Big Ideas Math Algebra 2 Answers PDF Download | Free BIM Algebra 2 Textbook Solution Key

Big Ideas Math Algebra 2 Answers

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Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures

Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures

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Big Ideas Math Book 6th Grade Answer Key Chapter 9 Statistical Measures

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Performance Task

Lesson: 1 Introduction to Statistics

Lesson: 2 Mean

Lesson: 3 Measures of Center

Lesson: 4 Measures of Variation

Lesson: 5 Mean Absolute Deviation

Chapter 9: Statistical Measures

Statistical Measures STEAM Video/Performance Task

STEAM Video
Daylight in the Big City
Averages can be used to compare different sets of data. How can you use averages to compare the amounts of day light in different cities? Can you think of any other real-life situations where averages are useful?
Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 1
Watch the STEAM Video “Daylight in the Big City.” Then answer the following questions.
1. Why do different cities have different amounts of daylight throughout the year?

Answer:
Our amount of daylight hours depends on our latitude and how Earth orbits the sun. This causes a seasonal variation in the intensity of sunlight reaching the surface and the number of hours of daylight. The variation in intensity results because the angle at which the sun’s rays hit the Earth changes with the time of year.

2. Robert’s table includes the difference of the greatest amount of daylight and the least amount of daylight in Lagos, Nigeria, and in Moscow, Russia.
Lagos: 44 minutes
Moscow:633 minutes
Use these values to make a prediction about the difference between the greatest amount of daylight and the least amount of daylight in a city in Alaska.

Answer:
The least daylight in Alaska is 1092 minutes in Juneau
The greatest daylight in Alaska is 1320 minutes in Fairbanks

Performance Task
Which Measure of Center Is Best: Mean, Median, or Mode?
After completing this chapter, you will be able to use the concepts you learned to answer the questions in the STEAM Video Performance Task. You will be given the greatest and least amounts of daylight in the 15 cities in the United States with the greatest populations.
s
Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 3
You will determine which measure of center best represents the data. Why might someone be interested in the amounts of daylight throughout the year in a city?

Statistical Measures Getting Ready for Chapter 9

Chapter Exploration
Work with a partner. Write the number of letters in each of your first names on the board.
Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 4
1. Write all of the numbers on a piece of paper. The collection of numbers is called data.
2. Talk with your partner about how you can organize the data. What conclusions can you make about the numbers of letters in the first names of the students in your class?
3. Draw a grid like the one shown below. Then use the grid to draw a graph of the data.
Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 5

Answer:
3,6,9,5,6,7,6,5,5,8,6,8,5,6,4,4,7,6,3,5,6,5,5

4. THE CENTER OF THE DATA Use the graph of the data in Exercise 3 to answer the following.
a. Is there one number that occurs more than any of the other numbers? If so, write a sentence that interprets this number in the context of your class.
b. Complete the sentence, “In my class, the average number of letters in a student’s first name is __________.” Justify your reasoning.
c. Organize your data using a different type of graph. Describe the advantages or disadvantages of this graph.

Answer:
a. Yes, 6, 5, 8 are more than other numbers given in the data.
b. “In my class, the average number of letters in a student’s first name is 5 and 6.

Vocabulary
The following vocabulary terms are defined in this chapter. Think about what each term might mean and record your thoughts.
statistical question
measure of center
measure of variation
mean
median
range

Lesson 9.1 Introduction to Statistics

EXPLORATION 1

Using Data to Answer a Question
Work with a partner.
a. Use your pulse to find your heart rate in beats per minute.
Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.1 1
b. Collect the recorded heart rates of the students in your class, including yourself. How spread out are the data? Use a diagram to justify your answer.
c. REASONING How would you answer the following question by using only one value? Explain your reasoning.
“What is the heart rate of a sixth-grade student?”
Answer: Your pulse is measured by counting the number of times your heart beats in one minute. For example, if your heart contracts 72 times in one minute, your pulse would be 72 beats per minute (BPM).

EXPLORATION 2

Identifying Types of Questions
Work with a partner.
a. Answer each question on your own. Then compare your answers with your partner’s answers. For which questions should your answers be the same? For which questions might your answers be different?
1. How many states are in the United States?
Answer: There are 50 states in the United States.

2. How much does a movie ticket cost? Math Practice
Answer: $9.16
3. What color fur do bears have? Build Arguments How can comparing your answers help you support your conjecture?
Answer: The color white becomes visible to our eyes when an object reflects back all.

4. How tall is your math teacher?
Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.1 2
b. CONJECTURE
Some of the questions in part(a) are considered statistical questions. Which ones are they? Explain.
Answer: 5.10 inches

Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.1 3

Statistics is the science of collecting, organizing, analyzing, and interpreting data. A statistical question is one for which you do not expect to get a single answer. Instead, you expect a variety of answers, and you are interested in the distribution and tendency of those answers.

Try It
Determine whether the question is a statistical question. Explain.
Question 1.
What types of cell phones do students have in your class?
Answer:
Smartphones, Cell phones give students access to tools and apps that can help them complete and stay on top of their class work. These tools can also teach students to develop better study habits, like time management and organization skills.

Question 2.
How many desks are in your classroom?
Answer: 25

Question 3.
How much do virtual-reality headsets cost?
Answer: $499

Question 4.
How many minutes are in your lunch period?
Answer: 45 minutes

A dot plot uses a number line to show the number of times each value in a data set occurs. Dot plots show the spread and the distribution of a data set.

Question 5.
Repeat parts (a)–(c)using the dot plot below that shows the times of students in a 100-meter race.
Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.1 7
Answer:

Self-Assessment for Concepts & Skills

Solve each exercise. Then rate your understanding of the success criteria in your journal.
Question 6.
VOCABULARY
What is a statistical question? Give an example and a non-example.
Answer:
Eg for statistical question: a. How much do bags of pretzels cost at the grocery store?
Because you can anticipate that the prices will vary, it is a statistical question. table at the right may represent the prices of several bags of pretzels at a grocery store.
Eg for non-statistical question: b. How many days does your school have off for spring break this year?
Answer: Because there is only one answer, it is not a statistical question.

Question 7.
OPEN-ENDED
Write and answer a statistical question using the dot plot. Then find and interpret the number of data values.
Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.1 8
Answer: There are 16 data values on the dot plot.

Question 8.
You record the amount of snowfall each day for several days. Then you create the dot plot.
Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.1 11
a. Find and interpret the number of data values on the dot plot.
Answer: There are 13 data values on the dot plot.

b. How can you collect these data? What are the units?
Answer: We can collect the data by using the dots given in the above figure.
c. Write a statistical question that you can answer using the dot plot. Then answer the question.
Answer: dot plots are best used to show a distribution of data.

Question 9.
You conduct a survey to answer, “How many hours does a typical sixth-grade student spend exercising during a week?” Use the data in the table to answer the question.
Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.1 12
Answer:
Given the data
5, 1, 5, 3, 5, 4, 5, 2, 5, 4, 3, 4, 6, 5, 6
The typical sixth-grade student spend exercising during a week is 6 hours.

Introduction to Statistics Homework & Practice 9.1

Review & Refresh

Solve the inequality. Graph the solution.
Question 1.
x – 16 > 8
Answer: x>3.

big ideas math answers grade 6 chapter 9 statistical measures img_1

Question 2.
p + 6 ≤ 8
Answer:   p ≤ 2

big ideas math answers grade 6 chapter 9 statistical measures img_2

Question 3.
54 > 6k
Answer: 9>k

big ideas math answers grade 6 chapter 9 statistical measures img_3

Question 4.
\(\frac{m}{12}\) ≥ 3
Answer: m ≤ 36

Tell whether the ordered pair is a solution of the equation.
Question 5.
y = 4x; (2, 8)
Answer: The given ordered pair is a solution of the equation.
Given : y = 4x;(2,8)
y=8;x=2
8=4 × 2
8=8 (satisfied)

Question 6.
y = 3x + 5; (3, 15)
Answer: Given order pair is not an absolute solution of ordered pair
Given: y = 3x + 5; (3, 15)
y=15;x=3
15=3(3)+5
15=9+5
15=14 (not satisfied)

Question 7.
y = 6x – 15; (4, 9)
Answer:
The given ordered pair is a solution of the equation.
Given: y = 6x – 15; (4, 9)
9=6(4)-15
9=24-15
9=9

Question 8.
A point is reflected in the x-axis. The reflected point is (4, −3). What is the original point?
A. (-3, 4)
B. (-4, 3)
C. (-4, -3)
D. (4, 3)
Answer: B,(-4,3)

Order the numbers from least to greatest.
Question 9.
24%, \(\frac{1}{4}\) , 0.2, \(\frac{7}{20}\) , 0.32
Answer:0.24,0.25,0.2.0.35,0.32
0.2,0.24,0.32,0.35

Question 10.
\(\frac{7}{8}\), 85%, 0.88, \(\frac{3}{4}\) , 78%
Answer:0.875,0.78,0.88,0.75,0.78
0.75,0.78,0.85,0.875,0.88

Concepts, Skills, &Problem Solving

IDENTIFYING TYPES OF QUESTIONS Answer the question. Tell whether your answer should be the same as your classmates’. (See Exploration 2, p. 413.)
Question 11.
How many inches are in 1 foot?
Answer: 12 inches

Question 12.
How many pets do you have?
Answer: none

Question 13.
On what day of the month were you born?
Answer: 27th April

Question 14.
How many senators are in Congress?
Answer: The Senate is composed of 100 Senators, 2 for each state. Until the ratification of the 17th Amendment in 1913, Senators were chosen by state legislatures, not by popular vote. Since then, they have been elected to six-year terms by the people of each state.

IDENTIFYING STATISTICAL QUESTIONS
Determine whether the question is a statistical question. Explain.
Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.1 13
Question 15.
What are the eye colors of sixth-grade students?
Answer: brown

Question 16.
At what temperature (in degrees Fahrenheit) does water freeze?
Answer: 32 degrees Fahrenheit

Question 17.
How many pages are in the favorite books of students your age?
Answer: 200 pages

Question 18.
How many hours do sixth-grade students use the Internet each week?
Answer: 1.5 hour each

Question 19.
MODELING REAL LIFE
The vertical dot plot shows the heights of the players on a recent NBA championship team.
a. Find and interpret the number of data values on the dot plot.
b. How can you collect these data? What are the units?
c. Write a statistical question that you can answer using the dot plot. Then answer the question.
Answer:

Question 20.
MODELING REAL LIFE
The dot plot shows the lengths of earthworms.
Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.1 14
a. Find and interpret the number of data values on the dot plot.
Answer: There are 21 data values on the plot.
b. How can you collect these data? What are the units?
Answer: Based on dot plots and units are measured in mm.
c. Write a statistical question that you can answer using the dot plot. Then answer the question.
Answer: Find the mode of the length of earthworms using the dot plot.
23 is repeated times.
So, the mode is 23.

DESCRIBING DATA
Display the data in a dot plot. Identify any clusters, peaks, or gaps in the data.
Question 21.
Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.1 15
Answer:
bim grade 6 chapter 9 statictical measures answers key img_5

Data are clustered around 22 and around 25
Peak at 25
The gap between 16 and 21

Question 22.
Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.1 16
Answer:
bim grade 6 chapter 9 statictical measures answers key img_6

No clusters
Peak at 83
No gaps

INTERPRETING DATA
The dot plot shows the speeds of cars in a traffic study. Estimate the speed limit. Explain your reasoning.
Question 23.
Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.1 17
Answer: Most of the data clustered around 44 and 45 , hence the estimated speed is between 44-45 miles per hour

Question 24.
Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.1 18
Answer: Most of the data clustered around 65 , there is a peak at 65 and gaps between”60-62″ and 63-65.

Question 25.
DIG DEEPER!
You conduct a survey to answer, “How many hours does a sixth-grade student spend on homework during a school night?” The table shows the results.
Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.1 19
a. Is this a statistical question? Explain.
Answer: yes, it is a statistical question because students work in the different time zone based on individual student capacity.
b. Identify any clusters, peaks, or gaps in the data.
Answer: cluster is around 2. There is a peak at 2 and there is no gap.
c. Use the distribution of the data to answer the question.
Answer: A total of 29 data values are distributed.

RESEARCH
Use the Internet to research and identify the method of measurement and the units used when collecting data about the topic.
Question 26.
wind speed
Answer: The instruments used to measure wind are known as anemometers and can record wind speed, direction, and the strength of gusts. The normal unit of wind speed is the knot (nautical mile per hour = 0.51 m sec-1 = 1.15 mph).

Question 27.
amount of rainfall
Answer:
The standard instrument for the measurement of rainfall is the 203mm (8 inches) rain gauge. This is essentially a circular funnel with a diameter of 203mm which collects the rain into a graduated and calibrated cylinder. The measuring cylinder can record up to 25mm of precipitation

Question 28.
earthquake intensity
Answer: The Richter scale measures the largest wiggle (amplitude) on the recording, but other magnitude scales measure different parts of the earthquake. The USGS currently reports earthquake magnitudes using the Moment Magnitude scale, though many other magnitudes are calculated for research and comparison purposes.

Question 29.
REASONING
Write a question about letters in the English alphabet that is not a statistical question. Then write a question about letters that is a statistical question. Explain your reasoning.
Answer: Statistical Question: How many letters in the English alphabet are used to spell a student’s name in class?
Reasoning: The original question has one answer. This Question will have many answers.

Question 30.
REASONING
A bar graph shows the favorite colors of 30 people. Does it make sense to describe clusters in the data? peaks? gaps? Explain.
Answer: No, It doesn’t make sense to describe the distribution. Colors are not measures numerically.

Lesson 9.2 Mean

EXPLORATION 1

Finding a Balance Point
Work with a partner. The diagrams show the numbers of tokens brought to a batting cage. Where on the number line is the data set balanced ? Is this a good representation of the average? Explain.
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures 9.2 1

EXPLORATION 2

Finding a Fair Share
Work with a partner. One token lets you hit 12 baseballs in a batting cage. The table shows the numbers of tokens six friends bring to the batting cage.
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures 9.2 2
a. Regroup the tokens so that everyone has the same amount. How many times can each friend use the batting cage? Explain how this represents a “fair share. “Use Clear Definitions What does it mean for data to have an average? How does this help you answer the question?
b. how can you find the answer in part(a) algebraically?
c. Write a statistical question that can be answered using the value in part(a).
Answer:

Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures 9.2 3

Try It

Find the mean of the data.
Question 1.
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures 9.2 6
Answer:
The sum of the data/no of values
The sum of the data=45+54+13+44+89+60+9+18;
no of values=8
The sum of the data=332:no of values=8; 332/8=41.5 is the mean of the data

Question 2.
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures 9.2 7
Answer:
555 is mean for the above-given data.

Question 3.
WHA IT?
The monthly rainfall in May was 0.5 inch in City A and 2 inches in City B. Does this affect your answer in Example 2? Explain.
Answer:

Self-Assessment for Concepts & Skills

Solve each exercise. Then rate your understanding of the success criteria in your journal.
Question 4.
NUMBER SENSE
Is the mean always equal to a value in the data set? Explain.
Answer: It is the value that is most common. You will notice, however, that the mean is not often one of the actual values that you have observed in your data set. In addition, the mean is the only measure of central tendency where the sum of the deviations of each value from the mean is always zero.

Question 5.
WRITING
Explain why the mean describes a typical value in a data set.
Answer:
A measure of central tendency is a single value that attempts to describe a set of data by identifying the central position within that set of data. The mean (often called the average) is most likely the measure of central tendency that you are most familiar with, but there are others, such as the median and the mode.

Question 6.
NUMBER SENSE
What can you determine when the mean of one data set is greater than the mean of another data set? Explain your reasoning.
Answer:

Question 7.
COMPARING MEANS
Compare the means of the data sets.
Data set A: 43, 32, 16, 41, 24, 19, 30, 27
Data set B: 44, 18, 29, 24, 36, 22, 26, 21
Answer:
An outlier is a data value that is much greater or much less than the other values. When included in a data set, it can affect the mean.

Question 8.
DIG DEEPER!
The monthly numbers of customers at a store in the first half of a year are 282, 270, 320, 351, 319, and 252. The monthly numbers of customers in the second half of the year are 211, 185, 192, 216, 168, and 144. Compare the mean monthly customers in the first half of the year with the mean monthly customers in the second half of the year.
Answer:

Question 9.
The table shows tournament finishes for a golfer. What place does the golfer typically finish in tournaments? Explain how you found your answer.
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures 9.2 12
Answer: Mean=sum of data/number of data values
Mean=118/16
Mean=7.375
a. The golfer’s mean finish was about 7th
b. The finishes 37 and 26 are much greater than other finishes. They are outliers

Mean Homework & Practice 9.2

Review & Refresh

Determine whether the question is a statistical question. Explain.
Question 1.
How tall are sixth-grade students?
Answer: The average height for a sixth grader (age 12) is about five feet. Girls tend to be about an inch taller on average. But there is a wide range. Any height from about 52 inches (4′4″) to 65 inches (5′5″) is in the normal range according to the CDC.

Question 2.
How many minutes are there in 1 Year?
Answer:
An average Gregorian year is 365.2425 days (52.1775 weeks, 8765.82 hours, 525949.2 minutes, or 31556952 seconds). For this calendar, a common year is 365 days (8760 hours, 525600 minutes, or 31536000 seconds), and a leap year is 366 days (8784 hours, 527040 minutes, or 31622400 seconds).

Question 3.
How many counties are in Tennessee?
Answer: Tennessee’s 95 counties are divided into four TDOT regions. Regional offices are located in Jackson (Region 4), Nashville (Region 3), Chattanooga (Region 2), and Knoxville (Region 1).

Question 4.
What is a student’s favorite sport?
Answer: cricket

Write the percent as a fraction or mixed number in simplest form.
Question 5.
84%
Answer:0.84

Question 6.
71%
Answer:0.71

Question 7.
353%
Answer:3.53

Question 8.
0.2%
Answer:0.002

Divide. Check your answer.
Question 9.
11.7 ÷ 9
Answer:1.3

Question 10.
\(\sqrt [ 5 ]{ 72.8 } \)
Answer: 2.35

Question 11.
\(\sqrt [ 6.8 ]{ 28.56 } \)
Answer: 1.63

Question 12.
93 ÷ 3.75
Answer:24.8

Concepts, Skills, & Problem Solving

FINDING A FAIR SHARE Regroup the amounts so that each person has the same amount. What is the amount? (See Exploration 2, p. 419.)
Question 13.
Dollars brought by friends to a fair: 11, 12, 12, 12, 12, 12, 13
Answer:
Given : 11,12,12,12,12,12,13.
Mean=Sum of data/number of data values
Mean=84/7
Mean=12
Answer = 12 dollars for each friend

Question 14.
Tickets earned by friends playing an arcade game: 0, 0, 0, 1, 1, 2, 3
Answer:
Given : 0,0,0,1,1,2,3.
Mean=Sum of data/number of data values
Mean= 7/7
Mean=1
Answer = 1 Tickets each friend

FINDING THE MEAN
Find the mean of the data.
Question 15.
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures 9.2 13
Answer: 2 is the mean of the data.

Question 16.
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures 9.2 14
Answer: 3 is the mean of the above-given data.

Question 17.
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures 9.2 15
Answer: 103 is the mean of the above-given data

Question 18.
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures 9.2 16
Answer: 14.8 is the mean of the above-given data.

Question 19.
MODELING REAL LIFE
You and your friends are watching a television show. One of your friends asks, “How long are the commercial breaks during this show?”Break Times (minutes)
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures 9.2 17
a. Is this a statistical question? Explain.
Answer: Yes it is a statistical question.

b.Use the mean of the values in the table to answer the question.
Answer:
Given the data,
4.2, 3.5, 4.55, 2.75, 2.25
x̄ = (4.2 + 3.5 + 4.55 + 2.75 + 2.25)/5
x̄ = 17.25/5
= 3.45

Question 20.
MODELING REAL LIFE
The table shows the monthly rainfall amounts at a measuring station.
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures 9.2 18
a. What is the mean monthly rainfall?
Answer:
x̄ = (22.5 + 1.51 + 1.86 + 2.06 + 3.48 + 4.47 + 3.37 + 5.40 + 5.45 + 4.34 + 2.64 + 2.14)/12
= 33.54/12
= 2.795

b. Compare the mean monthly rainfall for the first half of the year with the mean monthly rainfall for the second half of the year.
Answer:
Mean:
x̄ = (22.5 + 1.51 + 1.86 + 2.06 + 3.48 + 4.47)/6
= 15.6/6
= 2.6
For second 6 months:
x̄ = (3.37 + 5.40 + 5.45 + 4.34 + 2.64 + 2.14)/6
= 23.34/6
= 3.89
The mean value of the second 6 months is greater than the first 6 months.

Question 21.
OPEN-ENDED
Create two different data sets that have six values and a mean of 21.
Answer:
Mean of 21:
Set 1:
12, 31, 21, 24, 13, 25 for these numbers we can calculate the mean we get 21
Set 2:
12, 31, 20, 30, 10, 18 for these numbers we can calculate the mean we get 21

Question 22.
MODELING REAL LIFE
The bar graph shows your cell phone data usage for five months. Describe how the outlier affects the mean. Then use the data to answer the statistical question, “How much cell phone data do you use in a month?”
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures 9.2 19
Answer: 288 is a lot less than the other data values so it is an outlier
Mean with outlier=10/5
Mean with outlier = 2
Mean without outlier = 6.18/5
Mean without outlier = 1.236
The outlier causes the mean to be about 0.76 data usage.

Question 23.
MODELING REAL LIFE
The table shows the heights of the volleyball players on two teams. Compare the mean heights of the two teams. Do outliers affect either mean? Explain.
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures 9.2 20
Answer:
Dolphins=59+65+53+56+58+61+64+68+51+56+54+57=702
Total no of observations=12;Mean=702\12=58.5
Tigers=63+68+66+58+54+55+61+62+53+70+64+64=683
Total no of observations=12; Mean=683/12=56.9

Question 24.
REASONING
Use a dot plot to explain why the mean of the data set below is the point where the data set is balanced.
11, 13, 17, 15, 12, 18, 12
Answer:
mean = (11 + 13 + 17 + 15 + 18 + 12)/6
= 86/6
= 14.3

Question 25.
DIG DEEPER!
In your class, 7 students do not receive a weekly allowance, 5 students receive $3, 7 students receive $5, 3 students receive $6, and 2 students receive $8.
a. What is the mean weekly allowance? Explain how you found your answer.
b. A new student who joins your class receives a weekly allowance of $3.50. Without calculating, explain how this affects the mean.
Answer:
Given number of students receive no amount = 7
Number of students receive $3 = 5
Then, total amount 5 students receive = 5 × 3 = $15
Then, total amount 7 students receive = 5 × 7 = $35
Number of students receive $6 = 3
Then total amount 3 students receive = 6 × 3 = $18
Number of students receive $8 = 2
Then, total amount 2 students receive = 2 × 8 = $16
Now, the total amount all students receive =
15 + 35 + 18 + 6 = 84
The total students = 7 + 5 + 7 + 3 + 2 = 24
Mean = total amount/total amount = 84/24 = $3.5
Hence, the mean weekly allowance is $3.5

Question 26.
PRECISION
A collection of 8 geodes has a mean weight of 14 ounces. A different collection of 12 geodes has a mean weight of 14 ounces. What is the mean weight of the 20 geodes? Explain how you found your answer.
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures 9.2 21
Answer:
Given,
A collection of 8 geodes has a mean weight of 14 ounces.
A different collection of 12 geodes has a mean weight of 14 ounces.
Total weight of the first 8 backpacks
8×14
112 pounds
Total weight of the second 12 backpacks
12×9
108
Total weight of the whole 20 backpacks
112+108
220
So the mean weight of the 20 backpacks
220 / 20
11

Lesson 9.3 Measures of Center

EXPLORATION 1

Finding the Median
Work with a partner.
a. Write the total numbers of letters in the first and last names of 15 celebrities, historical figures, or people you know. One person is already listed for you.
Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 1

Dr. B. R. Ambedkar-8
Otto von Bismarck-15
A. P. J. Abdul Kalam-10
Vallabhbhai Patel-16
Alexander Hamilton-17
Jawaharlal Nehru -15
Mother Teresa -12
Thomas Jefferson-15
J. R. D. Tata -4
Indira Gandhi -12
Sachin Tendulkar-15
Napoleon Bonaparte-17
John Adams-9
Karl Marx-8
Andrew Jackson-13
b. Order the values in your data set from least to greatest. Then write the data on a strip of grid paper with 15 boxes.
Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 2
c. The middle value of the data set is called the median. The value (or values) that occur most often is called the mode. Find the median and the mode of your data set. Explain how you found your answers.
Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 3
d. Why are the median and the mode considered averages of a data set?
Answer:

Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 4

A measure of center is a measure that describes the typical value of a data set. The mean is one type of measure of center. Here are two others.

