimeters
b. 350 cubic centimeters
c. 450 cubic centimeters
d. 476 cubic centimeters

Answer: 476 cubic centimeters

Explanation:
Split the figure into 2 parts
Figure 1:
V1 = 10 cm × 7 cm × 5 cm
V1 = 350 cu. cm
Figure 2:
V2 = 3 cm × 7 cm × 6 cm
V2 = 126 cu. cm
V = V1 + V2
V = 350 cu. cm + 126 cu. cm
V = 476 cu. cm

Chapter Review/Test – Page No. 705

Question 1.
Fran drew a triangle with no congruent sides and 1 right angle. Which term accurately describes the triangle? Mark all that apply.
Options:
a. isosceles
b. scalene
c. acute
d. right

Answer: Right

Explanation:
A right triangle is a type of triangle that has one angle that measures 90°. Right triangles, and the relationships between their sides and angles, are the basis of trigonometry.
Thus the correct answer is option D.

Question 2.
Jose stores his baseball cards in a box like the one shown.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 130
Use the numbers and symbols on the tiles to write a formula that represents the volume of the box. Symbols may be used more than once or not at all.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 131
What is the volume of the box?
V = ______ cubic inches

Answer:
Volume of the box is l × w × h
V = 8 in × 10 in × 3 in
V = 240 cu. in
Thus the volume of the box is 240 cu. in

Question 3.
Mr. Delgado sees this sign while he is driving. For 3a–3b, choose the values and term that correctly describes the shape Mr. Delgado saw.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 132
3a. The figure has Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 133 sides and Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 134angles.
Type below:
________

Answer: The figure has 3 sides and 3 angles.

Explanation:
From the above figure we can say that there are three sides and three angles.

Question 3.
3b. All of the sides are congruent, so the figure is Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 135
________

Answer: a regular polygon
If all the sides are congruent then the polygon is a regular polygon.

Chapter Review/Test – Page No. 706

Question 4.
What is the volume of the composite figure?
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 136
______ cubic feet

Answer: 36 cubic feet

Explanation:
Figure 1:
length = 2 ft
width = 3 ft
height = 1 ft
Volume of 1st figure = l × w × h
V = 2 ft × 3 ft × 1 ft = 6 cu. ft
Figure 2:
length = 4 ft
width = 3 ft
height = 1 ft
Volume of 1st figure = l × w × h
V = 4 ft × 3 ft × 1 ft = 12 cu. ft
Figure 3:
length = 6 ft
width = 3 ft
height = 1 ft
Volume of 1st figure = l × w × h
V = 6 ft × 3 ft × 1 ft = 18 cu. ft
Add all the volumes = 6 cu. ft + 12 cu. ft + 18 cu. ft
Volume = 36 cu. ft

Question 5.
Match the figure with the number of unit cubes that would be needed to build each figure. Not every number of unit cubes will be used.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 137

Answer:
Go-Math-Grade-5-Answer-Key-Chapter-11-Geometry-and-Volume-img-137

Explanation:
Count the number of unit cubes in the first figure.
There are 10 unit cubes in figure 1 so match the figure 1 to 10 unit cubes.
Count the number of unit cubes in the second figure.
There are 12 unit cubes in figure 2 so match figure 2 to 12 unit cubes.
Count the number of unit cubes in the third figure.
There are 9 unit cubes in figure 3 so match figure 3 to 9 unit cubes.

Question 6.
Chuck is making a poster about polyhedrons for his math class. He will draw figures and organize them in different sections of the poster.
Part A
Chuck wants to draw three-dimensional figures whose lateral faces are rectangles. He says he can draw prisms and pyramids. Do you agree?
Explain your answer.
i. yes
ii. no

Answer: No

Explanation:
The lateral faces of a pyramid are triangles.
The lateral faces of a prism are rectangles.

Question 6.
Part B
Chuck says that he can draw a cylinder on his polyhedron poster because it has a pair of bases that are congruent. Is Chuck correct?
Explain your reasoning.
i. yes
ii. no

Answer: No

Explanation:
A cylinder does have 2 congruent bases, but a cylinder is not a polyhedron.
A cylinder has 1 curved surface, while a polyhedron has faces that are polygons

Chapter Review/Test – Page No. 707

Question 7.
Javier drew the shape shown. For 7a–7b, choose the values and term that correctly describe the shape Javier drew.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 138
7a. The figure has Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 139 sides and Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 140 angles.
Type below:
_________

Answer: 8, 8
The above figure has 8 sides and 8 angles.

Question 7.
7b. The figure is a Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 141
Type below:
_________

Answer: The polygon with 8 sides is known as the octagon. The above figure is congruent thus it is a regular octagon.

Question 8.
Victoria used 1-inch cubes to build the rectangular prism shown. Find the volume of the rectangular prism Victoria built.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 142
______ cubic inches

Answer: 72

Explanation:
Given,
l = 6 in
w = 3 in
h = 4 in
The volume of the rectangular prism is l × w × h
V = 6 in × 3 in × 4in
V = 72 cu in.
Hence, the volume of the rectangular prism Victoria built is 72 cu. in.

Question 9.
Nathan drew a scalene, obtuse triangle. For 9a–9c, choose Yes or No to indicate whether the figure shown could be the triangle that Nathan drew.
a. Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 143
i. yes
ii. no

Answer: Yes

Explanation:
The above different have different sizes thus the triangle is scalene. The angle for the above triangle is more than 90° thus the angle is an obtuse angle. So, the answer is yes.

Question 9.
b. Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 144
i. yes
ii. no

Answer: No

Explanation:
The above different have different sizes thus the triangle is scalene. It has one right angle thus the statement is not correct.

Question 9.
c. Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 145

Answer: No

Explanation:
The above different have different sizes thus the triangle is scalene. It has one right angle thus the statement is not correct.

Chapter Review/Test – Page No. 708

Question 10.
A shipping crate holds 20 shoeboxes. The dimensions of a shoebox are 6 inches by 4 inches by 12 inches. For 10a–10b, select True or False for each statement.
a. Each shoebox has a volume of 22 cubic inches.
i. True
ii. False

Answer: False

Explanation:
Shoebox volume:
V = 6 in × 4 in × 12 in
V = 288 cu. in
Thus the statement is false.

Question 10.
b. Each crate has a volume of about 440 cubic inches.
i. True
ii. False

Answer: False

Explanation:
Crate Volume:
V = 288 cu. in × 20
V = 5760 cu. in
Thus the statement is false.

Question 10.
c. If the crate could hold 27 shoeboxes the volume of the crate would be about 7,776 cubic inches.
i. True
ii. False

Answer: True

Explanation:
Crate Volume:
V = 288 cu. in × 27
V = 7776 cu. in
Thus the statement is true.

Question 11.
Mario is making a diagram that shows the relationship between different kinds of quadrilaterals. In the diagram, each quadrilateral on a lower level can also be described by the quadrilateral(s) above it on higher levels.
Part A
Complete the diagram by writing the name of one figure from the tiles in each box. Not every figure will be used.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 146

Answer:
Go-Math-Grade-5-Answer-Key-Chapter-11-Geometry-and-Volume-img-146

Question 11.
Part B
Mario claims that a rhombus is sometimes a square, but a square is always a rhombus. Is he correct? Explain your answer.
i. yes
ii. no

Answer: Yes

Explanation:
A square is a quadrilateral with all sides equal in length and all interior angles right angles. A square however is a rhombus since all four of its sides are of the same length.

Chapter Review/Test – Page No. 709

Question 12.
Write the letter in the box that correctly describes the three-dimensional figure.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 147
Type below:
___________

Answer:
Go-Math-Grade-5-Answer-Key-Chapter-11-Geometry-and-Volume-img-147

Explanation:
Prism: In geometry, a prism is a polyhedron comprising an n-sided polygonal base, a second base which is a translated copy of the first, and n other faces joining corresponding sides of the two bases.
Figure B and C are prisms
Pyramid: In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle called a lateral face. All the edges meet at the same point in the pyramid. Thus the figures A and D are pyramids.

Question 13.
Mark packed 1-inch cubes into a box with a volume of 120 cubic inches. How many layers of 1-inch cubes did Mark pack?
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 148
______ layers

Answer: 5

Explanation:
Mark packed 1-inch cubes into a box with a volume of 120 cubic inches.
By seeing the figure we can say that there are 24 unit cubes.
To find the number of layers we need to divide 120 by 24
= 120 ÷ 24 = 5
There are 5 layers of 1-inch cubes.

Question 14.
A composite figure is shown. What is the volume of the composite figure?
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 149
Volume = ______ cubic centimeters

Answer: 312

Explanation:
Split the figure into 2 parts.
Figure 1:
h = 3 cm
w = 6 cm
b = 4 cm
V = 4 cm × 6 cm × 3 cm = 72 cu. cm
Figure 2:
b = 10 cm
w = 6 cm
h = 4 cm
V = 10 cm × 6 cm × 4 cm = 240 cu. cm
Now add the volume of 2 figures
72 cu. cm + 240 cu. cm = 312 cu cm
Thus the volume of the composite figure is 312 cu. cm

Chapter Review/Test – Page No. 710

Question 15.
For 15a–15c, write the name of one quadrilateral from the tiles to complete a true statement. Use each quadrilateral once only.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 150
a. A Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 151 is always a parallelogram.
_________

Answer: rectangle

Explanation: Parallelograms are quadrilaterals with two sets of parallel sides. Since squares must be quadrilaterals with two sets of parallel sides, then all squares are parallelograms.

Question 15.
b. A Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 152 is always a rhombus.
_________

Answer: square

Explanation: A square is a quadrilateral with all sides equal in length and all interior angles right angles.

Question 15.
c. A Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 153 is sometimes a parallelogram.
_________

Answer: trapezoid

Explanation: A trapezoid has one pair of parallel sides and a parallelogram has two pairs of parallel sides. So a parallelogram is also a trapezoid.

Question 16.
Megan’s aquarium has a volume of 4,320 cubic inches. Which could be the dimensions of the aquarium? Mark all that apply.
Options:
a. 16 in. by 16 in. by 18 in.
b. 14 in. by 18 in. by 20 in.
c. 12 in. by 15 in. by 24 in.
d. 8 in. by 20 in. by 27 in.

Answer: C, D

Explanation:
The volume of a prism = l × w × h
1. V = 16 in × 16 in × 16 in
V = 4608 cu. in
2. V = 14 in × 18 in × 20 in = 5040 cu. in
3. V = 12 in × 15 in × 24 in = 4320 cu. in
4. V = 8 in × 20 in × 27 in = 4320 cu in
Thus the suitable answers are C and D.

Question 17.
Ken keeps paper clips in a box that is the shape of a cube. Each side of the cube is 3 inches. What is the volume of the box?
______ cubic inches

Answer: 27

Explanation:
Ken keeps paper clips in a box that is the shape of a cube.
Each side of the cube is 3 inches.
The volume of a cube = 3 in × 3 in × 3 in = 27 cu. in
Therefore the volume of the box is 27 cubic inches.

Question 18.
Monica used 1-inch cubes to make the rectangular prism shown. For 18a–18d, write the value that makes each statement true. Each value can be used more than once or not at all.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 154
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 155
a. Each cube has a volume of ____ cubic inch(es).

Answer: 1

Explanation:
Monica used 1-inch cubes to make the rectangular prism
Volume = 1 in × 1 in × 1 in = 1 cu. in.
Each cube has a volume of 1 cubic inch.

Question 18.
b. Each layer of the prism is made up of ____ cubes.
______ cubes

Answer: 20

Explanation:
We can calculate the layer by calculating the base and width
4 × 5 = 20 cubes
Each layer of the prism is made up of 20 cubes.

Question 18.
c. There are ____ layers of cubes.
______ layers

Answer: 3
By seeing the figure we can say that there are 3 layers of the cube.
You can also find the layers of the cube by calculating the height of the figure.

Question 18.
d. The volume of the prism is ____ cubic inches.
______ cubic inches

Answer: 60

Explanation:
The volume of a prism = l × w × h
V = 4 in × 5 in × 3 in
Volume = 60 cu. inches
Therefore, the volume of the prism is 60 cubic inches.

Chapter Review/Test – Vocabulary – Page No. 4910

Choose the best term from the box.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 156

Question 1.
A _____ has two congruent polygons as bases and rectangular lateral faces.
__________

Answer: prism
A prism has two congruent polygons as bases and rectangular lateral faces.

Question 2.
A _____ has only one base and triangular lateral faces.
__________

Answer: pyramid
A pyramid has only one base and triangular lateral faces.

Concepts and Skills

Name each polygon. Then tell whether it is a regular polygon or not a regular polygon.

Question 3.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 157
Name: __________
Type: __________

Answer:
i. hexagon
ii. regular

Explanation:
A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. It is named by the number of sides and angles it has.
The above figure has six sides and 6 angles. Thus the name of the polygon is hexagon.
Two polygons are congruent when they have the same size and the same shape. The above figure has same size and angles. Thus it is a regular polygon.

Question 4.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 158
Name: __________
Type: __________

Answer:
i. pentagon
ii. regular

Explanation:
A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. It is named by the number of sides and angles it has.
The above figure has five sides and 5 angles. Thus the name of the polygon is pentagon.
Two polygons are congruent when they have the same size and the same shape. The above figure has same size and angles. Thus it is a regular polygon.

Question 5.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 159
Name: __________
Type: __________

Answer:
i. pentagon
ii. not regular

Explanation:
A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. It is named by the number of sides and angles it has.
The above figure has five sides and 5 angles. Thus the name of the polygon is the pentagon.
Two polygons are congruent when they have the same size and the same shape. The above figure does not have the same size and angles. Thus it is not a regular polygon.

Question 6.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 160
Name: __________
Type: __________

Answer:
i. octagon
ii. not regular

Explanation:
A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. It is named by the number of sides and angles it has.
The above figure has 8 sides and 8 angles. Thus the name of the polygon is octagon.
Two polygons are congruent when they have the same size and the same shape. The above figure does not have same size and angles. Thus it is not a regular polygon.

Classify each figure in as many ways as possible.

Question 7.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 161
1. __________
2. __________

Answer:
1. quadrilateral
2. trapezoid

Explanation:
1. A general quadrilateral has 4 sides and 4 angles.
2. A trapezoid is a 4-sided flat shape with straight sides that has a pair of opposite sides parallel.

Question 8.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 162
△ __________
∠ __________

Answer:
△ – scalene
∠ – right

Explanation:
The above triangle has different sides. Thus the triangle is a scalene triangle.
The triangle with one right angle is known as a right angled triangle.

Classify the solid figure. Write prism, pyramid, cone, cylinder, or sphere.

Question 9.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 163
__________

Answer: prism

Explanation:
In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides.

Question 10.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 164
__________

Answer: pyramid

Explanation:
In geometry, a pentagonal pyramid is a pyramid with a pentagonal base upon which are erected five triangular faces that meet at a point (the vertex). Like any pyramid, it is self-dual.

Count the number of cubes used to build each solid figure.

Question 11.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 165
_____ unit cubes

Answer: 4

Explanation:
The figure shows that there are 4 unit cubes.

Question 12.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 166
_____ unit cubes

Answer: 7

Explanation:
By seeing the above figure we can say that there are 7 unit cubes.

Question 13.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 167
_____ unit cubes

Answer: 5

Explanation:
The figure above shows that there are 5 unit cubes.

Chapter Review/Test – Page No. 4920

Fill in the bubble completely to show your answer.

Question 14.
What type of triangle is shown below?
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 168
Options:
a. acute; isosceles
b. acute; scalene
c. obtuse; scalene
d. obtuse; isosceles

Answer: obtuse; scalene

Explanation:
The sides of the triangle is different. Thus it is a scalene triangle. The angle of the triangle is an obtuse angle.
Thus the correct answer is option C.

Question 15.
Angela buys a paperweight at the local gift shop. The paperweight is in the shape of a hexagonal pyramid.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 169
Which of the following represents the correct number of faces, edges, and vertices in a hexagonal pyramid?
Options:
a. 6 faces, 12 edges, 18 vertices
b. 7 faces, 7 edges, 12 vertices
c. 7 faces, 12 edges, 7 vertices
d. 8 faces, 18 edges, 12 vertices

Answer: 7 faces, 12 edges, 7 vertices

Explanation:
In geometry, a hexagonal pyramid is a pyramid with a hexagonal base upon which are erected six isosceles triangular faces that meet at a point.
The hexagonal pyramid has 7 faces, 12 edges and 7 vertices.
Therefore the correct answer is option C.

Question 16.
A manufacturing company constructs a shipping box to hold its cereal boxes. Each cereal box has a volume of 40 cubic inches. If the shipping box holds 8 layers with 4 cereal boxes in each layer, what is the volume of the shipping box?
Options:
a. 160 cu in.
b. 320 cu in.
c. 480 cu in.
d. 1,280 cu in.

Answer: 1,280 cu in.

Explanation:
A manufacturing company constructs a shipping box to hold its cereal boxes.
Each cereal box has a volume of 40 cubic inches.
If the shipping box holds 8 layers with 4 cereal boxes in each layer
Multiply the number of layers with boxes
= 8 × 4 = 32
The volume of 8 layers is 40 × 32 = 1280 cubic inches
Thus the correct answer is option D.

Chapter Review/Test – Page No. 4930

Fill in the bubble completely to show your answer.

Question 17.
Sharri packed away her old summer clothes in a storage tote that had a length of 3 feet, a width of 4 feet, and a height of 3 feet. What was the volume of the tote that Sharri used?
Options:
a. 36 cu ft
b. 24 cu ft
c. 21 cu ft
d. 10 cu ft

Answer: 36 cu ft

Explanation:
Given,
Sharri packed away her old summer clothes in a storage tote that had a length of 3 feet, a width of 4 feet, and a height of 3 feet.
Volume = l × w × h
V = 3 ft × 4 ft × 3 ft
V = 36 cu. ft
Thus the volume of the tote that Sharri used is 36 cu. ft.
The correct answer is option A.

Question 18.
Which quadrilateral is NOT classified as a parallelogram?
Options:
a. Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 170
b. Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 171
c. Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 172
d. Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 173

Answer: Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 171

Explanation:
The opposite sides of figure b are not parallel. Thus the figure b quadrilateral is NOT classified as a parallelogram.

Question 19.
What is the volume of the composite figure below?
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 174
Options:
a. 1,875 cm3
b. 480 cm3
c. 360 cm3
d. 150 cm3

Answer:
Volume of 1st cube is 5 cm × 4 cm × 5 cm = 100 cu. cm
Volume of 2nd cube is 5 cm × 4 cm × 8 cm = 160 cu. cm
Volume of 3rd cube is 5 cm × 4 cm × 5 cm = 100 cu. cm
Add all the volumes to find the volume of the composite figure
That means 100 cu. cm + 160 cu. cm + 100 cu. cm = 360 cu. cm
Therefore the volume of the composite figure is 360 cm3
The correct answer is option C.

Chapter Review/Test – Page No. 4940

Constructed Response

Question 20.
a. A video game store made a display of game console boxes shown at the right. The length, width, and height of each game console box is 2 feet.
Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume Chapter Review/Test img 175
What is the volume of the display of game console boxes? Show your work and explain your answer.
_____ cu ft.

Answer: 512 cu. ft

Explanation:
length = 2 ft
width = 2 ft
height = 2 ft
Volume of the display of game console boxes = 2 ft × 2 ft × 2 ft = 8 cu. ft
Number of console boxes = 64
64 × 8 cu. ft = 512 cu ft
The volume of the display of game console boxes = 512 cu ft

Question 20.
b. On a busy Saturday, the video game store sold 22 game consoles.
What is the volume of the game console boxes that are left?
_____ cu ft.

Answer: 336 cu. ft

length = 2 ft
width = 2 ft
height = 2 ft
The volume of the display of game console boxes = 2 ft × 2 ft × 2 ft = 8 cu. ft
Number of console boxes = 22
The volume of the game console boxes that are left
22 × 8 cu. ft = 176 cu. ft
The volume of the game console boxes that are left = 512 – 176 = 336 cu. ft

Performance Task

Question 21.
Look for two pictures of three-dimensional buildings in newspapers and magazines. The buildings should be rectangular prisms.
A. Paste the pictures on a large sheet of paper. Leave room to write information near the picture.
B. Label each building with their name and location.
C. Research the buildings, if the information is available. Find things that are interesting about the buildings or their location. Also find their length, width, and height to the nearest foot. If the information is not available, measure the buildings on the page in inches or centimeters, and make a good estimate of their width (such as 1/2 the height, rounded to the nearest whole number). Find their volumes.
D. Make a class presentation, choosing one of the buildings you found.

Conclusion

Hoping the knowledge shared about Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume has helped you clear your queries to the possible extent. Download the 5th Grade Go Math Ch 11 Geometry and Volume Answer Key free of cost and take your preparation to next level.

Go Math Grade 4 Answer Key Homework FL Chapter 9 Relate Fractions and Decimals Review/Test

go-math-grade-4-chapter-9-relate-fractions-and-decimals-review-test-answer-key

Are you looking for the best option to do self-study & score the highest marks in the exam? Then, Go Math Grade 4 Answer Key Homework FL Chapter 9 Relate Fractions and Decimals Review/Test is the one you need. You can ace up your preparation & perform practice tests by using the Go Math 4th Grade Answer Key Homework FL Chapter 9 Relate Fractions and Decimals Review/Test. Each and every question explained in a step-wise manner so that 4th-grade students can easily grasp the concepts and practice in an effective way.

Go Math Grade 4 Answer Key Homework FL Chapter 9 Relate Fractions and Decimals Review/Test

Is Go Math 4th Grade Solution Key Homework FL Chapter 9 Relate Fractions and Decimals Review/Test enough to practice & score high? What do you think? From our subject experts’ point of view, it is very helpful in securing max. marks. So, Download Go Math Grade 4 Answer Key Homework FL Chapter 9 Relate Fractions and Decimals Review/Test pdf and increase your math skills. This Go Math Grade 4 Answer Key aids the students to score the highest marks as well as gain more subject knowledge.

Review/Test – Page No. 373

Choose the best term from the box.
Go Math Grade 4 Answer Key Homework FL Chapter 9 Relate Fractions and Decimals Review Test img 1

Question 1.
One of ten equal parts is one __________.
_______

Answer: tenth
One of ten equal parts is one-tenth.

Question 2.
A __________ is a symbol used to separate dollars from cents in money amounts and to separate the ones and the tenths places in decimals.
_______

Answer: decimal point
A decimal point is a symbol used to separate dollars from cents in money amounts and to separate the ones and the tenths places in decimals.

Question 3.
A ________________ is a number with one or more digits to the right of the decimal point.
_______

Answer: decimal
A decimal  is a number with one or more digits to the right of the decimal point.

Write the fraction and the decimal shown by the model.

Question 4.
Go Math Grade 4 Answer Key Homework FL Chapter 9 Relate Fractions and Decimals Review Test img 2
\(\frac{□}{□}\)

Answer: \(\frac{7}{10}\)

Explanation:
We can see from the above figure that there are 10 blocks and among them, 7 are shaded. So, the fraction of the shaded part is \(\frac{7}{10}\)

Question 4.
Go Math Grade 4 Answer Key Homework FL Chapter 9 Relate Fractions and Decimals Review Test img 3
\(\frac{□}{□}\)

Answer: \(\frac{52}{100}\)

Explanation:
We can see from the above figure that there are 100 boxes, in which 52 are shaded. So, the fraction of the shaded part is \(\frac{52}{100}\)

Write the number as hundredths in fraction form and decimal form.

Question 6.
\(\frac{9}{10}\)
Type below:
________

Answer: 0.9

Explanation:
The hundredth of the fraction \(\frac{9}{10}\) is \(\frac{90}{100}\). And the decimal form of the given fraction is 0.9

Question 7.
\(\frac{3}{10}\)
Type below:
________

Answer: 0.3

Explanation:
The hundredth of the fraction \(\frac{3}{10}\) is \(\frac{30}{100}\). And the decimal form of the given fraction is 0.3.

Question 8.
0.2
Type below:
________

Answer: \(\frac{2}{10}\)

Explanation:
The hundredth of the fraction \(\frac{2}{10}\) is \(\frac{20}{100}\). And the decimal form of the given fraction is 0.2

Find the sum.

Question 9.
\(\frac{5}{10}+\frac{30}{100}\) = \(\frac{□}{□}\)

Answer: \(\frac{80}{100}\)

Explanation:
Given the fractions 5/10 and 30/100
The denominators of both the fractions are different. Make the denominators common.
\(\frac{5}{10}\) × \(\frac{10}{10}\) = \(\frac{50}{100}\)
\(\frac{50}{100}\) + \(\frac{30}{100}\) = \(\frac{80}{100}\)

Question 10.
\(\frac{6}{10}+\frac{4}{100}\) = \(\frac{□}{□}\)

Answer: \(\frac{64}{100}\)

Explanation:
Given the fractions 6/10 and 4/100
The denominators of both the fractions are different. Make the denominators common.
\(\frac{6}{10}\) × \(\frac{10}{10}\) = \(\frac{60}{100}\)
\(\frac{60}{100}\) + \(\frac{4}{100}\) = \(\frac{64}{100}\)
\(\frac{6}{10}+\frac{4}{100}\) = \(\frac{64}{100}\)

Question 11.
0.24 + 0.1 = _____

Answer: 0.34

Explanation:
0.1 = 0.10
0.24 + 0.10 = 0.34

Compare. Write <, >, or =.

Question 12.
3.45 _____ 3.54

Answer: <

Explanation:
The decimal 3.45 is less than 3.54

Question 13.
1.7 _____ 1.70

Answer: =

Explanation:
The decimal 1.7 and 1.70 are same. Thus 1.7 = 1.70

Question 14.
8.1 _____ 8.01

Answer: >

Explanation:
8.1 is greater than 8.01

Question 15.
$4.25 _____ $3.75

Answer: >

Explanation:
$4.25 is greater than $3.75

Review/Test – Page No. 374

Fill in the bubble completely to show your answer.

Question 16.
Which fraction or mixed number and decimal is shown by the model?
Go Math Grade 4 Answer Key Homework FL Chapter 9 Relate Fractions and Decimals Review Test img 4
Options:
a. \(\frac{24}{100}\), 0.24
b. 1 \(\frac{24}{100}\), 1.24
c. 1 \(\frac{76}{100}\), 1.76
d. 1 \(\frac{24}{10}\), 1.24

Answer: 1 \(\frac{24}{100}\), 1.24

Explanation:
There are 100 blocks in each box. In that 124 blocks are shaded. So, the mixed fraction of the shaded part is 1 \(\frac{24}{100}\), 1.24
Thus the correct answer is option b.

Question 17.
Bethany collected 0.7 inch of rain in her rain gauge. How many hundredths of an inch did she collect?
Go Math Grade 4 Answer Key Homework FL Chapter 9 Relate Fractions and Decimals Review Test img 5
Options:
a. \(\frac{7}{100}\)
b. \(\frac{7}{10}\)
c. \(\frac{70}{100}\)
d. \(\frac{7}{1}\)

Answer: \(\frac{7}{10}\)

Explanation:
The fraction of the decimal 0.7 is \(\frac{7}{10}\)
Thus the correct answer is option b.

Question 18.
Pam paid for her lunch with the amount of money shown below.
Go Math Grade 4 Answer Key Homework FL Chapter 9 Relate Fractions and Decimals Review Test img 6
How much money did she spend?
Options:
a. 2 \(\frac{62}{100}\) dollars
b. 2 \(\frac{77}{100}\) dollars
c. 2 \(\frac{87}{100}\) dollars
d. 3 \(\frac{2}{100}\) dollars

Answer: 2 \(\frac{62}{100}\) dollars

Review/Test – Page No. 375

Fill in the bubble completely to show your answer.

Question 19.
Carson shaded a model to represent the part of his book he read this weekend. Which decimal represents the part of the book he read?
Go Math Grade 4 Answer Key Homework FL Chapter 9 Relate Fractions and Decimals Review Test img 7
Options:
a. 4.0
b. 0.44
c. 0.4
d. 0.04

Answer: 0.4

Explanation:
There are 10 blocks and among them, 4 are shaded. Thus the decimal form of the shaded part is 0.4.
Thus the correct answer is option c.

Question 20.
Christelle is making a doll house. The doll house is \(\frac{6}{10}\) meter high without the roof. The roof is \(\frac{15}{100}\) meter high. What will the height of the doll house be, with the roof?
Options:
a. \(\frac{21}{100}\) meter
b. \(\frac{75}{100}\) meter
c. 1 \(\frac{6}{100}\) meter
d. \(\frac{60}{100}\) meter

Answer: \(\frac{75}{100}\) meter

Explanation:
Given,
Christelle is making a doll house. The doll house is \(\frac{6}{10}\) meter high without the roof.
The roof is \(\frac{15}{100}\) meter high.
\(\frac{6}{10}\) and \(\frac{15}{100}\) the denominators are different. So make the denominators equal first.
\(\frac{6}{10}\) × \(\frac{10}{10}\) = \(\frac{60}{100}\)
\(\frac{60}{100}\) + \(\frac{15}{100}\) = \(\frac{75}{100}\) meter
Thus the correct answer is option b.

Question 21.
Amie has three quarters and one nickel. If she and three girls share the money equally, what will each person get?
Options:
a. $0.10
b. $0.15
c. $0.20
d. $0.25

Answer: $0.25

Explanation:
1 quarter = $0.25
3 quarters = 3 × $0.25 = $0.75
1 nickel = $0.05
$0.75 + $0.05 = $0.80
If she and three girls share the money equally = $0.80/3 = $0.25
Thus the correct answer is option d.

Review/Test – Page No. 376

Question 22.
There is \(\frac{30}{100}\) of a liter of orange juice in one container and \(\frac{5}{10}\) of a liter of pineapple juice in another container. If Mrs. Morales combines the two juices, how much orange-pineapple juice will she have? Explain how you found your answer.
Type below:
________

Answer:
The total quantity was found by adding the quantities of individual kinds of juice. The addition was performed by expressing each fraction using the common denominator of 10, then reducing the final result.
\(\frac{30}{100}\) + \(\frac{5}{10}\)
= \(\frac{30}{100}\) + \(\frac{50}{100}\)
= \(\frac{80}{100}\)
= \(\frac{4}{5}\)

Question 23.
Write the amount of orange-pineapple juice as a decimal.
_____

Answer:
\(\frac{4}{5}\)
= 0.8
Thus the amount of orange-pineapple juice as a decimal is 0.8

Question 24.
Luke lives 0.4 kilometer from a skating rink. Mark lives 0.25 kilometer from the skating rink.
A. Who lives closer to the skating rink? Explain.
Type below:
________

Answer:
Let’s take a look at their decimal places.
For 0.4, the four is in the tenths place, therefore it’s 4/10
For 0.25, the number ends in the hundredths place, therefore it’s 25/100
To compare them, I can make the 4/10 out of 100 and we’ll see which has the larger denominator.
To do this, we multiply 4/10 by 10/10 to get 40/100.
40/100 is greater than 25/100, so Luke lives closer to the skating rink.