Try It

Question 1.
Find the median and mode of the data.1, 2, 20, 4, 17, 8, 12, 9, 5, 20, 13
Answer: Given the data,
1, 2, 20, 4, 17, 8, 12, 9, 5, 20, 13
First, write the numbers in the ascending or descending order.
1, 2, 4, 5, 8, 9, 12, 13, 17, 20, 20
The Median is 9.
The mode is 20 because it is repeated more than once.

Question 2.
100, 75, 90, 80, 110, 102
Answer:
Given the data,
100, 75, 90, 80, 110, 102
First, write the numbers in the ascending or descending order.
75, 80, 90, 100, 102, 110
= (90+100)/2
= 85
Mode:
No mode in the data.

Question 3.
One member of the class was absent and ends up voting for horror. Does this change the mode? Explain.
Answer: No

Question 4.
The times (in minutes) it takes six students to travel to school are 8, 10, 10, 15, 20, and 45. Find the mean, median, and mode of the data with and without the outlier. Which measure does the outlier affect the most?
Answer:
Median:
Write the numbers in ascending or descending order
8, 10, 10, 15, 20, and 45
= (10 + 15)/2 = 25/2 = 12.5
Mode:
10 is the mode. Because it is the most repeated number.
Mean:
Adding up the values and then dividing by the number of values.
= (8 + 10 + 10 + 15 + 20 + 45)/6
= 108/6
= 18

Question 5.
WHAT IF?
The store decreases the price of each video game by$3. How does this decrease affect the mean, median, and mode?
Answer:

Self-Assessment for Concepts & Skills

Solve each exercise. Then rate your understanding of the success criteria in your journal.
Question 6.
FINDING MEASURES OF CENTER
Consider the data set below.
15, 18, 13, 11, 12, 21, 9, 11
a. Find the mean, median, and mode of the data.

Answer:
Given the data,
15, 18, 13, 11, 12, 21, 9, 11
x̄ = (15 + 18 + 13 + 11 + 12 + 21 + 9 + 11)/8
x̄ = 110/8
x̄ = 13.75
Median:
Write the numbers in ascending order and descending order.
9, 11, 11, 12, 13, 15, 18, 21
= (12 + 13)/2
= 12.5
Mode:
11 is the mode because this is repeated more than one time.

b. Each value in the data set is decreased by 7. How does this change affect the mean, median, and mode?
Answer:
Each value is decreased by 7 in the given data
8, 11, 6, 4, 5, 14, 2, 4
x̄ = (8 + 11 + 6 + 4 + 5 + 14 + 2 + 4)/8
x̄ = 54/8
x̄ = 6.75

Question 7.
WRITING
Explain why a typical value in a data set can be described by the median or the mode.
Answer:
For data from skewed distributions, the median is better than the mean because it isn’t influenced by extremely large values. The mode is the only measure you can use for nominal or categorical data that can’t be ordered

Question 8.
How does removing the outlier affect your answer in Example 5?
Answer:

Question 9.
It takes 10 contestants on a television show 43, 41, 62, 40, 44, 43, 44, 46, 45, and 41 seconds to cross a canyon on a zipline. Find the mean, median, and mode of the data with and without the outlier. Which measure does the outlier affect the most?
Answer:

Question 10.
The table shows the weights of several great white sharks. Use the data to answer the statistical question, “What is the weight of a great white shark?”
Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 12
Answer:

Measures of Center Homework & Practice 9.3

Review & Refresh

Find the mean of the data.
Question 1.
1, 5, 8, 4, 5, 7, 6, 6, 2, 3
Answer: 4.7

Explanation:
Given the data,
1, 5, 8, 4, 5, 7, 6, 6, 2, 3
x̄ = ∑x/n
x̄ = (1 + 5 + 8 + 4 + 5 + 7 + 6 + 6 + 2 + 3)/16
x̄ = 49/16
x̄ = 3.06

Question 2.
9, 12, 11, 11, 10, 7, 4, 8
Answer: 9

Explanation:
Given the data,
9, 12, 11, 11, 10, 7, 4, 8
x̄ = ∑x/n
x̄ = (9 + 12 + 11 + 11 + 10 + 7 + 4 + 8)/8
x̄ = 72/8
x̄ = 9

Question 3.
26, 42, 31, 50, 29, 37, 44, 31
Answer: 36.25

Explanation:
Given the data,
26, 42, 31, 50, 29, 37, 44, 31
x̄ = ∑x/n
x̄ = (26+42+31+50+29+37+44+31)/8
x̄ = 290/8
x̄ = 36.25

Question 4.
53, 45, 43, 55, 28, 21, 61, 29, 24, 40, 27, 42
Answer: 39

Explanation:
Given the data,
53, 45, 43, 55, 28, 21, 61, 29, 24, 40, 27, 42
x̄ = ∑x/n
x̄ = (53+45+43+55+28+21+61+29+24+40+27+42)/12
x̄ = 468/12
x̄ = 39

Question 5.
A shelf in your room can hold at most 30 pounds.  ere are 12 pounds of books already on the shelf. Which inequality represents the number of pounds you can add to the shelf?
A. x < 18
B. x ≥ 18
C. x ≤ 42
D. x ≤ 18
Answer: x ≤ 18

Explanation:
12+x ≤ 30
12+x -12 ≤ 30-12
x ≤ 18

Find the missing values in the ratio table. Then write the equivalent ratios.
Question 6.
Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 13
Answer:
Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-9.3-13

Question 7.
Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 14
Answer:
Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-9.3-14

Find the surface area of the prism.

Question 8.
Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 15
Answer:
Given,
l = 6m
w = 5m
h = 5m
We know that,
Surface Area of the Prism = 2lw + 2lh + 2hw
= 2(6 × 5) + 2(6 × 8) + 2(8 × 5)
= 60 + 96 + 80
= 236 sq. meters

Question 9.
Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 16
Answer:
Given,
l = 4.5 ft
w = 2ft
h = 3.5ft
We know that,
Surface Area of the Prism = 2lw + 2lh + 2hw
= 2(4.5 × 2) + 2(4.5 × 3.5) + 2(2 × 3.5)
= 18 + 31.5 + 14
= 63.5 sq. ft

Question 10.
Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 17
Answer:
Given,
l = 6 yd
w = 4 yd
h = 2 yd
We know that,
Surface Area of the Prism = bh + 2lh + lb
= 2 × 4 + 2(6 × 5) + 6 × 2
= 8 + 60 + 12
= 80 sq. yards

Concepts, Skills, & Problem Solving

FINDING THE MEDIAN Use grid paper to find the median of the data. (See Exploration 1, p. 425.)
Question 11.
9, 7, 2, 4, 3, 5, 9, 6, 8, 0, 3, 8
Answer:
First, arrange the numbers in ascending or descending order.
= 0, 2, 3, 3, 4, 5, 6, 7, 8, 8, 9, 9
= (5 + 6)/2
= 11/2
= 5.5

Question 12.
16, 24, 13, 36, 22, 26, 22, 28, 25
Answer:
First, arrange the numbers in ascending or descending order.
13, 16, 22, 22, 24, 25, 26, 28, 36
24 is the median.
The median is the middle score in a set of given data.

FINDING THE MEDIAN AND MODE
Find the median and mode of the data.
Question 13.
3, 5, 7, 9, 11, 3, 8
Answer: The Median is 7; The Mode is 3.
Given: 3, 5, 7, 9, 11, 3, 8
Sorted list: 3,3,5,7,8,9,11
Median is the middle number in a sorted list of numbers = 7
The mode is the value that appears most frequently in a data set = 3

Question 14.
14, 19, 16, 13, 16, 14
Answer: The Median is 15; The Modes are 14 and 16.
Given: 13,14,14,16,16,19
Sorted list: 14, 19, 16, 13, 16, 14
Median is the middle number in a sorted list of numbers = 15
The mode is the value that appears most frequently in a data set = 14,16

Question 15.
16. 93, 81, 94, 71, 89, 92, 94, 99
Answer: The Median is 90.5; The Mode is 94.
Given: 16, 93, 81, 94, 71, 89, 92, 94, 99
Sorted list: 16,71,81,89,92,93,94,94,99
Median is the middle number in a sorted list of numbers = 92
The mode is the value that appears most frequently in a data set = 94

Question 16.
44, 13, 36, 52, 19, 27, 33
Answer: The Median is 33; There are no modes.
Given: 44, 13, 36, 52, 19, 27, 33
Sorted list: 13,19,27,33,36,44,52
Median is the middle number in a sorted list of numbers = 33
The mode is the value that appears most frequently in a data set = no mode

Question 17.
12, 33, 18, 28, 29, 12, 17, 4, 2
Answer: The Median is 17; The Modes are 12.
Given: 12, 33, 18, 28, 29, 12, 17, 4, 2
Sorted list: 2,4,12,12,17,18,28,29,33
Median is the middle number in a sorted list of numbers = 17
The mode is the value that appears most frequently in a data set = 12

Question 18.
55, 44, 40, 55, 48, 44, 58, 67
Answer:
The Median is 51.5
The Modes are 44 and 55.
Given: 55, 44, 40, 55, 48, 44, 58, 67
Sorted list: 40,44,44,48,55,55,58,67
Median is the middle number in a sorted list of numbers = 51.5
The mode is the value that appears most frequently in a data set = 44,55

Question 19.
YOU BE THE TEACHER
Your friend finds the median of the data. Is your friend correct? Explain your reasoning.
Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 18
Answer: No, first the given data is arranged in ascending order then after median is to be found. The median is 55

FINDING THE MODE
Find the mode of the data.
Question 20.
Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 19
Answer: The modes are Black and Blue.

Question 21.
Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 20
Answer: The modes are singing, dancing, comedy.

Question 22.
REASONING
In Exercises 20 and 21, can you find the mean and median of the data? Explain.
Answer: You can’t find the mean and median in exercises 20 and 21.
The data set is not made up of numbers

FINDING MEASURES OF CENTER
Find the mean, median, and mode of the data.
Question 23.
4.7, 8.51, 6.5, 7.42, 9.64, 7.2, 9.3
Answer: Given: 4.7, 8.51, 6.5, 7.42, 9.64, 7.2, 9.3
Sorted list: 4.7, 6.5, 7.2, 7.42, 8.51, 9.64
Mean: x̄ = ∑x/n
x̄ = (4.7+6.5+7.2+7.42+8.51+9.64)/6
x̄ = 43.97/6
x̄ =7.32
Median: 7.42.
Mode: no mode.

Question 24.
8\(\frac{1}{2}\), 6\(\frac{5}{8}\), 3\(\frac{1}{8}\), 5\(\frac{3}{4}\), 6\(\frac{5}{8}\), 5\(\frac{1}{4}\), 10\(\frac{5}{8}\), 4\(\frac{1}{2}\)
Answer: Given: 8.5, 6.62, 3.12, 5.75, 6.62, 5.25, 10.62, 4.5
Sorted list: 3.12, 4.5, 5.25, 5.75, 6.62, 6.62, 8.5, 10.62
Mean: x̄ = ∑x/n
x̄ = (3.12, 4.5, 5.25, 5.75, 6.62, 6.62, 8.5, 10.62)/8
x̄ =
x̄ =
Median: 6.18
Mode: 6.62

Question 25.
MODELING REAL LIFE
The weights (in ounces) of several moon rocks are shown in the table. Find the mean, median, and mode of the weights.
Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 21
Answer:
Mean
x̄ = (2.2 + 2.2 + 3.2 + 2.4 + 2.8 + 3.4 + 2.6 + 3.0 + 2.5)/9
Median:
Write the moon rock weights in ascending or descending order.
2.6 is the median
Mode:
2.2 is repeated move times
So, 2.2 is the mode.

REMOVING AN OUTLIER Find the mean, median, and mode of the data with and without the outlier. Which measure does the outlier affect the most?
Question 26.
45, 52, 17, 63, 57, 42, 54, 58
Answer:
Outliners means removing of the small data value
17 is the outliner
x̄ = ∑x/n
= (45 + 52 + 17 + 63 + 57 + 42 + 54 + 58)/8
= 388/8 = 48.5
Mean without outliner:
= (45 + 52 + 63 + 57 + 42 + 54 + 58)/7
= 371/7 = 53
Median with outliner:
17, 42, 45, 52, 54, 57, 58, 63
= (52 + 54)/2
= 106/2
= 53
Median without outliner:
42, 45, 52, 54, 57, 58, 63
54 is the median
Mode:
There is no change of value in the without outliner and with the outliner.
So, there is no mode in the data values.

Question 27.
85, 77, 211, 88, 91, 84, 85
Answer:
77 is the outliner
Mean with outliner:
x̄ = (85 + 77 + 211 + 88 + 91 + 84 + 85)/7
=721/7
= 103
Mean without outliner:
x̄ = (85 + 211 + 88 + 91 + 84 + 85)/6
= 644/6
= 107
Median with outliner:
Write the data values in ascending or descending order.
77, 84, 85, 88, 91, 211
85 is the median.
Median without outliner:
84, 85, 85, 88, 91, 211
= (85 + 88)/2
= 173/2
= 86.5
Mode:
There is no change of value in the without outliner and with the outliner.
85 is the mode.

Question 28.
23, 73, 45, 27, 23, 25, 43, 45
Answer:
73 is the outliner
Mean with outliner:
Mean = (23 + 45 + 27 + 23 + 25 + 43 + 45)
= 231/7
= 33
Mean with outliner:
Mean = (23 + 45 + 27 + 23 + 25 + 43 + 45+ 73)
= 304/8
= 38

Question 29.
101, 110, 99, 100, 64, 112, 110, 111, 102
Answer:
64 is the outliner
Mean with outliner:
x̄ = (101 + 110 + 99 + 100 + 64 + 112 + 110 + 111 + 102)/9
= 901/9 = 101
Mean with outliner:
x̄ = (101 + 110 + 99 + 100 + 112 + 110 + 111 + 102)/8
= 755/8
= 94.37
Median:
Write the data values in ascending or descending order
64, 99, 100, 101, 102, 110, 111, 112
Median without outliner:
= (101 + 102)/2
= 203/2
= 101.5
Mode:
Mode with and without outliner = 110

Question 30.
REASONING
The table shows the monthly salaries for employees at a company.
Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 22
a. Find the mean, median, and mode of the data.
b. Each employee receives a 5% raise. Find the mean, median, and mode of the data with the raise. How does this increase affect the mean, median, and mode of the data?
c. How are the mean, median, and mode of the monthly salaries related to the mean, median, and mode of the annual salaries?
Answer:

CHOOSING A MEASURE OF CENTER
Find the mean, median, and mode of the data. Choose the measure that best represents the data. Explain your reasoning.
Question 31.
48, 12, 11, 45, 48, 48, 43, 32
Answer:
Write the data in ascending order or descending order.
11, 12, 32, 43, 45, 48, 48, 48
= (32 + 43)/2
= 75/2
= 37.5
48 is the mode of the data

Question 32.
12, 13, 40, 95, 88, 7, 95
Answer:
Mean:
x̄ = ∑x/n
= (12 + 13 + 40 + 95 + 88 + 7 + 95)/7
= 350/7 = 50
Median:
7, 12, 13, 40, 88, 95, 95
40 is the median
mode:
95 is the mode.

Question 33.
2, 8, 10, 12, 56, 9, 5, 2, 4
Answer:
Mean:
x̄ = ∑x/n
= (2 + 8 + 10 + 12 + 56 + 9 + 5 + 2 + 4)/9
= 108/9
= 12
Median:
2, 2, 4, 5, 8, 9, 10, 12, 56
8 is the median
Mode:
2 is the mode.

Question 34.
126, 62, 144, 81, 144, 103
Answer:
Mean:
x̄ = ∑x/n
= (126 + 62 + 144 + 81 + 144 + 103)6
= 660/60
= 11
Median:
62, 81, 103, 126, 144, 144
= (103 + 126)/2
= 114.5

Question 35.
MODELING REAL LIFE
The weather forecast for a week is shown. Which measure of center best represents the high temperatures? the low temperatures? Explain your reasoning.
Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 23
Answer:

Question 36.
RESEARCH
Find the costs of 10 different boxes of cereal. Choose one cereal whose cost will be an outlier.
a. Which measure of center does the outlier affect the most? Justify your answer.
b. Use the data to answer the statistical question, “How much does a box of cereal cost?”
Answer:

Question 37.
PROBLEM SOLVING
The bar graph shows the numbers of hours you volunteered at an animal shelter. What is the minimum number of hours you need to volunteer in the seventh week to justify that you volunteered an average of 10 hours per week for the 7 weeks? Explain your answer using measures of center.
Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 24
Answer:

Question 38.
REASONING
Why is the mode the least frequently used measure of center to describe a data set? Explain.
Answer:
The mode can be helpful in some analyses, but generally it does not contain enough accurate information to be useful in determining the shape of a distribution. When it is not a “Normal Distribution” the Mode can be misleading, although it is helpful in conjunction with the Mean for defining the amount of skewness in a distribution.

Question 39.
DIG DEEPER!
The data are the prices of several fitness wristbands at a store.
$130 $170 $230 $130
$250 $275 $130 $185
a. Does the price shown in the advertisement represent the prices well? Explain.
Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 25
b. Why might the store use this advertisement?
c. In this situation, why might a person want to know the mean? the median? the mode? Explain.
Answer:

Question 40.
CRITICAL THINKING
The expressions 3x, 9x, 4x, 23x, 6x, and 3x form a data set. Assume x> 0.
a. Find the mean, median, and mode of the data.
b. Is there an outlier? If so, what is it?
Answer:
Mean: This is an average of all the numbers. Add up the numbers and then divide by how many numbers there are.
(3 + 9 + 4 + 23 + 6 + 3)/6 = 48/6 = 8
Median: The number in the middle, when the numbers are in order. If there are 2 middle numbers, average them together.
3, 3, 4, 6, 9, 23 : 4 and 6 are the middle numbers. 4+6/2 = 10/2 = 5
Mode: What value occurs most frequently? 3 is the only duplicate
Outlier: What value is abnormal to our set of data? All of our numbers are small (single digits), except for 23. That makes it an outlier.

Lesson 9.4 Measures of Variation

EXPLORATION 1

Interpreting Statements
Work with a partner. There are 24 students in your class. Your teacher makes the following statements.
Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 1
• “The exam scores range from 75% to 96%.”
a. What does each statement mean? Explain.
b. Use your teacher’s statements to make a dot plot that can represent the distribution of the exam scores of the class.
c. Compare your dot plot with other groups’. How are they alike? different?

EXPLORATION 2

Grouping Data
Work with a partner. The numbers of U.S.states visited by students in a sixth-grade class are shown.
Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 2
a. Represent the data using a dot plot. Between what values do the data range?
b. Use the dot plot to make observations about the data.
c. How can you describe the middle half of the data?

A measure of variation is a measure that describes the distribution of a data set. A simple measure of variation to find is the range. The range of a data set is the difference of the greatest value and the least value.

Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 3

Try It
Question 1.
The ages of people in line for a roller coaster are 15, 17, 21, 32, 41, 30, 25, 52, 16, 39, 11, and 24. Find and interpret the range of the ages.
Answer:
Given,
The ages of people in line for a roller coaster are 15, 17, 21, 32, 41, 30, 25, 52, 16, 39, 11, and 24.
Range = (upper value – lower value)/2
= (52 – 11)/2
= 41/2
= 20.5

Question 2.
The data are the number of pages in each of an author’s novels. Find and interpret the interquartile range of the data.
356, 364, 390, 468, 400, 382, 376, 396, 350
Answer:
Given,
The data are the number of pages in each of an author’s novels.
356, 364, 390, 468, 400, 382, 376, 396, 350
Lower quartile = 360
Upper quartile = 398
Interquartile range = 38

Self-Assessment for Concepts & Skills

Solve each exercise. Then rate your understanding of the success criteria in your journal.
Question 3.
WRITING
Explain why the variability of a data set can be described by the range or the interquartile range.
Answer:
The interquartile range is the third quartile (Q3) minus the first quartile (Q1). But the IQR is less affected by outliers: the 2 values come from the middle half of the data set, so they are unlikely to be extreme scores. The IQR gives a consistent measure of variability for skewed as well as normal distributions.

Question 4.
DIFFERENT WORDS, SAME QUESTION
Which is different? Find “both” answers.
Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 8
Answer:

Question 5.
The table shows the distances traveled by a paper airplane. Find and interpret the range and interquartile range of the distances.
Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 11
Answer: Given: 13.5, 12.5, 21, 16.75, 10.25, 19, 32, 26.5, 29,16.25, 28.5, 18.5.

Question 6.
The table shows the years of teaching experience of math teachers at a school. How do the outlier or outliers affect the variability of the data?
Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 12
Answer:
Given the data
5, 10, 7, 8, 10, 11, 22, 8, 6, 35
22 is added to the data set
22 is the outliner
so there is no effect to measure of center and the measure of variability.

Measures of Variation Homework & Practice 9.4

Review & Refresh

Find the mean, median, and mode of the data.
Question 1.
4, 8, 11, 6, 4, 5, 9, 10, 10, 4
Answer:
Mean = x̄ = (4 + 8 + 11 + 6 + 4 + 5 + 9 + 10 + 10 + 4)/10
= 71/10
= 7.1
Median:
Write the data in ascending or descending order.
4, 4, 4, 5, 6, 8, 9, 10, 10, 11
= (5 + 8)/2
= 13/2
=6.5
Mode:
More number if data repeated is called mode.
4 is the mode.

Question 2.
74, 78, 86, 67, 80
Answer:
Mean = x̄ = (74 + 78 + 86 + 67 + 80)/5
= 385/5
= 77
Median:
Write the data in ascending or descending order.
67, 74, 78, 80, 86
78 is the median
Mode:
There is no mode in the data.

Question 3.
15, 18, 17, 17, 15, 16, 14
Answer:
Mean = x̄ = (15 + 18 + 17 + 17 + 15 + 16 + 14)/7
= 112/7 = 16
Median:
Write the data in ascending or descending order.
14, 15, 15, 16, 17, 17, 18
16 is the median
Mode:
17, 15 are the median.

Question 4.
31, 14, 18, 26, 17, 32
Answer:
Mean:
x̄ = (31 + 14 + 18 + 26 + 17 + 32)/6
Median:
Write the data in ascending or descending order.
14, 17, 18, 26, 31, 32
= (18 + 26)/2
= 44/2
= 22
Mode:
There is no mode in the data.

Copy and complete the statement using < or >.
Question 5.
Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 13
Answer:
A negative number is less than the positive number
6 > -7

Question 6.
Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 14
Answer:
A negative number is less than the positive number
-3 < 0

Question 7.
Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 15
Answer:
A negative number is less than the positive number
14 > -14

Question 8.
Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 16
Answer:
A negative number is less than the positive number
8 > -10

Find the surface area of the pyramid.
Question 9.
Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 17
Answer:
Given,
Length = 12 mm
Height = 14 mm
A = a² + 2a √a²/4 + h²
Area = 509.56 sq. mm

Question 10.
Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 18
Answer:
Given,
Length = 5 in
Height = 8.5 in
A = a² + 2a √a²/4 + h²
Area = 113.6 sq. inches

Question 11.
Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 19
Answer:
Given,
Length = 6 ft
Height = 9 ft
A = a² + 2a √a²/4 + h²
Area = 149.84 sq.ft

Concepts, Skills, &Problem Solving

INTERPRETING STATEMENTS There are 20 students in your class. Your teacher makes the two statements shown. Use your teacher’s statements to make a dot plot that can represent the distribution of the scores of the class. (See Exploration 1, p. 433.)
Question 12.
“The quiz scores range from 65% to 95%.”
“The scores were evenly spread out.”
Answer:

Question 13.
“The project scores range from 78% to 93%.”
“Most of the students received low scores.”
Answer:

FINDING THE RANGE Find the range of the data.
Question 14.
4, 8, 2, 9, 5, 3
Answer: 7

Explanation:
Range is the difference of higher value and lower value
lowest value = 2
highest value = 9
R = 9 – 2
R = 7

Question 15.
28, 42, 36, 23, 14, 47, 40
Answer: 33

Explanation:
The range is the difference between higher value and lower value
Lowest value: 14
Highest value: 47
Range = 47 – 14
R = 33

Question 16.
26, 21, 27, 33, 24, 29
Answer: 12

Explanation:
The range is the difference between higher value and lower value
Lowest value: 21
Highest value: 33
Range = 33 – 21
R = 12

Question 17.
52, 40, 49, 48, 62, 54, 44, 58, 39
Answer: 23

Explanation:
The range is the difference between higher value and lower value
Lowest value: 39
Highest value: 62
Range = 62 – 39
R = 23

Question 18.
133, 117, 152, 127, 168, 146, 174
Answer: 57

Explanation:
The range is the difference between higher value and lower value
Lowest value: 117
Highest value: 174
Range = 174 – 117
R = 57

Question 19.
4.8, 5.5, 4.2, 8.9, 3.4, 7.5, 1.6, 3.8
Answer: 7.3

Explanation:
The range is the difference of higher value and lower value
Lowest value: 1.6
Highest value: 8.9
Range = 8.9 – 1.6
R = 7.3

Question 20.
YOU BE THE TEACHER
Your friend finds the range of the data. Is your friend correct? Explain your reasoning.
Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 20
Answer:
The range is the difference between higher value and lower value
Lowest value: 28
Highest value: 59
Range =  59 – 28
Range = 31

FINDING THE INTERQUARTILE RANGE Find the interquartile range of the data.
Question 21.
4, 6, 4, 2, 9, 1, 12, 7
Answer: 6

Explanation:
This simple formula is used for calculating the interquartile range:
IQR = Xu – Xl
Lower quartile (xL): 2.5
Upper quartile (xU): 8.5
IQR = 8.5 – 2.5
IQR = 6

Question 22.
18, 22, 15, 16, 15, 13, 19, 18
Answer: 3.75

Explanation:
This simple formula is used for calculating the interquartile range:
IQR = Xu – Xl
Lower quartile (xL): 15
Upper quartile (xU): 18.75
IQR = 18.75 – 15
= 3.75

Question 23.
40, 33, 37, 54, 41, 34, 27, 39, 35
Answer: 7

Explanation:
This simple formula is used for calculating the interquartile range:
IQR = Xu – Xl
Lower quartile (xL): 33.5
Upper quartile (xU): 40.5
IQR = 40.5 – 33.5
= 7

Question 24.
84, 75, 90, 87, 99, 91, 85, 88, 76, 92, 94
Answer: 8

Explanation:
This simple formula is used for calculating the interquartile range:
IQR = Xu – Xl
Lower quartile (xL): 84
Upper quartile (xU): 92
IQR = 92 – 84
= 8

Question 25.
132, 127, 106, 140, 158, 135, 129, 138
Answer: 12

Explanation:
This simple formula is used for calculating the interquartile range:
IQR = Xu – Xl
Lower quartile (xL): 127.5
Upper quartile (xU): 139.5
IQR = 139.5 – 127.5
= 12

Question 26.
38, 55, 61, 56, 46, 67, 59, 75, 65, 58
Answer: 12.75

Explanation:
This simple formula is used for calculating the interquartile range:
IQR = Xu – Xl
Lower quartile (xL): 52.75
Upper quartile (xU): 65.5
IQR = 65.5  – 52.75
= 12.75

Question 27.
MODELING REAL LIFE
The table shows the number of tornadoes in Alabama each year for several years. Find and interpret the range and interquartile range of the data. Then determine whether there are any outliers.
Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 21
Answer:
The data is 65, 32, 54, 23, 55, 145,37, 80, 94, 42, 69, 77
Range:
Lowest value: 23
Highest value: 145
R = Highest value – Lowest value
R = 145 – 23
R = 122
IQR:
This simple formula is used for calculating the interquartile range:
IQR = Xu – Xl
Lower quartile (xL): 38.25
Upper quartile (xU): 79.25
IQR = 79.25 – 38.25
= 41

Question 28.
WRITING
Consider a data set that has no mode. Which measure of variation is greater, the range or the interquartile range? Explain your reasoning.
Answer:
It would be based on the set of numbers you have, but in most cases, it is the interquartile range, because the mode is usually closer to the median. This leaves the interquartile range as a larger number.

Question 29.
CRITICAL THINKING
Is it possible for the range of a data set to be equal to the interquartile range? Explain your reasoning.
Answer:
The interquartile range (IQR) is a measure of variability, based on dividing a data set into quartiles. Quartiles divide a rank-ordered data set into four equal parts.

Question 30.
REASONING
How does an outlier affect the range of a data set? Explain.
Answer:
Outlier An extreme value in a set of data that is much higher or lower than the other numbers. Outliers affect the mean value of the data but have little effect on the median or mode of a given set of data.

Question 31.
MODELING REAL LIFE
The table shows the numbers of points scored by players on a sixth-grade basketball team in a season.
Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 22
a. Find the range and interquartile range of the data.
b. Identify the outlier(s) in the data set. Find the range and interquartile range of the data set without the outlier(s). Which measure does the outlier or outliers affect more?
Answer:

Question 32.
DIG DEEPER!
Two data sets have the same range. Can you assume that the interquartile ranges of the two data sets are about the same? Give an example to justify your answer.
Answer:
Yes,
A data set with the least value of 2 and the greatest value of 20 will have the same range as a data set with the least value of 82 and the greatest value of 100 will have the same range of 18.

Question 33.
MODELING REAL LIFE
The tables show the ages of the finalists for two reality singing competitions.
Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 23
a. Find the mean, median, range, and interquartile range of the ages for each show. Compare the results.

Answer:
18, 15, 22, 18, 24, 17, 21, 16, 28, 21
Mean:
x̄ = ∑x/n = (18 + 15 + 22 + 18 + 24 + 17 + 21 + 16 + 28 + 21)/10
=200/10 = 20
Median:
15, 16,  17,  18,  18, 21, 22, 24, 28
= (18 + 21)/2
= 39/2
= 19.5
Range:
(28 – 15)/2
= 13/2
= 6.5
interquartile range:
Number of observations: 10
Xl = 16.75
Xu = 22.5
Xu – Xl = 5.75
Ages of show B:
Mean:
x̄ = ∑x/n = (21 + 20 + 23 + 13 + 15 + 18 + 17 + 22 + 36 + 25)/10
= 210/10 = 21
Median:
13, 15, 17, 18, 20, 21, 22, 23, 25, 36
= (20 + 21)/2 = 41/2 = 20.5
Range:
(36 – 13)/2
= 23/2
= 11.5
Interquartile Range:
Samples = 10
Xl = 16.5
Xu = 23.5

b. A 21-year-old is voted off Show A, and the 36-year-old is voted off Show B. How do these changes affect the measures in part(a)? Explain.
Answer:
Mean:
x̄ = ∑x/n = (18 + 17 + 15 + 22 + 16 + 18 + 28 + 24)/8
= 158/8
= 79
Median: 15, 16, 17, 18, 18, 22, 24, 28
(18 + 18)/2
= 36/2
= 18
Range:
(28 – 15)/2
= 13/2
= 6.5
Interquartile Range:
Samples = 8
Xl = 16.25
Xu = 23.5
Interquartile Range = 23.5 – 16.25
= 7.25
21, 20, 23, 13, 15, 18, 17, 22, 25
Mean = (21 + 20 + 23 + 13 + 15 + 18 + 17 + 22 + 25)/9
= 174/2
= 87
Median:
13, 15, 17, 18, 21, 20, 22, 23, 25
21 is the median
Range:
(25 – 13)/2
= 12/2
= 6
Interquartile Range:
data = 9
Xl = 16
Xu = 22.5
(Xu – Xl) = 22.5 – 16
= 6.5
In Part A there is no effect on the range and it affects the mean, median, interquartile.

Question 34.
OPEN-ENDED
Create a set of data with 7 values that has a mean of 30, a median of 26, a range of 50, and an interquartile range of 36.
Answer:
The first thing we need to do is to put the data in increasing order. This is needed to calculate the median:
30,31,32,33,34,35,35,36,37,39

Lesson 9.5 Mean Absolute Deviation

Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.5 1

EXPLORATION 1

Finding Distances from the Mean
Work with a partner. The table shows the exam scores of 14 students in your class.
Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.5 2
a. Which exam score deviates the most from the mean? Which exam score deviates the least from the mean? Explain how you found your answers.
b. How far is each data value from the mean?
c. Divide the sum of the values in part(b) by the number of values. In your own words, what does this represent?
d. REASONING Ina data set, what does it mean when the value you found in part(c) is close to 0? Explain.

Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.5 3

Another measure of variation is the mean absolute deviation. The mean absolute deviation is an average of how much data values differ from the mean.

Try It
Question 1.
Find and interpret the mean absolute deviation of the data.
5, 8, 8, 10, 13, 14, 16, 22
Answer: Number of observations : 8
Mean: 12

Question 2.
WHAT IF?
The pitcher allows 4 runs in the next game. How would you expect the mean absolute deviation to change? Explain.
Answer:

Self-Assessment for Concepts & Skills

Solve each exercise. Then rate your understanding of the success criteria in your journal.
Question 3.
WRITING
Explain why the variability of a data set can be described by the mean absolute deviation.
Answer:

Question 4.
FINDING THE MEAN ABSOLUTE DEVIATION
Find and interpret the mean absolute deviation of the data. 8, 12, 4, 3, 14, 1, 9, 13
Answer: number of observations:8
Mean: 8
mean absolute deviation: 4

Question 5.
WHICH ONE do DOESN’T BELONG?
Which one does not belong with the other three? Explain your reasoning.
Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.5 6
Answer: MEAN
A mean is different from all the above-given factors
A mean is the simple mathematical average of a set of two or more numbers.
The mean for a given set of numbers can be computed in more than one way, including the arithmetic mean method, which uses the sum of the numbers in the series, and the geometric mean method, which is the average of a set of products.

Question 6.
The tables show the numbers of questions answered correctly by members of two teams on a game show. Compare the mean, median, and mean absolute deviation of the numbers of correct answers for each team. What can you conclude?
Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.5 9
Answer:
Tiger sharks
3, 6, 5, 4, 4, 2
Mean: (3 + 6 + 5 + 4 + 4 + 2)/6
= 24/6
= 4
Median:
2, 3, 4, 4, 5, 6
= (4 + 4)/2
= 4
MAD:
Number of observations: 6
Mean = 4
MAD = 1
Bear Cats:
Mean:
6, 1, 4, 1, 8, 4
(6 + 1 + 4 + 1 + 8 + 4)/6
= 24/6
= 4
Median:
1, 1, 4, 4, 6, 8
= (4 + 4)/2
= 4
MAD:
Number of observations: 6
Mean = 4
MAD = 2
The mean, Median, Mean Absolute Deviation of both tiger sharks and Bear Cats are the same.

Question 7.
DIG DEEPER!
The data set shows the numbers of books that students in your book club read last summer.
8, 6, 11, 12, 14, 12, 11, 6, 15, 9, 7, 10, 9, 13, 5, 8
A new student who read 18 books last summer joins the club. Is18 an outlier? How does including this value in the data set affect the measures of center and variation? Explain.
Answer: 8 is added to the dataset.
Yes, 18 is an outliner
No, it does not affect the measures of the center and variation by removing the outliner.
If the outliner is not removed then it affects the measures of center and variation.

Mean Absolute Deviation Homework & Practice 9.5

Review & Refresh

Find the range and interquartile range of the data.
Question 1.
23, 45, 39, 34, 28, 41, 26, 33
Answer:
Number of observations:8
Lower quartile (xL): 26.5
Upper quartile (xU): 40.5
interquartile range = 14
Range:
Number of observations:8
Lowest value: 23
Highest value: 45
Range = 45 – 23
= 22

Question 2.
63, 53, 48, 61, 69, 63, 57, 72, 46
Answer:
Number of observations:9
Lower quartile (xL): 50.5
Upper quartile (xU): 66
interquartile range = 15.5
Range:
Number of observations:9
Lowest value: 46
Highest value: 72
Range = 26

Graph the integer and its opposite.
Question 3.
15
Answer:
Big Ideas Math Grade 6 Chapter 9 Statistics Answer Key img_5

Question 4.
17
Answer:
Big Ideas Math Grade 6 Chapter 9 Statistics Answer Key img_6

Question 16.
– 22
Answer:
Big Ideas Math Grade 6 Chapter 9 Statistics Answer Key img_7

Question 7.
Find the numbers of faces, edges, and vertices of the solid.
Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.5 10
Answer:
The name of the solid is a pentagon.
Number of vertices = 5
Number of faces = 5
Numver of edges = 5

Write the word sentence as an equation.
Question 8.
17 plus a number q is 40.
Answer:
We have to write the equation for the word sentence.
The phrase ‘plus’ indicates ‘+’
17 + q = 40

Question 9.
The product of a number s and 14 is 49.
Answer:
We have to write the equation for the word sentence.
The phrase product indicates ‘×’
s × 14 = 49

Question 10.
The difference of a number b and 9 is 32.
Answer:
We have to write the equation for the word sentence.
The phrase difference indicates ‘-‘
b – 9 = 32

Question 11.
The quotient of 36 and a number g is 9.
Answer:
We have to write the equation for the word sentence.
The phrase quotient indicates ‘÷’
36 ÷ g = 9

Concepts, Skills, &Problem Solving

FINDING DISTANCES FROM THE MEAN Find the average distance of each data value in the set from the mean. (See Exploration 1, p. 439.)
Question 12.
Model years of used cars on a lot: 2014, 2006, 2009, 2011, 2005
Answer:

Question 13.
Prices of kites at a shop: $7, $20, $9, $35, $12, $15, $7, $10, $20, $25
Answer:

FINDING THE MEAN ABSOLUTE DEVIATION Find and interpret the mean absolute deviation of the data.
Question 14.
69, 51, 71, 77, 71, 80, 75, 63, 73
Answer:
Given the data
69, 51, 71, 77, 71, 80, 75, 63, 73
Number of samples = 9
Mean Absolute Deviation = 70

Question 15.
94, 86, 95, 99, 88, 90
Answer:
Given the data
94, 86, 95, 99, 88, 90
Number of samples = 6
Mean Absolute Deviation = 92

Question 16.
46, 54, 43, 57, 50, 62, 78, 42
Answer:
Given the data
46, 54, 43, 57, 50, 62, 78, 42
Number of samples = 8
Mean Absolute Deviation = 54

Question 17.
25, 28, 20, 22, 32, 28, 35, 34, 30, 36
Answer:
Given the data
25, 28, 20, 22, 32, 28, 35, 34, 30, 36
Number of samples = 10
Mean Absolute Deviation = 29

Question 18.
101, 115, 124, 125, 173, 165, 170
Answer:
Given the data
101, 115, 124, 125, 173, 165, 170
Number of samples = 7
Mean Absolute Deviation = 139

Question 19.
1.1, 7.5, 4.9, 0.4, 2.2, 3.3, 5.1
Answer:
Given the data
1.1, 7.5, 4.9, 0.4, 2.2, 3.3, 5.1
Number of samples = 7
Mean Absolute Deviation = 3.5

Question 20.
\(\frac{1}{4}, \frac{5}{8}, \frac{3}{8}, \frac{3}{4}, \frac{1}{2}\)
Answer:
Number of observations:5
Mean (x̄): 0.5
Mean Absolute Deviation (MAD): 0.15

Question 21.
4.6, 8.5, 7.2, 6.6, 5.1, 6.2, 8.1, 10.3
Answer:
Number of observations:8
Mean (x̄): 7.075
Mean Absolute Deviation (MAD): 1.45

Question 22.
YOU BE THE TEACHER
Your friend finds and interprets the mean absolute deviation of the data set 35, 40, 38, 32, 42, and 41. Is your friend correct? Explain your reasoning.
Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.5 11
Answer:
x̄ = ∑x/n = (35 + 40 + 38)/3
= 113/3
= 37.6
Yes, the data values are different from the mean by an average of 3.

Question 23.
MODELING REAL LIFE
The data set shows the admission prices at several glass-blowing workshops.
$20, $20, $16, $12, $15, $25, $11
Find and interpret the range, interquartile range, and mean absolute deviation of the data.
Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.5 12
Answer:
Range = (25 – 11)
= 14/2
= 7
Interquartile range:
Samples = 7
Xl = 12
Xu = 20
Xu – Xl = 20 – 12
= 8
Absolute Deviation of the data:
Data = 7
Mean = 17
Mean Absolute Deviation = 4

Question 24.
MODELING REAL LIFE
The table shows the prices of the five most-expensive and least-expensive dishes on a menu. Find the MAD of each data set. Then compare their variations.
Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.5 13
Answer:
Five expensive dishes
$28, $30, $28, $39, $25
MAD:
Dishes = 5
Mean $30
MAD = $3.6
First leasr expensive dishes:
$7, $7, $10, $8, $12
MAD:
Dishes = 5
Mean $8.8
MAD = $1.76
Mean Absolute Deviation of five most expensive dishes is greater than Mean Absolute Deviation of five least expensive dishes.

Question 25.
REASONING
The data sets show the years of the coins in two collections.
Your collection: 1950, 1952, 1908, 1902, 1955, 1954, 1901, 1910
Your friend’s collection: 1929, 1935, 1928, 1930, 1925, 1932, 1933, 1920
Compare the measures of center and the measures of variation for each data set. What can you conclude?
Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.5 14
Answer:
The measure of center is a value of the center or middle of a data set.
There are 4 measures of center they are
Mean
Median
Mode
Midrange
four measures of variations
Range
Interquartile range
Variance
Standard deviation
your collection:
Mean: (1950 + 1952 + 1908 + 1902 + 1955 + 1954 + 1901 + 1910)/8
= 1,929
Median: 1901, 1902, 1908, 1910, 1950, 1952, 1954, 1955
= (1910 + 1952)/2
= 1930
Mode: There is no mode
Midrange:
(1955 + 1901)/2
= 3856/2
= 1928
Range:
(1955 – 1901)/2
= 54/2
= 27
Interquartile range:
Number of observations = 8
Xl = 1903.5
Xu = 1953.5
Interquartile range = 50
Variance = 655.14
Standard deviation = 25.59

Question 26.
MODELING REAL LIFE
You survey students in your class about the numbers of movies they watched last month. A new student joins the class who watched 22 movies last month. Is22 an outlier? How does including this value affect the measures of center and the measures of variation? Explain.
Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.5 15
Answer:

REASONING
Which data set would have the greater mean absolute deviation? Explain your reasoning.
Question 27.
guesses for number of gumballs in a jar
guesses for number of baseballs in a jar
Answer:
Gumballs in the jar have a greater mean absolute deviation because baseballs are larger than baseballs.

Question 28.
monthly rainfall amounts in a city
monthly amounts of water used in a home
Answer:

Question 29.
REASONING
Range, interquartile range, and mean absolute deviation are all measures of variation. Which measure of variation is most reliable? Explain your reasoning.
Answer:

Question 30.
DIG DEEPER!
Add and subtract the MAD from the mean in the original data set in Exercise 26.
a. What percent of the values are within one MAD of the mean? two MADs of the mean? Which values are more than twice the MAD from the mean?
b. What do you notice as you get more and more MADs away from the mean? Explain.
Answer:

Statistical Measures Connecting Concepts

Using the Problem-Solving Plan

Question 1.
Six friends play a carnival game in which a person throws darts at balloons. Each person throws the same number of darts and then records the portion of the balloons that pop. Find and interpret the mean, median, and MAD of the data.
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures cc 1
Understand the problem.
You know that each person throws the same number of darts. You are given the portion of balloons popped by each person as a fraction, a decimal, or a percent.

Make a plan.
First, write each fraction and each decimal as a percent. Next, order the percents from least to greatest. Then find and interpret the mean, median, and MAD of the data.