Question 24.
B. How can you write each distance as a fraction? Explain.
Type below:
________

Answer:
For 0.4, the four is in the tenths place, therefore it’s 4/10
For 0.25, the number ends in the hundredths place, therefore it’s 25/100

Question 24.
C. Luke is walking to the skating rink to pick up a practice schedule. Then he is walking to Mark’s house. Will he walk more than a kilometer or less than a kilometer? Explain.
Type below:
________

Answer: Less than a kilometer

Explanation:
4/10 < 5/10 or 1/2 and 25/100 < 50/100 or 1/2.
Therefore 4/10 + 25/100 < 1/2 + 1/2.
Since 1/2 + 1/2 = 1, you know that 4/10 + 25/100 < 1.

Conclusion:

If you want to do a review test, then go through the Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals pdf because you may know the concept of fractions and decimals precisely. In case you have any doubts about the questions and answers covered in the Go Math Grade 4 Answer Key, don’t hesitate to share with us. We the team of CCSSMathAnswer.com will work on it to clarify your dilemmas at the earliest possible. All the Best!!!

Go Math Grade 7 Answer Key Chapter 5 Percent Increase and Decrease

go-math-grade-7-chapter-5-percent-increase-and-decrease-answer-key

Download Go Math Grade 7 Answer Key for Chapter 5 Percent Increase and Decrease pdf for free. Quick and easy learning is possible with Go Math 7th Grade Answer Key Chapter 5 Percent Increase and Decrease. So, we suggest the students of 7th standard to go through the HMH Go Math Grade 7 Key Chapter 5 Percent Increase and Decrease. Our team of Go Math Answer Key will help the Grade 7 students to score the highest marks.

Go Math Grade 7 Answer Key Chapter 5 Percent Increase and Decrease

Get a brief explanation for all the questions in Chapter 5 Percent Increase and Decrease Go Math Answer Key Grade 7. Tap on the links provided below and get the solutions according to the topics. So, utilize the time in the proper way and practice Go Math 7th Grade Solution Key Chapter 5 Percent Increase and Decrease.

Chapter 5 – Percent Increase and Decrease

Chapter 5 – Rewriting Percent Expressions

Chapter 5 – Applications of Percent

Chapter 5

Percent Increase and Decrease – Guided Practice – Page No. 144

Find each percent increase. Round to the nearest percent.

Question 1.
From $5 to $8
______ %

Answer: 60%

Explanation:
Percent Charge = Amount of Change/Original Amount
Original amount = 5
Final amount = 8
8 – 5 = 3
Percent change = 3/5 = 0.6 = 60%

Question 2.
From 20 students to 30 students
______ %

Answer: 50%

Explanation:
Percent Charge = Amount of Change/Original Amount
Original amount = 20
Final amount = 30
We find the amount of change
30 – 20 = 10
We determine the percent of the increase
Percent change = 10/20 = 0.5 = 50%

Question 3.
From 86 books to 150 books
______ %

Answer: 74%

Explanation:
Percent Charge = Amount of Change/Original Amount
Original amount = 86
Final amount = 150
We find the amount of change
150 – 86 = 64
We determine the percent of increase and round it to the nearest percent
Percent Change = 64/86 ≈ 0.74 = 74%

Question 4.
From $3.49 to $3.89
______ %

Answer: 11%

Explanation:
Percent Charge = Amount of Change/Original Amount
Original amount = 3.49
Final amount = 3.89
We find the amount of change
3.89 – 3.49 = 0.40
We determine the percent of increase and round it to the nearest percent
Percent Change = 0.40/0.39 ≈ 0.11 = 11%

Question 5.
From 13 friends to 14 friends
______ %

Answer: 8%

Explanation:
Percent Charge = Amount of Change/Original Amount
Original amount = 13
Final amount = 14
We find the amount of change
14 – 13 = 1
We determine the percent of increase and round it to the nearest percent
Percent Change = 1/13 ≈ 0.08 = 8%

Question 6.
From 5 miles to 16 miles
______ %

Answer: 220%

Explanation:
Percent Charge = Amount of Change/Original Amount
Original amount = 5
Final amount = 16
We find the amount of change
16 – 5 = 11
We determine the percent of increase and round it to the nearest percent
Percent Change = 11/5 = 2.2 = 220%

Question 7.
Nathan usually drinks 36 ounces of water per day. He read that he should drink 64 ounces of water per day. If he starts drinking 64 ounces, what is the percent increase? Round to the nearest percent.
______ %

Answer: 78%

Explanation:
Given,
Nathan usually drinks 36 ounces of water per day. He read that he should drink 64 ounces of water per day.
Original Amount: 36
Final Amount: 64
Percent Charge = Amount of Change/Original Amount
We find the amount of change
64 – 36 = 28
We determine the percent of increase and round it to the nearest percent
Percent Change = 28/36 ≈ 0.78 = 78%
Thus the nearest percent is 78%

Find each percent decrease. Round to the nearest percent.

Question 8.
From $80 to $64
______ %

Answer: 20%

Explanation:
Percent Charge = Amount of Change/Original Amount
Original amount = 80
Final amount = 64
We find the amount of change
Amount of change = Greater value – Lesser value
= 80 – 64 = 16
We determine the percent of increase and round it to the nearest percent
Percent Change = 16/80 = 0.20 = 20%
Thus the nearest percent is 20%

Question 9.
From 95 °F to 68 °F
______ %

Answer: 28%

Explanation:
Percent Charge = Amount of Change/Original Amount
Original amount = 95
Final amount = 68
We find the amount of change
Amount of change = Greater value – Lesser value
= 95 – 68 = 27
We determine the percent of increase and round it to the nearest percent
Percent Change = 27/98 ≈ 0.28 = 28%
Thus the nearest percent is 28%

Question 10.
From 90 points to 45 points
______ %

Answer: 50%

Explanation:
Percent Charge = Amount of Change/Original Amount
Original amount = 90
Final amount = 45
We find the amount of change
Amount of change = Greater value – Lesser value
90 – 45 = 45
We determine the percent of increase and round it to the nearest percent
Percent Change = 45/90 = 0.50 = 50%
Thus the nearest percent is 50%

Question 11.
From 145 pounds to 132 pounds
______ %

Answer: 9%

Explanation:
Percent Charge = Amount of Change/Original Amount
Original amount = 145
Final amount = 132
We find the amount of change
Amount of change = Greater value – Lesser value
145 – 132 = 13
We determine the percent of increase and round it to the nearest percent
Percent Change = 13/145 ≈ 0.09 = 9%
The nearest percent is 9%

Question 12.
From 64 photos to 21 photos
______ %

Answer: 67%

Explanation:
Percent Charge = Amount of Change/Original Amount
Original amount = 64
Final amount = 21
We find the amount of change
Amount of change = Greater value – Lesser value
64 – 21 = 43
We determine the percent of increase and round it to the nearest percent
Percent Change = 43/64 ≈ 0.67 = 67%
Therefore the nearest percent is 67%

Question 13.
From 16 bagels to 0 bagels
______ %

Answer: 100%

Explanation:
Percent Charge = Amount of Change/Original Amount
Original amount = 16
Final amount = 0
We find the amount of change
Amount of change = Greater value – Lesser value
16 – 0 = 16
We determine the percent of increase and round it to the nearest percent
Percent Change = 16/16 = 1.0% = 100%

Question 14.
Over the summer, Jackie played video games 3 hours per day. When school began in the fall, she was only allowed to play video games for half an hour per day. What is the percent decrease? Round to the nearest percent.
______ %

Answer: 83%

Explanation:
Percent Charge = Amount of Change/Original Amount
Original amount = 3
Final amount = 0.5
We find the amount of change
Amount of change = Greater value – Lesser value
3 – 0.5 = 2.5
We determine the percent of increase and round it to the nearest percent
Percent Change = 2.5/3 ≈ 0.83 = 83%
The nearest percent is 83%

Find the new amount given the original amount and the percent of change.

Question 15.
$9; 10% increase
$ ______

Answer: $9.90

Explanation:
Percent Charge = Amount of Change/Original Amount
Original amount = 9
Increase = 10%
We find the amount of change
0.1 × 9 = 0.90
New Amount = Original Amount + Amount of Change
9 + 0.90 = 9.90

Question 16.
48 cookies; 25% decrease
______ cookies

Answer: 36 cookies

Explanation:
Original amount = 48
Decrease = 25%
We find the amount of change
0.25 × 48 = 12
New Amount = Original Amount – Amount of Change
48 – 12 = 36
Thus the answer is 36 cookies.

Question 17.
340 pages; 20% decrease
______ pages

Answer: 272 pages

Explanation:
Original Amount: 340 pages
Decrease: 20%
We find the amount of change
0.20 × 340 = 68
New Amount = Original Amount – Amount of Change
340 – 68 = 272
The answer is 272 pages.

Question 18.
28 members; 50% increase
______ members

Answer: 42 members

Explanation:
Original Amount: 28
Increase: 50%
We find the amount of change
0.5 × 28 = 14
New amount = Original Amount + Amount of Change
28 + 14 = 42
The answer is 42 members

Question 19.
$29,000; 4% decrease
$ ______

Answer: $27,840

Explanation:
Original Amount: 29000
Decrease: 4%
We find the amount of change
0.04 × 29000 = 1160
New Amount = Original Amount – Amount of Change
29000 – 1160 = 27840
The answer is $27,840

Question 20.
810 songs; 130% increase
______ songs

Answer: 1863 songs

Explanation:
Original Amount: 810
Increase: 130%
We find the amount of change
1.3 × 810 = 1053
New amount = Original Amount + Amount of Change
810 + 1053 = 1863 songs

Question 21.
Adam currently runs about 20 miles per week, and he wants to increase his weekly mileage by 30%. How many miles will Adam run per week?
______ miles

Answer: 26 miles

Explanation:
Given,
Adam currently runs about 20 miles per week, and he wants to increase his weekly mileage by 30%.
Original Amount: 20
Increase: 30%
We find the amount of change
0.3 × 20 = 6
New amount = Original Amount + Amount of Change
= 20 + 6 = 26
Therefore Adam run 26 miles per week.

Essential Question Check-In

Question 22.
What process do you use to find the percent change of a quantity?
Type below:
_____________

Answer: In order to find the percent change of a quantity, we determine the amount of change in the quantity and divide it by the original amount.

Percent Increase and Decrease – Independent Practice – Page No. 145

Question 23.
Complete the table.
Go Math Grade 7 Answer Key Chapter 5 Percent Increase and Decrease Lesson 1: Percent Increase and Decrease img 1
Type below:
_____________

Answer: bike: 13%, scooter 24%, increase, tennis racket: $83, skis: $435

Go-Math-Grade-7-Answer-Key-Chapter-5-Percent-Increase-and-Decrease-img-1

Explanation:
Since the new price is less than the original price, it is a percent decrease. percent decreases can be found using the equation percent decrease = (original – new)/original
Bike: 110 – 96/110 = 14/110 ≈ 13%
Scooter: 56 – 45/45 = 11/45 ≈ 24%
Use the equation percent increase = new – original/original
let x be the new price
skis: (580 – x)/580 = 0.25
580 – x = 0.25 × 580
580 – x = 145
x = 580 – 145 = 435
The new price is $435

Question 24.
Multiple Representations
The bar graph shows the number of hurricanes in the Atlantic Basin from 2006–2011.
Go Math Grade 7 Answer Key Chapter 5 Percent Increase and Decrease Lesson 1: Percent Increase and Decrease img 2
a. Find the amount of change and the percent of decrease in the number of hurricanes from 2008 to 2009 and from 2010 to 2011. Compare the amounts of change and percents of decrease.
Type below:
_____________

Answer: 2008 to 2009 has a smaller amount of change but a larger percent of decrease.

Explanation:
2008 to 2009:
amount of change: 8 – 3 = 5
percent decrease: 5/8 = 0.625 = 62.5%
2010 to 2011:
amount of change: 12 – 7 = 5
percent decrease: 5/12 ≈ 0.416 = 41.6%
The amount of change for 2010 to 2011 was greater than the amount of change for 2008 to 2009 but 2008 to 209 had a greater percent decrease than 2010 to 2011.

Question 24.
b. Between which two years was the percent of change the greatest? What was the percent of change during that period?
_______ %

Answer: 2009 and 2010, 300%

Explanation:
Use the percent change = amount of change/original amount.
The biggest change in heights is between 2009 and 2010.
The percent change is (12-3)/3 = 9/3 = 3 = 300%

Question 25.
Represent Real-World Problems
Cheese sticks that were previously priced at “5 for $1” are now “4 for $1”. Find each percent of change and show your work.
a. Find the percent decrease in the number of cheese sticks you can buy for $1.
_______ %

Answer: 20% decrease

Explanation:
Use the percent change = amount of change/original amount.
(5 – 4)/5 = 1/5 = 0.2 = 20% decrease

Question 25.
b. Find the percent increase in the price per cheese stick.
_______ %

Answer: 25% increase

Explanation:
First, find the price per cheese stick at each price.
Use the percent change = amount of change/original amount.
1.00/5 = 0.20
1/4 = 0.25
(0.25 – 0.20)/0.20 = 0.05/0.20 = 25% increase

Percent Increase and Decrease – Page No. 146

Question 26.
Percent error calculations are used to determine how close to the true values, or how accurate, experimental values really are. The formula is similar to finding percent of change.
Go Math Grade 7 Answer Key Chapter 5 Percent Increase and Decrease Lesson 1: Percent Increase and Decrease img 3
chemistry class, Charlie records the volume of a liquid as 13.3 milliliters. The actual volume is 13.6 milliliters. What is his percent error? Round to the nearest percent.
_______ %

Answer: 2%

Explanation:
Use the formula
Go Math Grade 7 Answer Key Chapter 5 Percent Increase and Decrease Lesson 1: Percent Increase and Decrease img 3
|13.3 – 13.6|/13.6 = |-0.3|/13.6 ≈ 0.02 = 2%

H.O.T.

Focus on Higher Order Thinking

Question 27.
Look for a Pattern
Leroi and Sylvia both put $100 in a savings account. Leroi decides he will put in an additional $10 each week. Sylvia decides to put in an additional 10% of the amount in the account each week.
a. Who has more money after the first additional deposit? Explain.
___________

Answer: the same

Explanation:
Since 10% of 100 is 100(0.10) = 10, they both make an additional deposit of 10, so they have the same amount of money after the first additional deposit.

Question 27.
b. Who has more money after the second additional deposit? Explain.
___________

Answer: Sylvia

Explanation:
Both Lerio and Sylvia have $110 in their account after their first deposits since they both started with $100 and both deposited $10 for their first deposit.
After the second deposit, Lerio has 110 + 10 = $120.
Sylvia has 110 + 0.10(110) = 110 + 11 = $121
So she has more money after the second deposit.

Question 27.
c. How do you think the amounts in the two accounts will compare after a month? A year?
Type below:
___________

Answer: Sylvia will continue to have more money after a month and a year since 10% of the balance is going to be greater than the 10 deposit that Leroi is making.

Question 28.
Critical Thinking
Suppose an amount increases by 100%, then decreases by 100%. Find the final amount. Would the situation change if the original increase was 150%? Explain your reasoning.
Type below:
___________

Answer: If an amount increases by 100%, then it will double. If it then decreases by 100%, it will become 0.
If you increase a number by 150% and then decrease it by 150%, you will not get to 0. 150% increase of 100 is 100 + 150 = 250.
A decrease of 150% is then 250 – 1.5(250) = 250 – 375 = -125

Question 29.
Look for a Pattern
Ariel deposited $100 into a bank account. Each Friday she will withdraw 10% of the money in the account to spend. Ariel thinks her account will be empty after 10 withdrawals. Do you agree? Explain.
___________

Answer: Ariel is incorrect. Her account balance will decrease as follows for the first 10 withdrawals:
1st withdrawal: 100 – 0.1(100) = 100 – 10 = 90
2nd withdrawal: 90 – 0.1(90) = 90 – 9 = 81
3rd withdrawal: 81 – 0.1(81) = 81 – 8.10 = 72.90
4th withdrawal: 72.90 – 0.1(72.90) = 72.90 – 7.29 = 65.61
5th withdrawal: 65.61 – 0.1(65.61) = 65.61 – 6.56 = 59.05
6th withdrawal: 59.05 – 0.1(59.05) = 59.05 – 5.91 = 53.14
7th withdrawal: 53.14 – 0.1(53.14) = 53.14 – 5.31 = 47.83
8th withdrawal: 47.83 – 0.1(47.83) = 47.83 – 4.78 = 43.05
9th withdrawal: 43.05 – 0.1(43.05) = 43.05 – 4.31 = 38.74
10th withdrawal: 38.74 – 0.1(38.74) = 38.74 – 3.87 = 34.87

Rewriting Percent Expressions – Guided Practice – Page No. 150

Question 1.
Dana buys dress shirts from a clothing manufacturer for s dollars each, and then sells the dress shirts in her retail clothing store at a 35% markup.
a. Write the markup as a decimal.
______

Answer: To convert a percent to a decimal, move the decimal place two places to the left. Therefore, 35% as a decimal is 0.35.

Question 1.
b. Write an expression for the retail price of the dress shirt.
Type below:
___________

Answer:
To write the expression, use the formula
retail price = original place + markup
Since s is the original place, if the markup is 35% = 0.35, then the markup is 0.35s.

Question 1.
c. What is the retail price of a dress shirt that Dana purchased for $32.00?
$ ______

Answer: Plugging in s = 32 into the expression gives a retail price of 1.35 = 1.35(32) = $43.20

Question 1.
d. How much was added to the original price of the dress shirt?
$ ______

Answer: The amount added to the original price is the amount of the markup. Since the amount of the markup is 0.35s and s = 32, then the amount of the markup was 0.35s = 0.35(32) = $11.20.
You can also find the amount of markup by subtracting the retail price and the original price. Since the retail price is $43.20 and the original price is $32, then the markup amount is $43.20 – $32 = $11.20

List the markup and retail price of each item. Round to two decimal places when necessary.

Question 2.
Go Math Grade 7 Answer Key Chapter 5 Percent Increase and Decrease Lesson 2: Rewriting Percent Expressions img 4
Markup: $ ______ Retail Price: $ ______

Answer: Markup: $ 2.70 Retail Price: $ 20.70

Explanation:
Go-Math-Grade-7-Answer-Key-Chapter-5-Percent-Increase-and-Decrease-img-4
Use the formula markup = price(markup%)
18(0.15) = 2.70
Use the retail price formula = price + markup
18 + 2.70 = 20.70

Question 3.
Go Math Grade 7 Answer Key Chapter 5 Percent Increase and Decrease Lesson 2: Rewriting Percent Expressions img 5
Markup: $ ______ Retail Price: $ ______

Answer:
Go-Math-Grade-7-Answer-Key-Chapter-5-Percent-Increase-and-Decrease-img-5
Use the formula markup = (price)(markup %)
22.50(0.42) = 9.45
Use the retail price formula = price + markup
22.50 + 9.45 = 31.95

Question 4.
Go Math Grade 7 Answer Key Chapter 5 Percent Increase and Decrease Lesson 2: Rewriting Percent Expressions img 6
Markup: $ ______ Retail Price: $ ______

Answer:
Go-Math-Grade-7-Answer-Key-Chapter-5-Percent-Increase-and-Decrease-img-6
Use the formula markup = (price)(markup %)
= 33.75(0.75) = 25.31
Use the formula retail price = price + markup
33.75 + 25.31 = 59.06

Question 5.
Go Math Grade 7 Answer Key Chapter 5 Percent Increase and Decrease Lesson 2: Rewriting Percent Expressions img 7
Markup: $ ______ Retail Price: $ ______

Answer:
Go-Math-Grade-7-Answer-Key-Chapter-5-Percent-Increase-and-Decrease-img-7
Use the formula markup = (price)(markup %)
= 74.99(0.33) = 24.75
Use the formula retail price = price + markup
74.99 + 24.75 = 99.74

Question 6.
Go Math Grade 7 Answer Key Chapter 5 Percent Increase and Decrease Lesson 2: Rewriting Percent Expressions img 8
Markup: $ ______ Retail Price: $ ______

Answer:
Go-Math-Grade-7-Answer-Key-Chapter-5-Percent-Increase-and-Decrease-img-8
Use the formula markup = (price)(markup %)
48.60(1.00) = 48.60
Use the formula retail price = price + markup
48.60 + 48.60 = 97.20

Question 7.
Go Math Grade 7 Answer Key Chapter 5 Percent Increase and Decrease Lesson 2: Rewriting Percent Expressions img 9
Markup: $ ______ Retail Price: $ ______

Answer:
Go-Math-Grade-7-Answer-Key-Chapter-5-Percent-Increase-and-Decrease-img-9
Use the formula markup = (price)(markup %)
= 185 × 1.25 = 231.25
Use the formula retail price = price + markup
185 + 231.25 = 461.25

Find the sale price of each item. Round to two decimal places when necessary.

Question 8.
Original price: $45.00; Markdown: 22%
$ ______

Answer:
Use the formula markup = (price)(markup %)
45(0.22) = 9.90
Markdown is 9.90
Use the formula retail price = price + markup
45 – 9.90 = 35.10
Sale price is $35.10

Question 9.
Original price: $89.00; Markdown: 33%
$ ______

Answer:
Use the formula markup = (price)(markup %)
89 × 0.33 = 29.37
Use the formula retail price = price – markup
89 – 29.37 = 59.63

Question 10.
Original price: $23.99; Markdown: 44%
$ ______

Answer:
Use the formula markup = (price)(markup %)
23.99 × 0.44 = 10.56
Use the formula retail price = price – markup
23.99 – 10.56 = 13.43

Question 11.
Original price: $279.99, Markdown: 75%
$ ______

Answer:
Use the formula markup = (price)(markup %)
279.99 × 0.75 = 209.99
Use the formula retail price = price – markup
279.99 – 209.99 = 70

Essential Question Check-In

Question 12.
How can you determine the sale price if you are given the regular price and the percent of markdown?
Type below:
____________

Answer:
Use the formula
Sale price = Original Price – Markdown
If the Sale price is S, Original Price p, and x the average reduction, then the formula becomes:|
S = p – x . p

Rewriting Percent Expressions – Independent Practice – Page No. 151

Question 13.
A bookstore manager marks down the price of older hardcover books, which originally sell for b dollars, by 46%.
a. Write the markdown as a decimal.
______

Answer: 0.46

Explanation:
To convert a percent to decimal form, move the decimal point 2 places to the left and don’t write the percent symbol. Therefore, 46% as a decimal is 0.46.

Question 13.
b. Write an expression for the sale price of the hardcover book.
Type below:
____________

Answer: 0.54b

Explanation:
The sale price is the original price minus the discount amount. If the original price is discounted 46% and the original price is b dollars, the amount of the discount is 46% of b = 0.46b.
The sale price is then b – 0.46b = (1 – 0.46)b = 0.54b

Question 13.
c. What is the sale price of a hardcover book for which the original retail price was $29.00?
$ ______

Answer: $15.66

Explanation:
From part (b), the sale price of an item with an original price of b dollars is 0.54b. If the original price is then b = 29 dollars, the sale price is 0.54b = 0.54 × 29 = $15.66

Question 13.
d. If you buy the book in part c, how much do you save by paying the sale price?
$ ______

Answer: $13.34

Explanation:
The amount of savings is the difference between the original price and the sale price. If the original price is $29 and the sale price is $15.66, then the amount of savings is $29.00 – $15.66 = $13.34

Question 14.
Raquela’s coworker made price tags for several items that are to be marked down by 35%. Match each Regular Price to the correct Sale Price, if possible. Not all sales tags match an item.
Go Math Grade 7 Answer Key Chapter 5 Percent Increase and Decrease Lesson 2: Rewriting Percent Expressions img 10
Type below:
_____________

Answer:
35% markdown means the expression for the sales price is p – 0.35p = 0.65p. Plug in the regular prices for p to find the sale prices. Remember the directions stated not all sales tags will match a regular price so you won’t be able to match every regular price ticket with a sale price ticket.
0.65(3.29) = 2.14
0.65(4.19) = 2.72
0.65(2.79) = 1.81
0.65(3.09) = 2.01
0.65(3.77) = 2.45

Question 15.
Communicate Mathematical Ideas
For each situation, give an example that includes the original price and final price after markup or markdown.
a. A markdown that is greater than 99% but less than 100%
Type below:
_____________

Answer:
A markdown that is greater than 99% but less than 100% could be 99.5%. If the original price is $100, then the final price is 100 – 100(0.995) = 100 – 99.50 = 0.50

Question 15.
b. A markdown that is less than 1%
Type below:
_____________

Answer:
A markdown that is less then 1% could be 0.5%. If the original price is $100, then the final price would be 100 – 0.005(100) = 100 – 0.50 = 99.50

Question 15.
c. A markup that is more than 200%
Type below:
_____________

Answer:
A markup that is more than 200% could be 300%. If the original price is $100, then the final price would be 100 + 100 (3.00) = 100 + 300 = 400

Rewriting Percent Expressions – Page No. 152

Question 16.
Represent Real-World Problems
Harold works at a men’s clothing store, which marks up its retail clothing by 27%. The store purchases pants for $74.00, suit jackets for $325.00, and dress shirts for $48.00. How much will Harold charge a customer for two pairs of pants, three dress shirts, and a suit jacket?
$ __________

Answer: $783.59

Explanation:
Given,
Harold works at a men’s clothing store, which marks up its retail clothing by 27%.
The store purchases pants for $74.00, suit jackets for $325.00, and dress shirts for $48.00.
If the markup is 27%, then the expression for the retail price is p + 0.27p = 1.27p
where p is the original price.
The retail price of the pants is then 1.27(74) = 93.98.
The retail price of the suit jackets is 1.27(325) = 412.75
The retail price of the dress shirts is 1.27(48) = 60.96
The total for two pants, three dress shirts, and one suit jacket would then be 2(93.98) + 3(60.96) + 412.75
= 187.96 + 182.88 + 412.75 = 783.59

Question 17.
Analyze Relationships
Your family needs a set of 4 tires. Which of the following deals would you prefer? Explain.
Go Math Grade 7 Answer Key Chapter 5 Percent Increase and Decrease Lesson 2: Rewriting Percent Expressions img 11
Type below:
____________

Answer: I and III

Explanation:
The percent discount for buying 3 tires and getting one free is 25% since you are getting 1/4 of the tires for free and 1/4 off = 25%.
This means deal (I) and deal (III) are the same. They are greater than a 20% discount so deals (I) and (III) are preferable.

H.O.T.

Focus on Higher Order Thinking

Question 18.
Critique Reasoning
Margo purchases bulk teas from a warehouse and marks up those prices by 20% for retail sale. When teas go unsold for more than two months, Margo marks down the retail price by 20%. She says that she is breaking even, that is, she is getting the same price for the tea that she paid for it. Is she correct? Explain.
_______

Answer:
She is not correct. If she originally purchases the teas for $100 and then marks the price up 20%, the retail price would then be 100 + 0.20(100) = 100 + 20 = 120.
The sales price would then be 120 – 0.2(120) = 120 – 24 = 96.
This less than the purchase price so she is losing money, not breaking even.

Question 19.
Problem Solving
Grady marks down some $2.49 pens to $1.99 for a week and then marks them back up to $2.49. Find the percent of increase and the percent of decrease to the nearest tenth. Are the percents of change the same for both price changes? If not, which is a greater change?
_______

Answer: The percent decrease is found by using the formula (original price – new price)/(original price). The percent decrease is then (2.49 – 1.99)/2.49 = 0.20 = 20%.
A percent increase is found by using the formula (new price – original price)/original price.
The percent increase is then (2.49 – 1.99)/1.99 = 0.25 = 25%
The percents of change are not the same. The percent increase is greater.

Question 20.
Persevere in Problem Solving
At Danielle’s clothing boutique, if an item does not sell for eight weeks, she marks it down by 15%. If it remains unsold after that, she marks it down an additional 5% each week until she can no longer make a profit. Then she donates it to charity.

Rafael wants to buy a coat originally priced $150, but he can’t afford more than $110. If Danielle paid $100 for the coat, during which week(s) could Rafael buy the coat within his budget? Justify your answer.
Type below:
_____________

Answer:
The expression for the markdown on the 8th week is p – 0.15p = 0.85p since it will get marked down 15% on the 8th week.
The expression for the additional markdowns is p – 0.05p = 0.95p since it will get marked down an additional 5% every week after the 8th week.
On the 8th week, it will be marked down to 0.85(150) = 127.50. This is more than Rafael can afford.
On the 9th week, it will be marked down to 0.95(127.50) = 121.13. This is still more than Rafael can afford.
On the 10th week, it will be marked down to 0.95(121.13) = 115.07. This is still more than Rafael can afford.
On the 11th week, it will be marked down to 0.95(115.07) = 109.32. Rafael can afford this price so he must wait until the 11th week.

Applications of Percent – Guided Practice – Page No. 156

Question 1.
5% of $30 =
$ _______

Answer: $1.5

Explanation:
We have to find:
5% of $30
0.50 × 30 = $1.5

Question 2.
15% of $70 =
$ _______

Answer: $10.5

Explanation:
We have to find:
15% of $70
0.15 × 70 = 10.5

Question 3.
0.4% of $100 =
$ _______

Answer: $0.40

Explanation:
We have to find:
0.4% of $100
0.004 × 100 = 0.40

Question 4.
150% of $22 =
$ _______

Answer: $33

Explanation:
We have to find:
150% of $22
1.5 × 22 = 33

Question 5.
1% of $80 =
$ _______

Answer: $0.8

Explanation:
We have to find:
1% of $80
0.01 × 80 = 0.8

Question 6.
200% of $5 =
$ _______

Answer: $10

Explanation:
We have to find:
200% of $5
2 × 5 = 10

Question 7.
Brandon buys a radio for $43.99 in a state where the sales tax is 7%.
a. How much does he pay in taxes?
$ _______

Answer: 3.08

Explanation:
We have to find the amount he pays in taxes by multiplying the cost by the sales tax percentage in decimal form remember to round to 2 decimal places.
43.99(0.07) = 3.08

Question 7.
b. What is the total Brandon pays for the radio?
$ _______

Answer: 47.07

Explanation:
To find the total Brandon pays for the radio we have to add the sales tax amount to the cost to find the total amount he pays.
43.99 + 3.08 = 47.07
Thus the total Brandon pays for the radio is $47.07.

Question 8.
Luisa’s restaurant bill comes to $75.50, and she leaves a 15% tip. What is Luisa’s total restaurant bill?
$ _______

Answer: $86.25

Explanation:
Given that,
Luisa’s restaurant bill comes to $75.50, and she leaves a 15% tip.
Use the formula for the total restaurant bill:
T = P + x. P
Where T represents the total bill, P represents Luisa’s bill and x represents percents for tip, then the total restaurant bill is:
T = 75 + 0.15 (75)
T = 75 + 11.25
T = $86.25
Therefore Lusia’s total restaurant bill is $86.25

Question 9.
Joe borrowed $2,000 from the bank at a rate of 7% simple interest per year. How much interest did he pay in 5 years?
$ _______

Answer: 700

Explanation:
Joe borrowed $2,000 from the bank at a rate of 7% simple interest per year.
We have to find the amount of interest per year
2000(0.07) = 140
Find the amount of interest for 5 years
140(5) = 700
Thus Joe pays $700 in 5 years.