Solve and check.
Use the plan to solve the problem. Then check your solution.
Answer:

Question 2.
The cost c (in dollars) to rent skis at a resort for n days is represented by the equation c = 22n. The durations of several ski rentals are shown in the table. Find the range and interquartile range of the costs of the ski rentals. Then determine whether any of the costs are outliers.
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures cc 2
Answer:
Given the equation c = 22n
c = 22(1) = 22
c = 22(5) = 1100
c = 22(1) = 22
c = 22(3) = 66
c = 22(5) = 110
c = 22(4) = 88
c = 22(3) = 66
c = 22(12) = 264
c = 22(1) = 22
c = 22(12) = 264
c = 22(5) = 110
c = 22(7) = 154
c = 22(4) = 88
c = 22(1) = 22
22, 110, 22, 66, 110, 88, 66, 264, 22, 264, 110, 154, 88, 22
Range = (264 – 22)/2 = 242/2
= 141
Interquartile range:
Number of observations: 14
lower quartile = 22
upper quartile = 121
Interquartile range = upper quartile – lower quartile
= 121 – 22
= 99

Performance Task
Which Measure of Center Is Best: Mean, Median, or Mode?
At the beginning of this chapter, you watched a STEAM Video called “Daylight in the Big City.“ You are now ready to complete the performance task related to this video, available at BigIdeasMath.com. Be sure to use the problem-solving plan as you work through the performance task.
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures cc 3

Statistical Measures Chapter Review

Review Vocabulary

Write the definition and give an example of each vocabulary term.
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures cr 1

Graphic Organizers

You can use a Definition and Example Chart to organize information about a concept. Here is an example of a Definition and Example Chart for the vocabulary term statistical question.
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures cr 2

Choose and complete a graphic organizer to help you study the concept.
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures cr 3
1. mean
2. outlier
3. median
4. mode
5. range
6. quartiles
7. interquartile range

Chapter Self-Assessment

As you complete the exercises, use the scale below to rate your understanding of the success criteria in your journal.
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures crr 1

9.1 Introduction to Statistics (pp. 413–418)
Learning Target: Identify statistical questions and use data to answer statistical questions.

Determine whether the question is a statistical question. Explain.
Question 1.
How many positive integers are less than 20?
Answer: There are only 19 numbers in that group

Question 2.
In what month were the students in a sixth-grade class born?
Answer: February

Question 3.
The dot plot shows the number of televisions owned by each family on a city block.
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures crr 3
a. Find and interpret the number of data values on the dot plot.
b. Write a statistical question that you can answer using the dot plot. Then answer the question.
Answer:

Display the data in a dot plot. Identify any clusters, peaks, or gaps in the data
Question 4.
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures crr 4
Answer:

Question 5.
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures crr 5
Answer:

Question 6.
You conduct a survey to answer, “What is the heart rate of a typical sixth-grade student?” e table shows the results. Use the distribution of the data to answer the question.
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures crr 6
Answer:

9.2 Mean (pp. 419–424)
Learning Target: Find and interpret the mean of a data set.

Question 7.
Find the mean of the data.
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures crr 7
Answer:
x̄ = ∑x/n =(1112+1409+675+536+1398+162)/6
x̄ = ∑x/n=6751/6
x̄ = ∑x/n=1125.16

Question 8.
The double bar graph shows the monthly profit for two toy companies over a four-month period. Compare the mean monthly profits.
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures crr 8
Answer:
Company A:
3.6, 3, 3.4, 4
Mean: (3.6 + 3 + 3.4 + 4)/4 = 14/4 = 3.5
Company B:
3, 4.3, 2.2, 4.1
Mean: (3 + 4.3 + 2.2 + 4.1)/4
= 13.6/4
= 3.4

Question 9.
The table shows the test scores for a class of sixth-grade students. Describe how the outlier affects the mean. Then use the data to answer the statistical question, “What is the typical test score for a student in the class?”
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures crr 9
Answer:

9.3 Measures of Center (pp. 425–432)
Learning Target: Find and interpret the median and mode of a data set.

Find the median and mode of the data.
Question 10.
8, 8, 6, 8, 4, 5, 6
Answer:
Median:
write the given data in ascending order or descending order.
4, 5, 6, 8, 8, 8
= (6 + 8)/2
= 14/2
= 7
Mode:
8 is the mode.

Question 11.
24, 74, 61, 29, 38, 27, 68, 54
Answer:
Median:
write the given data in ascending order or descending order.
24, 74, 61, 29, 38, 27, 68, 54
= 24, 27, 29, 38, 54, 61, 68, 74
= (38 + 54)/2
= 92/2
= 48
Mode:
There is no mode in the data.

Question 12.
Find the mean, median, and mode of the data set 67, 52, 50, 99, 66, 50, and 57 with and without the outlier. Which measure does the outlier affect the most?
Answer:
Given the data,
67, 52, 50, 99, 66, 50, and 57
Mean with outliner:
(67 + 52 + 50 + 99 + 66 + 50 + 57)/7
= 441/7
= 63
Mean without outliner:
66 is the median
Mode with outliner: 50
Mode without outliner:
No mode
Outliners affect the mean value of the data but have little effect on the median or mode of a given set of data.

Question 13.
The table shows the lengths of several movies. Which measure of center best represents the data? Explain your reasoning.
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures crr 13
Answer:

Question 14.
Give an example of a data set that does not have a median. Explain why the data set does not have a median.
Answer:

9.4 Measures of Variation (pp. 433–438)
Learning Target: Find and interpret the range and interquartile range of a data set.

Find the range of the data.
Question 15.
45, 76, 98, 21, 52, 39
Answer:
Lowest value = 21
Highest value = 98
Range = (98 – 21)/2
= 77/2
= 38.5

Question 16.
95, 63, 52, 8, 93, 16, 42, 37, 62
Answer:
Lowest value = 8
Highest value = 95
Range = (95 – 8)/2
= 87/2
= 43.5

Find the interquartile range of the data.
Question 17.
28, 46, 25, 76, 18, 25, 47, 83, 44
Answer:
Given the data
28, 46, 25, 76, 18, 25, 47, 83, 44
Number of observations: 9
lower quartile: 25
upper quartile: 61.5
Interquartile range (Xu – Xl) = 36.5

Question 18.
14, 25, 97, 55, 66, 28, 92, 38, 94
Answer:
Given the data
14, 25, 97, 55, 66, 28, 92, 38, 94
Number of observations: 9
lower quartile: 26.5
upper quartile: 93
Interquartile range (Xu – Xl) = 66.5

Question 19.
The table shows the weights of several adult emperor penguins. Find and interpret the range and interquartile range of the data. Then determine whether there are any outliers.
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures crr 19
Answer:
25, 27, 36, 23.5, 33.5, 31.25, 30.75, 32, 24, 29.25
Yes there are outliner
Range: (36  – 25)/2
= 11/2
= 5.5
Interquartile range:
Number of observations = 10
Mean = 29.225
MAD = 3.98

Question 20.
Two data sets have the same interquartile range. Can you assume that the ranges of the two data sets are about the same? Give an example to justify your answer.
Answer:
23
Yes, a data set with the least value of 2 and the greatest value of 20 will have the same range as a data set with the least value of 82 and the greatest value of 100 will have the same range of 18.

9.5 Mean Absolute Deviation (pp. 439–444)
Learning Target: Find and interpret the mean absolute deviation of a data set.

Find and interpret the mean absolute deviation of the data.
Question 21.
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures crr 21
Answer:
Given data,
6, 8.5, 6, 9, 10, 7, 8, 9.5
No. of observations: 8
Mean = 8
Mean Absolute Deviation: 1.25

Question 22.
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures crr 22
Answer:
Given data,
130, 150, 190, 100, 175, 120, 165, 140, 180, 190
No. of observations: 10
Mean = 154
Mean Absolute Deviation: 26

Question 23.
The table shows the prices of the five most-expensive and least-expensive manicures given by a salon technician on a particular day. Find the MAD of each data set. Then compare their variations.
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures crr 23
Answer:
five most-expensive:
$58, $52, $70, $49, $56
No. of observations: 5
Mean = 57
Mean Absolute Deviation: 5.6
5 least-expensive manicures:
$10, $10, $15, $10, $15
No. of observations: 5
Mean = 12
Mean Absolute Deviation: 2.4
The Mean Absolute Deviation of the five most-expensive is greater than the Mean Absolute Deviation of the 5 least-expensive manicures.

Question 24.
You record the lengths of songs you stream. The next song is 276 seconds long. Is 276 an outlier? How does including this value affect the measures of center and the measures of variation? Explain.
Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures crr 24
Answer:
Given the data,
233, 219, 163, 213, 224, 208, 225, 220, 222, 240, 228, 219, 260, 249, 209, 236,  206
The next song is 276 seconds long.
276 is the outliner.
We can remove 276 from the given data set.
So, there is no effect on the center and the measure of variations.

Statistical Measures Practice Test

Find the mean, median, mode, range, and interquartile range of the data.
Question 1.
5, 6, 4, 24, 10, 6, 9, 8
Answer:
Mean = (5 + 6 + 4 + 24 + 10 + 6 + 9 + 8)/8
= 72/8
= 9
Median:
4, 5, 6, 6, 8, 9, 10, 24
= (6 + 8)/2 = 14/2
= 7
Mode:
6 is the mode
range = (24 – 4)/2
= 20/2
= 10
Range:
Lowest value: 4
Highest value: 24
Range: 20
Interquartile range:
Lower quartile (xL): 5.25
Upper quartile (xU): 9.75
Interquartile range (xU-xL): 4.5

Question 2.
46, 27, 94, 56, 53, 65, 43
Answer:
Given the data,
46, 27, 94, 56, 53, 65, 43
Mean = (46 + 27 + 94 + 56 + 53 + 65 + 43)/7
= 16.75
Median = 15.5
Mode: There is no mode
Range:
Number of observations = 7
Lowest value: 27
Highest value: 94
Range: 67
Interquartile range:
Lower quartile (xL): 43
Upper quartile (xU): 65
Interquartile range (xU-xL): 22

Question 3.
32, 58, 19, 36, 44, 57, 11, 26, 74
Answer:
Given the data,
32, 58, 19, 36, 44, 57, 11, 26, 74
Mean = (32 + 58 + 19 + 36 + 44 + 57 + 11 + 26 + 74)/9
= 357/9
= 39.66
Median:
Arrange the data in ascending or descending order.
11, 19, 26, 32, 36, 44, 57, 58, 74
Median = 36
Mode: There is no mode in the data
Range:
Lowest value: 11
Highest value: 74
Range: 63
Interquartile range:
Lower quartile (xL): 22.5
Upper quartile (xU): 57.5
Interquartile range (xU-xL): 35

Question 4.
36, 24, 49, 32, 37, 28, 38, 40, 39
Answer:
Given the data
36, 24, 49, 32, 37, 28, 38, 40, 39
Arrange the data in ascending or descending order.
24, 28, 32, 36, 37, 38, 39, 40, 49
Mean = (24 + 28 + 32 + 36 + 37 + 28 + 38 + 40 + 49)/9
= 34.66
Median: 37
Mode: There is no mode
Range:
Lowest value: 24
Highest value: 49
Range: 25
Interquartile range:
Lower quartile (xL): 30
Upper quartile (xU): 39.5
Interquartile range (xU-xL): 9.5

Find and interpret the mean absolute deviation of the data.
Question 5.
Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures pt 5
Answer:
Given the data,
312, 286, 196, 201, 158, 225, 206, 192
Mean (x̄): 0.5
Mean Absolute Deviation (MAD): 0.15

Question 6.
Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures pt 6
Answer:
Given the data,
15, 8, 19, 20, 18, 20, 22, 14, 10, 15
Mean (x̄): 16.1
Mean Absolute Deviation (MAD): 3.7

Question 7.
You conduct a survey to answer, “How many Times (minutes)minutes does it take a typical sixth-grade student to run a mile?” The table shows the results. Use the distribution of the data to answer the question.
Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures pt 7
Answer:

Question 8.
The table shows the weights of Alaskan malamute 8181808281dogs at a veterinarian’s office. Which measure of center best represents the weight of an Alaskan malamute? Explain your reasoning.
Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures pt 8
Answer:

Question 9.
The table shows the numbers of guests Numbers of Guests at a hotel on different days.
Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures pt 9
a. Find the range and interquartile range of the data.
b. Use the interquartile range to identify the outlier(s) in the data set. Find the range and interquartile range of the data set without the outlier(s). Which measure did the outlier or outliers affect more?
Answer:

Question 10.
The data sets show the numbers of hours worked each week by two people for several weeks.
Person A: 9, 18, 12, 6, 9, 21, 3, 12
Person B: 12, 18, 15, 16, 14, 12, 15, 18
Compare the measures of center and the measures of variation for each data set. What can you conclude?
Answer:

Question 11.
The table shows the lengths of several bearded dragons captured for a study. Find the mean, median, and mode of the data in centimeters and in inches. How does converting to inches affect the mean, median, and mode?
Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures pt 11
Answer:

Statistical Measures Cumulative Practice

Question 1.
Which statement can be represented by a negative integer?
A. The temperature rises 15 degrees.
B. A hot-air balloon ascends 450 yards.
C. You earn $50 completing chores.
D. A submarine submerges 260 feet.
Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures cp 1
Answer: D. A submarine submerges 260 feet.

Question 2.
What is the height h (in inches) of the prism?
Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures cp 2
Answer:
h = v/lw
h = 5850/30(12 1/4)
h = 5850/(30 × 12.25)
h = 5850/367.50
h = 15.91 inches

Question 3.
Which is the solution of the inequality \(\frac{2}{3}\)x < 6?
F. x < 4
G. x < 5\(\frac{1}{3}\)
H. x < 6\(\frac{2}{3}\)
I. x < 9
Answer: I. x < 9

Question 4.
The number of hours that each of six students spent reading last week is shown in the bar graph.
Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures cp 4
For the data in the bar graph, which measure is the?
A. mean
B. median
C. mode
D. range
Answer: C. mode

Explanation:
In the above bar graph, 10 is repeated two ways.
Thus the correct answer is option C.

Question 5.
Which list of numbers is in order from least to greatest?
F. – 5.41, – 3.6, – 3.2, – 3.06, – 1
G. – 1, – 3.06, – 3.2, – 3.6, – 5.41
H. – 5.41, – 3.06, – 3.2, – 3.6, – 1
I. – 1, – 3.6, – 3.2, – 3.06, – 5.41
Answer: F. – 5.41, – 3.6, – 3.2, – 3.06, – 1

Explanation:
We have to write the numbers from least to greatest
The negative sign with the highest number will be the least.
– 5.41, – 3.6, – 3.2, – 3.06, – 1
Thus the correct answer is option F.

Question 6.
What is the mean absolute deviation of the data shown in the dot plot, rounded to the nearest tenth?
Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures cp 6
A. 1.4
B. 3
C. 3.2
D. 57.
Answer:
Data from the dot plot
5, 5, 4, 4, 6, 1
Number of observations: 6
Mean = 4.166
Mean absolute deviation = 1.66
Thus the correct answer is option A.

Question 7.
A family wants to buy tickets to a theme park. There are separate ticket prices for adults and children.
Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures cp 7
Which expression represents the total cost (in dollars) for adult tickets c and child tickets?
F. 600 (a + c)
G. 50(a × c)
H. 30a + 20c
I. 30a × 20c
Answer: H. 30a + 20c

Question 8.
The dot plot shows the leap distances (in feet) of a tree frog. How many leaps were recorded?
Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures cp 8
Answer: 7 leaps were recorded

Question 9.
What is the value of the expression when a = 6 and b = 14?
0.8a + 0.02b
A. 0.4828
B. 0.8814
C. 5.08
D. 16.4
Answer:
Given the expression,
0.8a + 0.02b
a = 6
b = 14
0.8(6) + 0.02(14)
4.8 + 0.28
= 5.08
Thus the correct answer is option C.

Question 10.
Which property was not used to simplify the expression?
Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures cp 10
F. Distributive Property
G. Associative Property of Addition
H. Multiplication Property of One
I. Commutative Property of Multiplication
Answer: I. Commutative Property of Multiplication

Question 11.
What are the coordinates of Point P?
Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures cp 11
A. (- 3, – 2)
B. (3, – 2)
C. (- 2, – 3)
D. (-2, 3)
Answer: B. (3, – 2)

Explanation:
By seeing the above graph we can write the ordered pair P.
the x-axis is on 3 and the y-axis is on -2
Thus the correct answer is option B.

Question 12.
Create a data set with 5 numbers that has the following measures.
Think
Solve
Explain
• a mean of 7
• a median of 9
Explain how you created your data set.
Answer:
The data set is 3, 2, 9, 1, 20

Final Words:

We hope that the article on Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures helps you in all over preparation. If you are lagging in this concept, then you can check the above material. Feel free to post your doubts or comments in the comments section. If you need solutions to any of the questions, then you can ask us in the comment section itself. We clear all your doubts as early as possible. Stay tuned to our site to get more updates on BIM All Grades materials.

Big Ideas Math Answers Grade K | Big Ideas Math Book Grade K Answer Key

Big Ideas Math Answers Grade K

Download Kindergarten Big Ideas Math Textbook Answer Key from here. You have different opportunities to problem-solving and communication skills through explore and grow, think and grow. Apply the concept of maths in real-time and enhance your skills. With the help of Big Ideas Math Answers Grade K, you can perform well in practice tests, Assessment tests, and chapter tests. BigIdeas Math Answers Grade K is an essential teaching practice for elementary school students.

Download Big Ideas Math Answers Grade K Pdf | BIM K Grade Answers

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Common Core 2019 – Grade K

Top 5 Preparation Tips for Exams

  1. Study the subject from the best material.
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  3. Fix the timetable and plan for preparation.
  4. First, you have to organize the study space
  5. Take breaks regularly for your relaxation.

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Big Ideas Math Answers Grade 2 | Big Ideas Math Book 2nd Grade Solutions

Big Ideas Math Answers Grade 2

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The best preparation strategy will help the students to manage their preparation time properly. So, it is advised that every student have to make a preparation plan using the following tips. We are giving the preparation tips for the 2nd grade students. Follow these tips and score good marks in the exam.

  • First, find out the amount of time you have for the preparation.
  • Collect the best study material to read.
  • Prepare all the chapters without leaving any choice.
  • Take Breaks after every chapter.
  • Drink plenty of water
  • Enough sleep
  • Set the best time of the day as study time
  • Study Everyday
  • Do not read everything the night before the exam.
  • Try to complete the preparation a few days before the test.
  • Understand the concept and write the revision notes.
  • Revise early in the morning.

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Big Ideas Math Answers Grade 6 Chapter 5 Algebraic Expressions and Properties

Big Ideas Math Answers Grade 6 Chapter 5 Algebraic Expressions and Properties

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Big Ideas Math Book 6th Grade Answer Key Chapter 5 Algebraic Expressions and Properties

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Algebraic Expressions and Properties STEAM Video/Performance

Lesson: 1 Algebraic Expressions

Lesson: 2 Writing Expressions

Lesson: 3 Properties of Addition and Multiplication

Lesson: 4 The Distributive Property

Lesson: 5 Factoring Expressions

Chapter: 5 – Algebraic Expressions and Properties

Algebraic Expressions and Properties STEAM Video/Performance

Shadow Drawings
Expressions can be used to represent the growth of living things over time. Can you think of any other real-life situations in which you would want to use an expression to represent a changing quantity?
Watch the STEAM Video “Shadow Drawings.” Then answer the following questions.

Question 1.
Tory traces the shadow of a plant each week on the same day of the week and at the same time of day. Why does she need to be so careful about the timing of the drawing?

Answer:
Tory traces the shadow of a plant each week on the same day of the week and at the same time of day.
Because she needs to represent the growth of the plant over time. Thus she needs to be very careful about the timing of the drawing.

Question 2.
The table shows the height of the plant each week for the first three weeks. About how tall was the plant after 1.5 weeks? Explain your reasoning.
Big Ideas Math Answers Grade 6 Chapter 5 Algebraic Expressions and Properties 1

Answer: 10.5 inches

Explanation:
The above table represents the height of the plant for 3 weeks.
1 week = 7 inches
0.5 week = 7/2 = 3.5 inches
1.5 week = 7 + 3.5 = 10.5 inches

Question 3.
Predict the height of the plant when Tory makes her next three weekly drawings.

Answer: 42 inches (approx)

Explanation:
The height of the plant is increased by 7 inches every week.
The height of the plant is increased to 22 inches for the first three weeks.
7 × 6 = 42 inches
Thus we predict the height of the plant when Tory makes her next three weekly drawings is 42 inches.

Performance Task

Describing Change

After completing this chapter, you will be able to use the concepts you learned to answer the questions in the STEAM Video Performance Task. You will be given data sets for the following real-life situations.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 2
You will be asked to use given data to write expressions and make predictions. Do the expressions provide accurate predictions far into the future?
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 3

Getting Ready for Chapter 5

Question 1.
Work with a partner.
a. You baby sit for 3 hours. You receive $24. What is your hourly wage?

  • Write the problem. Underline the important numbers and units you need to solve the problem.
  • Read the problem carefully a second time. Circle the key phrase for the question.
    Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 4
  • Write each important number or phrase, with its units, on a piece of paper. Write +, −, ×, ÷, and = on five other pieces of paper.
    Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 5
  • Arrange the pieces of paper to answer the question, “What is your hourly wage?”
  • Evaluate the expression that represents the hourly wage.
    Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 6

Answer:
Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-6
According to the given details, Babysit receives $24 for 3 hours.
3 hours = $24
1 hour = 24/3 = $8
Thus your hourly wage is $8

b. How can you use your hourly wage to find how much you will receive for any number of hours worked?

Answer:
You can multiply by $8 in given any number of hours worked to get the total receive.

Vocabulary

The following vocabulary terms are defined in this chapter. Think about what each term might mean and record your thoughts.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 7

Lesson 5.1 Algebraic Expressions

EXPLORATION 1
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 8
Work with a partner. Identify any missing information that is needed to answer each question. Then choose a reasonable quantity and write an expression for each problem. After you have written the expression, evaluate it using mental math or some other method.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 9
a. You receive $24 for washing cars. How much do you earn per hour?

Answer:
Let the number of hours 8.
24 ÷ 8 = 3
Thus you earn $3 per hour.

b. You buy 5 silicone baking molds at a craft store. How much do you spend?
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 10

Answer:
Let the cost of each silicone baking molds is $3
5 × $3 = $15
Thus you spend $15 to buy 5 silicone baking molds.
c. You are running in a mud race. How much farther do you have to go after running 2000 feet?
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 11

Answer:
You are running a 4500-foot race.
4500 – 2000 = 2500 feet
Thus you have to run 2500 feet more.

d. A rattlesnake is 25 centimeters long when it hatches. The snake grows at a rate of about 1.6 centimeters per month for several months. What is the length of the rattlesnake?
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 12

Answer:
Given,
A rattlesnake is 25 centimeters long when it hatches. The snake grows at a rate of about 1.6 centimeters per month for several months.
Let the number of months be m
25 + 1.6m
If months = 12
1.6 × 12 = 19.2 cms
25 + 19.2 = 44.2 centimeters

5.1 Lesson

Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 13

An algebraic expression is an expression that may contain numbers, operations, and one or more variables. A variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 14

Try It

Identify the terms, coefficients, and constants in the expression.

Question 1.
12 + 10c

Answer:
12 – constant
10 – coefficient
c – variable or term
A term without a variable is called a constant.
The numerical factor of a term that contains a variable is called a coefficient.
A variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.

Question 2.
15 + 3w + \(\frac{1}{2}\)

Answer:
15 and \(\frac{1}{2}\) – constant
3 – coefficient
w – variable or term
A term without a variable is called a constant.
The numerical factor of a term that contains a variable is called a coefficient.
A variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.

Question 3.
z2 + 9z

Answer:
2 – exponent
9 – coefficient
z – variable or term
An exponent is a number or letter written above and to the right of a mathematical expression called the base
The exponent tells us how many times the base is used as a factor
The numerical factor of a term that contains a variable is called a coefficient.
A variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.

write the expression using exponents.

Question 4.
j . j . j . j . j . j

Answer:
j raised to the sixth power
An exponent is a number or letter written above and to the right of a mathematical expression called the base
The exponent tells us how many times the base is used as a factor

Question 5.
9 . k . k . k . k . k

Answer:
9 – constant
k raised to the fifth power
An exponent is a number or letter written above and to the right of a mathematical expression called the base
The exponent tells us how many times the base is used as a factor

Question 6.
Evaluate 24 + c when c = 9.

Answer: 33

Explanation:
Given equation
24 + c
and also given c is equal to 9
substitute c value in the equation we get
24 + 9 = 33

Question 7.
Evaluate d − 17 when d = 30.

Answer: 13

Explanation:
Given equation
d – 17
and also given d is equal to 30
substitute d value in the equation we get
30 – 17 = 13

Question 8.
Evaluate 18 ÷ q when q = \(\frac{1}{2}\)

Answer: 36

Explanation:
Given equation
18 ÷ q
and also given q is equal to \(\frac{1}{2}\)
substitute q value in the equation we get
18 ÷ \(\frac{1}{2}\) = 36

Evaluate the expression when p = 24 and q = 8.

Question 9.
p ÷ q

Answer:
p = 24
q = 8
p ÷ q
Substitute the value of p and q in the expression
24 ÷ 8 = 3

Question 10.
q + p

Answer:  32

Explanation:
Given,
p = 24
q = 8
q + p
Substitute the value of p and q in the expression
8 + 24 = 32
Hence we get the answer is 32

Question 11.
p – q

Answer: 16

Explanation:
Given,
p = 24
q = 8
p – q
Substitute the value of p and q in the expression
24 – 8 = 16
Hence we get the answer is 16

Question 12.
p . q

Answer: 192

Explanation:
Given,
p = 24
q = 8
p . q
Substitute the value of p and q in the expression
24 . 8  by multiplying 24 with 8 we get 192
Hence  the answer is 192

Evaluate the expression when y = 6.

Question 13.
5y + 1

Answer: 31

Explanation:
Given equation
5y + 1
and also given y = 6
Now substitute 6 in the given equation
5.6 + 1 is
5 multiply with 6 and then add with 1 we get 30 + 1 is 31
hence answer is 31

Question 14.
30 – 24 ÷ y

Answer: 1

Explanation:
Given equation
30 – 24 ÷ y
and also given y = 6
Now substitute 6 in the given equation
30 – 24 ÷ y is
30 – 24 ÷6
6 ÷ 6
six divided by six
we get 1
Hence answer is 1

Question 15.
y2 – 7

Answer: 29

Explanation:
Given equation
y² – 7
and also given y = 6
Now substitute 6 in the given equation
y2 – 7
6² – 7
6 × 6 – 7
36 – 7
29
Hence answer is 29

Question 16.
1.5 + y2

Answer: 37.5

Explanation:
Given equation
1.5 + y²
and also given y = 6
Now substitute 6 in the given equation
1.5 + 6²
1.5 +36
37.5
Hence answer is 37.5

Self-Assessment for Concepts & Skills

Solve each exercise. Then rate your understanding of the success criteria in your journal.

Question 17.
WHICH ONE DOESN’T BELONG?
Which expression does not belong with the other three? Explain your reasoning.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 15

Answer: The expression 3(4) + 5 does not belong to the other three. Because it does not contain any variable in the expression.

Question 18.
ALGEBRAIC EXPRESSIONS
Identify the terms, coefficients, and constants in the expression 9h + 1.

Answer:
1 – constant
9 – coefficient
h – variable or term
A term without a variable is called a constant.
The numerical factor of a term that contains a variable is called a coefficient.
A variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.

EVALUATING EXPRESSIONS
Evaluate the expression when m = 8.

Question 19.
m – 7

Answer: 1
Given equation
m – 7
given m value is 8
Now substitute m value 8  in the given equation we get
m – 7
8 – 7
1
Hence the answer is 1

Question 20.
5m + 4

Answer: 44
Given equation
5m + 4
given m value is 8
Now substitute m value 8  in the given equation we get
5 . 8 + 4
40 + 4
44
Hence the answer is 44

Question 21.
NUMBER SENSE
Does the value of the expression 20 − x increase, decrease, or stay the same as x increases? Explain.

Answer:
When the value of x increases, the value of 20 – x decreases. And when the value of x does not change, 20 – x remains the same. When greater values of x are subtracted from 20, you will have a lower value left. Therefore, as x increases, the value of the expression 20 – x will decrease.

Question 22.
OPEN-ENDED
Write an algebraic expression using more than one operation. When you evaluate the expression, how do you know which operation to perform first?

Answer:
Example  40 – 2(6 – 4)²
40 – 2 (2)²
40 – 2(4)
40 – 8
32

When evaluating an expression, proceed in this order:

parentheses are done first.
exponents are done next.
multiplication and division are done as they are encountered from left to right.
addition and subtraction are done as they are encountered from left to right.

Question 23.
STRUCTURE
Is the expression 8.2 ÷ m . m . m . m the same as the expression 8.2 ÷ m4? Explain your reasoning.

Answer: Yes
An exponent is a number or letter written above and to the right of a mathematical expression called the base
The exponent tells us how many times the base is used as a factor
Hence the expression 8.2 ÷ m . m . m . m the same as the expression 8.2 ÷ m⁴

Self-Assessment for Problem Solving

Solve each exercise. Then rate your understanding of the success criteria in your journal.

Question 24.
The expression 12.25m + 29.99 gives the cost (in dollars) of a gym membership for m months. You have $180 to spend on a membership. Can you buy a one-year membership?

Answer: Yes.
Given
The expression 12.25m + 29.99
gym membership for m months
You have $180 to spend on a membership
Let’s solve your equation step-by-step.
12.25m+29.99=180
Step 1: Subtract 29.99 from both sides.
12.25m+29.99−29.99=180−29.99
12.25m=150.01
Step 2: Divide both sides by 12.25.
12.25m/12.25=150.01/12.25
m=12.245714
The expression 12.25m + 29.99= 12.25(12.24)+29.99 = 179.93

Question 25.
DIG DEEPER!
The expression p −15 gives the amount (in dollars) you pay after using the coupon when the original amount of a purchase is p dollars. The expression 30 + 6n gives the amount of money (in dollars) you save after n weeks. A jacket costs $78. Can you buy the jacket after 6 weeks? Explain.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 16

Answer:
The amount you pay using coupon = p (purchase) -15
so we simply plug in our value into this equation
$78- $15 = $63
so $63 is the amount you pay after using the coupon on an original purchase of $78
n = 6 weeks
30 + 6n
30 + 6(6)
30 + 36 = 66
No, you cannot buy the jacket after 6 weeks.

Algebraic Expressions Homework & Practice 5.1

Review & Refresh

You ask 40 students which of three items from the cafeteria they like the best. You record the results on the piece of paper shown.

Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 500

Question 1.
What percent of students answered salad?

Answer: 25%

Explanation:
Total number of students = 40
The number of students who like a salad in the Cafeteria food is 10 students
40/10 = 4
The percentage of the students is
(10/40) × 100 = 25%
Thus the percentage of students who answered salad is 25%.

Question 2.
How many students answered pizza?

Answer: 12 students

Explanation:
Total number of students = 40
The number of students who like a salad in the Cafeteria food is 10 students
The number of students who answered pasta is 18
40 – 18 – 10 = 12
Thus the number of students who answered pizza is 12.

Question 3.
What percent of students answered pasta?

Answer: 45%

Explanation:
Total number of students = 40
The number of students who answered pasta is 18
(18/40) × 100 = 45
Thus the percentage of students who answered pasta is 45%

Find the missing quantity in the double number line.

Question 4.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 17

Answer:
Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-17
The ratio of 2 and 10 is 1:5
The equivalent ratio of 1:5 is 6:30
So, the missing quantity is 6.

Question 5.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 18

Answer:
Based on the ratios we can find the missing quantity.
The cost of 1 pastry is $2.5
The cost of 9 pastries is $22.5
Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-18

Divide. Write the answer in simplest form.

Question 6.
1\(\frac{3}{8}\) ÷ \(\frac{3}{4}\)

Answer: \(\frac{1}{2}\)
To simplify a fraction, divide the top and bottom by the highest number that
can divide into both numbers exactly.
Simplifying (or reducing) fractions means making the fraction as simple as possible

Question 7.
2\(\frac{7}{9}\) ÷ 2

Answer: \(\frac{7}{9}\)
To simplify a fraction, divide the top and bottom by the highest number that
can divide into both numbers exactly.
Simplifying (or reducing) fractions means making the fraction as simple as possible

Question 8.
4 ÷ 4\(\frac{2}{5}\)

Answer: \(\frac{5}{2}\)
To simplify a fraction, divide the top and bottom by the highest number that
can divide into both numbers exactly.
Simplifying (or reducing) fractions means making the fraction as simple as possible

Question 9.
3\(\frac{2}{3}\) ÷ 1\(\frac{2}{7}\)

Answer: latex]\frac{14}{3}[/latex]
To simplify a fraction, divide the top and bottom by the highest number that
can divide into both numbers exactly.
Simplifying (or reducing) fractions means making the fraction as simple as possible

Concepts, Skills, & Problem Solving

EVALUATING EXPRESSIONS
Write and evaluate an expression for the problem. (See Exploration 1, p. 201.)

Question 10.
The scores on your first two history tests are 82 and 95. By how many points did you improve on your second test?

Answer: 13

Explanation:
The scores on your first two history tests are 82 and 95.
95 – 82 = 13
Thus you have to improve 13 points on your second test.

Question 11.
You buy a hat for $12 and give the cashier a $20 bill. How much change do you receive?

Answer: $8

Explanation:
Given,
You buy a hat for $12 and give the cashier a $20 bill.
20 – 12 = 8
Thus you receive $8 change.

Question 12.
You receive $8 for raking leaves for 2 hours. What is your hourly wage?

Answer: $4

Explanation:
Given,
You receive $8 for raking leaves for 2 hours.
2 hour = $8
1 hour = ?
8/2 = 4
Thus the hourly wage is $4.

Question 13.
Music lessons cost $20 per week. How much do 6 weeks of lessons cost?

Answer: $120

Explanation:
Given,
Music lessons cost $20 per week.
1 week = $20
$20 × 6 = $120
Thus the cost of 6 weeks is $120.

ALGEBRAIC EXPRESSIONS
Identify the terms, coefficients, and constants in the expression.

Question 14.
7h + 3

Answer:
3 – constant
7 – coefficient
h – variable or term
A term without a variable is called a constant.
The numerical factor of a term that contains a variable is called a coefficient.
A variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.

Question 15.
g + 12 + 9g

Answer:
12 – constant
9 – coefficient
g – variable or term
A term without a variable is called a constant.
The numerical factor of a term that contains a variable is called a coefficient.
A variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.

Question 16.
5c2 + 7d

Answer:
2 – exponent
5 and 7 – coefficient
c and d – variable or term
An exponent is a number or letter written above and to the right of a mathematical expression called the base
The exponent tells us how many times the base is used as a factor
The numerical factor of a term that contains a variable is called a coefficient.
A variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.

Question 17.
2m2 + 15 + 2p2

Answer:
15 – constant
2 – exponent
2 – coefficient
m and p – variable or term
A term without a variable is called a constant.
An exponent is a number or letter written above and to the right of a mathematical expression called the base
The exponent tells us how many times the base is used as a factor
The numerical factor of a term that contains a variable is called a coefficient.
A variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.

Question 18.
6 + n2 + \(\frac{1}{2}\)d

Answer:
6 – constant
\(\frac{1}{2}\)– exponent
2 – coefficient
n and d – variable or term
A term without a variable is called a constant.
An exponent is a number or letter written above and to the right of a mathematical expression called the base
The exponent tells us how many times the base is used as a factor
The numerical factor of a term that contains a variable is called a coefficient.
A variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.

Question 19.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 19

Answer:
2 – exponent
8 and \(\frac{1}{3}\)– coefficient
x – variable or term
A term without a variable is called a constant.
An exponent is a number or letter written above and to the right of a mathematical expression called the base
The exponent tells us how many times the base is used as a factor
The numerical factor of a term that contains a variable is called a coefficient.
A variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.

Question 20.
YOU BE THE TEACHER
Your friend finds the terms, coefficients, and constants in the algebraic expression 2x2y. Is your friend correct? Explain your reasoning.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 20

Answer:
Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-20
A term without a variable is called a constant.
An exponent is a number or letter written above and to the right of a mathematical expression called the base
The exponent tells us how many times the base is used as a factor
The numerical factor of a term that contains a variable is called a coefficient.
A variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.

Question 21.
PERIMETER
You can use the expression 2ℓ + 2w to find the perimeter of a rectangle, where ℓ is the length and w is the width.
a. Identify the terms, coefficients, and constants in the expression.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 21

Answer:
Given Expression 2ℓ + 2w
The coefficients of the expression are 2.
terms – l, w
b. Interpret the coefficients of the terms.

Answer: The coefficients of the terms are 2, 2
2 + 2 = 4

USING EXPONENTS
Write the expression using exponents.

Question 22.
b . b . b

Answer:
b raised to the third power
An exponent is a number or letter written above and to the right of a mathematical expression called the base
The exponent tells us how many times the base is used as a factor

Question 23.
g . g . g . g . g

Answer:
g raised to the fifth power
An exponent is a number or letter written above and to the right of a mathematical expression called the base
The exponent tells us how many times the base is used as a factor

Question 24.
8 . w . w . w . w

Answer:
8 – constant
w raised to the fourth power
An exponent is a number or letter written above and to the right of a mathematical expression called the base
The exponent tells us how many times the base is used as a factor

Question 25.
5 . 2 . y . y . y

Answer:
5 and 2 – constant
y raised to the third power
An exponent is a number or letter written above and to the right of a mathematical expression called the base
The exponent tells us how many times the base is used as a factor

Question 26.
a . a . c . c

Answer:
a and c  raised to the two power
An exponent is a number or letter written above and to the right of a mathematical expression called the base
The exponent tells us how many times the base is used as a factor

Question 27.
2 . 1 . x . z . z .z . z

Answer:
2 and 1 – constant
x raised to the 1 power
z raised to the fourth power
An exponent is a number or letter written above and to the right of a mathematical expression called the base
The exponent tells us how many times the base is used as a factor

Question 28.
YOU BE THE TEACHER
Your friend writes the product using exponents. Is your friend correct? Explain your reasoning.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 22

Answer: correct
5  – constant
n  raised to the fourth power
An exponent is a number or letter written above and to the right of a mathematical expression called the base
The exponent tells us how many times the base is used as a factor

Question 29.
AREA
Write an expression using exponents that represents the area of the square.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 23

Answer:
Side = 5d
Area of the square = s × s
A = 5d × 5d
A = 25d²

Question 30.
REASONING
Suppose the man in the St. Ives poem has x wives, each wife has x sacks, each sack has x cats, and each cat has x kits. Write an expression using exponents that represent the total number of kits, cats, sacks, and wives.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 24

Answer:
Suppose the man in the St. Ives poem has x wives, each wife has x sacks, each sack has x cats, and each cat has x kits.
x = 7
7 × 7 × 7 × 7

EVALUATING EXPRESSIONS
Evaluate the expression when a = 3, b = 2, and c = 12.

Question 31.
6 + a

Answer: 9

Explanation:
Given equation
6 + a
given data
a = 3
now substitute given data in the equation we get
6 + 3 = 9
hence the answer is 9

Question 32.
b.5

Answer: 10

Explanation:
Given equation
b.5
given data
b = 2
now substitute given data in the equation we get
2 . 5= 10 (2 multiply by 5)
hence the answer is 10

Question 33.
c – 1

Answer: 11

Explanation:
Given equation
c – 1
given data
c = 12
now substitute given data in the equation we get
12 – 1 = 11
hence the answer is 11

Question 34.
27 ÷ a

Answer: 9

Explanation:
Given equation
27 ÷a
given data
a = 3
now substitute given data in the equation we get
27 ÷ 3 = 9
Hence the answer is 9

Question 35.
12 – b

Answer: 10

Explanation:
Given equation
12 -b
given data
b = 2
now substitute given data in the equation we get
12 – 2 = 10
Hence the answer is 10

Question 36.
c + 5

Answer: 17

Explanation:
Given equation
c + 5
given data
c = 12
now substitute given data in the equation we get
12+ 5 = 17
Hence the answer is 17

Question 37.
2a

Answer: 6

Explanation:
Given equation
2a
given data
a = 3
now substitute given data in the equation we get
2(3) = 6
Hence the answer is 6

Question 38.
c ÷ 6

Answer: 2

Explanation:
Given equation
c ÷ 6
given data
c = 12
now substitute given data in the equation we get
12 ÷ 6 = 2
Hence the answer is 2

Question 39.
a + b

Answer: 5

Explanation:
Given equation
a + b
given data
a = 3, b = 2
now substitute given data in equation we get
3 + 2 = 5
hence the answer is 5

Question 40.
c + a

Answer: 15

Explanation:
Given equation
a + b
given data
a = 3, b = 2
now substitute given data in equation we get
3 + 2 = 5
hence the answer is 5

Question 41.
c – a

Answer: 11

Explanation:
Given equation
c – a
given data
a = 3, c = 12
now substitute given data in equation we get
12 – 3 = 11
hence the answer is 11

Question 42.
a – b

Answer: 1

Explanation:
Given equation
a – b
given data
a = 3, b = 2
now substitute given data in equation we get
3 – 2 = 1
hence the answer is 1

Question 43.
\(\frac{c}{a}\)

Answer: 4

Explanation:
Given equation
\(\frac{c}{a}\)
given data
a = 3, c = 12
now substitute given data in equation we get
\(\frac{12}{3}\) = 4
hence the answer is 4

Question 44.
\(\frac{c}{b}\)

Answer: 6

Explanation:
Given equation
\(\frac{c}{b}\)
given data
b = 2, c = 12
now substitute given data in equation we get
\(\frac{12}{2}\) = 6
hence the answer is 6

Question 45.
b.c

Answer: 24

Explanation:
Given equation
b . a
given data
b = 2, c = 12
now substitute given data in equation we get
2(12) = 24
hence the answer is 24

Question 46.
c(a)

Answer: 36

Explanation:
Given equation
c(a)
given data
a = 3, c = 12
now substitute given data in equation we get
12(3) = 36
hence the answer is 36

Question 47.
PROBLEM SOLVING
You earn 15n dollars for mowing n lawns. How much do you earn for mowing 1 lawn? 7 lawns?

Answer:
Given,
You earn 15n dollars for mowing n lawns.
n = 1
15 × 1 = 15
n = 7
15 × 7 = 105
Thus you earn $15 for mowing 1 lawn and $105 for mowing 7 lawns.

EVALUATING EXPRESSIONS
Copy and complete the table.

Question 48.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 25

Answer:
Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-25
Explanation:
Given data from the table
x = 3 ,6, and 9
substitute x values in the given equation x . 8
3(8) = 24
6(8) = 48
9(8) = 72

Question 49.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 26

Answer:
Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-26
Explanation:
Given data from the table
x = 2 ,4, and 8
substitute x values in the given equation 64 ÷ x = 24
64 ÷ 2 = 32
64 ÷ 4 = 16
64 ÷ 8 = 8

Question 50.
MODELING REAL LIFE
Due to gravity, an object falls 16t2 feet in t seconds. You drop a rock from a bridge that is 75 feet above the water. Will the rock hit the water in 2 seconds? Explain.

Answer:  No
Given
Due to gravity, an object falls 16t2 feet in t seconds. You drop a rock from a bridge that is 75 feet above the water
d = 16t² (d in ft, t in sec)
Set d = 75 ft and solve for t.
75 = 16t²
t = √(75/16) sec ≅ 2.17 sec
It hits the water in 2.17 sec.

EVALUATING EXPRESSIONS
Evaluate the expression when a = 10, b = 9, and c = 4.

Question 51.
2a + 3

Answer: 23
Given equation
2a + 3
given data
a = 10,
now substitute given data in equation we get
2(10)+3
= 20 + 3
= 23
hence the answer is 23

Question 52.
4c – 7.8

Answer:
Given equation
4c – 7.8
given data
a = 10,
now substitute given data in equation we get
4(4) – 7.8
= 16 – 7.8
= 8.2
Hence the answer is 8.2

Question 53.
\(\frac{a}{4}\) + \(\frac{1}{3}\)

Answer: \(\frac{17}{6}\) or 2.83
Given equation
\(\frac{a}{4}\) + \(\frac{1}{3}\)
given data
a = 10,
now substitute given data in equation we get
\(\frac{10}{4}\) + \(\frac{1}{3}\)
= \(\frac{17}{6}\)
= 2.83
hence the answer is \(\frac{17}{6}\) or 2.83

Question 54.
\(\frac{24}{b}\) + 8

Answer:
\(\frac{32}{3}\) or 10.66
Given equation
\(\frac{24}{b}\) + 8
given data
b = 9,
now substitute given data in equation we get
\(\frac{24}{9}\) + 8
= \(\frac{8}{3}\) + 8
= \(\frac{32}{3}\)
= 10.66
Hence the answer is \(\frac{32}{3}\) or 10.66

Question 55.
c2 + 6

Answer: 22
Given equation
c² + 6
given data
c = 4,
now substitute given data in equation we get
c² + 6
= 4² + 6
= (4 × 4) + 6
= 16 + 6
= 22
Hence the answer is 22

Question 56.
a2 – 18

Answer: 82
Given equation
a² – 18
given data
a = 10,
now substitute given data in equation we get
a² – 18
= 10² – 18
= (10 × 10) – 18
= 100 – 18
= 82
Hence the answer is 82

Question 57.
a + 9c

Answer: 40
Given equation
a  + 9c
given data
a = 10, c = 4
now substitute given data in equation we get
10 + 9(4)
= 10 + 36
= 46
Hence the answer is 46

Question 58.
bc + 12.3

Answer: 48.3
bc + 12.3
given data
b = 9, c = 4
now substitute given data in equation we get
9(4) + 12.3
= 36 + 12.3
= 48.3
Hence the answer is 48.3

Question 59.
3a + 2b – 6c

Answer: 24
3a + 2b – 6c
given data
a = 10, b = 9, c = 4
now substitute given data in equation we get
3(10) + 2(9) – 6(4)
= 30 + 18 – 24
= 24
Hence the answer is 24

Question 60.
YOU BE THE TEACHER
Your friend evaluates the expression when m = 8. Is your friend correct? Explain your reasoning.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 27

Answer:  incorrect.

Explanation:
Given the expression 5m + 3
m = 8
5 × 8 + 3
40 + 3 = 43
By this we can say that your friend is incorrect.

Question 61.
PROBLEM SOLVING
After m months, the height of a plant is (10 + 3m) millimeters. How tall is the plant after 8 months? 3 years?

Answer:
8 months = 34 millimeters
EXPLANATION:
You have to plug in the number 8 as “m” in the equation then solve. 10 + 3(8)
3 years = 118 millimeters
3 years converted to months would be 12×3 which equals 36. Then put it into the equation 10 + 3(36) and you do the multiplication first.