Question 10.
You have $550 in a savings account that earns 3% simple interest each year. How much will be in your account in 10 years?
$ _______

Answer: $715

Explanation:
Given,
You have $550 in a savings account that earns 3% simple interest each year.
Use the formula for simple interest:
Bt = B0(1 + tr)
Where t is time interval, Bt is money after t years, B0 is deposit and r is interest for one year, then the formula becomes:
B10 = B0(1 + 10.r)
B10 = 550(1 + 10 (0.03))
B10 = $715
In your account after 10 years will be $715.

Question 11.
Martin finds a shirt on sale for 10% off at a department store. The original price was $20. Martin must also pay 8.5% sales tax.
a. How much is the shirt before taxes are applied?
$ _______

Answer: 18

Explanation:
We have to find the sales price of the shirt
20 – 0.1(20) = 20 – 2 = 18
The price of the shirt before taxes are applied is $18.

Question 11.
b. How much is the shirt after taxes are applied?
$ _______

Answer: 19.53

Explanation:
We have to find the price after sales tax
18 + 0.085(18) = 18 + 1.53 = 19.53
The price of the shirt after taxes are applied is $19.53

Question 12.
Teresa’s restaurant bill comes to $29.99 before tax. If the sales tax is 6.25% and she tips the waiter 20%, what is the total cost of the meal?
$ _______

Answer: 37.86

Explanation:
Given,
Teresa’s restaurant bill comes to $29.99 before tax. If the sales tax is 6.25% and she tips the waiter 20%.
Find the amount of sales tax
29.99(0.0625) = 1.87
Find the amount of the tip
29.99(0.20) = 6.00
The total cost by adding the bill account, sales tax, and tip amount.
29.99 + 1.87 + 6.00 = 37.86
Thus the total cost of the meal is $37.86

Essential Question Check-In

Question 13.
How can you determine the total cost of an item including tax if you know the price of the item and the tax rate?
Type below:
_____________

Answer: You can find the total cost of an item including tax by first multiplying the price of the item by the tax rate in decimal form to get the amount of sales tax. Then add the amount of sales tax to the price to get the total cost.

Applications of Percent – Independent Practice – Page No. 157

Question 14.
Emily’s meal costs $32.75 and Darren’s meal costs $39.88. Emily treats Darren by paying for both meals, and leaves a 14% tip. Find the total cost.
$ _______

Answer: 82.80

Explanation:
Emily’s meal costs $32.75 and Darren’s meal costs $39.88.
So, the total cost of the meals before tip is $32.75 + $39.88 = $72.63
Emily treats Darren by paying for both meals and leaves a 14% tip.
$72.63 = 0.14(72.63) ≈ $10.17
Round to two decimal places since dollar amounts must be rounded to the nearest cent.
The total cost that Dareen pays is then cost before tip + amount of tip = $72.63 + $10.17 = $82.80

Question 15.
The Jayden family eats at a restaurant that is having a 15% discount promotion. Their meal costs $78.65, and they leave a 20% tip. If the tip applies to the cost of the meal before the discount, what is the total cost of the meal?
$ _______

Answer: 82.58

Explanation:
The Jayden family eats at a restaurant that is having a 15% discount promotion.
The total cost of the meal = cost of meal + tip amount – discount amount
Their meal costs $78.65, and they leave a 20% tip.
We need to find the tip amount and the discount amount using the given cost of the meal, tip percent, and discount percent.
20% of 78.65 = 0.20 × 78.65 = $15.73
Since the cost of the meal before the discount is $78.65 and the discount percent is 15%, then the amount of the discount is
15% of 78365 = 0.15 × $78.65 ≈ $11.80
The total cost is then
78.65 + 15.73 – 11.80 = $82.58

Question 16.
A jeweler buys a ring from a jewelry maker for $125. He marks up the price by 135% for sale in his store. What is the selling price of the ring with 7.5% sales tax?
$ _______

Answer: 315.78

Explanation:
A jeweler buys a ring from a jewelry maker for $125. He marks up the price by 135% for sale in his store.
125 × 1.35 = 168.75
We can find the retail price by adding the markup to the purchase price
125 + 168.75 = 293.75
The amount of sales tax is 293.75 × 0.075 = 22.03
We can find the selling price by adding the tax amount to the retail price.
293.75 + 22.03 = 315.78
Therefore the selling price of the ring with 7.5% sales tax is $315.78

Question 17.
Luis wants to buy a skateboard that usually sells for $79.99. All merchandise is discounted by 12%. What is the total cost of the skateboard if Luis has to pay a state sales tax of 6.75%?
$ _______

Answer: 75.14

Explanation:
Given,
Luis wants to buy a skateboard that usually sells for $79.99. All merchandise is discounted by 12%.
79.99 × 0.12 = 9.60
79.99 – 9.60 = 70.39
First, we need to find the amount paid in taxes and then add that to the discount price to get the total cost.
70.39 × 0.0675 = 4.75
70.39 + 4.75 = 75.14
The total cost of the skateboard if Luis has to pay a state sales tax of 6.75% is $75.14

Question 18.
Kedar earns a monthly salary of $2,200 plus a 3.75% commission on the amount of his sales at a men’s clothing store. What would he earn this month if he sold $4,500 in clothing? Round to the nearest cent.
$ _______

Answer: 2368.75

Explanation:
Given,
Kedar earns a monthly salary of $2,200 plus a 3.75% commission on the amount of his sales at a men’s clothing store.
4500 × 0.0375 = 168.75
The total earnings can be known by adding his monthly salary and his commission.
2200 + 168.75 = 2368.75

Question 19.
Danielle earns a 7.25% commission on everything she sells at the electronics store where she works. She also earns a base salary of $750 per week. How much did she earn last week if she sold $4,500 in electronics merchandise? Round to the nearest cent.
$ _______

Answer: 1076.25

Explanation:
Danielle earns a 7.25% commission on everything she sells at the electronics store where she works.
She also earns a base salary of $750 per week.
The amount she made in the commission is 4500 × 0.0725 = 326.25
We can find the total earnings by adding her weekly pay and commission.
750 + 326.25 = 1076.25
Thus she earns $1076.25 last week if she sold $4,500 in electronics merchandise.

Question 20.
Francois earns a weekly salary of $475 plus a 5.5% commission on sales at a gift shop. How much would he earn in a week if he sold $700 in goods? Round to the nearest cent.
$ _______

Answer: 513.50

Explanation:
Given that, Francois earns a weekly salary of $475 plus a 5.5% commission on sales at a gift shop.
The amount he made in commission
700 × 0.055 = 38.50
We can find the total amount he earned by adding his weekly pay and commission
475 + 38.50 = $513.50

Question 21.
Sandra is 4 feet tall. Pablo is 10% taller than Sandra, and Michaela is 8% taller than Pablo
a. Explain how to find Michaela’s height with the given information.
Type below:
_____________

Answer:
First we have to find 10% of Sandra’s height: 0.10 × 4 = 0.4
This means that Pablo is then 4 + 0.4 = 4.4 feet tall.
Next find 8% of Pablo’s height: 4.4 × 0.08 = 0.352
This means that Michaela is 4.4 + 0.353 = 4.752 feet tall.

Question 21.
b. What is Michaela’s approximate height in feet and inches?
_______ feet _______ inches

Answer:
Convert from feet to inches.
1 feet = 12 inches
4.752 = 4 + 0.752
0.752 = 12 × 0.752 = 9 inches
4 feet = 12 × 4 = 48 inches
Thus the approximate height of Michaela is 4 feet 9 inches.

Question 22.
Eugene wants to buy jeans at a store that is giving $10 off everything. The tag on the jeans is marked 50% off. The original price is $49.98.
a. Find the total cost if the 50% discount is applied before the $10 discount.
$ _______

Answer: $14.99

Explanation:
Given that,
Eugene wants to buy jeans at a store that is giving $10 off everything.
The tag on the jeans is marked 50% off. The original price is $49.98.
0.5 × 49.98 = 24.99
Now subtract $10 discount.
24.99 – 10 = 14.99
The total cost if the 50% discount is applied before the $10 discount is $14.99

Question 22.
b. Find the total cost if the $10 discount is applied before the 50% discount.
$ _______

Answer: $19.99

Explanation:
We have to find the price after the $10 discount then find 50% of that price to find the discounted price.
49.98 – 10 = 39.98
0.5 × 39.98 = 19.99
Thus the total cost if the $10 discount is applied before the 50% discount is $19.99

Applications of Percent – Page No. 158

Question 23.
Multistep
Eric downloads the coupon shown and goes shopping at Gadgets Galore, where he buys a digital camera for $95 and an extra battery for $15.99.
a. What is the total cost if the coupon is applied to the digital camera?
Go Math Grade 7 Answer Key Chapter 5 Percent Increase and Decrease Lesson 3: Applications of Percent img 12
$ _______

Answer: 101.49

Explanation:
Use the formula for the discount price:
DP = P – x.P
Price for the digital camera:
DP = 95 – 0.1(95)
DP = 95 – 9.5
DP = $85.5
Total cost = 85.5 + 15.99 = $101.49

Question 23.
b. What is the total cost if the coupon is applied to the extra battery?
$ _______

Answer: 109.391

Explanation:
Use the formula for the discount price:
DP = P – x.P
Price for the digital camera:
DP = 15.99 – 0.1(15.99)
DP = 15.99 – 1.599
DP = $14.399
Total cost = 95 + 14.399 = $109.391

Question 23.
c. To which item should Eric apply the discount? Explain.
____________

Answer: He should apply the discount to the digital camera because then the total cost is the lower.

Question 23.
d. Eric has to pay 8% sales tax after the coupon is applied. How much is his total bill?
$ _______

Answer:
Use formula for Discount price
If he uses coupon for the digital camera then his total cost will be
T = DP + 0.08 × DP
T = 101.49 + 8.1192
T = $109.6029
If he uses coupon for the extra battery his total cost will be
T = DP + 0.08 × DP
T = 109.391 + 0.08(109.391)
T = $118.14228

Question 24.
Two stores are having sales on the same shirts. The sale at Store 1 is “2 shirts for $22” and the sale at Store 2 is “Each $12.99 shirt is 10% off”.
a. Explain how much will you save by buying at Store 1.
$ _______

Answer:
For store 1, the shirts are 2 for $22. Ecah shirt then costs $22 ÷ 2 = $11
At store 2, each shirt is 10% off of $12.99 so each shirt costs:
$12.99 – 0.1(12.99) = $12.99 – $1.30 = $11.69
You will then save $11.69 – $11.00 = 0.69 per shirt if you buy them from Store 1.

Question 24.
b. If Store 3 has shirts originally priced at $20.98 on sale for 55% off, does it have a better deal than the other stores? Justify your answer.
_______

Answer:
If Store 3 sells shirts at 55% off of $20.98, then each shirt costs:
$20.98 – 0.55($20.98) = $20.98 – $11.54 = $9.44
This is lower than the costs per shirt of Store 1 and Store 2 so it has a better deal.

H.O.T.

Focus on Higher Order Thinking

Question 25.
Analyze Relationships
Marcus can choose between a monthly salary of $1,500 plus 5.5% of sales or $2,400 plus 3% of sales. He expects sales between $5,000 and $10,000 a month. Which salary option should he choose? Explain.
_______

Answer: Second Salary option is better

Explanation:
E = 1500 + 0.055(5000)
E = 1500 + 275
E = $1775
In the second case he will earn
E = 2400 + 0.03(5000)
E = 2400 + 150
E = $2550

Question 26.
Multistep
In chemistry class, Bob recorded the volume of a liquid as 13.2 mL. The actual volume was 13.7 mL. Use the formula to find percent error of Bob’s measurement to the nearest tenth of a percent.
_______ %

Answer: 3.6%

Explanation:
Go Math Grade 7 Answer Key Chapter 5 Percent Increase and Decrease Lesson 1: Percent Increase and Decrease img 3
|13.2 – 13.7|/13.7 = |-0.5|/13.7
0.5/13.7 ≈ 0.036 = 3.6%

MODULE QUIZ – 5.1 Percent Increase and Decrease – Page No. 159

Find the percent change from the first value to the second.

Question 1.
36; 63
_______ %

Answer: 75%

Explanation:
Use the formula percent change = amount of change/first value
amount of change = 27
First value = 36
(63 – 36)/36 = 27/36 = 0.75 = 75%

Question 2.
50; 35
_______ %

Answer: 30%

Explanation:
Use the formula percent change = amount of change/first value
amount of change = 15
First value = 50
(50 – 35)/35 = 15/50 = 0.3 = 30%

Question 3.
40; 72
_______ %

Answer: 80%

Explanation:
Use the formula percent change = amount of change/first value
amount of change = 32
First value = 40
(72 – 40)/40 = 32/40 = 0.8 = 80%

5.2 Markup and Markdown

Use the original price and the markdown or markup to find the retail price.

Question 5.
Original price: $60; Markup: 15%
$ _______

Answer: $69

Explanation:
Use the formula retail price = original price + markup
60 + 60 × 0.15 = 60 + 9= 69

Question 6.
Original price: $32; Markup: 12.5%
$ _______

Answer: 36

Explanation:

Use the formula retail price = original price + markup

32 + 32 × 0.125 = 32 + 4 = $36

Question 7.
Original price: $50; Markdown: 22%
$ _______

Answer: 39

Explanation:

Use the formula retail price = original price + markup

50 – 50 × 0.22 = 50 – 11 = 39

Question 8.
Original price: $125; Markdown: 30%
$ _______

Answer: 87.50

Explanation:

Use the formula retail price = original price + markup

125 – 125 × 0.3 = 125 – 37.50 = 87.50

5.3 Applications of Percent

Question 9.
Mae Ling earns a weekly salary of $325 plus a 6.5% commission on sales at a gift shop. How much would she make in a work week if she sold $4,800 worth of merchandise?
$ _______

Answer: 637

Explanation:

Mae Ling weekly earnings is equal to her weekly salary plus her commission.

Since she earns 6.5 % commission on sales, if she sold $4800 worth of merchandise, her commission earnings  would be 6.5 % of 4800 = 0.065 × 4800 = $312.

Since her weekly salary is 325, then her total weekly earnings is $325 + $312 = $637

Question 10.
Ramon earns $1,735 each month and pays $53.10 for electricity. To the nearest tenth of a percent, what percent of Ramon’s earnings are spent on electricity each month?
_______ %

Answer: 3.1%

Explanation:

Divide the electric payment by his monthly pay

53.10/1735 = 0.031 = 3.1%

Question 11.
James, Priya, and Siobhan work in a grocery store. James makes $7.00 per hour. Priya makes 20% more than James, and Siobhan makes 5% less than Priya. How much does Siobhan make per hour?
$ _______

Answer: 7.98 per hour

Explanation:

Since James makes $7 per hour and priya makes 20% more than this, find 20% of 7 and then add that to 7 to find the pay per hour for Priya.

7 + 0.2(7) = 7 + 1.40 = 8.40

Since Priya makes $8.40 per hour and Siobhan makes 5% less than this, find 5% of 8.40 and subtract that from 8.40 to find the pay per hour of Siobhan.

8.40 – 0.05(8.40) = 8.40 – 0.42 = 7.98

Question 12.

The Hu family goes out for lunch, and the price of the meal is $45. The sales tax on the meal is 6%, and the family also leaves a 20% tip on the pre-tax amount. What is the total cost of the meal?
$ _______

Answer: 56.70

Explanation:

Find the amount of tax

45 × 0.06 = 2.70

Find the amount of tip

45 × 0.20 = 9

Find the total cost by adding the cost of the meal, the tax, and the tip.

45 + 2.70 + 9 = $56.70

Essential Question

Question 13.
Give three examples of how percents are used in the real-world. Tell whether each situation represents a percent increase or a percent decrease.
Type below:
____________

Answer:

One example could be giving a tip when you eat at a restaurant. Since the cost increases, it represents a percent increase.

Second example is tax on purchase. Since the price increases it is a percent increase.

Third example is using a coupon when buying an item. Since the price decreases, it is a percent decrease.

Selected Response – Page No. 160

Question 1.
Zalmon walks \(\frac{3}{4}\) of a mile in \(\frac{3}{10}\) of an hour. What is his speed in miles per hour?
Options:
a. 0.225 miles per hour
b. 2.3 miles per hour
c. 2.5 miles per hour
d. 2.6 miles per hour

Answer: 2.5 miles per hour

Explanation:
Given that,
Zalmon walks \(\frac{3}{4}\) of a mile in \(\frac{3}{10}\) of an hour.
Divide the number of miles by the number of hours to get his speed in miles per hour.
\(\frac{3}{4}\) ÷ \(\frac{3}{10}\)
\(\frac{3}{4}\) ÷ \(\frac{10}{3}\) = \(\frac{5}{2}\)
Convert the fraction into the decimal form.
\(\frac{5}{2}\) = 2.5 miles per hour
Thus the correct answer is option C.

Question 2.
Find the percent change from 70 to 56.
Options:
a. 20% decrease
b. 20% increase
c. 25% decrease
d. 25% increase

Answer: 20% increase

Explanation:
Use the percent change = amount of change/original amount.
Since the number decreased from 70 to 56, it is a percent decrease.
= (70 – 56)/70 = \(\frac{14}{70}\) = 0.2 = 20%
Thus the correct answer is option A.

Question 3.
The rainfall total two years ago was 10.2 inches. Last year’s total was 20% greater. What was last year’s rainfall total?
Options:
a. 8.16 inches
b. 11.22 inches
c. 12.24 inches
d. 20.4 inches

Answer: 12.24 inches

Explanation:
Given,
The rainfall total two years ago was 10.2 inches. Last year’s total was 20% greater.
Find 20% of 10.2
10.2 × 0.20 = 2.04
Add the value to the original amount of 10.2
10.2 + 2.04 = 12.24
Therefore the correct answer is option C.

Question 4.
A pair of basketball shoes was originally priced at $80, but was marked up 37.5%. What was the retail price of the shoes?
Options:
a. $50
b. $83
c. $110
d. $130

Answer: $110

Explanation:
A pair of basketball shoes was originally priced at $80, but was marked up 37.5%.
Use the formula retail price = original price + markup
80 + 80 × 0.375 = 80 + 30 = 110
Thus the correct answer is option C.

Question 5.
The sales tax rate in Jan’s town is 7.5%. If she buys 3 lamps for $23.59 each and a sofa for $769.99, how much sales tax does she owe?
Options:
a. $58.85
b. $63.06
c. $67.26
d. $71.46

Answer: $63.06

Explanation:
The sales tax rate in Jan’s town is 7.5%.
If she buys 3 lamps for $23.59 each and a sofa for $769.99
Total cost before tax is 3 × 23.59 + 769.99
= 70.77 + 769.99 = 840.76
Find the amount of tax by multiplying the tax rate and total cost from the above solution and then round to 2 decimal place.
840.76 × 0.075 = 63.06
Thus the correct answer is option B.

Question 6.
The day after a national holiday, decorations were marked down 40%. Before the holiday, a patriotic banner cost $5.75. How much did the banner cost after the holiday?
Options:
a. $1.15
b. $2.30
c. $3.45
d. $8.05

Answer: $3.45

Explanation:
The day after a national holiday, decorations were marked down 40%. Before the holiday, a patriotic banner cost $5.75.
use the formula retail price = original price – markdown
5.75 – 5.75 × 0.4 = 5.75 – 2.30 = 3.45
Thus the correct answer is option C.

Question 7.
Dustin makes $2,330 each month and pays $840 for rent. To the nearest tenth of a percent, what percent of Dustin’s earnings are spent on rent?
Options:
a. 84%
b. 63.9%
c. 56.4%
d. 36.1%

Answer: 36.1%

Explanation:
Dustin makes $2,330 each month and pays $840 for rent.
Divide his rent by his monthly income. round to three decimal places and then convert to percent form.
840/2330 = 0.361 = 36.1%
Thus the correct answer is option D.

Question 8.
A scuba diver is positioned at -30 feet. How many feet will she have to rise to change her position to -12 feet?
Options:
a. -42 ft
b. -18 ft
c. 18 ft
d. 42 ft

Answer: 18 ft

Explanation:
Given,
A scuba diver is positioned at -30 feet.
-12 – (-30) = 12 + 30 = 18 feet
Thus the correct answer is option C.

Question 9.
A bank offers an annual simple interest rate of 8% on home improvement loans. Tobias borrowed $17,000 over a period of 2 years. How much did he repay altogether?
Options:
a. $1360
b. $2720
c. $18360
d. $19720

Answer: $19720

Explanation:
Given that,
A bank offers an annual simple interest rate of 8% on home improvement loans.
Tobias borrowed $17,000 over a period of 2 years
Find the amount of interest he paid using the formula
I = prt
where p is the amount borrowed
r is the interest rate
t is the number of years
17000 × 0.08 × 2 = 2720
Add the amount borrowed and amount of interest
17000 + 2720 = 19720.
Thus the correct answer is option D.

Mini-Task

Question 10.
The granola Summer buys used to cost $6.00 per pound, but it has been marked up 15%.
a. How much did it cost Summer to buy 2.6 pounds of granola at the old price?
$ ___________

Answer: $15.60

Explanation:
Multiply 2.6 by the old price of $6
2.6 × 6 = 15.60
It costs $15.60 to buy 2.6 pounds of granola at the old price.

Question 10.
b. How much does it cost her to buy 2.6 pounds of granola at the new price?
$ _______

Answer: $17.94

Explanation:
Find the new price using the formula retail price = original price + markup
Then find the total cost by buying 2.6 pounds at the new price.
6 + 6 × 0.15 = 6 + 0.9 = 6.90
2.6 × 6.90 = 17.94
The new price is $17.94

Question 10.
c. Suppose Summer buys 3.5 pounds of granola. How much more does it cost at the new price than at the old price?
$ _______

Answer: $3.15

Explanation:
3.5 × 6 = 21
3.5 × 6.90 = 24.15
24.15 – 21 = 3.15

Module 5 – Page No. 162

EXERCISES

Question 1.
Michelle purchased 25 audio files in January. In February she purchased 40 audio files. Find the percent increase.
_______ %

Answer: 60%

Explanation:
Given,
Michelle purchased 25 audio files in January. In February she purchased 40 audio files.
Use the percent change = amount of change/original amount.
(40 -25)/25 = 15/25 = 0.6 = 60%
Thus the percent increase is 60%

Question 2.
Sam’s dog weighs 72 pounds. The vet suggests that for the dog’s health, its weight should decrease by 12.5 percent. According to the vet, what is a healthy weight for the dog?
_______ pounds

Answer: 63 pounds

Explanation:
Given,
Sam’s dog weighs 72 pounds. The vet suggests that for the dog’s health, its weight should decrease by 12.5 percent.
72 × 0.125 = 9
Find a healthy weight by subtracting the change in weight from the original weight
72 – 9 = 63
The healthy weight of the dog is 63 pounds.

Question 3.
The original price of a barbecue grill is $79.50. The grill is marked down 15%. What is the sale price of the grill?
$ _______

Answer: 67.57

Explanation:
Given,
The original price of a barbecue grill is $79.50. The grill is marked down 15%.
Use the formula sale price = original price – markdown
= 79.50 – 79.50 × 0.15 = 79.50 – 11.93 = $67.57
Thus the sale price of the grill is $67.57

Question 4.
A sporting goods store marks up the cost s of soccer balls by 250%. Write an expression that represents the retail cost of the soccer balls. The store buys soccer balls for $5.00 each. What is the retail price of the soccer balls?
$ _______

Answer: $17.5

Explanation:
Use the formula retail price = original price + markup to find the expression for an original price of s and a markup percentage of 250%
s + 2.5s = 3.5s
substitute s = 5 into the expression to find the retail price
3.5 × 5 = 17.50
Thus the retail price of the soccer balls is $17.50

Unit 2 Performance Tasks – Page No. 163

Question 1.
Viktor is a bike tour operator and needs to replace two of his touring bikes. He orders two bikes from the sporting goods store for a total of $2,000 and pays using his credit card. When the bill arrives, he reads the following information:
Balance: $2000
Annual interest rate: 14.9%
Minimum payment due: $40
Late fee: $10 if payment not received by 3/1/2013
a. To keep his good credit, Viktor promptly sends in a minimum payment of $40. When the next bill arrives, it looks a lot like the previous bill.
Balance: $1,984.34
Annual interest rate: 14.9%
Minimum payment due: $40
Late fee: $10 if payment not received by 4/1/2013
Explain how the credit card company calculated the new balance. Notice that the given interest rate is annual, but the payment is monthly.
Type below:
_____________

Answer:
We have to find the balance after the first bill by subtracting the $40 payment from the original balance of $2000.
Balance after first bill: 2000 – 40 = 1960
Then find the amount of interest charged on the second bill by multiplying the balance of $1960 by the interest rate.
Remember since the interest rate is annually you have to divide it by 12 to get the monthly interest rate.
Interest on the second bill: 1960 × 0.149/12 = 24.34
And then add this interest amount to the balance of $1960 to get the balance on the second bill.
New balance: 1960 + 24.34 = 1984.34

Question 1.
b. Viktor was upset about the new bill, so he decided to send in $150 for his April payment. The minimum payment on his bill is calculated as 2% of the balance (rounded to the nearest dollar) or $20, whichever is greater. Fill out the details for Viktor’s new bill.
Type below:
_____________

Answer:
Find the balance after the $150 payment. The interest rate hasn’t changed so the annual interest rate on this new bill is the same as the previous bills.
balance after payment: 1984.34 – 150 = 1834.34
annual interest rate: 14/9%
Find the interest charged on the third bill. find the balance on the third bill by adding the interest charged to the balance of $1834.34.
interest on the third bill: 1834.34 × 0.149/12 = 22.78
balance: 1834.34 + 22.78 = 1857.12
To find what the minimum payment will be, first find 2% of the balance.
2% of balance: 0.02 × 1857.12 = 37.14
Minimum payment due: $37.00
Since this is greater than $20, the minimum payment is 2% of the balance rounded to the nearest dollar giving $37 as the payment.
The later fee date is one month after the late fee date of 04/01/2013 on the previous bill which gives 05/01/2013.

Question 1.
c. Viktor’s bank offers a credit card with an introductory annual interest rate of 9.9%. He can transfer his current balance for a fee of $40. After one year, the rate will return to the bank’s normal rate, which is 13.9%. The bank charges a late fee of $15. Give two reasons why Viktor should transfer the balance and two reasons why he should not
Type below:
_____________

Answer: Two reasons he should transfer is that the lower introductory rate would mean less interest charged in the first year and a lower normal rate would mean less interest charged after that first year as well. Two reasons he shouldn’t transfer the balance is that he would have to pay a transfer fee of $40 and that the late fee is $15 instead of $10 if he transfers the balance.

Unit 2 Performance Tasks (con’td) – Page No. 164

Question 2.
The table below shows how far several animals can travel at their maximum speeds in a given time.
a. Write each animal’s speed as a unit rate in feet per second.
Go Math Grade 7 Answer Key Chapter 5 Percent Increase and Decrease img 13
Elk: _________ feet per second
Giraffe: _________ feet per second
Zebra: _________ feet per second

Answer:
By seeing the above table we can find the unit rates by dividing the distance traveled by the time in second.
elk: 33 ÷ 1/2 = 33 ×  2 = 66 feet per second
Giraffe: 115 ÷ 2 1/2 = 115 ÷ 5/2 = 115 2/5 = 46 feet per second
Zebra: 117 ÷ 2 = 58.5 feet per second

Question 2.
b. Which animal has the fastest speed?
_____________

Answer: The elk had the greatest unit rate so it has the fastest speed.

Question 2.
c. How many miles could the fastest animal travel in 2 hours if it maintained the speed you calculated in part a? Use the formula d = rt and round your answer to the nearest tenth of a mile. Show your work.
Elk: _________ miles
Giraffe: _________ miles
Zebra: _________ miles

Answer:
Elk: 90 miles
Giraffe: 62 miles
Zebra: 72 miles

Explanation:

There are 60 seconds in a minute and 60 minutes in an hour so there are 2 × 60 × 60 = 7200 seconds in 2 hours.
Multiply the unit rate of the elk by 7200 seconds to get the distance traveled in feet.
There are 5280 feet in 1 mile so divide the distance in feet by 5280 to get the distances in miles.
Elk:
66 × 7200 =  475200 feet
Now convert from feet to miles
475200 feet = 90 miles
Giraffe: 46 feet per second
62 × 7200 = 331200 feet
Now convert from feet to miles.
331200 = 62 miles
Zebra: 58.5 feet per second
58.5 × 7200 = 421200 feet
Now convert from feet to miles.
421200 feet = 72 miles

Question 3.
d. The data in the table represents how fast each animal can travel at its maximum speed. Is it reasonable to expect the animal from part b to travel that distance in 2 hours? Explain why or why not.
______

Answer: It is not reasonable. An animal can only travel at its maximum speed for a short amount of time which is usually only for a couple of minutes.

Selected Response – Page No. 165

Question 1.
If the relationship between distance y in feet and time x in seconds is proportional, which rate is represented by \(\frac{y}{x}\) = 0.6?
Options:
a. 3 feet in 5 s
b. 3 feet in 9 s
c. 10 feet in 6 s
d. 18 feet in 3 s

Answer: 3 feet in 5 s

Explanation:
\(\frac{y}{x}\) = 0.6
0.6 = \(\frac{6}{10}\)
Since \(\frac{6}{10}\) = \(\frac{3}{5}\), it represents a rate of 3 feet in 5 seconds,
Therefore the correct answer is option A.

Question 2.
The Baghrams make regular monthly deposits in a savings account. The graph shows the relationship between the number x of months and the amount y in dollars in the account.
What is the equation for the deposit?
Go Math Grade 7 Answer Key Chapter 5 Percent Increase and Decrease img 14
Options:
a. \(\frac{y}{x}\) = $25/month
b. \(\frac{y}{x}\) = $40/month
c. \(\frac{y}{x}\) = $50/month
d. \(\frac{y}{x}\) = $75/month

Answer: \(\frac{y}{x}\) = $50/month

Explanation:
By seeing the above graph we can say that the point is (2, 100). This means that \(\frac{y}{x}\) = \(\frac{100}{2}\) = 50.
Thus the correct answer is option C.

Question 3.
What is the decimal form of −4 \(\frac{7}{8}\)?
Options:
a. -4.9375
b. -4.875
c. -4.75
d. -4.625

Answer: -4.875

Explanation:
Given the fraction
−4 \(\frac{7}{8}\)
First divide \(\frac{7}{8}\) = 0.875
4 + 0.875 = 4.875
So, −4 \(\frac{7}{8}\) = -4.875
Therefore the answer is option B.

Question 4.
Find the percent change from 72 to 90.
Options:
a. 20% decrease
b. 20% increase
c. 25% decrease
d. 25% increase

Answer: 25% increase

Explanation:
Use the formula percent change = amount of change/original amount.
the value increased from 72 to 90 so it is a percent increase.
(90-72)/72 = 18/72 = 0.25 = 25%
Thus the correct answer is option D.

Question 5.
A store had a sale on art supplies. The price p of each item was marked down 60%. Which expression represents the new price?
Options:
a. 0.4p
b. 0.6p
c. 1.4p
d. 1.6p

Answer: 0.4p

Explanation:
Given that,
A store had a sale on art supplies.
The price p of each item was marked down 60%
Use the formula sale price = original price – markdown
p is the original price and the markdown percent is 40% then combine the like terms.
p – 0.6p = 0.4p
Therefore the correct answer is option A.

Question 6.
Clarke borrows $16,000 to buy a car. He pays simple interest at an annual rate of 6% over a period of 3.5 years. How much does he pay altogether?
Options:
a. $18800
b. $19360
c. $19920
d. $20480

Answer: $19360

Explanation:
Given,
Clarke borrows $16,000 to buy a car.
He pays simple interest at an annual rate of 6% over a period of 3.5 years.
Find the total amount of interest using the formula
I = prt
where p is the amount borrowed
r is the rate of interest
t is the number of years
16000 × 0.06 × 3.5 = 3360
Now add the amount of interest to the amount borrowed to find the total amount
16000 + 3360 = 19,360
Thus the correct answer is option B.

Question 7.
To which set or sets does the number 37 belong?
Options:
a. integers only
b. rational numbers only
c. integers and rational numbers only
d. whole numbers, integers, and rational numbers

Answer: whole numbers, integers, and rational numbers

Explanation:
37 can be written as 37/1 so it is a rational number. 37 doesn’t have a decimal or fraction so it is an integer. Since it is a positive integer, it is also a whole number.
Thus a suitable answer is option D.

Page No. 166

Question 8.
In which equation is the constant of proportionality 5?
Options:
a. x = 5y
b. y = 5x
c. y = x + 5
d. y = 5 – x

Answer: y = 5x

Explanation:
Directly proportional equations are of the form y = kx
where k is the constant of proportionality.
If k = 5, then the equation is y = 5x.
Thus the correct answer is option B.

Question 9.
Suri earns extra money by dog walking. She charges $6.25 to walk a dog once a day 5 days a week and $8.75 to walk a dog once a day 7 days a week. Which equation represents this relationship?
Options:
a. y = 7x
b. y = 5x
c. y = 2.50x
d. y = 1.25x

Answer: y = 1.25x

Explanation:
Given that,
Suri earns extra money by dog walking. She charges $6.25 to walk a dog once a day 5 days a week and $8.75 to walk a dog once a day 7 days a week.
Since 6.25/5 = 1.25
So, the equation is y = 1.25x
where x is the number of days and y is the total charge.
So, the correct answer is option D.

Question 10.
Randy walks \(\frac{1}{2}\) mile in each \(\frac{1}{5}\) hour. How far will Randy walk in one hour?
Options:
a. \(\frac{1}{2}\) miles
b. 2 miles
c. 2 \(\frac{1}{2}\) miles
d. 5 miles

Answer: 2 \(\frac{1}{2}\) miles

Explanation:
Given,
Randy walks \(\frac{1}{2}\) mile in each \(\frac{1}{5}\) hour.
\(\frac{1}{2}\) ÷ \(\frac{1}{5}\)
\(\frac{1}{2}\) × \(\frac{5}{1}\) = \(\frac{5}{2}\)
Convert the fraction to the improper fractions.
\(\frac{5}{2}\) = 2 \(\frac{1}{2}\) miles
Therefore the correct answer is option C.

Question 11.
On a trip to Spain, Sheila bought a piece of jewelry that cost $56.75. She paid for it with her credit card, which charges a foreign transaction fee of 3%. How much was the foreign transaction fee?
Options:
a. $0.17
b. $1.07
c. $1.70
d. $17.00

Answer: $1.70

Explanation:
On a trip to Spain, Sheila bought a piece of jewelry that cost $56.75.
She paid for it with her credit card, which charges a foreign transaction fee of 3%
Find the foreign transaction fee amount by multiplying the cost by the foreign transaction fee percentage.
56.75 × 0.03 = 1.70
Thus the correct answer is option C.

Question 12.
A baker is looking for a recipe that has the lowest unit rate for flour per batch of muffins. Which recipe should she use?
Options:
a. \(\frac{1}{2}\) cup flour for \(\frac{2}{3}\) batch
b. \(\frac{2}{3}\) cup flour for \(\frac{1}{2}\) batch
c. \(\frac{3}{4}\) cup flour for \(\frac{2}{3}\) batch
d. \(\frac{1}{3}\) cup flour for \(\frac{1}{4}\) batch

Answer: \(\frac{1}{2}\) cup flour for \(\frac{2}{3}\) batch

Explanation:
a. \(\frac{1}{2}\) ÷ \(\frac{2}{3}\) = \(\frac{1}{2}\) × \(\frac{3}{2}\) = \(\frac{3}{4}\)
b. \(\frac{2}{3}\) ÷ \(\frac{1}{2}\) = \(\frac{2}{3}\) × \(\frac{2}{1}\) = \(\frac{4}{3}\) = 1 \(\frac{1}{3}\)
c. \(\frac{3}{4}\) ÷ \(\frac{2}{3}\) = \(\frac{3}{4}\) × \(\frac{3}{2}\) = \(\frac{9}{8}\) = 1 \(\frac{1}{8}\)
d. \(\frac{1}{3}\) ÷ \(\frac{1}{4}\) = \(\frac{1}{3}\) ÷ \(\frac{4}{1}\) = 1 \(\frac{1}{3}\)
Thus the correct answer is option A.

Mini-Task

Question 13.
Kevin was able to type 2 pages in 5 minutes, 3 pages in 7.5 minutes, and 5 pages in 12.5 minutes.
a. Make a table of the data.
Type below:
___________

Answer:

Number of Pages235
Minutes57.512.5

Question 13.
b. Graph the relationship between the number of pages typed and the number of minutes.
Go Math Grade 7 Answer Key Chapter 5 Percent Increase and Decrease img 15
Type below:
___________

Answer:

Go-Math-Grade-7-Answer-Key-Chapter-5-Percent-Increase-and-Decrease-img-15

Question 13.
c. Explain how to use the graph to find the unit rate.
Type below:
___________

Answer: The unit rate is 2.5 pages per minute

Explanation:
By using the graph we need to find the slope of the line.
We can do this by using the formula of a slope:
m = (y2-y1)/(x2-x1) = (7.5-5)/(3-2) = 2.5
Thus the unit rate is 2.5 pages per minute.

Conclusion:

Hope the answers provided in Go Math Answer Key Grade 7 Chapter 5 Percent Increase and Decrease are quite satisfactory for all the students. Refer to our Go Math 7th Grade Chapter 5 Percent Increase and Decrease to get the solutions with best explanations. After your preparation test your math skills by solving the questions in the performance tasks.

Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships

go-math-grade-8-chapter-4-nonproportional-relationships-answer-key

Are you searching for Go Math 8th Grade Answer Key Chapter 4 Nonproportional Relationships? If yes, then download Go Math Grade 8 Answer Key pdf from here in this article. It helps the students to score good marks in the exams. All the solutions are prepared by the math experts according to the latest edition. Get free access for all topics on Go Math Grade 8 Chapter 4 Nonproportional Relationships from here.

Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships

Check the list of the exercises contained in Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships. With the help of this Go Math Grade 8 Chapter 4 Nonproportional Relationships Solution Key students can improve their performance in the tests or assignments. Refer to HMH Go Math Grade 8 Chapter 4 Answer Key to complete your homework in time.

Lesson 1: Representing Linear Nonproportional Relationships

Lesson 2: Determining Slope and y-intercept

Lesson 3: Graphing Linear Nonproportional Relationships Using Slope and y-intercept

Lesson 4: Proportional and Nonproportional Situations 

Lesson 5: Representing Linear Nonproportional Relationships – Model Quiz

Mixed Review 

Guided Practice – Representing Linear Nonproportional Relationships – Page No. 98

Make a table of values for each equation.

Question 1.
y = 2x + 5
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 1: Representing Linear Nonproportional Relationships img 1
Type below:
____________

Answer:
grade 8 chapter 4 image 13

Explanation:
y = 2x + 5
Choose several values for x and substitute in the equation to find y.
x = 2(-2) + 5 = 1
x = 2(-1) + 5 = 3
x = 2(0) + 5 = 5
x = 2(1) + 5 = 7
x = 2(2) + 5 = 9

Question 2.
y = \(\frac{3}{8}\)x − 5
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 1: Representing Linear Nonproportional Relationships img 2
Type below:
____________

Answer:
grade 8 chapter 4 image 14

Explanation:
y = \(\frac{3}{8}\)x − 5
Choose several values for x and substitute in the equation to find y.
x = 3/8(-8) – 5 = -8
x = 3/8(0) – 5 = -5
x = 3/8(8) – 5 = -2
x = 3/8(16) – 5 = 1
x = 3/8(24) – 5 = 4

Explain why each relationship is not proportional.

Question 3.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 1: Representing Linear Nonproportional Relationships img 3
First calculate \(\frac{y}{x}\) for the values in the table.
____________

Answer:
The relationship is not proportional

Explanation:
Find y/x
3/0 = undefined
7/2 = 3.5
11/4 = 2.75
15/6 = 2.5
19/8 = 2.375
The ratio is not constant, hence relationship is not proportional.

Question 4.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 1: Representing Linear Nonproportional Relationships img 4
__________________

Answer:
The graph is a straight line but does not pass through the origin. So, the relationship is not proportional.

Complete the table for the equation. Then use the table to graph the equation.

Question 5.
y = x − 1
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 1: Representing Linear Nonproportional Relationships img 5
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 1: Representing Linear Nonproportional Relationships img 6
Type below:
____________

Answer:
grade 8 chapter 4 image 15

grade 8 chapter 4 image 16

Explanation:
y = x – 1
Choose several values of x and substitute in the equation to find y to draw a table.
x = -2; y = -2 – 1 = -2
x = -1; y = -1 -1 = -2
x = 0; y = 0 -1 = -1
x = 1; y = 1 – 1 = 0
x = 2; y = 2 -1 = 1
Also, Plot the ordered pairs from the table. Then draw a line connecting the points to represent all the possible solutions

Essential Question Check-In

Question 6.
How can you choose values for x when making a table of values representing a real world situation?
Type below:
____________

Answer:
When choosing values for x in a real-world situation, you choose positive values with an appropriate interval to represent the array of data.

Independent Practice – Representing Linear Nonproportional Relationships – Page No. 99

State whether the graph of each linear relationship is a solid line or a set of unconnected points. Explain your reasoning.

Question 7.
The relationship between the number of $4 lunches you buy with a $100 school lunch card and the money remaining on the card
____________

Answer:
Set of unconnected points.

Explanation:
You cannot buy a fractional part of a lunch.
Set of unconnected points.

Question 8.
The relationship between time and the distance remaining on a 3-mile walk for someone walking at a steady rate of 2 miles per hour.
____________

Answer:
A solid line

Explanation:
The relationship between time and the distance remaining on a 3-mile walk for someone walking at a steady rate of 2 miles per hour. The distance remaining can be a fraction. The time can be in a fraction as well.
A solid line

Question 9.
Analyze Relationships
Simone paid $12 for an initial year’s subscription to a magazine. The renewal rate is $8 per year. This situation can be represented by the equation y = 8x + 12, where x represents the number of years the subscription is renewed and y represents the total cost.
a. Make a table of values for this situation.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 1: Representing Linear Nonproportional Relationships img 7
Type below:
____________

Answer:
grade 8 chapter 4 image 17

Explanation:
y = 8x + 12
Choose several values for x and substitute in the equation to find y.

Question 9.
b. Draw a graph to represent the situation. Include a title and axis labels.
Type below:
____________

Answer:
grade 8 chapter 4 image 18

Explanation:
Plot the ordered pairs from the table. Then draw a line connecting the points to represent all the possible solutions

Question 9.
c. Explain why this relationship is not proportional.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 1: Representing Linear Nonproportional Relationships img 8
Type below:
____________

Answer:
It is not proportional as the graph does not pass through the origin

Explanation:
When a relationship is proportional, the graph of the equation passes through the origin.
It is not proportional as the graph does not pass through the origin

Question 9.
d. Does it make sense to connect the points on the graph with a solid line? Explain.
Type below:
____________

Answer:
No

Explanation:
No; The subscription is rewened for the entire year and cannot be done for a fraction of the year. The number of years must be a whole numb, so the total cost goes up in $8 increments.

Representing Linear Nonproportional Relationships – Page No. 100

Question 10.
Analyze Relationships
A proportional relationship is a linear relationship because the rate of change is constant (and equal to the constant of proportionality). What is required of a proportional relationship that is not required of a general linear relationship?
Type below:
____________

Answer:
The ratio between one quantity to the other quantity should be constant for a proportional linear relationship. The graph should be a straight line that passes through the origin.

Question 11.
Communicate Mathematical Ideas
Explain how you can identify a linear non-proportional relationship from a table, a graph, and an equation.
Type below:
____________

Answer:
In a table, the ratios y/x will not be equal. A graph will not pass through the origin. An equation will be in the form y = mx + b where b is not equal to 0.

Focus on Higher Order Thinking

Question 12.
Critique Reasoning
George observes that for every increase of 1 in the value of x, there is an increase of 60 in the corresponding value of y. He claims that the relationship represented by the table is proportional. Critique George’s reasoning.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 1: Representing Linear Nonproportional Relationships img 9
Type below:
____________

Answer:
The ratio is not constant, hence the relationship cannot be proportional.

Explanation:
Find y/x
90/1 = 90
150/2 = 75
210/3 = 70
270/4 = 67.5
330/5 = 66
The ratio is not constant, hence the relationship cannot be proportional.

Question 13.
Make a Conjecture
Two parallel lines are graphed on a coordinate plane. How many of the lines could represent proportional relationships? Explain.
Type below:
____________

Answer:
Maximum one

Explanation:
When there are two parallel lines, only one can pass through the origin and a line representing a proportional relationship must pass through the origin.
Maximum one

Guided Practice – Determining Slope and y-intercept – Page No. 104

Find the slope and y-intercept of the line in each graph.

Question 1.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 2: Determining Slope and y-intercept img 10
slope m = _____ y-intercept b = _____
m = ____________
b = ____________

Answer:
slope m = -2 y-intercept b = 1
m = -2
b = 1

Explanation:
Find the slope using two points from the grapgh by
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (0, 1) and (x2, y2) = (2, -3)
Slope m = (y2 -y1)/(x2 – x1) = (-3 – 1)/(2 – 0) = -4/2 = -2
From the graph when x = 0
y-intercept (b) = 1

Question 2.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 2: Determining Slope and y-intercept img 11
slope m = _____ y-intercept b = _____
m = ____________
b = ____________

Answer:
slope m = 5 y-intercept b = -15
m = 5
b = -15

Explanation:
Find the slope using two points from the grapgh by
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (3, 0) and (x2, y2) = (0, -15)
Slope m = (y2 -y1)/(x2 – x1) = (-15 – 0)/(0 – 3) = 15/3 = 5
From the graph when x = 0
y-intercept (b) = -15

Question 3.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 2: Determining Slope and y-intercept img 12
slope m = _____ y-intercept b = _____
Type below:
____________

Answer:
slope m = 3/2 y-intercept b = -2
m = 3/2
b = -2

Explanation:
Find the slope using two points from the grapgh by
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (0, -2) and (x2, y2) = (2, 1)
Slope m = (y2 -y1)/(x2 – x1) = (1 – (-2))/(2 – 0) = 3/2
From the graph when x = 0
y-intercept (b) = -2

Question 4.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 2: Determining Slope and y-intercept img 13
slope m = _____ y-intercept b = _____
m = ____________
b = ____________

Answer:
slope m = -3 y-intercept b = 9
m = -3
b = 9

Explanation:
Find the slope using two points from the grapgh by
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (3, 0) and (x2, y2) = (0, 9)
Slope m = (y2 -y1)/(x2 – x1) = (9 – 0))/(0 – 3) = -9/3 = -3
From the graph when x = 0
y-intercept (b) = 9

Find the slope and y-intercept of the line represented by each table.

Question 5.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 2: Determining Slope and y-intercept img 14
slope m = _____ y-intercept b = _____
m = ____________
b = ____________

Answer:
slope m = 3 y-intercept b = 1
m = 3
b = 1

Explanation:
Find the slope using two points from the grapgh by
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (8, 25) and (x2, y2) = (6, 19)
Slope m = (y2 -y1)/(x2 – x1) = (19 – 25)/(6 – 8) = 6/2 = 3
From the graph when x = 0
y-intercept (b) = 1

Question 6.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 2: Determining Slope and y-intercept img 15
slope m = _____ y-intercept b = _____
m = ____________
b = ____________

Answer:
slope m = -4 y-intercept b = 140
m = -4
b = 140

Explanation:
Find the slope using two points from the grapgh by
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (5, 120) and (x2, y2) = (15, 80)
Slope m = (y2 -y1)/(x2 – x1) = (80 – 120)/(15 – 5) = -40/10 = -4
From the graph when x = 0
y-intercept (b) = 140

Essential Question Check-In

Question 7.
How can you determine the slope and the y-intercept of a line from a graph?
Type below:
____________

Answer:
Choose any two points on the line from the graph and use it to find the slope. Determine the point where the line crosses the y-axis to find the y-intercept.

Independent Pratice – Determining Slope and y-intercept – Page No. 105

Question 8.
Some carpet cleaning costs are shown in the table. The relationship is linear. Find and interpret the rate of change and the initial value for this situation.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 2: Determining Slope and y-intercept img 16
Type below:
_____________

Answer:
Find the slope using two points
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (1, 125) and (x2, y2) = (3, 225)
Slope m = (y2 -y1)/(x2 – x1) = (225 – 125)/(3 – 1) = 100/2 = 50
Find the initial value when the value of x is 0
Work backward from x = 1 to x = 0
(175 – 125)/(2 – 1) = 50/1 = 50
Subtract the difference of x and y from the first point.
x = 1 – 1 = 0
y = 125 – 50 = 75
y intercept (b) = 75
The slope/rate of change represents the increase in the cost of cleaning the rooms for a unit increase in the number of rooms. The y-intercept shows the initial cost of carpet cleaning.

Question 9.
Make Predictions
The total cost to pay for parking at a state park for the day and rent a paddleboat are shown.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 2: Determining Slope and y-intercept img 17
a. Find the cost to park for a day and the hourly rate to rent a paddleboat.
Type below:
_____________

Answer:
$5

Explanation:
Find the slope using two points
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (1, 17) and (x2, y2) = (2, 29)
Slope m = (y2 -y1)/(x2 – x1) = (29 – 17)/(2 – 1) = 12/1 = 12
Find the initial value when the value of x is 0
Work backward from x = 1 to x = 0
(29 – 17)/(2 – 1) = 12/1 = 12
Subtract the difference of x and y from the first point.
x = 1 – 1 = 0
y = 17 – 12 = 5
The cost to park for a day is $5.

Question 9.
b. What will Lin pay if she rents a paddleboat for 3.5 hours and splits the total cost with a friend? Explain.
$ _____________

Answer:
$23.5

Explanation:
When Lin paddles for 3.5hr
Total Cost = 3.5(12) + 5 = 47
Lin’s cost = 47/2 = 23.5

Question 10.
Multi-Step
Raymond’s parents will pay for him to take sailboard lessons during the summer. He can take half-hour group lessons or half-hour private lessons. The relationship between cost and number of lessons is linear.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 2: Determining Slope and y-intercept img 18
a. Find the rate of change and the initial value for the group lessons.
Type below:
____________

Answer:
$25

Explanation:
Find the slope using two points
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (1, 55) and (x2, y2) = (2, 85)
Slope m = (y2 -y1)/(x2 – x1) = (85 – 55)/(2 – 1) = 30/1 = 30
Rate of change is $30 for per lesson
Find the initial value when the value of x is 0
Work backward from x = 1 to x = 0
(85 – 55)/(2 – 1) = 30/1 = 30
Subtract the difference of x and y from the first point.
x = 1 – 1 = 0
y = 55 – 30 = 25
The initial value of the group lesson is $25.

Question 10.
b. Find the rate of change and the initial value for the private lessons.
Type below:
_____________

Answer:
$25

Explanation:
Find the slope using two points
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (1, 75) and (x2, y2) = (2, 125)
Slope m = (y2 -y1)/(x2 – x1) = (125 – 75)/(2 – 1) = 50/1 = 50
Rate of change is $50 for per lesson
Find the initial value when the value of x is 0
Work backward from x = 1 to x = 0
(125 – 75)/(2 – 1) = 50/1 = 50
Subtract the difference of x and y from the first point.
x = 1 – 1 = 0
y = 75 – 50 = 25
The initial value of the private lesson is $25.

Question 10.
c. Compare and contrast the rates of change and the initial values.
Type below:
_____________

Answer:
The initial value for both types of lessons is the same. The rate of change is higher for private lessons then group lesson

Explanation:
Compare the results of a and b
The initial value for both types of lessons is the same. The rate of change is higher for private lessons then group lesson

Vocabulary – Determining Slope and y-intercept – Page No. 106

Explain why each relationship is not linear.

Question 11.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 2: Determining Slope and y-intercept img 19
Type below:
_____________

Answer:
The rate of change is not constant, hence the relationship is not linear

Explanation:
Find the rate of change using two points Slope m = (y2 -y1)/(x2 – x1)
(6.5 – 4.5)/(2 – 1) = 2
(8.5 – 6.5)/(3 – 2) = 2
(11.5 – 8.5)/(4 – 3) = 3
The rate of change is not constant, hence the relationship is not linear

Question 12.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 2: Determining Slope and y-intercept img 20
Type below:
_____________

Answer:
The rate of change is not constant, hence the relationship is not linear

Explanation:
Find the rate of change using two points Slope m = (y2 -y1)/(x2 – x1)
(126 – 140)/(5 – 3) = -7
(110 – 126)/(7 – 5) = -8
(92 – 110)/(9 – 7) = -9
The rate of change is not constant, hence the relationship is not linear

Question 13.
Communicate Mathematical Ideas
Describe the procedure you performed to derive the slope-intercept form of a linear equation.
Type below:
_____________

Answer:
Express the slope m between a random point (x, y) on the line and the point (0, b) where the line crosses the y-axis. Then solve the equation for y.

H.O.T.

Focus on Higher Order Thinking

Question 14.
Critique Reasoning
Your teacher asked your class to describe a realworld situation in which a y-intercept is 100 and the slope is 5. Your partner gave the following description: My younger brother originally had 100 small building blocks, but he has lost 5 of them every month since.
a. What mistake did your partner make?
Type below:
_____________

Answer:
If the brother loses 5 blocks every month, the slope would be -5 and not 5.

Explanation:
When the initial value is decreasing, the slope is negative.
If the brother loses 5 blocks every month, the slope would be -5 and not 5.

Question 14.
b. Describe a real-world situation that does match the situation.
Type below:
_____________

Answer:
I bought a 100 card pack and buy 5 additional cards every month.

Explanation:
Real world situation
I bought a 100 card pack and buy 5 additional cards every month.

Question 15.
Justify Reasoning
John has a job parking cars. He earns a fixed weekly salary of $300 plus a fee of $5 for each car he parks. His potential earnings for a week are shown in the graph. At what point does John begin to earn more from fees than his fixed salary? Justify your answer.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 2: Determining Slope and y-intercept img 21
Type below:
_____________

Answer:
After parking 60 cars, John’s earning become $600 double of his initial base salary of $300.
Hence, after parking 61 cars, his earning from the fee becomes more than his fixed salary.

Explanation:
He earns the same in fees as his fixed salary for perking 300/5 = 60
After parking 60 cars, John’s earning become $600 double of his initial base salary of $300.
Hence, after parking 61 cars, his earning from the fee becomes more than his fixed salary.

Guided Practice – Graphing Linear Nonproportional Relationships Using Slope and y-intercept – Page No. 110

Graph each equation using the slope and the y-intercept.

Question 1.
y = \(\frac{1}{2}\)x − 3
slope = _____ y-intercept = _____
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 3: Graphing Linear Nonproportional Relationships Using Slope and y-intercept img 22
Type below:
_____________

Answer:
slope = 1/2 y-intercept = -3
Grade 8 Chapter 4 image 1

Explanation:
y = 1/2 x – 3
The y-intercept is b = -3. Plot the point that contains the y-intercept (0, -3)
The slope m = 1/2. Use the slope to find a second point. From (0, -3) count 1 unit up and 2 unit right. The new point is (2, -2)
Draw a line through the points

Question 2.
y = −3x + 2
slope = _____ y-intercept = _____
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 3: Graphing Linear Nonproportional Relationships Using Slope and y-intercept img 23
Type below:
_____________

Answer:
slope = -3 y-intercept = 2
Grade 8 Chapter 4 image 2

Explanation:
y = -3x + 2
The y-intercept is b = 2. Plot the point that contains the y-intercept (0, 2)
The slope m = -3/1. Use the slope to find a second point. From (0, 2) count 3 unit down and 1 unit right. The new point is (1, -1)
Draw a line through the points

Question 3.
A friend gives you two baseball cards for your birthday. Afterward, you begin collecting them. You buy the same number of cards once each week. The equation y = 4x + 2 describes the number of cards, y, you have after x weeks.
a. Find and interpret the slope and the y-intercept of the line that represents this situation. Graph y = 4x + 2. Include axis labels.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 3: Graphing Linear Nonproportional Relationships Using Slope and y-intercept img 24
Type below:
_____________

Answer:
Grade 8 Chapter 4 image 3

Explanation:
y = 4x + 2
The y-intercept is b = 2. Plot the point that contains the y-intercept (0, 2)
The slope m = 4. Use the slope to find a second point. From (0, 2) count 4 unit up and 1 unit right. The new point is (1, 6)
Draw a line through the points

Question 3.
b. Discuss which points on the line do not make sense in this situation. Then plot three more points on the line that do make sense.
Type below:
_____________

Answer:
Grade 8 Chapter 4 image 4

Explanation:
The points with a negative value of x or y do not make sense as the number of cards or weeks cannot be negative.

Essential Question Check-In

Question 4.
Why might someone choose to use the y-intercept and the slope to graph a line?
Type below:
_____________

Answer:
When the relationship is given in the form y = mx + b, the y-intercept (b) and the slope (m) are easily accessible and easily calculable. Therefore, it is a good practice to use them to graph the line.

Independent Practice – Graphing Linear Nonproportional Relationships Using Slope and y-intercept – Page No. 111

Question 5.
Science
A spring stretches in relation to the weight hanging from it according to the equation y = 0.75x + 0.25 where x is the weight in pounds and y is the length of the spring in inches.
a. Graph the equation. Include axis labels.
Type below:
_____________

Answer:
grade 8 chapter 4 image 7

Explanation:
y = 0.75x + 0.25
Slope m = 0.75 and y-intercept = 0.25
Plot the point that contains the y-intercept (0, 0.25)
The slope is m = 0.75/1. Use the slope to find a second point. From (0,0.25) count 0.75 unit up and 1 unit right. The new point is (1, 1)

Question 5.
b. Interpret the slope and the y-intercept of the line.
Type below:
_____________

Answer:
The slope represents the increase in the length of spring in inches for each increase of pound of weight. y-intercept represents the unstretched length of the spring When there is no weight attached.

Question 5.
c. How long will the spring be if a 2-pound weight is hung on it? Will the length double if you double the weight? Explain
Type below:
_____________

Answer:
When there is a 2-pound weight hung, the length of the spring would be 1.75 inches. No, When there is a 4-pound weight hung, the length of the spring would be 3.25 inches and not 3.5 inches.

Look for a Pattern

Identify the coordinates of four points on the line with each given slope and y-intercept.

Question 6.
slope = 5, y-intercept = -1
Type below:
_____________

Answer:
(2, 9)
(3, 14)

Explanation:
slope = 5, y-intercept = -1
Plot the point that contains the y-intercept (0, -1)
The slope is m = 5/1. Use the slope to find a second point. From (0, -1) count 5 unit up and 1 unit right. The new point is (1, 4)
Follow the same procedure to find the remaining three points.
(2, 9)
(3, 14)

Question 7.
slope = -1, y-intercept = 8
Type below:
_____________

Answer:
(2, 6)
(3, 5)

Explanation:
slope = -1, y-intercept = 8
Plot the point that contains the y-intercept (0, 8)
The slope is m = -1/1. Use the slope to find a second point. From (0, 8) count 1 unit down and 1 unit right. The new point is (1, 7)
Follow the same procedure to find the remaining three points.
(2, 6)
(3, 5)

Question 8.
slope = 0.2, y-intercept = 0.3
Type below:
_____________

Answer:
(2, 0.7)
(3, 0.9)

Explanation:
slope = 0.2, y-intercept = 0.3
Plot the point that contains the y-intercept (0, 0.3)
The slope is m = 0.2/1. Use the slope to find a second point. From (0, 0.3) count 0.2 unit up and 1 unit right. The new point is (1, 0.5)
Follow the same procedure to find the remaining three points.
(2, 0.7)
(3, 0.9)

Question 9.
slope = 1.5, y-intercept = -3
Type below:
_____________

Answer:
(2, 0)
(3, 1.5)

Explanation:
slope = 1.5, y-intercept = -3
Plot the point that contains the y-intercept (0, -3)
The slope is m = 1.5/1. Use the slope to find a second point. From (0, -3) count 1.5 unit up and 1 unit right. The new point is (1, -1.5)
Follow the same procedure to find the remaining three points.
(2, 0)
(3, 1.5)

Question 10.
slope = −\(\frac{1}{2}\), y-intercept = 4
Type below:
_____________

Answer:
(4, 2)
(6, 1)

Explanation:
slope = −\(\frac{1}{2}\), y-intercept = 4
Plot the point that contains the y-intercept (0, 4)
The slope is m = −\(\frac{1}{2}\)/1. Use the slope to find a second point. From (0, 4) count 1 unit down and 2 unit right. The new point is (2, 3)
Follow the same procedure to find the remaining three points.
(4, 2)
(6, 1)

Question 11.
slope = \(\frac{2}{3}\), y-intercept = -5
Type below:
_____________

Answer:
(6, -1)
(9, 1)

Explanation:
slope = \(\frac{2}{3}\), y-intercept = -5
Plot the point that contains the y-intercept (0, -5)
The slope is m = \(\frac{2}{3}\). Use the slope to find a second point. From (0, -5) count 2 unit up and 3 unit right. The new point is (3, -3)
Follow the same procedure to find the remaining three points.
(6, -1)
(9, 1)

Question 12.
A music school charges a registration fee in addition to a fee per lesson. Music lessons last 0.5 hour. The equation y = 40x + 30 represents the total cost y of x lessons. Find and interpret the slope and y-intercept of the line that represents this situation. Then find four points on the line.
Type below:
_____________

Answer:
y = 40x + 30
Slope = 40
y-intercept = 30
The slope represents the fee of the classes per lesson and y-intercept represents the registration fee.
Plot the point that contains the y-intercept (0, 30)
The slope is m = 40/1. Use the slope to find a second point. From (0, 30) count 40 unit up and 1 unit right. The new point is (1, 70)
Follow the same procedure to find the remaining three points.
(2, 110)
(3, 150)

Graphing Linear Nonproportional Relationships Using Slope and y-intercept – Page No. 112

Question 13.
A public pool charges a membership fee and a fee for each visit. The equation y = 3x + 50 represents the cost y for x visits.
a. After locating the y-intercept on the coordinate plane shown, can you move up three gridlines and right one gridline to find a second point? Explain.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 3: Graphing Linear Nonproportional Relationships Using Slope and y-intercept img 25
Type below:
_____________

Answer:
Yes

Explanation:
Yes; Since the horizontal and vertical gridlines each represents 25 units, hence moving up 3 gridlines and right 1 gridline represent a slope a 75/25 or 3

Question 13.
b. Graph the equation y = 3x + 50. Include axis labels. Then interpret the slope and y-intercept.
Type below:
_____________

Answer:
grade 8 chapter 4 image 8
The slope represents the fee per visit and the y-intercept represents the membership fee.