Question 62.
STRUCTURE
You use a video streaming service to rent x new releases and y standard rentals. Which expression tells you how much money you will need?
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 28
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 29

Answer:
4x+3y

Explanation:
It is given that,
The number of new releases are represented by ‘x’ and number of standard rentals are represented by ‘y’.
Also, the cost for one new release = $4 and the cost of one standard rental = $3.
Thus, the cost of ‘x’ new releases = $4x and the cost of ‘y’ new releases = $3y.
So, the total cost = cost of ‘x’ new releases + cost of ‘y’ standard rentals.
i.e. Total cost = 4x + 3y in dollars.
Thus, the expression to tell the money required is 4x+3y.

Question 63.
OPEN-ENDED
You float 2000 feet along a lazy river water ride. The ride takes less than 10 minutes. Give two examples of possible times and speeds.

Answer:
if you travel at 200 feet per minute you can make in ten minutes

Question 64.
DIG DEEPER!
The expression 20a + 13c is the cost (in dollars) for a adults and c students to enter a science center.
a. How much does it cost for an adult? a student? Explain your reasoning.

Answer:
It costs $20 per adult. If this is a cost function,
which it is because the wording is “the cost (in dollars) for adults and c students”, the adult is the cost for 1 adult, 1a, is 20.
That relates the number of adults to the cost of 1 adult.
It costs $13 per student. Again, this is a cost function, so since the student is c,
the cost for 1 student, 1c, is 13. That relates the number of students to the cost of 1 student.

b. Find the total cost for 4 adults and 24 students.

Answer:
The total cost for 4 adult and 24 students looks like this:
20(4) + 13(24) which is 80 + 312 = $392

c. You find the cost for a group. Then the numbers of adults and students in the group both double. Does the cost double? Explain your answer using an example.

Answer:
If you have 3 adults and 3 students in your group, the cost is 20(3) + 13(3) which is $99.
If you double the number of each, let’s see if the cost doubles.
We will “up” the numbers to 6 each. 20(6) + 13(6) = $198. Is $198 the double of $99.
Yes it is. Let’s do it again to check. Let’s double the 6.
20(12) + 13(12) = $396, and $198 doubled does in fact equal $396

d. In part(b), the number of adults is cut in half, but the number of students doubles. Is the cost the same? Explain your answer.

Answer:
20(12) + 13(12) = $396, and $198 doubled does in fact equal $396.

Question 65.
REASONING
The volume of the cube (in cubic inches) is equal to four times the area of one of its faces (in square inches). What is the volume of the cube?
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 30

Answer:
Given,
The volume of the cube (in cubic inches) is equal to four times the area of one of its faces (in square inches).
We know that,
The volume of a cube = x³
Multiply 3 sides = x × x × x = x³

Lesson 5.2 Writing Expressions

EXPLORATION 1
Writing Expressions
Work with a partner. You use a $20 bill to buy lunch at a café. You order a sandwich from the menu board shown.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 31
a. Complete the table. In the last column, write a numerical expression for the amount of change you receive.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 32

Answer:
Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-32
b. Write an algebraic expression that represents the amount of change you receive when you order any sandwich from the menu board.

Answer:
You have only $20 for lunch, so if you order any sandwich from the menu
the board then the amount will be change
if you ordered chicken salad then your changing amount is
price = $ 4.95
change Received = $20 – $4.95 = $15.05
change Received = $15.05

c. The expression 20 − 4.65 represents the amount of change one customer receives after ordering from the menu board. Explain what each part of the expression represents. Do you know what the customer ordered? Explain your reasoning.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 32.1

Answer:
calculated changing amount for chicken salad in part (b),
so comparison between chicken salad expression and beef expression
For Chicken salad
Price = $4.95
change Recived = $20 – $4.95 = $15.05
change Recieved = $15.05
For Roast Beef
price = $6.75
Change Recived = $20 – $6.75 = $13.25
change Recived = $13.25

5.2 Lesson

Some words can imply math operations.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 33

Try It

Write the phrase as an expression.

Question 1.
the sum of 18 and 35

Answer: 53
Given
the sum of 18 and 35
so by add 18 with 35
we get 18+35
=53
So the answer is 53

Question 2.
6 times 50

Answer: 300
given
6 times 50
so multiply 6 with 50 we get
300
Hence the answer is 300

Write the phrase as an expression.

Question 3.
25 less than a number b

Answer: b – 25

Question 4.
a number x divided by 4

Answer:  \(\frac{x}{4}\)

Question 5.
the total of a number t and 11

Answer: t + 11

Question 6.
100 decreased by a number k.

Answer: 100 – k

Try It

Question 7.
Your friend has 5 more than twice as many game tokens as you. Let t be the number of game tokens you have. Write an expression for the number of game tokens your friend has.

Answer: 5+2t
given
Your friend has 5 more than twice as many game tokens as you
5+2t because 5 more then is adding 5 and twice as many is doubling or multiplying by 2

Self-Assessment for Concepts & Skills
Solve each exercise. Then rate your understanding of the success criteria in your journal.

WRITING EXPRESSIONS
Write the phrase as an expression.

Question 8.
the sum of 7 and 11

Answer: 7 + 11 we get 18

Question 9.
5 subtracted from 9

Answer: 9 – 5 we get 4

Question 10.
DIFFERENT WORDS, SAME QUESTION
Which is different? Write “both” expressions.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 34

Answer: 12 more than x and x increased by 12 has different words but the question is same.

Question 11.
PRECISION
Your friend says that the phrases below have the same meaning. Is your friend correct? Explain your reasoning.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 35

Answer: No your friend is incorrect.
“the difference of number x and 12” is x – 12
“the diffrence of 12 and number x” is 12 – x

Self-Assessment for Problem Solving

Solve each exercise. Then rate your understanding of the success criteria in your journal.

Question 12.
A company rents paddleboards by charging a rental fee plus an hourly rate. Write an expression that represents the cost (in dollars) of renting a paddleboard for h hours. How much does an eight-hour rental cost?
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 36

Answer:
The independent variable is that whose values do not take into account the values of other variables.
That is the time in hours for this item. Then, for the dependent variable, the answer would be the cost of renting.
The value of the dependent variable is based on the changes done in the values of the independent variable.

Question 13.
DIG DEEPER!
A county fair charges an entry fee of $7 and $0.75 for each ride token. You have $15. Write an expression that represents the amount (in dollars) you have left after entering the fair and purchasing n tokens. How many tokens can you purchase? How much money do you have left after purchasing 6 tokens?
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 37

Answer:
Given,
A county fair charges an entry fee of $7 and $0.75 for each ride token.
You have $15.
15.00 – 7.00 = 8.00
6 x .75 = 4.50
8.00- 4.5 = 3.50

Writing Expressions Homework & Practice 5.2

Review & Refresh

Identify the terms, coefficients, and constants in the expression.

Question 1.
4f + 8

Answer:
8 – constant
4 – coefficient
f- variable or term
A term without a variable is called a constant.
The numerical factor of a term that contains a variable is called a coefficient.
A variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.

Question 2.
\(\frac{4}{5}\) + 3s + 2

Answer:
\(\frac{4}{5}\) and 2 – constant
3 – coefficient
s- variable or term
A term without a variable is called a constant.
The numerical factor of a term that contains a variable is called a coefficient.
A variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.

Question 3.
9h2 + \(\frac{8}{9}\)p + 1

Answer:
1 – constant
2 – exponent
9 and \(\frac{8}{9}\)  – coefficient
h and p – variable or term
An exponent is a number or letter written above and to the right of a mathematical expression called the base
The exponent tells us how many times the base is used as a factor
The numerical factor of a term that contains a variable is called a coefficient.
A variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.

Copy and complete the statement.

Question 4.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 38

Answer: 7.5 gallon per hour

Explanation:
Convert from cup per minute to gallon per hour
1 Cup per minute = 3.75 gallon per hour
2 cup per minute = 2 × 3.75 = 7.5 gallon per hour

Question 5.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 39

Answer: 2362.2 feet per minute

Explanation:
Convert from meter per second to feet per minute
1 meter per second = 196.85 feet per minute
12 minute per second = 2362.2 feet per minute

Question 6.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 40

Answer: 4898.79 kg per hour

Explanation:
Convert from lb per second to kg per hour
1 lb per second = 1632.93 kg per hour
3 lb per second = 4898.79 kg per hour

Divide. Write the answer in simplest form.

Question 7.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 41

Answer:  \(\frac{8}{9}\) or 0.533

Explanation:
by dividing \(\frac{1}{2}\) with \(\frac{5}{8}\)
we get \(\frac{1}{2}\) ÷ \(\frac{5}{8}\)
\(\frac{8}{9}\)
0.533

Question 8.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 42

Answer: \(\frac{4}{9}\)

Explanation:
by dividing \(\frac{1}{3}\) with \(\frac{3}{4}\)
we get \(\frac{1}{3}\) ÷ \(\frac{3}{4}\)
\(\frac{4}{9}\)
0.44

Question 9.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 43

Answer: \(\frac{2}{15}\) or 0.133

Explanation:
by dividing \(\frac{2}{5}\) with \(\frac{3}{1}\)
we get \(\frac{2}{5}\) ÷ \(\frac{3}{1}\)
\(\frac{2}{15}\)
0.133

Question 10.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 44

Answer: \(\frac{7}{2}\) or 3.5

Explanation:
by dividing \(\frac{3}{1}\) with \(\frac{6}{7}\)
we get \(\frac{3}{1}\) ÷ \(\frac{6}{7}\)
\(\frac{7}{2}\)
3.5

Concepts, Skills, & Problem Solving

STRUCTURE
The expression represents the amount of change you receive after buying n sandwiches. Explain what each part of the expression represents. (See Exploration 1, p. 209.)

Question 11.
10 – 5.25n

Answer:
Let us assume that you buy 1 sandwich.
10 – 5.25(1)
= 10 – 5.25
= 4.75

Question 12.
20 – 4.95n

Answer:
Let us assume that you buy 2 sandwiches.
20 – 4.95(2)
20 – 9.9 = 10.1

Question 3.
100 – 6.75n

Answer:
Let us assume that you buy 6 sandwiches.
100 – 6.75(6)
= 100 – 40.50
= 59.50

WRITING EXPRESSIONS
Write the phrase as an expression.

Question 14.
5 less than 8

Answer: 5 < 8

Explanation:
The phrase “less than” indicates < symbol.
So, the expression is 5 < 8

Question 15.
the product of 3 and 12

Answer: 3 × 12

Explanation:
The phrase “product” indicates multiplication.
So, the expression is 3 × 12

Question 16.
28 divided by 7

Answer: 28 ÷ 7

Explanation:
The phrase “divided by” indicates ÷ symbol
So, the expression is 28 ÷ 7

Question 17.
the total of 6 and 10

Answer: 6 + 10 = 16

Explanation:
The phrase “total” indicates ‘+’ symbol.
So, the expression is 6 + 10 = 16

Question 18.
3 fewer than 18

Answer: 18 – 3

Explanation:
The phrase fewer than indicates ‘subtraction’
So, the expression is 18 – 3

Question 19.
17 added to 15

Answer: 17 + 15

Explanation:
Given 17 added to 15
so add 17 with 15

Question 20.
13 subtracted from a number x

Answer: 13 – x

Explanation:
The number represents the variable x
So here we have to subtract number x from 13
That gives the expression 13 – x

Question 21.
5 times a number d

Answer: 5d

Explanation:
The number represents variable d.
The word “times” represents ×
So the expression is 5d

Question 22.
the quotient of 18 and a number a

Answer: 18 ÷ a

Explanation:
a represents the number
So, the expression would be 18 ÷ a

Question 23.
the difference of a number s and 6

Answer: s – 6

Question 24.
7 increased by a number w

Answer: 7 + w

Question 25.
a number t cubed

Answer: t³

YOU BE THE TEACHER
Your friend writes the phrase as an expression. Is your friend correct? Explain your reasoning.

Question 26.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 45

Answer: incorrect

Explanation:
Given,
The quotient of 8 and a number is y is 8 ÷ y
By this, we can say that your friend is incorrect.

Question 27.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 46

Answer: correct

Explanation:
Given,
16 decreased by a number x
It means we have to subtract x from 16.
Thus the expression is 16 – x.

Question 28.
NUMBER SENSE
Five friends share the cost of a dinner equally.
a. Write an expression that represents the cost (in dollars) per person.

Answer: 600 ÷ p

b. Make up a reasonable total cost and test your expression.

Answer:
The total cost of dinner is $600.
Now divide the cost per person.
There are 5 friends.
The expression is 600 ÷ p
p = 5
600 ÷ 5 = 12
The cost per person is $120

Question 29.
MODELING REAL LIFE
A biologist analyzes 15 bacteria samples each day.
a. Copy and complete the table.
b. Write an expression that represents the total number of samples analyzed after n days.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 47

Answer:
Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-47
The expression that represents the total number of samples analyzed after n days is 15n

Question 30.
PROBLEM SOLVING
To rent a moving truck for the day, it costs $33 plus $1 for each mile driven.
a. Write an expression that represents the cost (in dollars) to rent the truck.

Answer: 33 + d
b. You drive the truck 300 miles. How much do you pay?

Answer:
Use the expression 33 + d to find how much do you pay.
33 + 300 = 333
Thus you pay $333 for 300 miles.

WRITING PHRASES
Give two ways to write the expression as a phrase.

Question 31.
n + 6

Answer:
According to the given details, we can write the expression in two ways
a number n more than 6
the sum of a number n and 6

Question 32.
4w

Answer:
According to the given details, we can write the expression in two ways
a number w is four times
The product of 4 and a number w

Question 33.
15 – b

Answer:
According to the given details we can write the expression in two ways.
15 decreased by a number d
The difference of 15 and a number b

Question 34.
14 – 3z

Answer:
According to the given details, we can write the expression in two ways.
The product of 3 and z subtracted from 14.
The difference of 14 and product of 3 and a number z.

EVALUATING EXPRESSIONS
Write the phrase as an expression. Then evaluate the expression when x = 5 and y = 20.

Question 35.
3 less than the quotient of a number y and 4

Answer:
given 3 less than the quotient of a number y and 4
The quotient of a number y and 4
Now we are given that 3 less than the quotient of a number y and 4
So, \(\frac{y}{4}\) – 3
Hence the expression becomes \(\frac{y}{4}\) – 3

Question 36.
the sum of a number x and 4, all divided by 3

Answer:
given
a sum, x and 4, so that becomes x + 4
All divided by denotes that we need to do the addition before division, so we need to put it in parentheses:
(x + 4)
And it is divided by 3.
So you can write the answer down in a few different ways:
(x + 4) ÷ 3
(x + 4) / 3
\(\frac{x + 4}{3}\)

Question 37.
6 more than the product of 8 and a number x

Answer:
A Product is an answer to a multiplication.
The product of 8 and a number is 8×n=8n
6 more than that means to add on 6
So the expression “6 more than the product of 8 and a number” is
8n+6

Question 38.
the quotient of 40 and the difference of a number y and 16

Answer:
as we know that
The expression ” the quotient of and the difference of a number y and ” is equivalent to the algebraic equation
\(\frac{40}{y-16}\)
For  y = 20  given problem
substitute the value of y in the equation
\(\frac{40}{20-16}\)  = \(\frac{40}{4}\) = 10

Question 39.
MODELING REAL LIFE
It costs $3 to bowl a game and $2 for shoe rental.
a. Write an expression that represents the total cost (in dollars) of g games.
b. Use your expression to find the total cost of 8 games.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 48

Answer:
a. If shoes are for all games in row, P=2+3g
b. If not, P=5g, with g the number of games
Explanation:
The price depends if shoes are included for the whole games, you just have to pay them once and then you have to pay g games, so P(g)=2+3g
Else, you have to pay for g shoes and g bowl party, so P(g)=2g+3g⇔P(g)=5g

Question 40.
MODELING REAL LIFE
Florida has 8 less than 5 times the number of counties in Arizona. Georgia has 25 more than twice the number of counties in Florida.
a. Write an expression that represents the number of counties in Florida.
b. Write an expression that represents the number of counties in Georgia.
c. Arizona has 15 counties. How many do Florida and Georgia have?

Answer:
Number of countries in Florida=5×a-8
Number of countries in Georgia=2×f+25
Explanation:
Given that the number of countries in Florida is denoted by f,
The number of countries in Arizona is given by a and the number of countries in Georgia is given by g.
as Florida has 8 less than five times the number of countries in Arizona
So f=5×a-8
Georgia has 25 more than twice the number of countries in Florida
So g=2×f+25
Now it is given that Arizona has 15 countries i.e. a=15
So f=5×15-8
f=67
g=2×67+25
g=159
Hence, the number of countries in Florida is:67
number of countries in Georgia is:159

Question 41.
PATTERNS
There are 140 people in a singing competition. The graph shows the results for the first five rounds.
a. Write an expression that represents the number of people after each round.
b. Assuming this pattern continues, how many people compete in the ninth round? Explain your reasoning.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 49

Answer:
a) The expression is y = 140 – 15 x
b ) There are 5 participants in the 9th round

Step-by-step explanation:
Step 1 :
From the graph we can see that,
Number of people in the singing competition = 140
Number of people in the first round = 125
Number of people in the second round = 110
Number of people in the third round = 95
Number of people in the fourth round = 80
Number of people in the fifth round = 65
Step 2 :
From the given data, We can get that the difference between the number of people participating in each round is 15 less than the previous round .
The first round has 15 people less than the total number of 140
Let x represent the number of the round and y represent the number of people participating in each round .
Then the expression to represent this would be
y = 140 – 15 x
Step 3 :
To find the number of participants in the 9th round given the same pattern continues.
For the 9th round x = 9, as x represents the number of the round
Substituting this in the equation obtained in step 2, we get
y = 140 -15 (9) = 140 – 135 = 5
There are 5 participants in the 9th round

Question 42.
NUMBER SENSE
The difference between two numbers is 8. The lesser number is a. Write an expression that represents the greater number.

Answer:
Given The difference between the two numbers is 8. The lesser number is a.
b-a=8
b is the greater number; b>a
So, b=a+8

Question 43.
NUMBER SENSE
One number is four times another. The greater number is x. Write an expression that represents the lesser number

Answer: y = x/4

Let us assume the smaller number y.
We know that four times the smaller number is equal to x. So, four times y is equal to x.
Turning this into an expression, you get 4y = x.
This means, to get y on its own, we need to divide by 4 on both sides, giving us the answer of y = x/4

Lesson 5.3 Properties of Addition and Multiplication

EXPLORATION 1

Identifying Equivalent Expressions
Work with a partner.
a. Choose four values for a variable x. Then evaluate each expression for each value of x. Are any of the expressions equivalent? Explain your reasoning.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 49.1

Answer:
Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-49.1
The equation x + 8, 4 + 4 + x, x + 4 + 4 are equal.
The equation 16x, 4.(x.4), (4.x).x are equal.
b. You have used the following properties in a previous course. Use the examples to explain the meaning of each property.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 50
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 51
Are these properties true for algebraic expressions? Explain your reasoning.

Answer:
Commutative property of addition: The commutative property of addition says that changing the order of addends does not change the sum. Here’s an example: 5 + 2 = 7 or 2 + 5 = 7
Commutative property of multiplication: The commutative property of multiplication tells us that we can multiply a string of numbers in any order. Basically: 2 x 3 x 5 will create the same answer as 3 x 5 x 2, or 2 x 5 x 3
Associative property of addition: The associative property of addition says that changing the grouping of the addends does not change the sum.
Example: 2 + (7 + 5) = (2 + 7) + 5
Associative Property of Multiplication: The associative property is a math rule that says that the way in which factors are grouped in a multiplication problem does not change the product.
Example: 2 × (7 × 5) = (2 × 7) × 5

5.3 Lesson

Expressions that result in the same number for any value of each variable are equivalent expressions. You can use the Commutative and Associative Properties to write equivalent expressions.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 52

Try It

Simplify the expression. Explain each step.

Question 1.
10 + (a + 9)

Answer: a+19
Step 1: Eliminate redundant parentheses
10+(a+9)=10+a+9
Step 2:Add the numbers
Step 3: Rearrange terms
a+19

Question 2.
(c + \(\frac{2}{3}\)) + \(\frac{1}{2}\)

Answer: c + \(\frac{7}{6}\)
(c + \(\frac{2}{3}\)) + \(\frac{1}{2}\)
c+ \(\frac{7}{6}\)

Question 3.
5(4n)

Answer: 20n
Multiply 5 with 4n
we get 20n

Simplify the expression. Explain each step.

Question 4.
12.b.0

Answer: 0
step 1
12 multiply with a number b
and then multiply with 0
we get 0

Question 5.
1.m.24

Answer: 24m
step 1
1 multiply with a number m
and then multiply with 24
we get 24m

Question 6.
(t + 15) + 0

Answer: t + 15
step 1
Add t + 15 with 0
and then
we get t + 15

Self-Assessment for Concepts & Skills

Solve each exercise. Then rate your understanding of the success criteria in your journal.

USING PROPERTIES
Simplify the expression. Explain each step.

Question 7.
(7 + c) + 4

Answer:
Step 1: Eliminate redundant parentheses
4+(7+c)= 4+7+c
Step 2:Add the numbers
Step 3: Rearrange terms
11 + c

Question 8.
4(b.6)

Answer: 24b
Step 1: Eliminate redundant parentheses
4 × b× 6 = 4 × 6× b
multiply 4 with 6 we get 24 and then with b
so we get 24b

Question 9.
0.b.9

Answer: 0
Step 1: Eliminate redundant parentheses
0 × b× 9 = 0 × 9× b
multiply 0 with 9 we get 0 and then with b
so we get 0

Question 10.
WRITING
Explain what it means for expressions to be equivalent. Then give an example of equivalent expressions.

Answer:
equivalent expressions are algebraic expressions that, although they look different, turn out to really be the same.

Example:
Let’s consider this algebraic expression: 2(x^2 + x). If we substitute 1 for the variable, the expression equals 4. But what about the expression
2x^2 + 2x? If, again, we substitute 1 for the variable x, we still get 4. How does this happen?
What we really did was simplify the original expression by distributing the 2 into the part in parentheses. So we really haven’t changed the expression at all – all we’ve done is rewrite it in a different form.
Because these two expressions are really the same, no matter what number we substitute for x, the results will always be identical. If we use 0, both expressions come out to 0. If we use 10, both expressions come out to 220. If we use 100, both expressions come out to 20,200. We get the same result no matter how large or small the number we use for x.

Question 11.
OPEN-ENDED
Write an algebraic expression that can be simplified using the Associative Property of Multiplication and the Multiplication Property of One.

Answer:
Let us consider an expression 4 × 30.
We can simplify the expression by using the Associative Property of Multiplication
4 × 30 = 4 × (5 × 6)
(4 × 5) × 6 = 4 × (5 × 6)
20 × 6 = 4 × 30
120 = 120

Self-Assessment for Problem Solving

Solve each exercise. Then rate your understanding of the success criteria in your journal.

Question 12.
You and five friends form a team for an outdoor adventure race. Your team needs to raise money to pay for $130 of travel fees, x dollars for each team member’s entry fee, and $85.50 for food. Use an algebraic expression to find the total amount your team needs to raise when the entry fee is $25.50 per person.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 53

Answer: (130+85)+25.5p=total amount

Step-by-step explanation:
130+85 is how much you’d need just for the fees and food, for the entry fee its per person
so it would be $25.5 for every person that is part of your team.

Question 13.
You have $50 and a $15 gift card to spend online. You purchase a pair of headphones for $34.99 and 8 songs for x dollars each. Use an algebraic expression to find the amount you have left when each song costs $1.10.

Answer: $21.21
Given
You have $50 and a $15 gift card to spend online
purchase a pair of headphones for $34.99 and 8 songs for x dollars each.
Use an algebraic expression to find the amount you have left when each song costs $1.10.
so
50 + 15 -34.99 – 8x
65 – 34.99 – 8(1.10)
30.01 – 8.8
$21.21

Properties of Addition and Multiplication Homework & Practice 5.3

Review & Refresh

Write the phrase as an expression.

Question 1.
10 added to a number p

Answer:  p + 10
First consider the expression for
10 added to a number p
we get p + 10
An algebraic expression is a mathematical phrase that contains a combination of numbers, variables and operational symbols.
A variable is a letter that can represent one or more numbers.

Question 2.
the product of 6 and a number m

Answer: 6m
First consider the expression for
the product of 6 and a number m
so multiply 6 with m
we get 6m
An algebraic expression is a mathematical phrase that contains a combination of numbers, variables and operational symbols.
A variable is a letter that can represent one or more numbers.

Question 3.
the quotient of a number b and 15

Answer: \(\frac{b}{15}\)
First consider the expression for
the quotient of a number b and 15
so divide b by 15
we get \(\frac{b}{15}\)
An algebraic expression is a mathematical phrase that contains a combination of numbers, variables and operational symbols.
A variable is a letter that can represent one or more numbers.

Question 4.
7 fewer than a number s

Answer:  s – 7
First consider the expression for
7 fewer than a number s
so subtract a number s with 7
we get s – 7
An algebraic expression is a mathematical phrase that contains a combination of numbers, variables and operational symbols.
A variable is a letter that can represent one or more numbers.

Write the prime factorization of the number.

Question 5.
36

Answer:
The number 36 can be written as a product of primes as
36 = 2² x 3².
The expression 2² x 3² is said to be the prime factorization of 36

Question 6.
144

Answer:
The prime factor of the 144 is 24 x 32.
144 = 2 x 2 x 2 x 2 x 3 x 3

Question 7.
147

Answer:
Factors of 147: 1, 3, 7, 21, 49, 147.
Prime factorization: 147 = 3 x 7 x 7,
which can also be written
147 = 3 x (7²)

Question 8.
205

Answer:
the prime factors of the number 205.
If we put all of it together we have the factors 5 x 41 = 205.
it can also be written in exponential form as 5¹ x 41¹.

Evaluate the expression.

Question 9.
8.092 + 3.5

Answer: 11.592
Given expression 8.092 + 3.5
now add 8.092 with 3.5 we get
11.592

Question 10.
16.78 – 12.237

Answer: 4.543
Given expression 16.78 – 12.237
now subtract  16.75 with 12.237  we get
4.543

Question 11.
9.17 + 1.83 + 2.641

Answer:  13.641
Given expression 9.17 + 1.83 + 2.641
now add 9.17  with 1.83  we get  11 then add with 2.641
we get 13.641

Question 12.
8.43 – 6.218 + 4.2

Answer:
Given expression 8.43 – 6.218 + 4.2
now subtract  8.43 with 6.218  we get 2.212  then add with 4.2
we get  6.412

Represent the ratio relationship using a graph.

Question 13.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 54

Answer:
Big Ideas Math Grade 6 Chapter 5 Algebraic Expressions and Properties Answers img_1

Question 14.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 55

Answer:
Big Ideas Math Grade 6 Chapter 5 Algebraic Expressions and Properties Answers img_2

Concepts, Skills, & Problem Solving
MATCHING
Match the expression with an equivalent expression. (See Exploration 1, p. 215.)

Question 15.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 56

Answer: B

Explanation:
3 + 3 + y is equivalent to y + 3 + 3
So, the correct answer is option B

Question 16.
Big Ideas Math Answers 6th Grade Chapter 5 Algebraic Expressions and Properties 57

Answer: C

Explanation:
(y.y).3 = y(3 . y)
So, the correct answer is option C.

Question 17.
Big Ideas Math Answers 6th Grade Chapter 5 Algebraic Expressions and Properties 58

Answer: A

Explanation:
3 . 1 . y = y . 3
So, the correct answer is option A.

Question 18.
Big Ideas Math Answers 6th Grade Chapter 5 Algebraic Expressions and Properties 59

Answer: D

Explanation:
(3 + 0) + (y + y)
(3 + y) + y
So, the correct answer is option D.

IDENTIFYING PROPERTIES
Tell which property the statement illustrates.

Question 19.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 60

Answer: commutative property of multiplication

Explanation:
The commutative property of multiplication tells us that we can multiply a string of numbers in any order.
5 . p = p . 5

Question 20.
2 + (12 + r) = (2 + 12) + r

Answer: associative property of addition

Explanation:
Associative property of addition: Changing the grouping of addends does not change the sum.
2 + (12 + r) = (2 + 12) + r

Question 21.
4 . (x . 10) = (4 . x) . 10

Answer: associative property of multiplication

Explanation:
The associative property is a math rule that says that the way in which factors are grouped in a multiplication problem does not change the product.

Question 22.
x + 7.5 = 7.5 + x

Answer: commutative property of addition

Explanation:
The commutative property of addition says that changing the order of addends does not change the sum.

Question 23.
(c + 2) + 0 = c + 2

Answer: Additive Identity

Explanation:
Additive identity is a number, which when added to any number, gives the sum as the number itself. It means that additive identity is “0” as adding 0 to any number, gives the sum as the number itself.

Question 24.
a . 1 = a

Answer: Multiplicative Identity

Explanation:
According to the multiplicative identity property of 1, any number multiplied by 1, gives the same result as the number itself. It is also called the Identity property of multiplication because the identity of the number remains the same.

Question 25.
YOU BE THE TEACHER
Your friend states the property that the statement illustrates. Is your friend correct? Explain your reasoning.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 61

Answer: correct

Explanation:
Associative property of addition: Changing the grouping of addends does not change the sum.
(7 + x) + 3 = (x + 7) + 3
Thus we can say that your friend is correct.

USING PROPERTIES
Simplify the expression. Explain each step.

Question 26.
6 + (5 + x)

Answer: 11 + x
Step 1: Eliminate redundant parentheses
6 + (5 + x) = 6+5+x
Step 2:Add the numbers
Step 3: Rearrange terms
11 + x

Question 27.
(14 + y) + 3

Answer: 17 + y
Step 1: Eliminate redundant parentheses
(14 + y) + 3 = 14 + 3 + y
Step 2:Add the numbers
Step 3: Rearrange terms
17 + y

Question 28.
6(2b)

Answer: 12b
Step 1: Eliminate redundant parentheses
6(2b) = 6 × 2 ×b
Step 2:multiply  the numbers
Step 3: Rearrange terms
we get 12b

Question 29.
7(9w)

Answer: 63w
Step 1: Eliminate redundant parentheses
7(9w) = 7 ×  ×w
Step 2:multiply  the numbers
Step 3: Rearrange terms
we get 63w

Question 30.
3.2 + (x + 5.1)

Answer: 8.3 + x
Step 1: Eliminate redundant parentheses
3.2 + (x + 5.1) = 3.2 + 5.1 + x
Step 2:Add the numbers
Step 3: Rearrange terms
8.3 + x

Question 31.
(0 + a) + 8

Answer: 8 + a
Step 1: Eliminate redundant parentheses
(0 + a) + 8 = 0 + 8 +a
Step 2:Add the numbers
Step 3: Rearrange terms
8 + a

Question 32.
9 . c . 4

Answer: 36c
Step 1: Eliminate redundant parentheses
9 . c . 4 = 9 . 4 . c
Step 2: multiply the numbers
Step 3: Rearrange terms
36c

Question 33.
(18.6 . d) . 1

Answer: 18.6 d
Step 1: Eliminate redundant parentheses
(18.6 . d) . 1 = (18.6 . 1) d
Step 2: multiply the numbers
Step 3: Rearrange terms
18.6 d

Question 34.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 62

Answer:
Step 1: Eliminate redundant parentheses
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 62 = 3k + (4\(\frac{1}{5}\) + 8\(\frac{3}{5}\))
Step 2: add the numbers
Step 3: Rearrange terms
3k + 12\(\frac{4}{5}\)

Question 35.
(2.4 + 4n) + 9

Answer:
Step 1: Eliminate redundant parentheses
(2.4 + 4n) + 9 = 2.4 + 9 + 4n
Step 2:Add the numbers
Step 3: Rearrange terms
11.4 + 4n

Question 36.
(3s) . 8

Answer: 24s
Step 1: Eliminate redundant parentheses
(3s) . 8 = (3 . 8) s
Step 2: multiply the numbers
Step 3: Rearrange terms
24s

Question 37.
z . 0 . 12

Answer: 0
Step 1: Eliminate redundant parentheses
z . 0 . 12 = z × 0 × 12
Step 2: multiply the numbers
Step 3: Rearrange terms
0

Question 38.
GEOMETRY
The expression 12 + x + 4 represents the perimeter of a triangle. Simplify the expression.

Answer: x+16

Explanation:
your simplifying so you only combine like terms.
12 and 4 dont have any variables following them so you add the two.
12+4=16
there is only 1 x in the expression so just add it on.
16+x

Question 39.
PRECISION
A case of scout cookies has 10 cartons. A carton has 12 boxes. The amount you earn on a whole case is 10(12x) dollars.
a. What does x represent?
b. Simplify the expression.

Answer:
Given
A case of scout cookies has 10 cartons. A carton has 12 boxes
A. x represents the money made per box
B. 10(12x) = 120x

Question 40.
MODELING REAL LIFE
A government estimates the cost to design new radar technology over a period of m months. The government estimates $840,000 for equipment, $15,000 for software,and $40,000 per month for wages. Use an algebraic expression to find the total cost the government estimates when the project takes 16 months to complete.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 63

Answer: $1,495,000.

Explanation:
The cost that is affected by the number of months mm is the wages while the first two costs are fixed. Hence, you multiply $40,000 by the number of months so that
840,000+15,000+40,000m
840,000+15,000+40,000m
For m=16m=16 (16 months),
=840,000+15,000+40,000(16)
=840,000+15,000+40,000(16)
=840,000+15,000+640,000
=840,000+15,000+640,000
=1,495,000
=1,495,000
So, the total cost is $1,495,000.

WRITING EXPRESSIONS
Write the phrase as an expression. Then simplify the expression.

Question 41.
7 plus the sum of a number x and 5

Answer:
7+(x+5)  sum means addition and it says x and 5. then it says 7 plus that so you put 7.
In reality, you wouldn’t need parenthesis,
but if you want it to match the phrase, you can put it in parenthesis.

Question 42.
the product of 8 and a number y, multiplied by 9

Answer: 8y x 9 ⇒ 72y
Given
the product of 8 and a number y ⇒ 8 × y = 8y
and also given multiplied by 9 ⇒ 8y × 9
so we get 72 y

USING PROPERTIES
Copy and complete the statement using the specified property.

Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 64

Answer:
Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-64

Question 48.
GEOMETRY
Five identical triangles form the trapezoid shown.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 65
a. What is the perimeter of the trapezoid?

Answer:
The perimeter of the trapezoid is a + b + c + d
P = sum of four sides
P = 3x + 7 + 7 + 2x
P = 5x + 14
Thus the perimeter of the trapezoid is 5x + 14
b. How can you use some or all of the triangles to form a new trapezoid with a perimeter of 3x +14? Explain your reasoning.

Answer:
You can reduce the size of the triangle to form a new trapezoid with a perimeter of 3x +14
The perimeter of the trapezoid is a + b + c + d
P = sum of four sides
P = 2x + 7 + 7 + 1x
P = 3x + 14

Question 49.
DIG DEEPER!
You and a friend sell hats at a fair booth. You sell 16 hats on the first shift and 21 hats on the third shift. Your friend sells x hats on the second shift.
a. The expression 37(14) + 10x represents the amount (in dollars) that you both earn. How can you tell that your friend is selling the hats for a lower price?
b. You earn more money than your friend. What can you say about the value of x?

Answer:
37+x

Explanation:
1st shift: 16 hats were sold
2nd shift: x hats were sold
3rd shift: 21 hats were sold
The total is
16+x+21
Simplifying
37+x
another step
16 + 21 + x = y
y = the number of hats sold
16 = hats sold on first shift
21 = hats on the third shift
x = hats on the second shift

Lesson 5.4 The Distributive Property

EXPLORATION 1
Using Models to Simplify Expressions
Work with a partner.
a. Use the models to simplify the expressions. Explain your reasoning.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 66

Answer:
Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-66
b. In part(a), check that the original expressions are equivalent to the simplified expressions.
c. You used the Distributive Property in a previous course. Use the example to explain the meaning of the property.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 67
Distributive Property: 6(20 + 3) = 6(20) + 6(3)
Is this property true for algebraic expressions? Explain your reasoning.

Answer:
The distributive property of multiplication over addition can be used when you multiply a number by a sum.
6(20 + 3) = 6(20) + 6(3)
6(23) = 120 + 18
138 = 138
Yes this property true for algebraic expressions

Try It

Use the Distributive Property to simplify the expression.

Question 1.
7(a + 2)

Answer: 7(a) + 7(2)

Explanation:
Given,
The distributive property of multiplication over addition can be used when you multiply a number by a sum.
7(a + 2) = (7 × a) + (7 × 2)
7a + 14
Thus 7(a + 2) = 7a + 14

Question 2.
3(d – 11)

Answer: 3(d) – 3(11)

Explanation:
Given,
The distributive property of multiplication over addition can be used when you multiply a number by a sum.
3(d – 11) = (3 × d) – (3 × 11)
3d – 33
Thus 3(d – 11) = 3d – 33

Question 3.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 68

Answer: 12a + 12\(\frac{2}{3}\)b

Explanation:
Given,
The distributive property of multiplication over addition can be used when you multiply a number by a sum.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 68= (12 × a) + (12 × \(\frac{2}{3}\)b)
= 12a + 12\(\frac{2}{3}\)b
Thus Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 68= 12a + 12\(\frac{2}{3}\)b

Question 4.
7(2 + 6 – 4d)

Answer: 7(2) + 7(6) – 7(4d)

Explanation:
Given,
The distributive property of multiplication over addition can be used when you multiply a number by a sum.
7(2 + 6 – 4d) = 7(8 – 4d)
56 – 28d
Thus 7(2 + 6 – 4d) = 56 – 28d

Simplify the expression.

Question 5.
8 + 3z – z

Answer: 8 + 2z

Explanation:
Combine the like terms and simplify the expression.
8 + 3z – z
8 + z(3 – 1)
8 + 2z
So, 8 + 3z – z = 8 + 2z

Question 6.
3(b + 5) + b + 2

Answer: 4b + 17

Explanation:
Combine the like terms and simplify the expression.
3(b + 5) + b + 2
= 3b + 15 + b + 2
= 3b + b + 15 + 2
= 4b + 17
Thus 3(b + 5) + b + 2 = 4b + 17

Self-Assessment for Concepts & Skills

Solve each exercise. Then rate your understanding of the success criteria in your journal.

Question 7.
WRITING
One meaning of the word distribute is to give something to each member of a group. How can this help you remember the Distributive Property?

Answer:
You must distribute or give the number outside the parenthesis to all the numbers inside the parenthesis

SIMPLIFYING EXPRESSIONS
Use the Distributive Property to simplify the expression.

Question 8.
3(x + 10)

Answer: 3(x) + 3(10)

Explanation:
We can simplify the expression by using the Distributive Property
The distributive property of multiplication over addition can be used when you multiply a number by a sum.
3(x + 10) = (3 × x) + (3 × 10)
= 3x + 30
So, 3(x + 10) = 3x + 30

Question 9.
15(4n – 2)

Answer: 15(4n) – 15(2)

Explanation:
We can simplify the expression by using the Distributive Property
The distributive property of multiplication over addition can be used when you multiply a number by a sum.
15(4n – 2) = (15 × 4n) – (15 × 2)
= 60n – 30
So, 15(4n – 2) = 60n – 30

Question 10.
2w + 4 + 13w + 1

Answer:15w + 5 = 5(3w + 1)

Explanation:
We can simplify the expression by using the Distributive Property
The distributive property of multiplication over addition can be used when you multiply a number by a sum.
2w + 4 + 13w + 1
Combine the like terms
=2w + 13w + 4 + 1
=15w + 5
=5(3w + 1)

Self-Assessment for Problem Solving

Solve each exercise. Then rate your understanding of the success criteria in your journal.

Question 11.
You purchase a remote-controlled drone for d dollars. Your friend purchases a drone that costs $35 more than your drone. Your brother purchases a drone that costs three times as much as your friend’s drone. Write and simplify an expression that represents the cost (in dollars) of your brother’s drone.

Answer:
Brother = 105+3d

Explanation:
Given
Drone = d
Friend = $35 more expensive than yours.
Brother = 3 times as much as your friend
Required
Write an expression for the cost of your brother’s drone
I’ll solve by analyzing the question one sentence after the other
You: Drone = d

Your friend:
Friend = $35 more expensive than yours.
This means
Brother = 3 × Friend
Substitute 35 + d for Friend
Brother = 3 × (35+d)
Open bracket
Brother = 3×35+3×d
Brother=105+3d

Question 12.
Write and simplify an expression that represents the total cost (in dollars) of buying the items shown for each member of a baseball team.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 68.1

Answer: 9(10 + x)

Explanation:
Number of members in the baseball team = 9
Cost of the pant = $10
Cost of a belt = $x
The expression that represents the total cost (in dollars) of buying the items shown for each member of a baseball team is 9(10 + x)

Question 13.
DIG DEEPER!
One molecule of caffeine contains x oxygen atoms, twice as many nitrogen atoms as oxygen atoms, 4 more carbon atoms than nitrogen atoms, and 1.25 times as many hydrogen atoms as carbon atoms. Write and simplify an expression that represents the number of hydrogen atoms in one molecule of caffeine.

Answer:
Given,
One molecule of caffeine contains x oxygen atoms, twice as many nitrogen atoms as oxygen atoms, 4 more carbon atoms than nitrogen atoms, and 1.25 times as many hydrogen atoms as carbon atoms.
One molecule of caffeine contains x oxygen atoms = x
twice as many nitrogen atoms as oxygen atoms = 2 . x
4 more carbon atoms than nitrogen atoms = 4 . x
1.25 times as many hydrogen atoms as carbon atoms = 1.25 × x
x + 2x + 6x + 1.25(6x)

The Distributive Property Homework & Practice 5.4

Review & Refresh

Simplify the expression. Explain each step.

Question 1.
(s + 4) + 8

Answer: s + 12

Explanation:
According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
(s + 4) + 8
= s + 4 + 8
= s + 12

Question 2.
(12 + x) + 2

Answer: 14 + x

Explanation:
According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
12 + x + 2
x + 12 + 2
x + 14

Question 3.
3(4n)

Answer: 12n

Explanation:
According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
3 × 4n = 12n

You are given the difference of the numbers of boys and girls in a class and the ratio of boys to girls. How many boys and how many girls are in the class?

Question 4.
3 more boys; 5 for every 4

Answer:
Let the total number of boys in the class be x.
The ratio of boys and girls is 5 : 4
Number of boys = 5x
Number of girls = 4x
5x – 4x = 3
x = 3
Number of boys = 5(3) = 15
15 + 3 = 18
Number of girls = 4(3) = 12
To find the total number of boys and girls in the class we have to add them
18 + 12 = 30
Thus there are 30 boys and girls in the class.

Question 5.
8 more girls; 3 for every 2

Answer:
Let the total number of boys in the class be x.
The ratio of boys and girls is 3 : 2
Number of boys = 3x
Number of girls = 2x
3x – 2x = 8
x = 8
Number of boys = 3x = 3(8) = 24
Number of girls = 2x = 2(8) = 16
More number of girls = 16 + 8 = 24
To find the total number of boys and girls in the class we have to add them
24 + 24 = 48
Thus there are 48 boys and girls in the class.

Question 6.
4 more girls; 9 for every 13

Answer:
Let the total number of boys in the class be x.
The ratio of girls and boys is 13 : 9
Number of boys = 9x
Number of girls = 13x
13x – 9x = 4
4x = 4
x = 1
Number of boys = 9x = 9(1) = 9
Number of girls = 13x = 13(1) = 13
13 + 4 = 17
To find the total number of boys and girls in the class we have to add them
9 + 17 = 26
Thus there are 26 boys and girls in the class.

Question 7.
6 more boys; 7 for every 4

Answer:
Let the total number of boys in the class be x.
The ratio of girls and boys is 7 : 4
Number of boys = 7x
Number of girls = 4x
7x – 4x = 6
3x = 6
x = 2
Number of boys = 7(2) = 14
Number of girls = 4(2) = 8
15 + 6 = 21
To find the total number of boys and girls in the class we have to add them
21 + 8 = 29
Thus there are 29 boys and girls in the class.

Divide.

Question 8.
301 ÷ 7

Answer: 43
So divide 301 with 7
then we get 43

Question 9.
1722 ÷ 14

Answer: 123
So divide 1722 with 14
then we get 123

Question 10.
629 ÷ 12

Answer: 52.41
So divide 629 with 12
then we get 52.14

Question 11.
8068 ÷ 31

Answer: 260.25
So divide 8068 with 31
then we get 260.25

Concepts, Skills, & Problem Solving
USING MODELS
Use the model to simplify the expression. Explain your reasoning. (See Exploration 1, p. 221.)

Question 12.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 69

Answer: 5z + 30

Explanation:
The shape of the above figure is a rectangle.
Area of the rectangle = l × b
A = (z + 6) × 5
A = 5z + 30

Question 13.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 70

Answer: 6s

Explanation:
Combine the like terms
There are 4s in the first block
There are 2s in the second block
4s + 2s = 6s

SIMPLIFYING EXPRESSIONS
Use the Distributive Property to simplify the expression.