Explanation:
Slope = 3
y-intercept = 50
The slope represents the fee of the classes per lesson and the y-intercept represents the registration fee.
Plot the point that contains the y-intercept (0, 50)
The slope is m = 3/1. Use the slope to find a second point. From (0, 50) count 3 unit up and 1 unit right. The new point is (1, 53)

Question 13.
c. How many visits to the pool can a member get for $200?
______ visits

Answer:
50 visits

Explanation:
You would get 50 visits for $200
grade 8 chapter 4 image 9

H.O.T.

Focus on Higher Order Thinking

Question 14.
Explain the Error
A student says that the slope of the line for the equation y = 20 − 15x is 20 and the y-intercept is 15. Find and correct the error.
Type below:
_____________

Answer:
The slope is -15 as it represents the change in y per unit change in x. The y-intercept is 20, when x = 0.

Explanation:
y = 20 − 15x
The slope is -15 as it represents the change in y per unit change in x. The y-intercept is 20, when x = 0.

Question 15.
Critical Thinking
Suppose you know the slope of a linear relationship and a point that its graph passes through. Can you graph the line even if the point provided does not represent the y-intercept? Explain.
Type below:
_____________

Answer:
Yes. You can plot the given point and use the slope to find a second point. Connect the points by drawing a line.

Question 16.
Make a Conjecture
Graph the lines y = 3x, y = 3x − 3, and y = 3x + 3. What do you notice about the lines? Make a conjecture based on your observation.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 3: Graphing Linear Nonproportional Relationships Using Slope and y-intercept img 26
Type below:
_____________

Answer:
grade 8 chapter 4 image 10

Explanation:
let’s tale the example
y = 3x
y = 3x – 3
y = 3x + 3
We notice that the lines are parallel to each other: the slopes of the lines are equal but the y-intersection point differs.

Guided Practice – Proportional and Nonproportional Situations – Page No. 117

Determine if each relationship is a proportional or nonproportional situation. Explain your reasoning.

Question 1.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 4: Proportional and Nonproportional Situations img 27
Look at the origin.
_____________

Answer:
Proportional relationship

Explanation:
Proportional relationship
The graph passes through the origin. Graph of a proportional relationship must pass through the origin

Question 2.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 4: Proportional and Nonproportional Situations img 28
_____________

Answer:
Non-proportional relationship

Explanation:
The graph does not pass through the origin. Graph of a proportional relationship must pass through the origin
Non-proportional relationship

Question 3.
q = 2p + \(\frac{1}{2}\)
Compare the equation with y = mx + b.
_____________

Answer:
q = 2p + \(\frac{1}{2}\)
The equation is in the form y = mx + b, with p being used es the variable instead of x and q instead of y. The value of m is 2, and the value b is 1/2. Since b is not 0, the relationship presented through the above equation is non-proportional.

Question 4.
v = \(\frac{1}{10}\)u
_____________

Answer:
Proportional relationship

Explanation:
v = \(\frac{1}{10}\)u
Compare with the form of equation y = mx + b. The equation represent proportional relationship if b = 0
Proportional relationship

Proportional and Nonproportional Situations – Page No. 118

The tables represent linear relationships. Determine if each relationship is a proportional or nonproportional situation.

Question 5.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 4: Proportional and Nonproportional Situations img 29
Find the quotient of y and x.
_____________

Answer:
proportional relationship

Explanation:
Find the ratio y/x
12/3 = 4
36/9 = 4
84/21 = 4
Since the ratio is constant, the relationship is proportional.

Question 6.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 4: Proportional and Nonproportional Situations img 30
_____________

Answer:
non-proportional

Explanation:
Find the ratio y/x
4/22 = 2/11
8/46 = 4/23
10/58 = 5/29
Since the ratio is not constant, the relationship is non-proportional.

Question 7.
The values in the table represent the numbers of households that watched three TV shows and the ratings of the shows. The relationship is linear. Describe the relationship in other ways.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 4: Proportional and Nonproportional Situations img 31
Type below:
_____________

Answer:
proportional relationship

Explanation:
Find the ratio y/x
12/15,000,000 = 0.0000008
16/20,000,000 = 0.0000008
20/25,000,000 = 0.0000008
Since the ratio is constant, the relationship is proportional.

Essential Question Check-In

Question 8.
How are using graphs, equations, and tables similar when distinguishing between proportional and nonproportional linear relationships?
Type below:
_____________

Answer:
The ratio between y to x is constant when the relationship is proportional. Graphs, tables, and equations all can be used to find the ratio. The ratio is not constant when the relationship is non-proportional.

Independent Practice – Proportional and Nonproportional Situations – Page No. 119

Question 9.
The graph shows the weight of a cross-country team’s beverage cooler based on how much sports drink it contains.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 4: Proportional and Nonproportional Situations img 32
a. Is the relationship proportional or nonproportional? Explain.
_____________

Answer:
Non-proportional

Explanation:
The graph does not pass through the origin. Graph of a proportional relationship must pass through the origin
Non-proportional

Question 9.
b. Identify and interpret the slope and the y-intercept.
Type below:
_____________

Answer:
Slope m = (y2 -y1)/(x2 – x1) = (12 – 10)/(4 – 0) = 0.5
y-intercept is the weight of the empty cooler, which is 10 lbs.

Explanation:
Find the slope using two points from the grapgh by
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (0, 10) and (x2, y2) = (4, 12)
Slope m = (y2 -y1)/(x2 – x1) = (12 – 10)/(4 – 0) = 0.5
From the graph when x = 0
y-intercept (b) = 10
y-intercept is the weight of the empty cooler, which is 10 lbs.

In 10–11, tell if the relationship between a rider’s height above the first floor and the time since the rider stepped on the elevator or escalator is proportional or nonproportional. Explain your reasoning.

Question 10.
The elevator paused for 10 seconds after you stepped on before beginning to rise at a constant rate of 8 feet per second.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 4: Proportional and Nonproportional Situations img 33
_____________

Answer:
Non-proportional

Explanation:
As there is a pause of 10 seconds, it would be the y-intercept of the graph (when x = 0)
Non-proportional

Question 11.
Your height, h, in feet above the first floor on the escalator is given by h = 0.75t, where t is the time in seconds.
_____________

Answer:
Proportional

Explanation:
Comparing with y = mx + b, where b = 0
Proportional

Analyze Relationships

Compare and contrast the two graphs.

Question 12.
Graph A       Graph B
y = \(\frac{1}{3}\) x        y = \(\sqrt { x } \)
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 4: Proportional and Nonproportional Situations img 34
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 4: Proportional and Nonproportional Situations img 35
Type below:
_____________

Answer:
Graph A represents a linear relationship while Graph B represents an exponential relationship. They both pass through the origin and the value of y increases with an increase in x.

Proportional and Nonproportional Situations – Page No. 120

Question 13.
Represent Real-World Problems
Describe a real-world situation where the relationship is linear and nonproportional.
Type below:
_____________

Answer:
The entrance fee to the amusement park is $8 and there is a fee of $2 per ride.

H.O.T.

Focus on Higher Order Thinking

Question 14.
Mathematical Reasoning
Suppose you know the slope of a linear relationship and one of the points that its graph passes through. How can you determine if the relationship is proportional or nonproportional?
Type below:
_____________

Answer:
Use the graph and the given point to determine the second point. Connect the two points by a straight line. If the graph passes through the origin, the relationship is proportional and if the graph does not pass through the origin, the relationship is non-proportional.

Question 15.
Multiple Representations
An entrant at a science fair has included information about temperature conversion in various forms, as shown. The variables F, C, and K represent temperatures in degrees Fahrenheit, degrees Celsius, and kelvin, respectively.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 4: Proportional and Nonproportional Situations img 36
a. Is the relationship between kelvins and degrees Celsius proportional? Justify your answer in two different ways.
_____________

Answer:
No, the relationship is not proportional.

Explanation:
Compare the equation B to the form: y = mx + b. Since b is not equal to 0, the relationship is non-proportional.
Find the ratio between the Kelvin and Degrees Celsius. Since the ration is not constant, the relationship is non-proportional.
281.15/8 = 35.14
288.15/15 = 19.21
309.15/36 = 8.59
No, the relationship is not proportional.

Question 15.
b. Is the relationship between degrees Celsius and degrees Fahrenheit proportional? Why or why not?
_____________

Answer:
No, the relationship is not proportional.

Explanation:
Compare the equation A to the form: y = mx + b. Since b is not equal to 0, the relationship is non-proportional.
No, the relationship is not proportional.

4.1 Representing Linear Nonproportional Relationships – Model Quiz – Page No. 121

Question 1.
Complete the table using the equation y = 3x + 2.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Model Quiz img 37
Type below:
_____________

Answer:
grade 8 chapter 4 image 11

Explanation:
Given y = 3x + 2
grade 8 chapter 4 image 11
x = -1; y = 3(-1) + 2 = -3 + 2 = -1
x = 0; y = 3(0) +2 = 2
x = 1; y = 3(1) + 2 = 3 + 2 = 5
x = 2; y = 3(2) + 2 = 6 + 2 = 8
x = 3: y = 3(3) + 2 = 9 + 2 = 11

4.2 Determining Slope and y-intercept

Question 2.
Find the slope and y-intercept of the line in the graph.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Model Quiz img 38
Type below:
_____________

Answer:
Slope = 3
y-intercept (b) = 1

Explanation:
Find the slope using two points from the grapgh by
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (0, 1) and (x2, y2) = (1, 4)
Slope m = (y2 -y1)/(x2 – x1) = (4 – 1)/(1 – 0) = 3/1
From the graph when x = 0
y-intercept (b) = 1

4.3 Graphing Linear Nonproportional Relationships

Question 3.
Graph the equation y = 2x − 3 using slope and y-intercept.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Model Quiz img 39
Type below:
_____________

Answer:
grade 8 chapter 4 image 12

Explanation:
Slope = 2
y-intercept = -3
Plot the point that contains the y-intercept (0, -3)
The slope is m = 2/1. Use the slope to find a second point. From (0, -3) count 2 unit up and 1 unit right. The new point is (1, -1)
Draw a line through the points

4.4 Proportional and Nonproportional Situations

Question 4.
Does the table represent a proportional or a nonproportional linear relationship?
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Model Quiz img 40
_____________

Answer:
Since the ratio is constant, the table represents a proportional linear relationship.

Explanation:
Find the ratio y/x
4/1 = 4
8/2 = 4
12/3 = 4
16/4 = 4
20/5 = 4
Since the ratio is constant, the table represents a proportional linear relationship.

Question 5.
Does the graph in Exercise 2 represent a proportional or a nonproportional linear relationship?
_____________

Answer:
It represents a non-proportional linear relationship

Explanation:
The line of the graph does not pass through the origin. The graph of a proportional relationship must pass through the origin.
It represents a non-proportional linear relationship

Question 6.
Does the graph in Exercise 3 represent a proportional or a nonproportional relationship?
_____________

Answer:
It represents a non-proportional linear relationship

Explanation:
The line of the graph does not pass through the origin. The graph of a proportional relationship must pass through the origin
It represents a non-proportional linear relationship

Essential Question

Question 7.
How can you identify a linear nonproportional relationship from a table, a graph, and an equation?
Type below:
_____________

Answer:
In a table, the ratio of y/x is not constant for non-proportional relationship.
In a graph, the line of the graph does not pass through the origin for non-proportional relationship.
In an equation, the b is not equal to for y = mx +b for non-proportional relationship.

Selected Response – Mixed Review – Page No. 122

Question 1.
The table below represents which equation?
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Mixed Review img 41
Options:
a. y = −x − 10
b. y = −6x
c. y = −4x − 6
d. y = −4x + 2

Answer:
c. y = −4x − 6

Explanation:
From the table, you can see that the y-intercept (when x = 0) is b = -6. Comparable to y = mx + b
The table is represented by Option C y = -4x – 6

Question 2.
The graph of which equation is shown below?
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Mixed Review img 42
Options:
a. y = −2x + 3
b. y = −2x + 1.5
c. y = 2x + 3
d. y = 2x + 1.5

Answer:
a. y = −2x + 3

Explanation:
From the table, you can see that the y-intercept (when x = 0) is b = 3. Comparable to y = mx + b
The Option B and D are rejected.
Since the graph is slanting downwards, the slope is negative.
Option C is rejected
The graph represents y = -2x + 3

Question 3.
The table below represents a linear relationship.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Mixed Review img 43
What is the y-intercept?
Options:
a. -4
b. -2
c. 2
d. 3

Answer:
b. -2

Explanation:
Find the rate of change
(7 – 4)/(3 – 2) = (10 – 7)/(4 – 3) = 3
Find the value of y for x = 0
Works backward from x = 2 to x = 1
x = 2 – 1 = 1
y = 4 – 3 = 1
x = 1 – 1 = 0
y = 1 – 3 = -2
y intercept = -2

Question 4.
Which equation represents a nonproportional relationship?
Options:
a. y = 3x + 0
b. y = −3x
c. y = 3x + 5
d. y = \(\frac{1}{3}\)x

Answer:
c. y = 3x + 5

Explanation:
For a non-proportional relationship, the equation is y = mx + b and b is not equal to 0.
Option C represents a non-proportional relationship y = 3x + 5

Question 5.
The table shows a proportional relationship. What is the missing y-value?
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Mixed Review img 44
Options:
a. 16
b. 20
c. 18
d. 24

Answer:
c. 18

Explanation:
Find the ratio y/x
6/4 = 3/2
Since the relationship is proportional, the ratio is constant.
Using the ratio to fins missing y
3/2 = y/12
y = 3/2 × 12 = 18

Question 6.
What is 0.00000598 written in scientific notation?
Options:
a. 5.98 × 10-6
b. 5.98 × 10-5
c. 59.8 × 10-6
d. 59.8 × 10-7

Answer:
c. 59.8 × 10-6

Explanation:
0.00000598
Move the decimal 6 points
59.8 × 10-6

Mini-Task

Question 7.
The graph shows a linear relationship.
Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Mixed Review img 45
a. Is the relationship proportional or nonproportional?
____________

Answer:
It represents a non-proportional linear relationship

Explanation:
The line of the graph does not pass through the origin. The graph of a proportional relationship must pass through the origin.
It represents a non-proportional linear relationship

Question 7.
b. What is the slope of the line?
_______

Answer:
Slope m = -2

Explanation:
Find the slope using two points from the grapgh by
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (0, -2) and (x2, y2) = (2, 1)
Slope m = (y2 -y1)/(x2 – x1) = (-3 -1)/(0 + 2) = -4/2 = -2

Question 7.
c. What is the y-intercept of the line?
_______

Answer:
y-intercept (b) = -3

Explanation:
From the graph when x = 0
y-intercept (b) = -3

Question 7.
d. What is the equation of the line?
Type below:
____________

Answer:
y = -2x – 3

Explanation:
Substitute m and b in the form: y = mx + b
y = -2x – 3

Conclusion:

I believe that our Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships pdf brought a smile to your face. All the beginners can easily start their practice with our step by step explanations. Bookmark our ccssmathanswers.com to get the latest information about the solutions.

Go Math Grade 3 Answer Key Chapter 8 Understand Fractions

go-math-grade-3-chapter-8-understand-fractions-answer-key

Go Math Grade 3 Answer Key Chapter 8 Understand Fractions includes all the topics covered in Chapter 8. Major Motto behind providing the Go Math Answer Key for Grade 3 Chapter 8 is to make the students familiar with the concepts. Download Go Math Grade 3 Answer Key Understand Fractions free of cost and prepare whenever you want. If you are preparing for 3rd standard exams you can always look up to HMH Go Math Solution Key Grade 3 Chapter 8 Understand Fractions.

Grade 3 Go Math Answer Key Chapter 8 Understand Fractions

Have an overview of Grade 3 HMH Go Math Solutions Key for Chapter 8 Understand Fractions and the lessons in Chapter 8. utilize the Answer Keys of Go Math 3rd Std Chapter 8 Understand Fractions and be prepared for the exams. Practice using the Practice Questions at the end of the chapter and test your preparation level and bridge the knowledge gap accordingly.

Lesson 1: Equal Parts of a Whole

Lesson 2: Equal Shares

Lesson 3: Unit Fractions of a Whole

Lesson 4: Fractions of a Whole

Lesson 5: Fractions on a Number Line

Chapter 8 Mid-Chapter Checkpoint

Lesson 6: Relate Fractions and Whole Numbers

Lesson 7: Fractions of a Group

Lesson 8: Find Part of a Group Using Unit Fractions

Lesson 9: Problem Solving

Chapter 8 Understand Fractions Review/Test

Equal Parts for a Whole – Page No 447

Write the number of equal parts. Then write the name for the parts.

Question 1:

Go Math Grade 3 Answer Key Chapter 8 - Equal Parts for a whole Image - 1

Equal Parts: ___________
Name: _______________

Answer:

i) 4
ii) Fourths

Explanation:
From the above figure, we can see that the circle is divided into 4 equal parts and the parts are named as fourths.

Question 2:

Go Math Grade 3 Answer Key Chapter 8 - Equal Parts for a whole Image 2

Equal Parts: ___________
Name: _______________

Answer:
i) 3
ii) Thirds

Explanation:
The rectangle is divided into 3 equal parts. The name for those parts is thirds.

Question 3:

Go Math Grade 3 Answer Key Chapter 8 - Equal Parts for a whole Image 3

Equal Parts: ____________
Name: ________________

Answer:
i) 2
ii) Halves

Explanation:
The square is diagonally cut into 2 triangles. As it is a square the triangles will be of the same size. Therefore the triangles are equal and the name for the parts is halves.

Question 4:

Go Math Grade 3 Answer Key Chapter 8 - Equal Parts for a whole Image 4

Equal Parts: _____________
Name: _________________

Answer:
i) 6
ii) Sixths

Explanation:
Here we can see a rectangle that is separated into 6 equal parts. As it is divided into 6 parts it is named as sixths.

Write whether the shape is divided into equal parts or unequal parts

Question 5:

Go Math Grade 3 Answer Key Chapter 8 - Equal Parts for a whole Image 5

____________ Parts

Answer:
Unequal

Explanation:
The triangle is cut into 2 but the size and shape are not the same. So, by seeing the figure we can say that the parts are unequal.

Question 6:

Go Math Grade 3 Answer Key Chapter 8 - Equal Parts for a whole Image 6

____________ Parts

Answer:
Equal

Explanation:
In the above figure, we can observe that the trapezium is divided into 3 triangles of equal parts.

Problem Solving

Question 7:
Diego cuts a round pizza into eight equal slices. What is the name for the parts?
____________

Answer:
Eighths

Explanation:
Diego cuts a round pizza into 8 equal slices. So the name for the parts is eighths.

Question 8:
Madison is making a placemat. She divides it into 6 equal parts to color. What is the name for the parts?____________

Answer:
Sixths

Explanation:
If the placemat is cut into 6 equal parts then the parts are named as sixths.

Equal Parts of a Whole – Lesson Check – Page No 448

Question 1:
How many equal parts are in this shape?

Go Math Grade 3 Answer Key Chapter 8 - lesson check img_1

Options:
i. 3
ii. 4
iii. 5
iv. 6

Answer:
ii (4)

Explanation:
In the figure, the rectangle is divided into 4 equal parts.

Question 2:
What is the name for the equal parts of the whole?

Go Math Grade 3 Answer Key Chapter 8 - lesson check img_2

Options:
i. Fourths
ii. Sixths
iii. Eighths
iv. Thirds

Answer:
iii (Eighths)

Explanation:
From the above fig, we can see 8 triangles. Therefore the name for the parts is eighths.

Spiral Review

Question 3:
Use a related multiplication fact to find the quotient.
49 ÷ 7 = ___

Options:
i. 6
ii. 7
iii. 8
iv. 9

Answer:
ii (7)

Explanation:
Given,
49 ÷ 7 = ___
49/7 = 7
49 is divisible by 7 by 7 times. Therefore the remainder is 0 and the quotient is 7.

Question 4:
Find the unknown factor and quotient.
9 × __ = 45
Options:
i. 4
ii. 5
iii. 6
iv. 7

Answer:
ii (5)

Explanation:
Given,
9 × __ = 45
45/9 = 5
Therefore the unknown factor of 9 × __ = 45 is 5.

Question 5:
There are 5 pairs of socks in one package. Matt buys 3 packages of socks. How many pairs of socks in all does Matt buy?
Options:
i. 30
ii. 15
iii. 10
iv. 8

Answer:
ii (15)

Explanation:
Given that, there are 5 pairs of socks in 1 package.
If Matt buys 3 packages of socks then multiply 5 with 3. We get 15.
Therefore, Matt buys 15 pairs of socks.

Question 6:
Mrs. McCarr buys 9 packages of markers for an art project. Each package has 10 markers. How many markers in all does Mrs. McCarr buy?
Options:
i. 10
ii. 19
iii. 81
iv. 90

Answer:
iv (90)

Explanation:
Given,
Mrs. McCarr buys 9 packages of marks for an art project
There are 10 markers in each package.

To find:
How many markers did Mrs. McCarr buy
In order to know the markers she bought we need to multiply the number of packages with total number of markers in each package.
i.e, 9 × 10 = 90
Therefore, the total number of markers in 9 packages is 90.

Equal Shares – Page No 453

Question 1:
6 friends share 3 sandwiches equally.

Go Math Grade 3 Answer Key Chapter 8 - Equal Shares Image_1

Answer:
3 Sixths of a Sandwich

Explanation:
There are 3 sandwiches and 6 friends need to share it equally
So, divide the total number of sandwiches by number of friends i.e., 3/6 = 1/2
So, the equal share of 6 sandwiches is 3 sixths or 1 half of a sandwich.

Question 2:
8 classmates share 4 pizzas equally.

Go Math Grade 3 Answer Key Chapter 8 - Equal Shares Image_2

Answer:
4 Eighths, or 1 half of a pizza.

Explanation:
Given,
Number of pizzas = 4
Number of classmates = 8
In order to share the pizzas equally, we need to divide 4 by 8
4/8 = 1/2
So, the 8 classmates can share 4 eighths or 1 half of a pizza.

Question 3:
4 teammates share 5 granola bars equally. Draw to show how much each person gets. Shade the amount that one person gets. Write the answer.
Go Math Grade 3 Answer Key Chapter 8 - Equal Shares Image_3

Answer:
5 fourths of a granola bar.

Explanation:
Given that, the number of teammates = 4
and number of granola bars = 5
Number of granola bars/Number of teammates= 5/4
So, the answer is 5 fourths of a granola bars.

Problem Solving

Question 4:
Three brothers share 2 sandwiches equally. How much of a sandwich does each brother get?

Answer:
2 thirds of a sandwich

Explanation:
To know how much sandwich does each brother get,
we have to divide no. of sandwiches by no. of brothers
i.e, 2/3
So, each brother gets 2 thirds of a sandwich.

Question 5:
Six neighbors share 4 pies equally. How much of a pie does each neighbor get?

Answer:
4 sixths or 1 sixth or 2 thirds of a pie

Explanation:
Given that, 6 neighbors share 4 pies equally
To know how much of a pie does each neighbor get
we need to divide number of pies by number of neighbors
4/6 = 2/3

(or)

1/6 of each pie

Equal Shares Lesson Check Page No 454

Question 1:
Two friends share 3 fruit bars equally. How much does each friend get?
Go Math Grade 3 Answer Key Chapter 8 - Equal Shares Lesson Check Img_1
Options:
i. 1 Half
ii. 2 Thirds
iii. 2 Halves
iv. 3 Halves

Answer:
iv (3 Halves)

Explanation:
Total number of fruit bars/ Number of friends = 3/2
So, each friend gets 3 halves of the fruit bar

Question 2:
Four brothers share 3 pizzas equally. How much of a pizza does each brother get?
Go Math Grade 3 Answer Key Chapter 8 - Equal Shares Lesson Check Img_2
Options:
i. 3 halves
ii. 4 third
iii. 3 fourths
iv. 2 fourths

Answer:
iii. (3 fourths)

Explanation:
Given,
No. of pizzas = 3
No. of brothers = 4
In order to share the pizzas,
we need to divide No. of pizzas/No. of brothers = 3/4
So, the answer is 3 fourths.

Spiral Review

Question 3:
Find the quotient.
3)27
Options:
i. 6
ii. 7
iii. 7
iv. 9

Answer:
iv (9)

Explanation:
To find quotient:
Divide 27/3 = 9
Therefore the quotient of 3)27 is 9

Question 4:
Tyrice put 4 cookies in each of 7 bags. How many cookies in all did he put in the bags?
Options:
i. 11
ii. 28
iii. 32
iv. 40

Answer:
ii (28)

Explanation:
Given that, Tyrice put 4 cookies in each of 7 bags
Total no. of cookies = 4
Total no. of bags = 7
To find:
How many cookies in all did he put in the bags,
We need to multiply No. of bags with No. of cookies
we get 7 × 4 = 28
Therefore, the Total Number of cookies in all the bags is 28.

Question 5:
Ryan earns $5 per hour raking leaves. He earned $35. How many hours did he rake leaves?
Options:
i. 5 hours
ii. 6 hours
iii. 7 hours
iv. 35 hours

Answer:
iii (7 hours)

Explanation:
Given,
Ryan earns $5 per hour
To find how many hours did he rake leaves to earn $35
Divide 35 by 5, we get
35/5 = 7
So, Ryan raked leaves for 7 hours to earn $35

Question 6:
Hannah has 229 horse stickers and 164 kitten stickers. How many more horse stickers than kitten stickers does Hannah have?
Options:
i. 45
ii. 65
iii. 145
iv. 293

Answer:
ii (65)

Explanation:
Total no. of horse stickers Hannah has is 229
No. of kitten stickers Hannah has is 164
To know how many more horse stickers than kitten stickers does Hannah have,
we need to subtract no. of horse stickers and no. of kitten stickers
i.e., 229 – 164 = 65
So, the answer is 65

Unit Fractions of a Whole Page No 459

Write the number of equal parts in the whole. Then write the fraction that names the shaded part.

Question 1:
Answer Key for Go Math Grade 3 Chapter 8 Unit Fractions of a Whole Image_1
__________ equal parts __________

Answer:
i) 6
ii) 1/6

Explanation:
The rectangle is divided into 6 equal parts. From the figure, we observe that one block is shaded. So, the fraction name of the shaded part is 1/6.

Question 2:
Answer Key for Go Math Grade 3 Chapter 8 Unit Fractions of a Whole Image_2

__________ equal parts

__________

Answer:

i) 2
ii) 1/2

Explanation:
There are 2 right-angled triangles in which one part is shaded. Therefore, the fractional name for the shaded part is 1/2

Question 3:
Answer Key for Go Math Grade 3 Chapter 8 Unit Fractions of a Whole Image_3

__________ equal parts

__________

Answer:

i) 4
ii) 1/4

Explanation:
The circle is divided into 4 equal parts and one part is shaded among them. The fraction that names the shaded part is 1/4

Question 4:
Answer Key for Go Math Grade 3 Chapter 8 Unit Fractions of a Whole Image_4

__________ equal parts

__________

Answer:

i) 3
ii) 1/3

Explanation:
In the above fig, we see that the trapezium is divided into 3 equal triangles and the fraction name of the shaded part is 1/3.

Question 5:
1/3 is  Answer Key for Go Math Grade 3 Chapter 8 Unit Fractions of a Whole Image_5

Answer:

Question 6:
1/8 is  Answer Key for Go Math Grade 3 Chapter 8 Unit Fractions of a Whole Image_6

Answer:

Question 7:
Tyler made a pan of cornbread. He cut it into 8 equal pieces and ate 1 piece. What fraction of the cornbread did Tyler eat?
________

Answer:
1/8

Explanation:
There are 8 pieces of cornbread. Tyler ate 1 piece out of 8 cornbread.
The fraction of cornbread that Tyler ate is 1/8

Question 8:
Anna cut an apple into 4 equal pieces. She gave 1 piece to her sister. What fraction of the apple did Anna give to her sister?
________

Answer:
1/4

Explanation:
Anna cut an apple into 4 pieces. She gave 1 piece of apple to her sister.
One piece of apple/ Total Number of pieces = 1/4

Unit Fractions of a Whole Lesson Check Page No 460

Question 1:
What fraction names the shaded part?
Answer Key for Go Math Grade 3 Chapter 8 Unit Fractions of a Whole Lesson Check
Options:
i. 1/3
ii. 1/4
iii. 1/6
iv. 1/8

Answer:
ii (1/4)

Explanation:
There are 4 blocks in the rectangle and one part is shaded among them. So the answer is 1/4

Question 2:
Tasha cut a fruit bar into 3 equal parts. She ate 1 part. What fraction of the fruit bar did Tasha eat?
Options:
i. 1/2
ii. 1/3
iii. 1/4
iv. 1/6

Answer:
ii (1/3)

Explanation:
The fruit bar is cut into 3 equal parts and Tasha ate one part. So, the fraction name of the fruit bar that Tasha ate is 1/3

Spiral Review
Question 3:
Alex has 5 lizards. He divides them equally among 5 cages. How many lizards do Alex put in each cage?
i. 0
ii. 1
iii. 5
iv. 10

Answer:
ii (1)

Explanation:
Alex has 5 lizards and put them equally in 5 cages. That means Alex has put one lizard in one cage.

Question 4:
Find the product.
8 × 1 = _
i. 0
ii. 1
iii. 8
iv. 9

Answer:
iii (8)

Explanation:
We know that any number multiplied with 1 is itself. Therefore the multiplication of 8 and 1 is 8.

Question 5:
Leo bought 6 chew toys for his new puppy. Each chew toy cost $4. How much did Leo spend in all for the chew toys?
i. $10
ii. $12
iii. $18
iv. $24

Answer:
iv ($24)

Explanation:
Given,
Leo bought 6 chew toys for his new puppy
Each toy costs $4.
1 — $4
6 —?
Cross multiplication is applied here,
we get 6 × 4 = 24
Therefore the cost of 6 chew toys is $24.

Question 6:
Lilly is making a picture graph. Each picture of a star is equal to two books she has read. The row for the month of December has 3 stars. How many books did Lilly read during the month of December?
i. 3
ii. 5
iii. 6
iv. 9

Answer:
iii (6)
Explanation:
Given that each picture of star equals 2 books
The row for the month of December has 3 stars.
Let’s apply the cross multiplication method here,
1 star — 2 books
3 stars —?
3 × 2 = 6
So, the answer to the above question is 6

Fractions of a Whole Page No 465

Write the fraction that names each part. Write a fraction in words and in numbers to name the shaded part.
Question 1:
Grade 3 HMH Go Math Answer Key Chapter 8 Fractions for a whole Image_1
Each Part is _______ . _______ sixths
____________

Answer:
i) 1/6
ii) Three
iii) 3/6

Explanation:
The above figure is Hexagon which consists of 6 sides. So each part of a hexagon is 1/6 and we can see that three parts are shaded. The fraction form of the shaded part is three sixths i.e., 3/6

Question 2:
Chapter 8 Go Math Grade 3 Answer Key Fractions for whole Image_2
Each Part is ________. ______ eighths
_____________

Answer:
i) 1/8
ii) Five
iii) 5/8

Explanation:
There are 8 blocks in the rectangle out of which 5 parts are shaded. Each part of the rectangle is 1/8 and the name for the shaded part is Five Eights. The fraction of the shaded part is 5/8.

Question 3:
Go Math 3rd Grade Answer for Chapter 8 Fractions for a whole Image_3
Each Part is ________. ______ thirds
_____________

Answer:
i) 1/3
ii) Two
iii) 2/3

Explanation:
Here we can see 3d form a triangle, each part is 1/3. Two sides are shaded in it so, the name for the shaded part is two thirds. The shaded part will be in the numerator and the total parts will be in the denominator. Hence the fraction form for the above fig is 2/3.

Question 4:
Go Math Grade 3 Chapter 8 Answer Key Fractions for a whole Image_4
Each Part is ________. ______ fourths
_____________

Answer:
i) 1/4
ii) Three
iii) 3/4

Explanation:
The square is divided into 4 equal triangles. Each part of the square is 1/4 and there are 3 shaded triangles in the square box. The name for the shaded parts is three fourths i.e., 3/4

Question 5:
Four out of six
Go Math Chapter 8 Grade 3 Answer Key Fractions for a whole Image_5
Each Part is ______________

Answer:
4/6

Explanation:
The circle is divided into 6 parts of which four parts are shaded. So, the numerator will be the shaded part and the denominator will be the total number of parts. So the answer is 4/6.

Question 6:
Eight out of eight
Grade 3 Go Math Solution Key Chapter 8 Fractions for a whole Image_6
Each Part is ______________

Answer:
8/8

Explanation:
The fig above shows that the circle is equally divided into 8 parts out of which all the parts are shaded. So, the fraction form of the shaded part is 8/8.

Question 7:
Emma makes a poster for the school’s spring concert. She divides the poster into 8 equal parts. She uses two of the parts for the title. What fraction of the poster does Emma use for the title?
_________________

Answer:
2/8

Explanation:
Given,
Emma divides the poster into 8 equal parts
She uses 2 parts for the title
So, the total number of parts will be in the denominator and the used parts will be in the numerator
Therefore the answer is 2/8.

Question 8:
Lucas makes a flag. It has 6 equal parts. Five of the parts are red. What fraction of the flag is red?
_________________

Answer:
5/6

Explanation:
Luca makes a flag which has 6 equal parts, in which 5 of the parts are red.
The fraction of the flag is which is in red is?
5 parts of red will be in the numerator and the 6 will be in the denominator
So, the fraction of the flag red is 5/6.

Fractions of a Whole Lesson Check Page No 466

Question 1:
What fraction names the shaded part?
Go Math Answer Key for Grade 3 Chapter 8 Fraction for a whole Lesson Check Img_1
Options:
i. 4/6
ii. 2/4
iii. 4/8
iv. 2/6

Answer:
i (4/6)

Explanation:
The rectangle is divided into 6 equal parts. Among them, 4 parts of the rectangle are shaded. So the fraction name of the shaded part is 4/6.

Question 2:
What fraction names the shaded part?
Chapter 8 Go Math Grade 3 Answer Key Understand Fractions Lesson Check Img_2
Options:
i. One fourth
ii. One third
iii. Three fourths
iv. Four thirds

Answer:
iii (Three fourths)

Explanation:
The above figure shows that the triangle is divided into 4 parts equally in which 3 parts are shaded. Therefore, the shaded part will be in the numerator and the total parts will be in the denominator. So, the fraction name of the shaded part is three fourths.

Question 3:
Sarah biked for 115 minutes last week. Jennie biked for 89 minutes last week. How many minutes in all did the girls bike?
Options:
i. 26 minutes
ii. 194 minutes
iii. 204 minutes
iv. 294 minutes

Answer:
iii (204 minutes)

Explanation:
Given that,
Sarah biked for 115 minutes and,
Jennie biked for 89 minutes
To find:
How many minutes in all did the girls bike
To find the total minutes we need to add the bike ride time of both Sarah and Jennie
i.e., 115 + 89 = 204 minutes

Question 4:
Harrison made a building using 124 blocks. Greyson made a building using 78 blocks. How many more blocks did Harrison use than Greyson did?
Options:
i. 46
ii. 56
iii. 154
iv. 202

Answer:
i (46)

Explanation:
i) Harrison made a building using 124 blocks
ii) Greyson made a building using 78 blocks
In order to know how many more blocks did Harrison use than Greyson did we need to subtract the blocks made by Harrison with Blocks made by Greyson
124 – 78 = 46
Therefore the answer is 46.

Question 5:
Von bought a bag of 24 dog treats. He gives his puppy 3 treats a day. How many days will the bag of dog treats last?
Options:
i. 3 days
ii. 6 days
iii. 8 days
iv. 21 days

Answer:
iii (8 days)

Explanation:
Given,
Von bought a bag of 24 dog treats
He gives his puppy 3 treats a day
To find:
How many days will the bag of dog treats last
Here we have to divide no. of bag treats by puppy treats a day
24/3 = 8

Question 6:
How many students chose swimming?
Go Math Grade 3 Chapter 8 Answer Key Understand Fractions Lesson Check Img_3
Options:
i. 5
ii. 10
iii. 20
iv. 25

Answer:
iv (25)

Explanation:
From the figure, we can observe that there are 5 students who choose swimming. But each student is equal to 5 votes.
So, 5 × 5 = 25
Therefore the students who swimming are 25

Fractions on a Number Line Page No 471

Use fraction strips to help you complete the number line. Then locate and draw a point for the fraction.
Question 1:
1/3
Answer key for Go Math Grade 3 Understand Fractions of a Number line image_1

Answer:

Question 2:
3/4
Chapter 8 Go Math Grade 3 Key understand fractions of a number line image_2

Answer:

Write the fraction that names the point.
Go Math Chapter 8 Grade 3 Solution Key Number line image_3

Question 3:
Point A ________

Answer: 2/8

Explanation:
The Number lies between 0 and 1 and each point is divided into 1/8. So, it starts from 0/8 to 8/8. Now we have to locate point A i.e., 2/8 because the number that lies after 1/8 is 2/8.

Question 4:
Point B ________

Answer: 5/8

Explanation:
As we have discussed before point B lies between 4/8 and 6/8. So, the location of point B is 5/8.

Question 5:
Point C ________

Answer: 7/8

Explanation:
The location of Point C lies between 6/8 and 8/8. Therefore the number between 6/8 and 8/8 is 7/8.

Problem Solving

Question 6:
Jade ran 6 times around her neighborhood to complete a total of 1 mile. How many times will she need to run to complete 5/6 of a mile?
_____

Answer: 5 times

Explanation:
Given,
6 laps around the neighborhood = 1 mile
That means each lap = 1/6th of a mile
In order to complete 5/6 of a mile she has to run 5 times

Question 7:
A missing fraction on a number line is located exactly halfway between 3/6 and 5/6. What is the missing fraction?
_____

Answer: 4/6

Explanation:
Given that the missing fraction on a number line is located between 3/6 and 5/6. The number that lies between 3 and 5 is 4. So, the missing fraction is 4/6.

Fractions on a Number Line Lesson Check Page No 472

Question 1:
Which fraction names point G on the number line?
Chapter 8 Go Math 3rd Grade Answer key for Number line lesson check image_1
Options:
i. 1/4
ii. 2/4
iii. 4/4
iv. 4/1

Answer:
i. (1/4)

Explanation:
The fraction on the number line lies between 0/4 and 4/4 i.e., 0 to 1. The location of point G lies between 0/4 and 2/4. The number between 0 and 2 is 1. Therefore the fraction of Point G is 1/4.

Question 2:
Which fraction names point R on the number line?

Grade 3 HMH Go Math Answer Key Chapter 8 Number line lesson check image_2
Options:
i. 1/3
ii. 2/3
iii. 3/3
iv. 3/2

Answer:
ii (2/3)

Explanation:
The number line starts from 0/3 and ends at 3/3. Point R is between 1/3 and 3/3. So, the fraction name of Point R on Number line is 2/3

Spiral Review

Question 3:
Each table in the cafeteria can seat 10 students. How many tables are needed to seat 40 students?
Options:
i. 10
ii. 8
iii. 5
iv. 4

Answer:
iv (4)

Explanation:
Given,
1 table in the cafeteria can seat 10 students
The tables are needed to seat 40 students =?
1 —- 10 students
?—- 40 students
40/10 = 4
Therefore tables are needed to seat 40 students = 4

Question 4:
Which is an example of the Commutative Property of Multiplication?

Options:
i. 6 × 1 = 6 × 1
ii. 4 + 9 = 4 × 9
iii. 4 × 9 = 9 × 4
iv. 6 × 3 = 2 × 9

Answer:
iii (4 × 9 = 9 × 4)

Explanation:
The multiplication rule for the commutative property is ab = ba. Therefore the answer is 4 × 9 = 9 × 4.

Question 5:
Pedro shaded part of a circle. Which fraction names the shaded part?
Solution Key for Go Math Grade 3 Chapter 8 Number Line Lesson Check image_3

Options:
i. 1/8
ii. 1/7
iii. 7/8
iv. 8/7

Answer:
iii (7/8)

Explanation:
The circle is divided into 8 equal parts. In that 7 parts are shaded. So, the fraction name for the shaded part is 7/8.

Question 6:
Which is true?
Options:
i. 8 ÷ 1 = 8
ii. 8 ÷ 8 = 8
iii. 8 × 0 = 8
iv. 1 =  8 × 1

Answer:
i (8 ÷ 1 = 8)

Explanation:
Any number divided by  1 is itself.
8/1 = 8
So the answer is 8 ÷ 1 = 8

Mid-Chapter Checkpoint Page No 473

Vocabulary

Choose the best term from the box to complete the sentence.

Grade 3 Go Math chapter 8 answer key mid chapter image_1

Question 1:
A ____________ is a number that names part of a whole or part of a group.

Answer: Fraction

Explanation:
The fraction is the one that divides the whole into equal parts or each part of the group.

Question 2:
The ___________ tells how many equal parts are in the whole or in the group.

Answer: Denominator

Explanation:
The part of a fraction that lies below the line and which shows the total number of equal parts in the whole.

Concept And Skills

Write the number of equal parts. Then write the name for the parts.

Question 3:
Go Math 3 Grade Chapter 8 Answer Key for Mid Chapter Checck point image_2

Equal Parts: ________
Name: ____________

Answer:
i. 2
ii. Halves

Explanation:
The trapezium is divided into two equal parts and the name for the parts is halves.

Question 4:

Key for Grade 3 Chapter 8 Go Math Mid Chapter Check Point Image_3

Equal Parts: ________
Name: ____________

Answer:
i. 8
ii. Eighths

Explanation:
From the above fig, we can observe that there are 8 equal parts that are in the shape of a square. The name for the parts of the figure is Eighths.

Question 5:

Go Math Solution Key for Grade 3 Chapter 8 Mid Chapter Checkpoint Image_4
Equal Parts: ________
Name: ____________

Answer:
i. 4
ii. Fourths

Explanation:
The figure is the shape of a rectangle and it is divided into 4 right triangles. So, the equal parts of the rectangle are 4 and the name for the parts is fourths.

Write the number of equal parts in the whole. Then write the fraction that names the shaded part.

Question 6:
Go Math Grade 3 Answer Key for Understand Fractions Mid Chapter Checkpoint Image_5
Equal Parts ________
Shaded Parts _______

Answer:
i. 3
ii. 1/3

Explanation:
A circle is divided equally into 3 parts and one part is shaded among them. So, the fraction that names the shaded part is 1/3

Question 7:
Grade 3 Go Math Key Chapter 8 Mid Chapter Checkpoint Image_6
Equal Parts ________
Shaded Parts _______

Answer:
i. 6
ii. 1/6

Explanation:
The above figure is divided into 6 equal parts in the shape of the triangle. Only one part of the triangle is shaded among them. Therefore the fraction name for it is 1/6.

Question 8:
Go Math Answer Key for Grade 3 Understand Fractions Mid Chapter Checkpoint Img_7

Equal Parts ________
Shaded Parts _______

Answer:
i. 4
ii. 1/4

Explanation:
Observe the above figure, there are 4 equal parts of the triangle in which one part is shaded. So, the fraction name for the shaded part is 1/4.

Mid-Chapter Checkpoint Page No 474

Write the fraction that names the point.

Question 9:
Point A ______

Answer: 1/6

Explanation:
The Number line lies from 0/6 and 6/6 in the fraction form. Point A lies between 0/6 and 3/6. So, the location of point A is 1/6

Question 10:
Point B ______

Explanation:
Point B lies between point A and 3/6. We know that Point A is 1/6. The number between 1/6 and 3/6 is 2/6. So, point B is 2/6.

Answer: 2/6

Question 11:
Point C ______

Explanation:
Point C is located between 4/6 and 6/6. The number between 4 and 6 is 5. Therefore the fraction that names Point C is 5/6.

Answer: 5/6

Question 12:
Jessica ordered a pizza. What fraction of the pizza has mushrooms? What fraction of the pizza does not have mushrooms?
Go Math grade 3 mid chapter checkpoint answer key image_9

Answer:
i. 2/8
ii. 6/8

Explanation:
Given,
Jessica ordered a pizza in which 2 parts of pizza has mushrooms
We need to write the fraction of the pizza that has mushrooms
Total Number of slices = 8
Pizza that has mushrooms = 2
Pizza that does not have mushrooms = 6
The fraction of the pizza that has mushrooms = 2/8
The fraction of the pizza that does not have mushrooms = 6/8

Question 13:
Which fraction names the shaded part?
Go Math Answer Key Grade 3 Chapter 8 Mid Chapter Checkpoint image_10

Answer:
i. 8 Equal Parts
ii. 5/8

Explanation:
The figure shows that the rectangle is divided into 8 equal parts. Five parts are shaded in that rectangle. So, the fraction name for the parts that are shaded is 5/8.

Question 14:
Six friends share 3 oatmeal squares equally. How much of an oatmeal square does each friend get?
Answer Key for Grade 3 Go Math Chapter 8 Mid Chapter Checkpoint Image_11

Answer: 3/6

Explanation:
Total no. of friends = 6
Number of oatmeal squares = 3
Total no. of friends will be in the denominator and the oatmeal in the numerator.
So the answer is 3/6 or 1/2.

Relate Fractions and Whole Numbers Page No 478

Make Connections Draw a model of the fraction or fraction greater than 1. Then write it as a whole number.

Question 12:
8/4 = _____

Answer:

Question 13:
6/6 = _____

Answer:

Question 14:
5/1 = _____

Answer:

Question 15:
Jeff rode his bike around a bike trail that was 1/3 of a mile long. He rode around the trail 9 times. Write a fraction greater than 1 for the distance. How many miles did Jeff ride?

Answer: 3 miles

Explanation:
Given,
Jeff rode his bike around a bike trail that was 1/3 of a mile long
He rode around the trail 9 times
In order to know how many miles did Jeff Ride
We need to multiply 1/3 with 9
= 9 × 1/3
= 3 miles

Question 16:
What’s the Error? Andrea drew the number line below. She said that 9/8 and 1 are equal. Explain her error
Go Math Solution Key for Chapter 8 Grade 3 Related fractions & whole no.s image_1

Answer:
The error of Andrea is that she has located the point 1 on 9/8, but it must lie on 8/8.

Explanation:
Not Equal. Because 9/8 and 1 are not the same. Point 1 must be located on 8/8.

Question 17:
Each shape is 1 whole. Which numbers name the parts that are shaded? Mark all that apply.
Chapter 8 Answer Key for Go Math Grade 3 related fractions & whole no.s image_2
Options:
i. 4
ii. 6
iii. 26/6
iv. 24/6
v. 6/4

Answer:
iv (24/6)

Explanation:
There are four circles and each circle is divided into six parts. All parts are shaded in each group. So, the total number of shaded parts is 24. The numerator consists of a number of shaded parts and the denominator contains a number of parts in each circle.
= 24/6

Relate Fractions and Whole Numbers Page No 479

Use the number line to find whether the two numbers are equal. Write equal or not equal.Go Math Answer Key Grade Chapter 8 Relate Fractions & whole numbers image_1

Question 1:
0/6 and 1
____

Answer:
Not equal

Explanation:
The points 0/6 and 1 does not lie on the same point. So, the numbers 0/6 and 1 are not equal

Question 2:
1 and 6/6
____

Answer:
Equal

Explanation:
6/6 = 1
So 6/6 and 1 are equal

Question 3:
1/6 and 6/6
____

Answer:
Not Equal

Explanation:
The points 1/6 and 6/6 does not lie on the same point. So, 1/6 and 6/6 are not equal.

Question 4:
Solution Key for Grade 3 Go Math Chapter 8 Related fractions and whole numbers image_2
2 = ____

Answer: 4/2

Explanation:
There are 2 circles and each circle is divided into two parts.
Total number of equal parts = 4
Number of circles =
So, 4/2 = 2

Question 5:
Go Math Chapter 8 for Grade 3 Answer Key Related Fractions & whole numbers img_3
4 = ____

Answer: 12/3

Explanation:
From the above figure, we can see 4 circles which are divided 3 parts individually.
Number of Equal parts = 12
So, 12/3 = 4

Question 6:
Go Math Grade 3 Key Chapter 8 Related Fractions and Whole Numbers Image_4
3 = ____

Answer: 12/4

Explanation:
Total Number of equal parts = 12
Equal parts in each circle = 4
Therefore, 12/4 = 3

Question 7:

Answer Key for Go Math Grade 3 Understanding Fractions Related Fractions and Whole Numbers Image_5
1 = _____

Answer: 8/8

Explanation:
A circle is divided into 8 equal parts and all are shaded. So, the fraction name for the shaded parts is 8/8.

Problem Solving

Question 8:
Rachel jogged along a trail that was 1/4 of a mile long. She jogged along the trail 8 times. How many miles did Rachel jog in all?
______ miles

Answer: 8/4 or 2 miles

Explanation:
Given,
Rachel jogged along a trail that was 1/4 of a mile long
And, She jogged along the trail 8 times
8 × 1/4 = 8/4 = 2
Therefore the answer is 2 miles.

Question 9:
Jon ran around a track that was 1/8 of a mile long. He ran around the track 24 times. How many miles did Jon run in all?
______ miles

Answer: 24/8 or 3 miles

Explanation:
Given that, Jon ran around a track that was 1/8 of a mile long
He ran around the track 24 times
24 × 1/8 = 24/8 = 3
So, the miles did Jon run in all is 3 miles

Relate Fractions and Whole Numbers Lesson Check Page No 480

Question 1:
Each shape is 1 whole. Which fraction greater than 1 names the parts that are shaded?
Go Math Grade 3 Answer Key Related Fractions & Whole Numbers Lesson Check img_1
Options:
i. 6/18
ii. 3/6
iii. 6/3
iv. 18/6

Answer:
iv (18/6)

Explanation:
There are 3 circles which are divided into 6 parts = 18 parts
Each circle has 6 shaded parts
= 18/6

Question 2:
Each shape is 1 whole. Which fraction greater than 1 names the parts that are shaded?
Solution Key of Grade 3 Go Math Chapter 8 Related Fractions & Whole No.s Lesson Check img_2

Options:
i. 8/2
ii. 16/8
iii. 8/16
iv. 2/8

Answer:
ii (16/8)

Explanation:
There are two are which are divided into 8 parts = 8 × 2 = 16
Number of shaded parts in 1 circle = 8
So the answer is 16/8

Spiral Review

Question 3:
Tara has 598 pennies and 231 nickels. How many pennies and nickels does she have in all?
598 + 231

Options:
i. 719
ii. 729
iii. 819
iv. 829

Answer:
iv (829)

Explanation:
598 + 231 = 829

Question 4:
Dylan read 6 books. Kylie read double the number of books that Dylan read. How many books did Kylie read?
Options:
i. 4
ii. 8
iii. 12
iv. 14

Answer:
iii (12)

Explanation:
Given,
Dylan read 6 books
Kylie read double the number of books that Dylan read
That means Kylie reads 2 times greater than Dylan
6 × 2 = 12
Therefore Kylie reads 12 books

Question 5:
Alyssa divides a granola bar into halves. How many equal parts are there?
Options:
i. 2
ii. 3
iii. 4
iv. 6

Answer:
i (2)

Explanation:
Given that, Alyssa divides a granola bar into halves
Halves mean 2. So there are 2 equal parts

Question 6:
There are 4 students in each small reading group. If there are 24 students in all, how many reading groups are there?
Options:
i. 5
ii. 6
iii. 7
iv. 8

Answer:
ii (6)

Explanation:
Given that there are 4 students in each small reading group
To find:
how many reading groups are there for 24 students
So, Total number of students/ No. of students in each small reading group
i.e., 24/4 = 6

Fractions of a Group Page No 485

Write a fraction to name the shaded part of each group.
Question 1:
Answer key for Go Math Grade 3 Chapter 8 Fractions of a Group img_1
______

Answer: 6/8

Explanation:
There are 8 triangles in 4 blocks and 6 triangles are shaded among them. So, the fraction to name the shaded part is 6/8.

Question 2:
Go Math Grade 3 Key Chapter 8 Fractions of a Group img_2
______

Answer: 3/6

Explanation:
In the above figure, we can observe that there are 6 stars in 2 groups and three stars are shaded. Shaded stars will be in the numerator and the total number of stars in the denominator. So, the answer is 3/6

Write a whole number and a fraction greater than 1 to name the part filled. Think: 1 container = 1

Question 3:
Answer Key for 3rd Grade Chapter 8 Fractions of group img_3
______

Answer:
i. 2
ii. 8/4

Explanation:
The figure shows that there are two containers and four circles are shaded. One container is the mirror image of another container. So, we can see 8 shaded circles. So, the fraction greater than 1 to name the part filled is 8/4.

Question 4:
Go Math Grade 3 Understanding fractions answer key fractions of a group img_4
______

Answer:
i. 3
ii. 18/6

Explanation:
Here we can see three egg trays and all six parts are filled. By seeing the above figure we can understand that egg tray is the mirror image of other trays. So, we can see 18 parts filled. So, the fraction to the part filled is 18/6

Draw a quick picture. Then, write a fraction to name the shaded part of the group.

Question 5:
Draw 4 circles. Shade 2 circles.
_____

Question 6:
Draw 6 circles. Make 3 groups. Shade 1 group.
_____

Problem Solving

Question 7:
Brian has 3 basketball cards and 5 baseball cards. What fraction of Brian’s cards are baseball cards?
______

Answer: 5/8

Explanation:
Given,
Brian has 3 basketball cards and 5 baseball cards
Total Number of cards = 5 + 3 = 8
The fraction of Brian’s cards are baseball cards =?
5/5+3 = 5/8

Question 8:
Sophia has 3 pink tulips and 3 white tulips. What fraction of Sophia’s tulips are pink?
______

Answer: 3/6 or 1/2

Explanation:
Number of pink tulips Sophia has = 3
and No. of white tulips Sophia has = 3
Total Number of tulips = 3 + 3 = 6
To find the fraction of Sophia’s tulips are pink
= No. of pink tulips/Total No. of tulips
= 3/6

Fractions of a Group Lesson Check Page No 486

Question 1:
What fraction of the group is shaded?
Fraction of Groups Lesson Check for Go Math Grade 3 Chapter 8 Img_1

Options:
i. 5/3
ii. 5/8
iii. 3/5
iv. 3/8

Answer:
ii (5/8)

Explanation:
There are a group of 8 circles and five are shaded in it. So, the fraction of the shaded group is 5/8

Question 2:
What fraction of the group is shaded?
Go Math Answer key for Chapter 8 Grade 3 Fractions of a group lesson check img_2
Options:
i. 1/4
ii. 1/2
iii. 2/4
iv. 4/1

Answer
i. (1/4)

Explanation:
It is a group of four squares in which one block is shaded. So, the fraction of the shaded part is 1/4

Spiral Review

Question 3:
Which number sentence does the array represent?
Go Math Solution Key for Grade 3 Chapter 8 Fractions of a Group Spiral Review img_1
Options:
i. 4 × 7 = 28
ii. 3 × 8 = 24
iii. 3 × 7 = 21
iv. 3 × 6 = 18

Answer:
iii (3 × 7 = 21)

Explanation:
Total Number of Rows = 3
Total Number of Columns = 7
Rows × Columns = 3 × 7 = 21

Question 4:
Juan has 436 baseball cards and 189 football cards. How many more baseball cards than football cards does Juan have?
Options:
i. 625
ii. 353
iii. 347
iv. 247

Answer:
iv (247)

Explanation:
No. of baseball cards that Juan has = 436
No. of football cards that Juan has = 189
To know how many more baseball cards than football cards does Juan have,
we need to subtract No. of baseball cards and No. of football cards
= 436 – 189
= 247

Question 5:
Sydney bought 3 bottles of glitter. Each bottle of glitter costs $6. How much did Sydney spend in all on the bottles of glitter?
Options:
i. $24
ii. $18
iii. $12
iv. $9

Answer:
ii ($18)

Explanation:
Given,
Sydney bought 3 bottles of glitter
Each bottle of glitter costs = $6
Cross multiplication method is applied here,
1 bottle — $6
3 bottles –?
3 × 6 = 18
Therefore, the cost of 3 bottles of glitter = $18

Question 6:
Add
262 + 119
Options:
i. 143
ii. 371
iii. 381
iv. 481

Answer:

iii (381)

Explanation:
Addition of 262 and 119
262 + 119 = 381

Find Part of a Group Using Unit Fractions Page No 491

Circle equal groups to solve. Count the number of items in 1 group.
Question 1:
Grade 3 Go Math Answer Key Chapter 8 Find Part of a Group Using Unit Fractions img_1
1/4 of 12 = ___

Answer: 3

Explanation:
To solve the problem we can multiply the numerator with the whole number and divide by the denominator
= (1 × 12)/4
= 12/4
= 3

Question 2:
Go Math Primary School Grade 3 Answer Key Find Part of a Group Using Unit Fractions img_2
1/8 of 16 = ___

Answer: 2

Explanation:
In order to solve the problem we have to do product of 16 and 1/8
= 16 × 1/8
= 16/8
=2

Question 3:
Chapter 8 HMH Go math grade 3 Anwer key Find Part of a Group Using Unit Fractions img_3
1/3 of 12 = ___

Answer: 4

Explanation:
The product of 1/3 and 12 is
(1 × 12)/3 = 12/3
We can cancel 12 in 3 table by 4 times
Therefore, 12/3 = 4

Question 4:
3rd Std HMH Go Math Solution Key chapter 8 Find Part of a Group Using Unit Fractions img_4
1/3 of 9 = ___

Answer:3

Explanation:
We can label 1/3 and 9 as number and denominator of a whole number
= 9 × 1/3
= 3

Question 5:
Go Math Solution Key for Grade 3 chapter 8 Find Part of a Group Using Unit Fractions img_5
1/6 of 18 = ___

Answer:3

Explanation:
The product of 1/6 and 18 is
(1 × 18)/3
= 6

Question 6:
chapter 8 HMH Go math grade 3 key Find Part of a Group Using Unit Fractions img_6
1/2 of 4 = ___

Answer:2

Explanation:
It is a product of a fraction and whole numbers
The numerator is 1 and 4 and denominator is 2
1 × 4/2
=2

Problem Solving

Question 7:
Marco drew 24 pictures. He drew 1/6 of them in art class. How many pictures did Marco draw in art class?
______ Pictures

Answer: 4

Explanation:
Given that Marco drew 24 picture
He drew 1/6 of them in art class
In order to know the pictures did Marco draw in art class
We have to multiply 1/6 with 24
we get,
24 ×1/6
= 24/6
= 4

Question 8:
Caroline has 16 marbles. One-eighth of them are blue. How many of Caroline’s marbles are blue?
______ Marbles

Answer: 2

Explanation:
Number of marbles that Caroline has = 16
In that 1/8 are blue

To find:
Number of Caroline’s marbles are blue
So we have to do product of 16 and 1/8
1/8 × 16
16/8 = 2

Therefore Number of Caroline’s marbles are blue is 2

Find Part of a Group Using Unit Fractions Lesson Check Page No 492

Question 1:
Ms. Davis made 12 blankets for her grandchildren. One third of the blankets are blue. How many blue blankets did she make?
Grade 3 Go Math Answer Key Find Part of a Group Using Unit Fractions lesson check img_1

Options:
i. 3
ii. 4
iii. 9
iv. 12

Answer:
ii (4)

Explanation:
Number of blankets made for her grandchildren = 12
1/3rd of the blankets are blue
In order to know the count of blue blankets
Multiply 12 with 1/3
= (12 ×1)/3
= 4

Question 2:
Jackson mowed 16 lawns. One fourth of the lawns are on Main Street. How many lawns on Main Street did Jackson mow?
3rd Std HMH Go Math Key for Find Part of a Group Using Unit Fractions lesson check img_2
Options:
i. 4
ii. 6
iii. 8
iv. 12

Answer:
i (4)

Explanation:
Given that Jackson mowed 16 lawns
One-fourth of the lawns are on Main Street

To find:
How many lawns on Main Street did Jackson mow?
Product of 16 and 1/4
= 16 × 1/4
= 4

Question 3:
Find the difference.
509 – 175
Options:
i. 334
ii. 374
iii. 434
iv. 474

Answer:
i.  (334)

Explanation:
The difference between the 1st number and 2nd number is
509 – 175 = 334

Question 4:
Find the quotient.
6)54
Options:
i. 6
ii. 7
iii. 8
iv. 9

Answer:
iv. (9)

Explanation:
Divide 54 by 6
54/6 = 9
So, the remainder is 0 and quotient is 9

Question 5:
There are 226 pets entered in the pet show. What is 226 rounded to the nearest hundred?
Options:
i. 200
ii. 220
iii. 300
iv. 400

Answer:
i. (200)

Explanation:
The word form of 226 is two hundred and twenty-six.
The number which is near to 226 is 200. Because the number is less than 250.
So, the nearest hundred to 226 is 200.

Question 6:
Ladonne made 36 muffins. She put the same number of muffins on each of 4 plates. How many muffins did she put on each plate?
Options:
i. 3
ii. 6
iii. 9
iv. 12

Answer:
iii (9)

Explanation:
Given,
Ladonne made 36 muffins
She put the same no. of muffins on each of 4 plates
No. of muffins on 4 plates/ Total No. of muffins
= 36/4
= 9

Problem Solving – Find the Whole Group Using Unit Fractions Page No 497

Draw a quick picture to solve.

Question 1:
Katrina has 2 blue ribbons for her hair. One fourth of all her ribbons are blue. How many ribbons does Katrina have in all?

Go Math Answer Key grade 3 chapter 8 Find whole Group Using Unit Fractions

____ ribbons

Answer:
8 ribbons

Explanation:
Given,
Katrina has 2 blue ribbons for her hair
1/4th of all ribbons are blue
To know how many ribbons that Katrina has,
we have to divide the number of blue ribbons by 1/4th of all ribbons are blue
we get, 2 ÷ 1/4 = (2 × 4)/1
= 2 × 4 = 8
Therefore, the answer to the above question is 8 ribbons.

Question 2:
One-eighth of Tony’s books are mystery books. He has 3 mystery books. How many books does Tony have in all?
______ Books

Answer:
24 Books

Explanation:
Given that, Tony has 3 mystery books
Out of which 1/8th of tony’s books are mystery books
So, to find how many books does Tony have in all
Divide 3 by 1/8, we get
3 ÷ 1/8
(3 ×8)/1 = 24

Question 3:
Brianna has 4 pink bracelets. One-third of all her bracelets are pink. How many bracelets does Brianna have?
______ Bracelets

Answer:
12 Bracelets

Explanation:
No. of pink bracelets that Brianna has = 4
1/3rd of all her bracelets are pink
Divide No. of pink bracelets by 1/3rd of all her pink bracelets
we get,
4 ÷ 1/3
4 × 3 = 12
So, the answer is 12 bracelets

Question 4:
Ramal filled 3 pages in a stamp album. This is one sixth of the pages in the album. How many pages are there in Ramal’s stamp album?
______ pages

Answer:
18 pages

Explanation:
Given,
Ramal filled 3 pages in a stamp album
one-sixth of the pages in the album
3 ÷ 1/6 = 3 × 6 = 18 pages

Question 5:
Jeff helped repair one half of the bicycles in a bike shop last week. If Jeff worked on 5 bicycles, how many bicycles did the shop repair in all last week?
______ bicycles

Answer:
10 bicycles

Explanation:
Jeff helped repair 1/2 of the bicycles in a bike shop last week
Jeff worked on 5 bicycles
5 divided by 1/2
5 × 2/1 = 10 bicycles

Question 6:
Layla collects postcards. She has 7 postcards from Europe. Her postcards from Europe are one third of her total collection. How many postcards in all does Layla have?
______ postcards

Answer:
21 postcards

Explanation:
Layla collects postcards in which 7 postcards are from Europe
Postcards from Europe of her total collection = 1/3
7 divided by 1/3
we get, 7 × 3 = 21
Therefore, the postcards in all do Layla has 21 postcards

Find the Whole Group Using Unit Fractions Lesson Check Page No 498

Question 1:
A zoo has 2 male lions. One-sixth of the lions are male lions. How many lions are there at the zoo?
Options:
i. 2
ii. 6
iii. 8
iv. 12

Answer:
iv (12)

Explanation:
Male lions in the Zoo = 2
1/6th of the lions are male in the zoo
2 ÷ 1/6
= 2 × 6
= 12

Question 2:
Max has 5 red model cars. One-third of his model cars are red. How many model cars does Max have?
Options:
i. 15
ii. 12
iii. 10
iv. 8

Answer:
i.  (15)

Explanation:
Given,
Max has 5 red model cars
1/3rd of the cars are red
So we need to divide 5 by 1/3,
we get 3 × 5 = 15
Therefore the answer is 15

Spiral Review

Question 3:
There are 382 trees in the local park. What is the number of trees rounded to the nearest hundred?
Options:
i. 300
ii. 380
iii. 400
iv. 500

Answer:
iii. (400)

Explanation:
Given that there are 382 trees in the local park.
This is nearer to the number 400. So the round figure of 382 is 400

Question 4:
The Jones family is driving 458 miles on their vacation. So far, they have driven 267 miles. How many miles do they have left to drive?
458 – 267
Options:
i. 191
ii. 201
iii. 211
iv. 291

Answer:
i.  (191)

Explanation:
Jones family is driving 458 miles on their vacation
They have driven 267 miles
In this, we have to subtract 458 with 267,
we get, 191

Question 5:
Ken has 6 different colors of marbles. He has 9 marbles of each color. How many marbles does Ken have in all?
Options:
i. 15
ii. 45
iii. 54
iv. 63

Answer:
iii (54)

Explanation:
Given,
Ken has 6 different colors of marbles
Ken has 9 marbles of each color
To know the total number of marbles multiply different colors of marbles with each marble color
= 6 × 9 = 54

Question 6:
Eight friends share two pizzas equally. How much of a pizza does each friend get?

HMH Go math grade 3 Anwer key Find the Whole Group Using Unit Fractions spiral review
Options:
i. 8 halves
ii. 4 eighths
iii. 2 sixths
iv. 2 eighths

Answer:
iv (2 eighths)

Explanation:
There are 2 pizzas and eight friends need to share those pizzas
so, we have 2 by 8
Each friend gets 2/8 and the fraction name is 2 eighths

Chapter 8 Understanding Fractions Review Test – Page No 499

Review/Test

Question 1:
Each shape is divided into equal parts. Select the shapes that show thirds. Mark all that apply.

Options:
i. Go Math Grade 3 Chapter 8 Review test (a)
ii. Go Math Solution Key for Grade 3 Review (b)
iii. Go Math Answer Key for Grade 3 Review (c)
iv. Chapter 8 Go Math Key for Grade 3 Review (d)

Answer: ii & iv

Explanation: From the given figures we can observe that there are thirds in Fig ii & iv.

Question 2:
What fraction names the shaded part of the shape?
Go Math Solution Key for Grade 3 Chapter Review Image_1

Options:
i. 8 sixths
ii. 8 eighths
iii. 6 eighths
iv. 2 sixths

Answer:
iii (6 eighths)

Explanation:
A rectangle is divided into a group of eight parts and 6 parts are shaded. The fraction name of the shaded parts is 6 eighths.

Question 3:
Omar shaded a model to show the part of the lawn that he finished mowing. What fraction names the shaded part? Explain how you know how to write the fraction.
HMH Go math grade 3 Anwer key Chapter 8 Review Image_2

Answer: 1/8

Explanation:
From the figure, we can see that there are eight triangles and only one part is shaded. So, the fraction of the shaded part is 1/8.

No. of Shaded parts must be given in the numerator and the number of parts or whole group will be in the denominator.

Chapter 8 Understanding Fractions Review Test – Page No 500

Question 4:
What fraction names point A on the number line?
Answer Key for 3rd Std HMH Go Math Chapter 8 Review img_3
Point A ___

Answer: 1/6

Explanation:
A number line is shown in the figure above,
Each point is equal to 1/6
The point is located after 0/6. So, Point A is 1/6.

Question 5:
Jamal folded this piece of paper into equal parts. Circle the word that makes the sentence true.
Go Math Key for Grade 3 Chapter 8 Review img_4
The Paper is folded into

Options:
i. Sixths
ii. Eighths
iii. Fourths

Answer: Eighths

Explanation:
From the figure, we can see that the paper is divided into 8 equal parts. So, the paper is folded into eighths.

Question 6:
Caleb took 18 photos at the zoo. One sixth of his photos are of giraffes. How many of Caleb’s photos are of giraffes?
_______ photos

Answer: 3 photos

Explanation:
Given that,
Caleb took 18 photos at the zoo
1/6th of the photos are giraffes
To know the no. of Caleb’s photos are of giraffes
Simplify 18 and 1/6
18/6 = 3

Question 7:
Three teachers share 2 packs of paper equally.
Go Math Primary School Grade 3 Answer Key Chapter 8 Review test img_5
How much paper does each teacher get? Mark all that apply.
Options:
i. 3 halves of a pack
ii. 2 thirds of a pack
iii. 3 sixths of a pack
iv. 1 half of a pack
v. 1 third of a pack

Answer:
ii (2 thirds of a pack)

Explanation:
No. of teachers = 3
No. of Packs of paper = 2
3 teachers should share 2 packs of paper
i.e., No. of Paper Packs/ No. of teachers = 2/3
The fraction name is 2 thirds of a pack

Chapter 8 Understanding Fractions Review Test – Page No 501

Question 8:
Lilly shaded this design.
Grade 3 HMH Go Math Answer Keys Chapter 8 Review Test Img_6
Select one number from each column to show the part of the design that Lilly shaded.
Answer Keys for HMH Go Math Chapter 8 Grade 3 Review img_7

Answer:
i. Numerator 1
ii. Denominator 4
iii. Numerator 5

Explanation:
The task is to observe the figure and identify the number from each column i.e., Numerator and Denominator Column. Lilly has Shaded the 1st column 1st block i.e, 1, Next 2nd Column 2nd block is shaded so 4, and at last 1st column 3rd block is shaded so numerator 5.

Question 9:
Marcus baked a loaf of banana bread for a party. He cut the loaf into equal size pieces. At the end of the party, there were 6 pieces left. Explain how you can find the number of pieces in the whole loaf if Marcus told you that 1/3 of the loaf was left. Use a drawing to show your work.
____ pieces

Answer: 18 pieces
Go Math Grade 3 Chapter 8 Answer Key review solution img_1

Explanation:
Given,
Marcus baked a loaf of banana bread for a party. He cut the loaf into equal size pieces
At the end of the party, there were 6 pieces left.
Marcus told you that 1/3 of the loaf was left
To find:
Number of pieces in the whole loaf = x
1/3 × x = 6
x = 6 × 3
x = 18
So, the total number of pieces in the whole loaf is 18

Chapter 8 Understanding Fractions Review Test – Page No 502

Question 10:
The model shows one whole. What fraction of the model is NOT shaded?
Answer key of Go math grade 3 chapter 8 Review img_8
____

Answer: 2/4

Explanation:
The square is divided to 4 equal triangles. In that two parts are shaded and two parts are not shaded.
Thus the fraction for the non shaded part is 2/4

Question 11:
Together, Amy and Thea make up 1/4 of the midfielders on the soccer team. How many midfielders are on the team? Show your work.
_____ midfielders

Answer: 8

Explanation:
1/4 of the midfielders on the soccer team represents 2 midfielders
If we divide no. of midfielders into 4 equal groups, then each group will have 2 midfielders
1/4 × x = 2
x = 4 × 2
x = 8
Thus 8 midfielders are on the team

Question 12:
Six friends share 4 apples equally. How much apple does each friend get?
HMH Go Math Chapter 8 Grade 3 Key Review img_9

Answer: 1 apple

Question 13:
Each shape is 1 whole.
Solution Key for HMH Go Math Grade 3 Understand Fractions Review img_10
For numbers, 13a–13e, choose Yes or No to show whether the number names the parts that are shaded.

a. 4
i. Yes
ii. No

Answer:
i. Yes

b. 8
i. Yes
ii. No

Answer:
i. Yes

c. 8/2
i. Yes
ii. No

Answer:
ii. No

d. 8/4
i. Yes
ii. No

Answer:
i. Yes

e. 2/8
i. Yes
ii. No

Answer:
ii. No

Chapter 8 Understanding Fractions Review Test – Page No 503

Question 14:
Alex has 3 baseballs. He brings 2 baseballs to school. What fraction of his baseballs does Alex bring to school?
____

Answer: 2/3

Explanation:
Total Number of baseballs that Alex have = 3
He brings 2 baseballs to school
The fraction of baseballs that brings to school = No. of baseballs brings to school/total no. of baseballs
= 2/3

Question 15:
Janeen and Nicole each made fruit salad for a school event.
Part A
Janeen used 16 pieces of fruit to make her salad. If 1/4 of the fruits were peaches, how many peaches did she use? Make a drawing to show your work.
____ peaches

Answer:4
No. of pieces Janeen used to make her fruit salad = 16
In that 1/4 of the fruits were peaches
how many peaches did she use is?
Multiply No. of fruit pieces with 1/4 of the fruits were peaches
we get,
16 × 1/4
= 16/4
= 4

Part B
Nicole used 24 pieces of fruit. If 1/6 of them were peaches, how many peaches in all did Janeen and Nicole use to make their fruit salads? Explain how you found your answer.
____ peaches

Answer: 8

Explanation:
No. of peaches Janeen used in her fruit salad = 4
Total number of fruit pieces Nicole used = 24
If 1/6 of them were peaches
24 × 1/6 = 4
To know total no. of peaches that Janeen and Nicole used
We have to add the number of peaches in the fruit salad of Janeen and Nicole
= 4 + 4
= 8

Question 16:
There are 8 rows of chairs in the auditorium. Three of the rows are empty. What fraction of the rows are empty?
_____ rows

Answer: 3/8

Explanation:
Given: Total Number of rows of chairs in the auditorium = 8
In that three rows are empty
The fraction of the rows that are empty is 3/8

Chapter 8 Understanding Fractions Review Test – Page No 504

Question 17:
Tara ran 3 laps around her neighborhood for a total of 1 mile yesterday. Today she wants to run 2/3 of a mile. How many laps will she need to run around her neighborhood?
Go Math HMH Grade 3 Answer Key for Understand Fractions Review img_11
____ laps

Answer: 2 laps

Explanation:
Given that,
Tara ran 3 laps around her neighborhood for a total of 1 mile
she wants to run 2/3 of a mile
1 mile —- 3 laps
2/3 mile — x
1 × x = (3 ×2)/3
x = 6/3
x = 2
Thus it takes 2 laps to run around her neighborhood

Question 18:
Gary painted some shapes.
Solution Key for Go Math Grade 3 Understand Fractions img_12
Select one number from each column to show a fraction greater than 1 that names the parts Gary painted.
Go Math 3rd std Answer Key for Understand fractions Review img_13
_____

Answer:

Question 19:
Angelo rode his bike around a bike trail that was 1/4 of a mile long. He rode his bike around the trail 8 times. Angelo says he rode a total of 8/4 miles. Teresa says he is wrong and that he actually rode 2 miles. Who is correct? Use words and drawings to explain how you know.
_____

Answer: 2 miles
Both Angelo and Teresa are correct
8/4 and 2 are same

Grade 3 HMH Go Math Answer Key PDF Chapter 8 covers questions from exercises, practice tests, assessment tests, etc. Improve your math knowledge and learn the concepts underlying effectively using our HMH Go Math 3rd Grade Chapter 8 Understand Fractions Anwer Key. To practice, more such questions check out Go Math Grade 3 Answer Key Chapter 8 Understand Fractions Extra Practice.

We wish the knowledge shared on Go Math Grade 3 Chapter 8 Understand Fractions has helped you in your preparation. If you need any help you can always look up to the Step by Step Solutions provided in our 3rd Grade Go Math Chapter 8 Understand Fractions.

Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts

Students who want to learn the fundamentals in Geometry and Fractions are suggest to go through the Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts. In this page we have provided the step by step expplanation for all the problems. Free Download pdf of Go Math 2nd Grade Chapter 11 Solution Key Geometry and Fraction Concepts is available here.

Go Math Grade 2 Chapter 11 Answer Key Geometry and Fraction Concepts

Quick and easy learning is possible with our Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts. We have covered all the topics as per the latest syllabus. The topics covered in Go Math Grade 2 Chapter 11 Answer Key Geometry and Fraction Concepts are Three-Dimensional Shapes, Attributes of Three-Dimensional Shapes, Partition Rectangles and so on. All you have to do is to click on the below attached links and start solving the problems.

Geometry and Fraction Concepts

Lesson: 1 Three-Dimensional Shapes

Lesson: 2 Attributes of Three-Dimensional Shapes

Lesson: 3 Build Three-Dimensional Shapes

Lesson: 4 Two-Dimensional Shapes

Lesson: 5 Angles in Two-Dimensional Shapes

Lesson: 6 Sort Two-Dimensional Shapes

Lesson: 7 Partition Rectangles

Mid-Chapter Checkpoint

Lesson: 8 Equal Parts

Lesson: 9 Show Equal Parts of a Whole

Lesson: 10 Describe Equal Parts

Lesson: 11 Problem Solving • Equal Shares

Review/Test

Geometry and Fraction Concepts Show What You Know

Equal Parts
Circle the shape that has two equal parts.
Question 1.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 1.1
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-1.1

Question 2.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 1.2
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-1.2

Identify Three-Dimensional Shapes
Question 3.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 1.3
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-1.3

Question 4.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 1.4
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-1.4

Identify Shapes
Circle all the shapes that match the shape name.
Question 5.
triangle
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 1.5
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-1.5

Question 6.
rectangle
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 1.6
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-1.6

Geometry and Fraction Concepts Vocabulary Builder

Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 2.1

Visualize It
Draw pictures to complete the graphic organizer.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 2.2

Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-2.2

Understand Vocabulary
Draw a shape to match the shape name.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 2.3

Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-2.3

Geometry and Fraction Concepts Game: Count the Sides

Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 2.4
2. Look for a shape that has the same number of sides as the number you tossed.
3. Put one of your counters on that shape.
4. Take turns. Cover all the shapes. The player with more counters on the board wins.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 2.5

Geometry and Fraction Concept Vocabulary

Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 3.1
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 3.2
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 3.3
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 3.4

Geometry and Fraction Concepts Vocabulary Game

Going to a Balloon Race
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 3.5
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 3.6
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 3.6
The Write Way
Reflect
Choose one idea. Write about it in the space below.

  • Draw and write about all of the words. Use a separate piece of paper for your drawings. face edge vertex
  • Choose one of these shapes. Write three things you know about it. quadrilateral pentagon hexagon
  • Explain how you know the difference between halves, thirds, and fourths. Draw pictures on a separate piece of paper if you need to.
    Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 3.8

Lesson 11.1 Three-Dimensional Shapes

Essential Question What objects match three-dimensional shapes?

Listen and Draw
Draw a picture of an object with the same shape shown.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.1 1

Answer:
Drawn a picture of an object with the same shape shown.
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.1-1

MATHEMATICAL PRACTICES

Appy Describe how the shapes are alike.
Describe how they are different.
Answer:
Two figures are said to be similar if they are the same shape. In more mathematical language, two figures are similar if their corresponding angles are congruent, and the ratios of the lengths of their corresponding sides are equal.

Share and Show
Circle the objects that match the shape name.
Question 1.
sphere
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.1 3
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.1-3

Question 2.
cube
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.1 4
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.1-4

On Your Own
Circle the objects that match the shape name.
Question 3.
cylinder
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.1 5
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.1-5

Question 4.
rectangular prism
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.1 6
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.1-6

Question 5.
cone
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.1 7
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.1-7

Question 6.
GO DEEPER
Julio used cardboard squares as the flat surfaces of a cube. How many squares did he use?
______ squares
Answer: 6 squares.
Explanation: Julio used cardboard squares as the flat surfaces of a cube. How many squares did he used 6 squares

Question 7.
THINK SMARTER
Circle the shapes that have a curved surface. Draw an X on the shapes that do not have a curved surface.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.1 8
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.1-8

Problem Solving • Applications
Question 8.
Make Connections
Reba traced around the bottom of each block. Match each block with the shape Reba drew.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.1 9
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.1-8

Question 9.
THINK SMARTER
Match the shapes.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.1 10
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.1-10

TAKE HOME ACTIVITY • Ask your child to name an object that has the shape of a cube

Three-Dimensional Shapes Homework & Practice 11.1

Circle the objects that match the shape name.
Question 1.
cube
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.1 11
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.1-11

Question 2.
cone
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.1 12
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.1-12

Question 3.
rectangular prism
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.1 13
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.1-13

Problem Solving
Question 4.
Lisa draws a circle by tracing around the bottom of a block. Which could be the shape of Lisa’s block? Circle the name of the shape.
cone cube rectangular prism
Answer: A cone, or a cylinder, Since the bottom of each 3D object is a circle compared to 2D it is a circle.
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts

Question 5.
WRITE
Describe one way that a cube and a cylinder are alike. Describe one way they are different.
Answer:
Same: Cude and a cylinder both alike as they are 3D shapes.
Different: A cube has vertices. where a cylinder doesn’t have any vertices.

Lesson Check
Question 1.
What is the name of this shape?
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.1 14
_______
Answer: Cube
Explanation:
a cube is a three-dimensional solid object bounded by six square faces, facets, or sides, with three meetings at each vertex.
The cube is the only regular hexahedron and is one of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices

Question 2.
What is the name of this shape?
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.1 15
______
Answer: cone
Explanation:
A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a point called the apex or vertex

Spiral Review
Question 3.
The string is about 6 centimeters long. What is a reasonable estimate for the length of the crayon?
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.1 16
_____ centimeters
Answer: 8 Centimeters

Question 4.
What is the total value of this group of coins?
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.1 17
______
Answer:  16 cents
Explanation:
By observing given picture we get penny nickel and dime
10 cents + 5 cents +  1 cent = 16 cents

Question 5.
What time is shown on this clock?
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.1 18
_______
Answer: 1030.
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.1-18

Lesson 11.2 Attributes of Three-Dimensional Shapes

Essential Question How would you describe the faces of a rectangular prism and the faces of a cube?

Listen and Draw
Circle the cones. Draw an X on the sphere.
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.2 1

Answers:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.2-1

MATHEMATICAL PRACTICES
Name the other shapes on this page. Describe how they are different.
Answer:
Other common shapes are points, lines, planes, and conic sections such as ellipses, circles, and parabolas. Among the most common 3-dimensional shapes are polyhedra, which are shapes with flat faces; ellipsoids, which are egg-shaped or sphere-shaped objects, cylinder,s and cones.

Share and Show

Write how many for each.
Question 1.
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.2 2
Answer:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.2-2

Question 2.
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.2 3
Answer:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.2-3Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.2-3

On Your Own
Question 3.
GO DEEPER
Use dot paper. Follow these steps to draw a cube.
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.2 4
Answer:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.2-4

Question 4.
THINK SMARTER
Trace all the faces of a rectangular prism on a sheet of paper. Write to tell about the shapes that you drew.
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.2 5
Answer:
a type of prism (a three-dimensional shape where the cross-section indicates the type of prism — so a triangular prism would have a triangular cross-section, a rectangular prism would have a rectangular cross-section, a square prism would have a square cross-section, and so on). “Cross-section” is just a fancy way of saying slicing the object like you would a loaf of bread — each “slice” of a prism is identical.

Problem Solving • Applications
Question 5.
Make Connections
Marcus traced around the faces of a three-dimensional shape. Circle the name of the shape he used.
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.2 6
Answer:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.2-6

Question 6.
THINK SMARTER
Use the words on the tiles to label the parts of the cube.
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.2 7
Describe the faces of a cube.
___________________
___________________
Answer:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.2-7

A cube is a 3D shape
Cube has 6 faces
All the 6 faces are of equal dimensions

TAKE HOME ACTIVITY • Have your child tell you about the faces on a cereal box or another kind of box.

Attributes of Three-Dimensional Shapes Homework & Practice 11.2

Circle the set of shapes that are the faces of the three-dimensional shape.
Question 1.
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.2 8
Answer:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.2-8

Question 2.
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.2 9
Answer:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.2-9

Problem Solving
Question 3.
Kevin keeps his marbles in a container that has the shape of a cube. He wants to paint each face a different color. How many different paint colors does he need?
______ different paint colors
Answer: 6 different paint colors

Question 4.
WRITE
Describe a cube. Use the words, faces, edges, and vertices in your description.
______________________
______________________
Answer: A cube is a three-dimensional solid object
Cube contains of 6 faces,12 edegs and 8 vertices.
One best elample of a cube is dies.

Lesson Check
Question 1.
How many faces does a cube have?
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.2 10
______ faces
Answer: 6 faces
a cube is a three-dimensional solid object bounded by six square faces, facets, or sides, with three meetings at each vertex.
The cube is the only regular hexahedron and is one of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices

Question 2.
How many faces does a rectangular prism have?
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.2 11
________ faces
Answer: 6 faces
A rectangular prism has 8 vertices, 12 sides, and 6 rectangular faces. All the opposite faces of a rectangular prism are equal.
A rectangular prism has a rectangular cross-section.

Spiral Review
Question 3.
What time is shown on this clock?
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.2 12
Answer: 0915
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.1-18

Question 4.
Circle the cone.
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.2 13
Answer:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.2-13

Question 5.
Use the line plot. How many books are 8 inches long?
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.2 14
Answer: 2 books.
Explanation: by observing the line plot there are 2 books

Lesson 11.3 Build Three-Dimensional Shapes

Essential Question How can you build a rectangular prism?

Listen and Draw
Circle the shapes with curved surfaces. Draw an X on the shapes with flat surfaces.
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.3 1

Answer:
Go-Math-Answer-Key-Grade-2-Chapter-11-Geometry-and-Fraction-Concepts-11.3-1

HOME CONNECTION • Your child sorted the shapes on this page using the attributes of the shapes.

MATHEMATICAL PRACTICES

Name the shapes you drew an X on. Describe how they are different.
Answer: The shapes with X on them are cube and rectangular prism.
Both cube and rectangular prism has equal number of faces, edegs and vetrices.
The cube and rectangular prism are diffrent from other shapes because they have edegs and vertices where as cone cylinder and sphere doesnt.

Share and Show
Build a rectangular prism with the given number of unit cubes. Shade to show the top and front views.
Question 1.
9 unit cubes
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.3 2
Answer:
Go-Math-Answer-Key-Grade-2-Chapter-11-Geometry-and-Fraction-Concepts-11.3-2

Question 2.
16 unit cubes
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.3 3
Answer:
Go-Math-Answer-Key-Grade-2-Chapter-11-Geometry-and-Fraction-Concepts-11.3-4

On Your Own
Build a rectangular prism with the given number of unit cubes. Shade to show the top and front views.
Question 3.
24 unit cubes
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.3 4
Answer:
Go-Math-Answer-Key-Grade-2-Chapter-11-Geometry-and-Fraction-Concepts-11.3-4

Question 4.
THINK SMARTER
The top, side, and front views of a rectangular prism are shown. Build the prism. How many unit cubes are used to build the solid?
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.3 5
__________ unit cubes
Answer: 30 unit cubes

Question 5.
Analyze
Jen uses 18 cubes to build a rectangular prism. The top and front views are shown. Shade to show the side view.
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.3 6
Answer:
Go-Math-Answer-Key-Grade-2-Chapter-11-Geometry-and-Fraction-Concepts-11.3-6

Problem Solving • Applications
Solve. Write or draw to explain.
Question 6.
GO DEEPER
Tomas built this rectangular prism. How many unit cubes did he use?
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.3 7
_____ cubes
Answer: 24 cubes
Explanation: Tomas built this rectangular prismhe used 24 unit cubes

Question 7.
Look for Structure
Theo builds the first layer of a rectangular prism using 4 cubes. He adds 3 more layers of 4 cubes each. How many cubes are used for the prism?
______ cubes
Answer: 12 cubes

Explanation:
Theo builds the first layer of a rectangular prism using 4 cubes. He adds 3 more layers of 4 cubes each. cubes are used for the prism are
24  cubes

Question 8.
THINK SMARTER
Tyler built this rectangular prism using unit cubes. Then he took it apart and used all of the cubes to build two new prisms. Fill in the bubble next to the two prisms he built.
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.3 8.1
Answer:
Go-Math-Answer-Key-Grade-2-Chapter-11-Geometry-and-Fraction-Concepts-11.3-8.1

TAKE HOME ACTIVITY • Ask your child to show how he or she solved an exercise in the lesson.

Build Three-Dimensional Shapes Homework & Practice 11.3

Build a rectangular prism with the given number of unit cubes. Shade to show the top and front views.
Question 1.
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.3 8
Answer:
Go-Math-Answer-Key-Grade-2-Chapter-11-Geometry-and-Fraction-Concepts-11.3-8

Problem Solving
Solve. Write or draw to explain.
Question 2.
Rosie built this rectangular prism. How many unit cubes did she use?
_____ unit cubes
Answer: 16 unit cubes

Explanation:
Rosie built this rectangular prism he used 16 cubes

Question 3.
WRITE
Build a rectangular prism using cubes. Then, draw in your journal the top, side, and bottom views of your prism.
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-img1
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-img1

Lesson Check
Question 3.
Milt builds the first layer of a rectangular prism using 3 cubes. He adds 2 more layers of 3 cubes each. How many cubes are used for the prism?
_____ cubes
Answer: 9 cubes.

Explanation:
Given Milt builds the first layer of a rectangular prism using 3 cubes. He adds 2 more layers of 3 cubes each.
then we get 9 cubes

Question 4.
Thea builds the first layer of a rectangular prism using 4 cubes. Raj adds 4 more layers of 4 cubes each. How many cubes are used for the prism?
_____ cubes
Answer: 12 cubes

Explanation:
Given Thea builds the first layer of a rectangular prism using 4 cubes. Raj adds 4 more layers of 4 cubes each.
then we get 12 cubes.

Spiral Review
Question 5.
Patti’s dance class will meet for 1 year. Her art class will meet for 32 weeks. Which is the greater amount of time?
___________
Answer: Dance class
As 1 year=356 days/366 days(leap year)=52 weeks which is more than 32 weeks.
Explanation:
Given Patti’s dance class will meet for 1 year. Her art class will meet for 32 weeks
Dance class
As 1 year=356 days/366 days(leap year)=52 weeks which is more than 32 weeks.

Question 6.
A large pack has 512 beads. A small pack has 346 beads. Estimate how many more beads the large pack has than the small pack.
about _____ more beads
Answer: about 166 more beads
Explanation:
Given A large pack has 512 beads. A small pack has 346 beads
There are 166 more beads the large pack has than the small pack.

Use the bar graph.
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.3 9
Question 7.
Which kind of fruit got the fewest votes?
_______
Answer: Apple

Question 8.
How many more votes did grape get than apple?
_____ more votes
Answer: 3 more votes

Lesson 11.4 Two-Dimensional Shapes

Essential Question What shapes can you name just by knowing the number of sides and vertices?

Listen and Draw
Use a ruler. Draw a shape with 3 straight sides. Then draw a shape with 4 straight sides.
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.4 1

Answer:
Go-Math-2nd-Grade-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.4-1

MATHEMATICAL PRACTICES
Describe how your shapes are different from the shapes a classmate drew.
Answer:

Share and Show

Write the number of sides and the number of vertices.
Question 1.
triangle
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.4 2
_____ sides
______ vertices
Answer:
3 sides
3 vertices
A triangle is a polygon with three sides and three vertices.

Question 2.
hexagon
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.4 3
_____ sides
______ vertices
Answer:
6 sides
6 vertices
a hexagon can be defined as a polygon with six sides. The two-dimensional shape has 6 sides, 6 vertices, and 6 angles.

Question 3.
pentagon
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.4 4
_____ sides
______ vertices
Answer:
5 sides
5 vertices
A pentagon has five straight sides and five vertices (corners). It has five angles inside it that add up to 540°

On Your Own
Write the number of sides and the number of vertices. Then write the name of the shape.
Question 4.
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.4 5
_____ sides
______ vertices
_______
Answer:
6 sides
6 vertices
Hexagon
a hexagon can be defined as a polygon with six sides. The two-dimensional shape has 6 sides, 6 vertices and 6 angles

Question 5.
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.4 6
Answer:
4 sides
4 vertices
Square
A square has 4 sides and 4 vertices. All the sides of a square are equal in length. All interior angles are equal and right angles.

Question 6.
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.4 7
Answer:
4 sides
4 vertices
Quadrilateral
A quadrilateral has 4 sides, 4 angles and 4 vertices. A quadrilateral can be regular or irregular

Question 7.
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.4 8
Answer:
3 sides
3 vertices
Triangle
A triangle is a polygon with three edges and three vertices.

Question 8.
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.4 9
Answer:
5 sides
5 vertices
Pentagon
A pentagon has five straight sides and five vertices (corners).

Question 9.
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.4 10
Answer:
4 sides
4 vertices
Quadrilateral
A quadrilateral has 4 sides, 4 angles and 4 vertices. A quadrilateral can be regular or irregular

GO DEEPER
Draw more sides to make the shape.
Question 10.
pentagon
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.4 11
Answer:
Go-Math-2nd-Grade-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.4-13

Question 11.
quadrilateral
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.4 12
Answer:
Go-Math-2nd-Grade-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.4-12

Question 12.
hexagon
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.4 13
Answer:
Go-Math-2nd-Grade-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.4-11

Problem Solving • Applications

Solve. Draw or write to explain.
Question 13.
THINK SMARTER
Alex draws a hexagon and two pentagons. How many sides does Alex draw altogether?
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.4 14.1
Answer: 6 sides.

Question 14.
Use Diagrams
Ed draws a shape that has 4 sides. It is not a square. It is not a rectangle. Draw a shape that could be Ed’s shape.
Answer:
Go-Math-2nd-Grade-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.4-12

Question 15.
THINK SMARTER
Count the sides and vertices of each two-dimensional shape. Draw each shape where it belongs in the chart.
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.4 14
Answer:
Go-Math-2nd-Grade-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.4-14

TAKE HOME ACTIVITY • Ask your child to draw a shape that is a quadrilateral.

Two-Dimensional Shapes Homework & Practice 11.4

Write the number of sides and the number of vertices. Then write the name of the shape.
Question 1.
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.4 15
______ sides
_______ vertices
Answer:
The above figure shows that there are:
3 sides
3 vertices
Triangle
A triangle is a polygon with three edges and three vertices.

Question 2.
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.4 16
______ sides
_______ vertices
Answer:
The above figure shows that there are:
6 sides
6 vetrices.
Hexagon
a hexagon can be defined as a polygon with six sides.

Question 3.
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.4 17
______ sides
_______ vertices
Answer:
The above figure shows that there are:
5 sides
5 vertices
Pentagon
A pentagon has five straight sides and five vertices (corners). It has five angles inside

Problem Solving
Solve. Draw or write to explain.
Question 4.
Oscar is drawing a picture of a house. He draws a pentagon shape for a window. How many sides does his window have?
______ sides
Answer: 5 sides.
house

Question 5.
WRITE
Draw and label a pentagon and a quadrilateral.
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-img1

Lesson Check
Question 1.
How many sides does a hexagon have?
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.4 18
_____ sides
Answer:
By seeing the above figure we can say that the hexagon contains 6 sides.
a hexagon can be defined as a polygon with six sides

Question 2.
How many vertices does a quadrilateral have?
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.4 19
______ vertices
Answer: By seeing the above figure we can say that the 4 vertices.
A quadrilateral has 4 sides, 4 angles and 4 vertices

Spiral Review
Question 3.
Use a centimeter ruler. What is the length of the ribbon to the nearest centimeter?
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.4 20
Answer: 11 centimeters
Go-Math-2nd-Grade-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.4-20

Question 4.
Look at the picture graph. How many more children chose apples than oranges?
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.4 21
______ children
Answer: 2 more children.

Lesson 11.5 Angles in Two-Dimensional Shapes

Essential Question How do you find and count angles in two-dimensional shapes?

Listen and Draw
Use a ruler. Draw two different triangles. Then draw two different rectangles.
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.5 1

Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.5-1

MATHEMATICAL PRACTICES
Describe a triangle and a rectangle. Tell about their sides and vertices.
Answer:
Triangle is a 3 faced shape with 3 sides and 3 vertices.
The rectangle is a 4 faces shape with 4 sides and 4 vertices.

Share and Show

Circle the angles in each shape. Write how many.
Question 1.
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.5 2
______ angles
Answer: 5 angles.
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.5-2

Question 2.
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.5 3
_____ angles
Answer: 6 angles.
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.5-3

Question 3.
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.5 4
_____ angles
Answer: 4 angles.
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.5-4

Question 4.
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.5 5
_____ angles
Answer: 5 angles
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.5-5

On Your Own
Circle the angles in each shape. Write how many.
Question 5.
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.5 6
______ angles
Answer: 3 angles.
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.5-6

Question 6.
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.5 7
_____ angles
Answer: 4 angles
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.5-7

Question 7.
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.5 8
_____ angles
Answer: 4 angles
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.5-8

Question 8.
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.5 9
_____ angles
Answer: 6 angles.
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.5-9

Question 9.
THINK SMARTER
Draw more sides to make the shape. Write how many angles.
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.5 10
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.5-10

Problem Solving • Applications

Question 10.
Draw two shapes that have 7 angles in all.
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.5 11
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.5-11

Question 11.
Use Diagrams
Ben drew 3 two-dimensional shapes that had 11 angles in all. Draw shapes Ben could have drawn.
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.5 12
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.5-12

Question 12.
THINK SMARTER
Fill in the bubble next to all the shapes that have 5 angles.
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.5 13
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.5-13

TAKE HOME ACTIVITY • Ask your child to draw a shape with 4 sides and 4 angles.

Angles in Two-Dimensional Shapes Homework & Practice 11.5

Circle the angles in each shape. Write how many.
Question 1.
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.5 14
______ angles
Answer: 4 angles.

Question 2.
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.5 15
_____ angles
Answer: 5 angles.

Problem Solving
Question 3.
Logan drew 2 two-dimensional shapes that had 8 angles in all. Draw shapes Logan could have drawn.
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.5 16
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.5-16

Question 4.
WRITE
Draw a two-dimensional shape with 4 angles. Circle the angles. Write the name of the two-dimensional shape you drew.
Answer: Quadrilateral
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.5-7

Lesson Check
Question 1.
How many angles does this shape have?
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.5 17
_____ angles
Answer: 5 angles

Question 2.
How many angles does this shape have?
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.5 18
______ angles
Answer: 3 angles

Spiral Review
Question 3.
Use an inch ruler. What is the length of the string to the nearest inch?
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.5 19
Answer: 14 inch
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.5-19

Question 4.
Look at the picture graph. How many children chose daisies?
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.5 20
_____ children
Answer: 5 childrens.

Lesson 11.6 Sort Two-Dimensional Shapes

Essential Question How do you use the number of sides and angles to sort two-dimensional shapes?

Listen and Draw
Make the shape with pattern blocks. Draw and color the blocks you used.
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.6 1

MATHEMATICAL PRACTICES
Describe how you could sort the blocks you used.
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.6-1

Share and Show

Circle the shapes that match the rule.
Question 1.
Shapes with 5 sides
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.6 2
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.6-2

Question 2.
Shapes with more than 3 angles
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.6 3
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.6-3

Question 3.
Shapes with fewer than 4 angles
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.6 4
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.6-4

Question 4.
Shapes with fewer than 5 sides
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.6 5
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.6-5

On Your Own
Circle the shapes that match the rule.
Question 5.
Shapes with 4 sides
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.6 6
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.6-6

Question 6.
Shapes with more than 4 angles
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.6 7
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.6-7

Question 7.
Shapes with fewer than 4 angles
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.6 8
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.6-8

Question 8.
Shapes with fewer than 5 sides
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.6 9
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.6-9

Question 9.
THINK SMARTER
Draw three shapes that match the rule. Circle them. Then draw two shapes that do not match the rule.
Shapes with fewer than 5 angles
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.6 10
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.6-9 (1)

Problem Solving • Applications

Question 10.
Make Connections
Sort the shapes.

  • Use red to color the shapes with more than 4 sides.
  • Use blue to color the shapes with fewer than 5 angles.
    2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.6 11
    Answer:
    2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.6-11

Question 11.
Draw each shape where it belongs in the chart.
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.6 12
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.6-12

TAKE HOME ACTIVITY • Ask your child to draw some shapes that each have 4 angles.

Sort Two-Dimensional Shapes Homework & Practice 11.6

Circle the shapes that match the rule.
Question 1.
Shapes with fewer than 5 sides
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.6 13
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.6-13

Question 2.
Shapes with more than 4 sides
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.6 14
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.6-14

Problem Solving
Question 3.
Tammy drew a shape with more than 3 angles. It is not a hexagon. Which shape did Tammy draw?
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.6 15
Answer: pentagon
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.6-15
Question 4.
WRITE
Think about the rules Shapes that have more than 3 angles. Draw three shapes that match this rule.
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.6-15

Lesson Check
Question 1.
Which shape has fewer than 4 sides?
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.6 16
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.6-16

Spiral Review
Question 2.
Use an inch ruler. What is the length of the pencil to the nearest inch?
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.6 17
Answer: 14 inch
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.6-17

Question 3.
Use the tally chart. How many children chose basketball as their favorite sport?
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.6 18
_____ children
Answer: 7 children chose basketball as their favorite sport

Lesson 11.7 Partition Rectangles

Essential Question How do you find the total number of same-size squares that will cover a rectangle?

Listen and Draw
Put several color tiles together. Trace around the shape to draw a two-dimensional shape.

HOME CONNECTION • After putting together tiles, your child traced around them to draw a two-dimensional shape. This activity is an introduction to partitioning a rectangle into several same-size squares.

MATHEMATICAL PRACTICES
Is there a different shape that can be made with the same number of tiles? Explain.
Answer:

Share and Show
Use color tiles to cover the rectangle.
Trace around the square tiles. Write how many.
Question 1.
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.7 1
Number of rows: ______
Number of columns: ______
Total: _____ square tiles
Answer:
Go-Math-2nd-Grade-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.7-1
Number of rows: 4
Number of columns: 4
Total: 16 square tiles

Question 2.
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.7 2
Number of rows: ______
Number of columns: ______
Total: _____ square tiles
Answer:
Go-Math-2nd-Grade-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.7-2
Number of rows: 2
Number of columns: 6
Total: 12 square tiles

On Your Own
Use color tiles to cover the rectangle.
Trace around the square tiles. Write how many.
Question 3.
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.7 3
Number of rows: ______
Number of columns: ______
Total: _____ square tiles
Answer:
Go-Math-2nd-Grade-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.7-3
Number of rows: 3
Number of columns: 5
Total: 15 square tiles

Question 4.
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.7 4
Number of rows: ______
Number of columns: ______
Total: _____ square tiles
Answer:
Go-Math-2nd-Grade-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.7-4
Number of rows: 2
Number of columns: 4
Total: 8 square tiles

Question 5.
THINK SMARTER
Mary started to cover this rectangle with ones blocks. Explain how you would estimate the number of ones blocks that would cover the whole rectangle.
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.7 5
Answer: 6 one blocks
Go-Math-2nd-Grade-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.7-5

TAKE HOME ACTIVITY • Have your child describe what he or she did in this lesson.

Partition Rectangles Homework & Practice 11.7

Use color tiles to cover the rectangle.
Trace around the square tiles. Write how many.
Question 1.
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.7 6
Number of rows: ______
Number of columns: ______
Total: _____ square tiles
Answer:
Go-Math-2nd-Grade-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.7-6
Number of rows: 4
Number of columns: 5
Total: 20 square tiles

Question 2.
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.7 7
Number of rows: ______
Number of columns: ______
Total: _____ square tiles
Answer:
Go-Math-2nd-Grade-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.7-7
Number of rows: 2
Number of columns: 4
Total: 8 square tiles

Problem Solving
Solve. Write or draw to explain.
Question 3.
Nina wants to put color tiles on a square. 3 color tiles fit across the top of the square. How many rows and columns of squares will Nina need? How many color tiles will she use in all?
______ tiles
Number of rows: ______
Number of columns: ______
Total: _____ square tiles
Answer:
Go-Math-Answer-Key-Grade-2-Chapter-11-Geometry-and-Fraction-Concepts-11.3-2
Number of rows: 3
Number of columns: 3
Total: 9 square tiles

Question 4.
WRITE
Look at Exercise 1 above. Is there a different-shaped rectangle that you could cover with 6 tiles? Explain.
Answer:

Lesson Check
Question 1.
Use color tiles to cover the rectangle. How many tiles did you use?
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.7 8
_____ tiles
Answer:
Go-Math-2nd-Grade-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.7-8
12 tiles

Spiral Review
Question 2.
How many faces does a cube have?
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.7 9
____ faces
Answer: 6 faces

Question 3.
How many angles does this shape have?
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.7 10
_____ angles
Answer: 6 angles

Question 4.
Use the tally chart. How many more children chose art than reading?
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.7 11
_____ children
Answer: 1 child

Geometry and Fraction Concepts Mid-Chapter Checkpoint

Concepts and Skills
Circle the objects that match the shape name.
Question 1.
cylinder
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.7 12
Answer:
Go-Math-2nd-Grade-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.7-12

Question 2.
cube
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.7 13
Answer:
Go-Math-2nd-Grade-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.7-13

Write the number of sides and the number of vertices.
Question 3.
quadrilateral
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.7 14
_____ sides
______ vertices
Answer:
4 sides
4 vertices

Question 4.
pentagon
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.7 15
_____ sides
_____ vertices
Answer:
4 sides
4 vertices

Question 5.
hexagon
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.7 16
_____ sides
_______ vertices
Answer:
6 sides
6 vertices

Question 6.
THINK SMARTER
How many angles does this shape have?
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts 11.7 17
______ angles
Answer: 5 angles

Lesson 11.8 Equal Parts

Essential Question What are halves, thirds, and fourths of a whole?

Listen and Draw
Put pattern blocks together to match the shape of the hexagon. Trace the shape you made.

MATHEMATICAL PRACTICES
Compare models
Describe how the shapes you used are different from the shapes a classmate used.
Answer:
Other common shapes are points, lines, planes, and conic sections such as ellipses, circles, and parabolas. Among the most common 3-dimensional shapes are polyhedra, which are shapes with flat faces; ellipsoids, which are egg-shaped or sphere-shaped objects, cylinders, and cones.

Share and Show
Write how many equal parts there are in the whole.
Write halves, thirds, or fourths to name the equal parts.
Question 1.
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.8 1
____ equal parts
__________
Answer: 2 equal parts
Halves

Question 2.
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.8 2
____ equal parts
__________
Answer:  3 equal parts
Thirds

Question 3.
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.8 3
____ equal parts
__________
Answer: 4 equal parts
Fourths

Question 4.
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.8 4
____ equal parts
__________
Answer: 3 equal parts
Thirds

Question 5.
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.8 5
____ equal parts
__________
Answer: 2 equal parts
Halves

Question 6.
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.8 6
____ equal parts
__________
Answer: 4 equal parts
Fourths

On Your Own
Write how many equal parts there are in the whole.
Write halves, thirds, or fourths to name the equal parts.
Question 7.
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.8 7
____ equal parts
__________
Answer: 2 equal parts
Halves

Question 8.
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.8 8
____ equal parts
__________
Answer: 4 equal parts
Fourths

Question 9.
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.8 9
____ equal parts
__________
Answer: 3 equal parts
Thirds

Question 10.
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.8 10
____ equal parts
__________
Answer: 3 equal parts
Thirds

Question 11.
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.8 11
____ equal parts
__________
Answer: 4 equal parts
Fourths

Question 12.
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.8 12
____ equal parts
__________
Answer: 2 equal parts
Halves

Question 13.
THINK SMARTER
Draw to show halves. Explain how you know that the parts are halves.
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.8 13
Answer:
Go-Math-Answer-Key-Grade-2-Chapter-11-Geometry-and-Fraction-Concepts-11.8-13

Problem Solving • Applications
Question 14.
Make Connections Sort the shapes.

  • Draw an X on shapes that do not show equal parts.
  • Use red to color the shapes that show thirds.
  • Use blue to color the shapes that show fourths.
    Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.8 14
    Answer:
    Go-Math-Answer-Key-Grade-2-Chapter-11-Geometry-and-Fraction-Concepts-11.8-14

Question 15.
Draw lines to show fourths three different ways.
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.8 15
Explain how you know that the parts are fourths.
___________________
____________________
Answer:

TAKE HOME ACTIVITY • Ask your child to fold one sheet of paper into halves and another sheet of paper into fourths.

Equal Parts Homework & Practice 11.8

Write how many equal parts there are in the whole.
Write halves, thirds, or fourths to name the equal parts.
Question 1.
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.8 16.1
______ equal parts
__________
Answer: 4 equal parts
Fourths

Question 2.
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.8 16
______ equal parts
__________
Answer: 2 equal parts
Halves

Question 3.
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.8 17
______ equal parts
__________
Answer: 3 equal parts
Thirds

Problem Solving
Question 4.
Sort the shapes.

  • Draw an X on the shapes that do not show equal parts.
  • Circle the shapes that show halves
    Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.8 18
    Answer:
    Go-Math-Answer-Key-Grade-2-Chapter-11-Geometry-and-Fraction-Concepts-11.8-18

Question 5.
WRITE
Look at the shapes in Exercise 4. Describe the shapes that you did not put an X on or circle.
____________________
_____________________
Answer:
the shapes that you did not put an X on or circle because other images have half divided quantity

Lesson Check
Question 1.
What are the 3 equal parts of the shape called?
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.8 19
________
Answer: thirds

Question 2.
What are the 4 equal parts of the shape called?
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.8 20
_______
Answer: fourths

Spiral Review
Question 3.
What is the sum?
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.8 21
Answer: 33

Question 4.
What is the difference?
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.8 22
Answer: 44

Question 5.
Circle the quadrilateral.
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.8 23
Answer:
Go-Math-Answer-Key-Grade-2-Chapter-11-Geometry-and-Fraction-Concepts-11.8-23

Question 6.
Circle the hexagon.
Go Math Answer Key Grade 2 Chapter 11 Geometry and Fraction Concepts 11.8 24
Answer:
Go-Math-Answer-Key-Grade-2-Chapter-11-Geometry-and-Fraction-Concepts-11.8-24

Lesson 11.9 Show Equal Parts of a Whole

Essential Question How do you know if a shape shows halves, thirds, or fourths?

Listen and Draw
Circle the shapes that show equal parts.
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.9 1
Answer:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.9-1

HOME CONNECTION • Your child completed this sorting activity with shapes to review the concept of equal parts.

MATHEMATICAL PRACTICES
Does the triangle show halves? Explain.
Answer: Yes,if the triangle id divided exactly at an angle of 90 degrees then it can be cut half.

Share and Show
Draw to show equal parts.
Question 1.
thirds
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.9 2
Answer:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.9-2

Question 2.
halves
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.9 3
Answer:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.9-3

Question 3.
fourths
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.9 4
Answer:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.9-4

Question 4.
halves
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.9 5
Answer:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.9-5

Question 5.
fourths
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.9 6
Answer:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.9-6

Question 6.
thirds
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.9 7
Answer:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.9-7

On Your Own
Draw to show equal parts.
Question 7.
halves
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.9 8
Answer:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.9-8

Question 8.
fourths
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.9 9
Answer:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.9-9

Question 9.
thirds
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.9 10
Answer:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.9-10

Question 10.
thirds
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.9 11
Answer:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.9-11

Question 11.
halves
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.9 12
Answer:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.9-12

Question 12.
fourths
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.9 13
Answer:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.9-13

Question 13.
halves
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.9 14
Answer:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.9-14

Question 14.
thirds
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.9 15
Answer:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.9-15

Question 15.
fourths
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.9 16
Answer:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.9-16

Question 16.
Does this shape show thirds? Explain.
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.9 17
Answer: No,The square is divided into three but thry are not equally divided.

Problem Solving • Applications
Question 17.
Colton and three friends want to share a pizza equally. Draw to show how the pizza should be divided.
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.9 18
Answer:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.9-18

Question 18.
GO DEEPER
There are two square pizzas. Each pizza is cut into fourths. How many pieces of pizza are there?
______ pieces
Answer: 8 Pieces

Question 19.
THINK SMARTER
Fill in the bubble next to the shapes that show thirds. Explain your answer.
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.9 19
________________
________________
Answer: The bubbled shapes are equally divided into thirds.
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.9-19

TAKE HOME ACTIVITY • Have your child describe how to show equal parts of a shape.

Show Equal Parts of a Whole Homework & Practice 11.9

Draw to show equal parts.
Question 1.
halves
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.9 20
Answer:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.9-20

Question 2.
fourths
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.9 21
Answer:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.9-21

Question 3.
thirds
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.9 22
Answer:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.9-22

Question 4.
thirds
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.9 23
Answer:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.9-23Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.9-23

Question 5.
halves
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.9 24
Answer:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.9-24

Question 6.
fourths
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.9 25
Answer:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.9-25

Problem Solving
Solve. Write or draw to explain.
Question 7.
Joe has one sandwich. He cuts the sandwich into fourths. How many pieces of sandwich does he have?
_____ pieces
Answer: 4 pieces

Question 8.
WRITE
Draw three rectangles. Then draw to show halves, thirds, and fourths. Write about each whole that you have drawn.
Answer:

Lesson Check
Question 1.
Circle the shape divided into fourths.
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.9 26
Answer:
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.9-26

Spiral Review
Question 2.
How many angles does this shape have?
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.9 27
______ angles
Answer: 5 angles

Question 3.
How many faces does a rectangular prism have?
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.9 28
______ Faces
Answer: 6 faces

Question 4.
Use a centimeter ruler. Measure the length of each object. How much longer is the ribbon than the string?
Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts 11.9 29
_____ centimeter long
Answer:
5 centimeter long
Go-Math-Grade-2-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.9-29

Lesson 11.10 Describe Equal Parts

Essential Question How do you find a half of, a third of, or a fourth of a whole?

Listen and Draw
Find shapes that show fourths and color them green.
Find shapes that show halves and color them red.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.10 1
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.10-1

HOME CONNECTION • Your child identified the number of equal parts in shapes to review describing equal parts of a whole.

MATHEMATICAL PRACTICES
Describe how the thirds in the unshaded shapes compare to each other.
Answer: In both the rectangles the thirds are equally divided but one is divided horizontally and the other is divided vertically, And the circle is equally divided into three.

Share and Show
Draw to show thirds.
Color a third of the shape.
Question 1.
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.10-2
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.10-2

Question 2.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.10 3
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.10-3

Question 3.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.10 4
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.10-4

Draw to show fourths.
Color a fourth of the shape.
Question 4.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.10 5
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.10-5

Question 5.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.10 6
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.10-6

Question 6.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.10 7
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.10-7

On Your Own
Draw to show halves.
Color a half of the shape
Question 7.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.10 8.1
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.10-8.1

Question 8.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.10 8.1
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.10-8

Question 9.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.10 9
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.10-9Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.10-9

Draw to show thirds.
Color a third of the shape.
Question 10.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.10 10
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.10-10

Question 11.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.10 11
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.10-11

Question 12.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.10 12
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.10-12

Draw to show fourths.
Color a fourth of the shape.
Question 13.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.10 13
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.10-14

Question 14.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.10 14
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.10-14

Question 15.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.10 15
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.10-15

Problem Solving • Applications
Question 16.
THINK SMARTER
Two posters are the same size. A third of one poster is red, and a fourth of the other poster is blue.
Is the red part or the blue part larger? Draw and write to explain.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.10 16
Answer:

Question 17.
THINK SMARTER
Draw to show halves, thirds, and fourths. Color a half, a third, or a fourth of the shape.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.10 17
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.10-17

Describe Equal Parts Homework & Practice 11.10

Draw to show halves.
Color a half of the shape.
Question 1.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.10 18
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.10-18

Question 2.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.10 19
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.10-19

Draw to show thirds.
Color a third of the shape.
Question 3.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.10 20
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.10-20

Question 4.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.10 21
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.10-21

Problem Solving
Question 5.
Circle all the shapes that have a third of the shape shaded.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.10 22
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.10-22 (1)

Question 6.
WRITE
Draw pictures to show a third of a whole and a fourth of a whole. Label each picture.
Answer:

Lesson Check
Question 1.
Circle the shape that is half-shaded.
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.10 23
Answer:
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.10-23

Spiral Review
Question 2.
What is the name of this shape?
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.10 24
_________
Answer: Hexagon

Question 3.
Use a centimeter ruler. What is the length of the string to the nearest centimeter?
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.10 25
______ centimeters
Answer:

Question 4.
The clock shows the time Chris finished his homework. What time did Chris finish his homework?
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.10 26
Answer: 0610
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.10-26

Question 5.
What time is shown on this clock?
Go Math Grade 2 Chapter 11 Answer Key Pdf Geometry and Fraction Concepts 11.10 27
Answer: 0815
Go-Math-Grade-2-Chapter-11-Answer-Key-Pdf-Geometry-and-Fraction-Concepts-11.10-27

Lesson 11.11 Problem Solving • Equal Shares

Essential Question How can drawing a diagram help when solving problems about equal shares?

There are two sandwiches that are the same size. Each sandwich is divided into fourths, but the sandwiches are cut differently. How might the two sandwiches be cut?
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.11 1

Unlock the Problem
What information do
I need to use?
There are ______ sandwiches.
Each sandwich is divided into _______
Answer: There are 2 sandwiches.
Each sandwich is divided into fourths.

Show how to solve the problem.
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.11 2
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.11-2

HOME CONNECTION • Your child drew a diagram to represent and solve a problem about dividing a whole in different ways to show equal shares.

Try Another Problem
Draw to show your answer.
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.11 3
Question 1.
Marquis has two square sheets of paper that are the same size. He wants to cut each sheet into halves. What are two different ways he can cut the sheets of paper?
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.11 4
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.11-4

Question 2.
Shanice has two pieces of cloth that are the same size. She needs to divide each piece into thirds. What are two different ways she can divide the pieces of cloth?
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.11 5
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.11-5

Share and Show

Draw to show your answer.
Question 3.
Brandon has two pieces of toast that are the same size. What are two different ways he can divide the pieces of toast into halves?
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.11 6
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.11-6

Question 4.
Mr. Rivera has two small trays of pasta that are the same size. What are two different ways he can cut the pasta into fourths?
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.11 7
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.11-7

Question 5.
THINK SMARTER
Erin has two ribbons that are the same size. What are two different ways she can divide the ribbons into thirds?
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.11 8
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.11-8

Problem Solving • Applications

Solve. Write or draw to explain.
Question 6.
Use Diagrams
David needs to divide two pieces of paper into the same number of equal shares. Look at how the first paper is divided. Show how to divide the second paper a different way.
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.11 9
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.11-9

Question 7.
GO DEEPER
Mrs. Lee cut two sandwiches into halves. How many equal shares does she have?
_______ equal shares
Answer: 2 equal shares

Question 8.
THINK SMARTER
Emma wants to cut a piece of paper into fourths. Fill in the bubble next to all the ways she could cut the paper.
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.11 10
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.11-10

TAKE HOME ACTIVITY • Ask your child to draw two rectangles and show two different ways to divide them into fourths.

Problem Solving • Equal Shares Homework & Practice 11.11

Draw to show your answer.
Question 1.
Max has square pizzas that are the same size. What are two different ways he can divide the pizzas into fourths?
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.11 11
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.11-11

Question 2.
Lia has two pieces of paper that are the same size. What are two different ways she can divide the pieces of paper into halves?
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.11 12
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.11-12

Question 3.
WRITE
Draw and write to explain how you can divide a rectangle into thirds in two different ways.
Answer: We can divide or partition a rectangle into thirds in two different ways by dividing the rectangle either horizontally or vertically
Such that each partition that is created on dividing it have equal area or equal share of the original rectangle and hence the partitions are similar.

Lesson Check
Question 1.
Bree cut a piece of cardboard into thirds like this.
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.11 13
Circle the other shape that is divided into thirds.
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.11 14
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.11-14

Spiral Review
Question 2.
Circle the shape with three equal parts.
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.11 15
Answer:
2nd-Grade-Go-Math-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-11.11-15

Question 3.
How many angles does this shape have?
2nd Grade Go Math Answer Key Chapter 11 Geometry and Fraction Concepts 11.11 16
______ angles
Answer: 5 angles

Question 4.
What is the best estimate for the width of a door?
_____ feet
Answer: 3 feet

Question 5.
Which is another way to write 10 minutes after 9?
_____ : _____
Answer: 0910

Geometry and Fraction Concepts Review/Test

Question 1.
Match the shapes.
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts rt 1
Answer:
Go-Math-2nd-Grade-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-rt-1

Question 2.
Do the sentences describe a cube?
Choose Yes or No.
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts rt 2
Rewrite each sentence with a mistake to make it a true sentence.
________________________
_______________________
Answer:
Go-Math-2nd-Grade-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-rt-2
A cube has 6 faces.
A cube has 8 vertuces.
A cube has 12 edges.
Each face of a cube is a square.

Question 3.
Draw lines to show thirds.
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts rt 3
Explain how you know that the parts are thirds.
__________________
_________________
Answer: Both the shaps are cut into thirds horizontally.
Go-Math-2nd-Grade-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-rt-3

Question 4.
Will and Ana have gardens that are the same size. They divide their gardens into fourths. What are two different ways they can divide the gardens? Draw to show your answer.
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts rt 4
Answer:
Go-Math-2nd-Grade-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-rt-4

Question 5.
Draw to show halves, thirds, and fourths. Color a half, a third, and a fourth.
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts rt 5
Answer:
Go-Math-2nd-Grade-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-rt-5

Question 6.
Max wants to cover the rectangle with blue tiles. Explain how you would estimate the number of blue tiles he would need to cover the rectangle.
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts rt 6
Answer: 5 tiles

Question 7.
THINK SMARTER +
Jenna built this rectangular prism. Circle the number of unit cubes Jenna used.
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts rt 7
Answer:
Go-Math-2nd-Grade-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-rt-7

Question 8.
Rachel makes a pentagon and a quadrilateral with toothpicks. She uses one toothpick for each side of a shape. How many toothpicks does Rachel need?
_____ toothpicks
Answer:
Given,
Rachel makes a pentagon and a quadrilateral with toothpicks. She uses one toothpick for each side of a shape.
Pentagon consists of 5 sides
Quadrilateral consits of 4 sides
5 + 4 = 9
Thus there are 9 toothpicks.
9 toothpicks

Question 9.
Kevin drew 2 two-dimensional shapes that had 9 angles in all. Draw the shapes Kevin could have drawn.
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts rt 8
Answer:
Go-Math-2nd-Grade-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-rt-8

Question 10.
Fill in the bubble next to the shapes that show fourths.
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts rt 10
Answer:
Go-Math-2nd-Grade-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-rt-10

Question 11.
GO DEEPER
Draw each shape where it belongs in the chart.
Go Math 2nd Grade Answer Key Chapter 11 Geometry and Fraction Concepts rt 11
Answer:
By using the above figure we can draw shapes with 3 and shapes with more than 3 angles in the table.
Go-Math-2nd-Grade-Answer-Key-Chapter-11-Geometry-and-Fraction-Concepts-rt-11

Conclusion:

Make use of the above links and start practicing the problems provided in Go Math Grade 2 Answer Key Chapter 11 Geometry and Fraction Concepts. Students who feel geometry as a difficult chapter can Download Grade 2 Go Math Chapter 11 Geometry and Fraction Concepts Answer key pdf for free. Share the pdf link with your friends and help them to score good marks in the exams.