Question 14.
3(x + 4)

Answer: 3x + 12

Explanation:
We can use the distributive property to simplify the expression.
3(x + 4) = (3 × x) + (3 × 4)
= 3x + 12

Question 15.
10(b – 6)

Answer: 10b – 60

Explanation:
We can use the distributive property to simplify the expression.
10(b – 6) = (10 × b) – (10 × 6)
= 10b – 60

Question 16.
6(s – 9)

Answer: 6s – 54

Explanation:
We can use the distributive property to simplify the expression.
6(s – 9) = (6 × s) – (6 × 9)
= 6s – 54

Question 17.
7(8 + y )

Answer: 56 + 7y

Explanation:
We can use the distributive property to simplify the expression.
7(8 + y) = (7 × 8) + (7 × y)
= 56 + 7y

Question 18.
8(12 + a)

Answer: 96 + 8a

Explanation:
We can use the distributive property to simplify the expression.
8(12 + a) = (8 × 12) + (8 × a)
= 96 + 8a

Question 19.
9(2n + 1)

Answer: 18n + 9

Explanation:
We can use the distributive property to simplify the expression.
9(2n + 1) = (9 × 2n) + (9 × 1)
= 18n + 9

Question 20.
12(6 – k)

Answer: 72 – 12k

Explanation:
We can use the distributive property to simplify the expression.
12(6 – k) = (12 × 6) – (12 × k)
= 72 – 12k

Question 21.
18(5 – 3w)

Answer: 90 – 54w

Explanation:
We can use the distributive property to simplify the expression.
18(5 – 3w) = (18 × 5) – (18 × 3w)
= 90 – 54w

Question 22.
9(3 + c + 4)

Answer: 63 + 9c

Explanation:
We can use the distributive property to simplify the expression.
9(3 + c + 4) = 9(7 + c)
(9 × 7) + ( 9 × c)
63 + 9c

Question 23.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 71

Answer: 3 + x/4

Explanation:
We can use the distributive property to simplify the expression.
1/4(8 + x + 4) = 1/4(12 + x)
= 3 + x/4

Question 24.
8(5g + 5 – 2)

Answer: 40g + 24

Explanation:
We can use the distributive property to simplify the expression.
8(5g + 5 – 2) = 8(5g) + 8(5) – 8(2)
40g + 40 – 16
40g + 24

Question 25.
6(10 + z + 3)

Answer: 78 + 6z

Explanation:
We can use the distributive property to simplify the expression.
6(10 + z + 3) = 6(10) + 6(z) + 6(3)
= 60 + 6z + 18
= 78 + 6z

Question 26.
4(x + y)

Answer: 4x + 4y

Explanation:
We can use the distributive property to simplify the expression.
4(x + y) = (4 × x) + (4 × y)
= 4x + 4y

Question 27.
25(x – y)

Answer: 25x – 25y

Explanation:
We can use the distributive property to simplify the expression.
25(x – y) = (25 × x) – (25 × y)
= 25x – 25y

Question 28.
7(p + q + 9)

Answer: 7p + 7q + 63

Explanation:
We can use the distributive property to simplify the expression.
7(p + q + 9) = (7 × p) + (7 × q) + (7 × 9)
= 7p + 7q + 63

Question 29.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 72

Answer: n + 3m + 2

Explanation:
We can use the distributive property to simplify the expression.
1/2 (2n + 4 + 6m) = 1/2 (2n) + 1/2 (4) + 1/2 (6m)
= n + 2 + 3m

MATCHING
Match the expression with an equivalent expression.

Question 30.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 73

Answer: C

Explanation:
Given,
6(n + 4) = 6n + 24
Now take 3 as common factor
3(2n + 8)
Thus the equivalent expression is option C.

Question 31.
Big Ideas Math Answers Grade 6 Chapter 5 Algebraic Expressions and Properties 74

Answer: A

Explanation:
Given,
2(3n + 9) = 6n + 18
Now take 3 as common factor
6n + 18 = 3(2n + 6)
Thus the equivalent expression is option A.

Question 32.
Big Ideas Math Answers Grade 6 Chapter 5 Algebraic Expressions and Properties 75

Answer: D

Explanation:
Given,
6(n + 2) = 6n + 12
Thus the equivalent expression is option D.

Question 33.
Big Ideas Math Answers Grade 6 Chapter 5 Algebraic Expressions and Properties 76

Answer: B

Explanation:
Given,
3(2n + 3) = 6n + 9
Thus the equivalent expression is option B.

Question 34.
STRUCTURE
Each day, you run on a treadmill for r minutes and lift weights for 15 minutes. Which expressions can you use to find how many minutes of exercise you do in 5 days? Explain your reasoning.
Big Ideas Math Answers Grade 6 Chapter 5 Algebraic Expressions and Properties 77

Answer: 5(r + 15)

Explanation:
Each day, you run on a treadmill for r minutes and lift weights for 15 minutes.
They are both expressions with r as the variable.
They are not equivalent expressions.
They are equivalent expressions.
Both expressions contain the terms 5, r, and 15.
5(15 + r) = 5(15) + 5(r)

Question 35.
MODELING REAL LIFE
A cheetah can run 103 feet per second. A zebra can run x feet per second. Write and simplify an expression that represents how many feet farther the cheetah can run in 10 seconds.
Big Ideas Math Answers Grade 6 Chapter 5 Algebraic Expressions and Properties 78

Answer:
Given,
A cheetah can run 103 feet per second. A zebra can run x feet per second.
We are given that the rate of cheetah Rc is:
Rc = 103 ft / sec
And the rate of zebra Rz is:
Rz = x ft / sec
We are to find the distance between the two after 10 seconds, that is:
distance = (103 – x) 10
distance = 1030 – 10 x

COMBINING LIKE TERMS
Simplify the expression.

Question 36.
6(x + 4) + 1

Answer: 6x + 25

Explanation:
Given the expression
6(x + 4) + 1
= (6 × x) + (6 × 4) + 1
= 6x + 24 + 1
= 6x + 25
Thus, 6(x + 4) + 1 = 6x + 25

Question 37.
5 + 8(3 + x)

Answer: 29 + 8x

Explanation:
Given the expression
5 + 8(3 + x)
= 5 + (8 × 3) + (8 × x)
= 5 + 24 + 8x
= 29 + 8x
Thus 5 + 8(3 + x) = 29 + 8x

Question 38.
x + 3 + 5x

Answer: 6x + 3

Explanation:
Given the expression
x + 3 + 5x
Combine the like terms
x + 5x + 3
6x + 3
So, x + 3 + 5x = 6x + 3

Question 39.
7y + 6 – 1 + 12y

Answer: 19y + 5

Explanation:
Given the expression
7y + 6 – 1 + 12y
Combine the like terms
7y + 12y + 6 – 1
= 19y + 5
So, 7y + 6 – 1 + 12y = 19y + 5

Question 40.
4d + 9 – d – 8

Answer: 3d + 1

Explanation:
Given the expression
4d + 9 – d – 8
Combine the like terms
4d – d + 9 – 8
3d + 1
So, 4d + 9 – d – 8 = 3d + 1

Question 41.
n + 3(n – 1)

Answer: 4n – 3

Explanation:
Given the expression
n + 3(n – 1)
n + (3 × n) – (3 × 1)
n + 3n – 3
4n – 3
So, n + 3(n – 1) = 4n – 3

Question 42.
2v + 8v – 5v

Answer: 5v

Explanation:
Given the expression
2v + 8v – 5v
Combine the like terms
v(2 + 8 – 5)
v(5) = 5v
Thus 2v + 8v – 5v = 5v

Question 43.
5(z + 4) + 5(2 – z)

Answer: 30

Explanation:
Given the expression
5(z + 4) + 5(2 – z)
= (5 × z) + (5 × 4) + (5 × 2) – (5 × z)
= 5z + 20 + 10 – 5z
Now combine the like terms
5z + 20 + 10 – 5z = 30

Question 44.
2.7(w – 5.2)

Answer: 2.7w – 14.04

Explanation:
Given the expression
2.7(w – 5.2)
= (2.7 × w) – (2.7 × 5.2)
= 2.7w – 14.04
Thus 2.7(w – 5.2) = 2.7w – 14.04

Question 45.
Big Ideas Math Answers Grade 6 Chapter 5 Algebraic Expressions and Properties 79

Answer:1 \(\frac{1}{2}\)y

Explanation:
Given the expression
\(\frac{2}{3}\)y + \(\frac{1}{6}\)y + y
y(\(\frac{2}{3}\) + \(\frac{1}{6}\) + 1)
= 1 \(\frac{1}{2}\)y
So, Big Ideas Math Answers Grade 6 Chapter 5 Algebraic Expressions and Properties 79 = 1 \(\frac{1}{2}\)y

Question 46.
Big Ideas Math Answers Grade 6 Chapter 5 Algebraic Expressions and Properties 80

Answer: 2\(\frac{3}{4}\)z + \(\frac{3}{10}\)

Explanation:
Given the expression
Big Ideas Math Answers Grade 6 Chapter 5 Algebraic Expressions and Properties 80
\(\frac{3}{4}\)z + \(\frac{3}{10}\) + 2z
2\(\frac{3}{4}\)z + \(\frac{3}{10}\)

Question 47.
7(x + y) – 7x

Answer: 7y

Explanation:
Given the expression
7(x + y) – 7x
= (7 × x) + (7 × y) – 7x
= 7x + 7y – 7x
= 7y
So, 7(x + y) – 7x = 7y

Question 48.
4x + 9y + 3(x + y)

Answer: 7x + 12y

Explanation:
Given the expression
4x + 9y + 3(x + y)
=4x + 9y + 3x + 3y
=4x + 3x + 9y + 3y
=7x + 12y
Thus 4x + 9y + 3(x + y) = 7x + 12y

Question 49.
YOU BE THE TEACHER
Your friend simplifies the expression. Is your friend correct? Explain your reasoning.
Big Ideas Math Answers Grade 6 Chapter 5 Algebraic Expressions and Properties 81

Answer: your friend is incorrect

Explanation:
8x – 2x + 5x
= 6x + 5x
= 11x
By this we can say that your friend is incorrect.

Question 50.
REASONING
Evaluate each expression by(1) using the Distributive Property and (2) evaluating inside the parentheses first. Which method do you prefer? Is your preference the same for both expressions? Explain your reasoning.
Big Ideas Math Answers Grade 6 Chapter 5 Algebraic Expressions and Properties 82

Answer:
a. 2(3.22 – 0.12)
We can solve this by using the Distributive Property
= 2(3.22) – 2(0.12)
= 6.44 – 0.24
= 6.20
2(3.22 – 0.12) = 6.20
b. 12(\(\frac{1}{2}\) + \(\frac{2}{3}\))
We can solve this by using the Distributive Property
(12 × \(\frac{1}{2}\)) + (12 × \(\frac{2}{3}\))
= 6 + 8
= 14
12(\(\frac{1}{2}\) + \(\frac{2}{3}\)) = 14

Question 51.
DIG DEEPER!
An art club sells 42 large candles and 56 small candles.
a. Write and simplify an expression that represents the profit.
b. A large candle costs $5, and a small candle costs $3. What is the club’s profit?
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 83

Answer:
For large candles, the selling price is $10 and its making cost is $x.
So, by selling a large candle the profit is $(10 – x)
Again for small candles, the selling price is $5 and its making cost is $y.
So, by selling a small candle the profit is $(5 – y)
Therefore, in a sale of 42 large candles and 56 small candles, the total profit will be, P = 42 (10 – x) + 56 (5 – y)
P = 420 – 42x + 280 – 56y
P = $(700 – 42x – 56y

Question 52.
REASONING
Find the difference between the perimeters of the rectangle and the hexagon. Interpret your answer.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 84

Answer:
Rectangle:
Perimeter of the Rectangle = 2l + 2w
P = 2(2x + 7) + 2(2x)
P = 4x + 14 + 4x
P = 8x + 14
Hexagon:
Perimeter of the Hexagon = 6a
P = x + x + 2x + 2x + x + 6 + x + 8
P = 8x + 14
The difference between the perimeters of the rectangle and the hexagon is (8x + 14) – (8x + 14) = 0

Question 53.
PUZZLE
Add one set of parentheses to the expression 7 . x + 3 + 8 . x + 3 . x + 8 − 9 so that it is equivalent to 2(9x + 10).

Answer:
7×(X+3)+8×X+3×X+8-9
=7×(X+3)+11×X-1
=7×X+21+11×X-1
=18×X+20
=2(9X+10)

Lesson 5.5 Factoring Expressions

EXPLORATION 1
Finding Dimensions
Work with a partner.
a. The models show the area (in square units) of each part of a rectangle. Use the models to find missing values that complete the expressions. Explain your reasoning.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 85
b. In part(a), check that the original expressions are equivalent to the expressions you wrote. Explain your reasoning.
c. Explain how you can use the Distributive Property to rewrite a sum of two whole numbers with a common factor.

Answer:
Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-85

Try It

Factor the expression using the GCF.

Question 1.
9 + 15

Answer: 3

Explanation:
The factors of 9 are: 1, 3, 9
The factors of 15 are: 1, 3, 5, 15
The number does not contain any common variable factors.
Then the greatest common factor is 3.

Question 2.
60 + 45

Answer: 15

Explanation:
The factors of 45 are: 1, 3, 5, 9, 15, 45
The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The number does not contain any common variable factors.
Then the greatest common factor is 15.

Question 3.
30 – 20

Answer: 10

Explanation:
The factors of 20 are: 1, 2, 4, 5, 10, 20
The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30
Then the greatest common factor is 10.

Factor the expression using the GCF.

Question 4.
7x + 49

Answer: 7

Explanation:
Since 7x, 49 contain both numbers and variables, there are two steps to find the GCF.
The factors of 7 are: 1, 7
The factors of 49 are: 1, 7, 49
Then the greatest common factor is 7.

Question 5.
8y – 44

Answer: 4

Explanation:
Since 8y, 44 contain both numbers and variables, there are two steps to find the GCF.
The factors of 8 are: 1, 2, 4, 8
The factors of 44 are: 1, 2, 4, 11, 22, 44
Then the greatest common factor is 4.

Question 6.
25a + 10b

Answer: 5

Explanation:
Since 25a, 10b contain both numbers and variables, there are two steps to find the GCF.
The factors of 10 are: 1, 2, 5, 10
The factors of 25 are: 1, 5, 25
Then the greatest common factor is 5.

Self-Assessment for Concepts & Skills
Solve each exercise. Then rate your understanding of the success criteria in your journal.

FACTORING EXPRESSIONS
Factor the expression using the GCF.

Question 7.
16 + 24

Answer: 8

Explanation:
The factors of 16 are: 1, 2, 4, 8, 16
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
Then the greatest common factor is 8.

Question 8.
49 – 28

Answer: 7

Explanation:
The factors of 28 are: 1, 2, 4, 7, 14, 28
The factors of 49 are: 1, 7, 49
Then the greatest common factor is 7.

Question 9.
8y + 14

Answer: 2

Explanation:
Since 8y, 14 contain both numbers and variables, there are two steps to find the GCF.
The factors of 8 are: 1, 2, 4, 8
The factors of 14 are: 1, 2, 7, 14
Then the greatest common factor is 2.

Question 10.
WHICH ONE DOESN’T BELONG?
Which expression does not belong with the other three? Explain your reasoning.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 86

Answer: 6(4n + 3)

Explanation:
i. 3(8n + 12)
= 24n + 36
ii. 4(6n + 9)
24n + 36
iii. 6(4n + 3)
24n + 18
iv. 12(2n + 3)
24n + 36
Thus the third expression does not belong to the other three.

Question 11.
REASONING
Use what you know about factoring to explain how you can factor the expression 18x + 30y + 9z. Then factor the expression.

Answer: 3 (6x + 10y + 3z)

Explanation:
Factoring is a mathematical representation of the expression with the help of common factors.
In this expression, we have given terms and their coefficients. Since we cannot factorize the terms, they will be intact in the process.
We can factorize this expression with the help of prime numbers:
2 × 3 × 3 × x + 2 × 3 × 5 × y + 3 × 3 × z
And finally, we will be able to obtain common factor from this expression:
3 ( 6x + 10y + 3z)

Question 12.
CRITICAL THINKING
Identify the GCF of the terms (x . x) and (4 . x). Explain your reasoning. Then use the GCF to factor the expression x2 + 4x.

Answer:
x2 + 4x
= x(x + 4)
The factors of 1 are: 1
The factors of 4 are: 1, 2, 4
Then the greatest common factor is 1.

Self-Assessment for Problem Solving

Solve each exercise. Then rate your understanding of the success criteria in your journal.

Question 13.
A youth club receives a discount on each pizza purchased for a party. The original price of each pizza is x dollars. The club leader purchases 8 pizzas for a total of (8x − 32) dollars. Factor the expression. What can you conclude about the discount?

Answer:
Given that,
A youth club receives a discount on each pizza purchased for a party.
The original price of each pizza is x dollars.
The club leader purchases 8 pizzas for a total of (8x − 32) dollars.

Question 14.
Three crates of food are packed on a shuttle departing for the Moon. Each crate weighs x pounds. On the Moon, the combined weight of the crates is (3x − 81) pounds. What can you conclude about the weight of each crate on the Moon?
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 87

Answer:
Three crates of food are packed on a shuttle departing for the Moon.
Each crate weighs x pounds. On the Moon, the combined weight of the crates is (3x − 81) pounds.
The factors of 3 are: 1, 3
The factors of 81 are: 1, 3, 9, 27, 81
Then the greatest common factor is 3.

Factoring Expressions Homework & Practice 5.5

Review & Refresh

Use the Distributive Property to simplify the expression.

Question 1.
2(n + 8)

Answer: 2n + 16

Explanation:
Given the expression 2(n + 8)
The distributive property explains that multiplying two numbers (factors) together will result in the same thing as breaking up one factor into two addends, multiplying both addends by the other factor, and adding together both products.
(2 × n) + (2 × 8)
= 2n + 16

Question 2.
3(4 + m)

Answer: 12 + 3m

Explanation:
The distributive property explains that multiplying two numbers (factors) together will result in the same thing as breaking up one factor into two addends, multiplying both addends by the other factor, and adding together both products.
3(4 + m)
= (3 × 4) + (3 × m)
= 12 + 3m

Question 3.
7(b – 3)

Answer: 7b – 21

Explanation:
The distributive property explains that multiplying two numbers (factors) together will result in the same thing as breaking up one factor into two addends, multiplying both addends by the other factor, and adding together both products.
7(b – 3)
= (7 × b) – (7 × 3)
= 7b – 21

Question 4.
10(4 – w)

Answer: 40 – 10w

Explanation:
The distributive property explains that multiplying two numbers (factors) together will result in the same thing as breaking up one factor into two addends, multiplying both addends by the other factor, and adding together both products.
10 (4 – w)
= (10 × 4) – (10 × w)
= 40 – 10w

Write the phrase as an expression.

Question 5.
5 plus a number p

Answer: 5 + p

Explanation:
The phrase plus indicates addition.
The Express would be 5 + p

Question 6.
18 less than a number r

Answer: 18 < r

Explanation:
The phrase less than indicates < symbol.
So the expression would be 18 < r

Question 7.
11 times a number d

Answer: 11d

Explanation:
The phrase times indicates × symbol.
So, the expression would be 11d

Question 8.
a number c divided by 25

Answer: c ÷ 25

Explanation:
The phrase divided by indicates ÷
So, the expression would be c ÷ 25

Decide whether the rates are equivalent.

Question 9.
84 feet in 12 seconds
217 feet in 31 seconds

Answer: The rates are equivalent

Explanation:
Given,
84 feet in 12 seconds
217 feet in 31 seconds
Here we have to check whether the rates are equivalent or not.
84 feet in 12 seconds = 7 : 1
217 feet in 31 seconds = 7 : 1
Thus the rates are equivalent.

Question 10.
12 cups of soda for every 54 cups of juice
8 cups of soda for every 36 cups of juice

Answer: the rates are equivalent

Explanation:
Given,
12 cups of soda for every 54 cups of juice
8 cups of soda for every 36 cups of juice
Here we have to check whether the rates are equivalent or not.
12 cups of soda for every 54 cups of juice = 2 : 9
8 cups of soda for every 36 cups of juice = 2 : 9
Thus the rates are equivalent.

Match the decimal with its equivalent percent.

Question 11.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 88

Answer: C

Explanation:
The fraction form of the decimal 0.36 is \(\frac{36}{100}\)
\(\frac{36}{100}\) × 100 = 36%
Thus the equivalent percent is option C.

Question 12.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 89

Answer: B

Explanation:
The fraction form of the decimal 3.6 is \(\frac{36}{10}\)
\(\frac{36}{10}\) × 100 = 36 × 10 = 360%
Thus the equivalent percent is option B.

Question 13.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 90

Answer: A

Explanation:
The fraction form of the decimal 0.0036 is \(\frac{36}{10000}\)
\(\frac{36}{10000}\) × 100 = \(\frac{36}{100}\) = 0.36%
Thus the equivalent percent is option A.

Question 14.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 91

Answer: B

Explanation:
Explanation:
The fraction form of the decimal 0.0036 is \(\frac{36}{1000}\)
\(\frac{36}{1000}\) × 100 = \(\frac{36}{10}\) =3.6%
Thus the equivalent percent is option D.

Concepts, Skills, & Problem Solving
FINDING DIMENSIONS
The model shows the area (in square units) of each part of a rectangle. Use the model to find missing values that complete the expression. Explain your reasoning. (See Exploration 1, p. 227.)

Question 15.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 92

Answer:4(3 + 4)

Explanation:
We can find the area of the rectangle by using the distributive property.
Let us take 4 as the common factor
(12 + 16) = 4(3 + 4)

Question 16.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 93

Answer: 8(6 + 4)

Explanation:
We can find the area of the rectangle by using the distributive property.
Let us take 8 as a common factor
48 + 32 = 8 (6 + 4)

FACTORING NUMERICAL EXPRESSIONS
Factor the expression using the GCF.

Question 17.
7 + 14

Answer: 7

Explanation:
The factors of 7 are: 1, 7
The factors of 14 are: 1, 2, 7, 14
Then the greatest common factor is 7.

Question 18.
12 + 42

Answer: 6

Explanation:
The factors of 12 are: 1, 2, 3, 4, 6, 12
The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42
Then the greatest common factor is 6.

Question 19.
22 + 11

Answer: 11

Explanation:
The factors of 11 are: 1, 11
The factors of 22 are: 1, 2, 11, 22
Then the greatest common factor is 11.

Question 20.
70 + 95

Answer: 5

Explanation:
The factors of 70 are: 1, 2, 5, 7, 10, 14, 35, 70
The factors of 95 are: 1, 5, 19, 95
Then the greatest common factor is 5.

Question 21.
60 – 36

Answer: 12

Explanation:
The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36
The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Then the greatest common factor is 12.

Question 22.
100 – 80

Answer: 20

Explanation:
The factors of 80 are: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
The factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100
Then the greatest common factor is 20.

Question 23.
84 + 28

Answer: 28

Explanation:
The factors of 28 are: 1, 2, 4, 7, 14, 28
The factors of 84 are: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Then the greatest common factor is 28.

Question 24.
48 + 80

Answer: 16

Explanation:
The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The factors of 80 are: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
Then the greatest common factor is 16.

Question 25.
19 + 95

Answer: 19

Explanation:
The factors of 19 are: 1, 19
The factors of 95 are: 1, 5, 19, 95
Then the greatest common factor is 19.

Question 26.
44 – 11

Answer: 11

Explanation:
The factors of 11 are: 1, 11
The factors of 44 are: 1, 2, 4, 11, 22, 44
Then the greatest common factor is 11.

Question 27.
18 – 12

Answer: 6

Explanation:
The factors of 12 are: 1, 2, 3, 4, 6, 12
The factors of 18 are: 1, 2, 3, 6, 9, 18
Then the greatest common factor is 6.

Question 28.
48 + 16

Answer: 16

Explanation:
The factors of 16 are: 1, 2, 4, 8, 16
The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Then the greatest common factor is 16.

Question 29.
98 – 70

Answer: 14

Explanation:
The factors of 70 are: 1, 2, 5, 7, 10, 14, 35, 70
The factors of 98 are: 1, 2, 7, 14, 49, 98
Then the greatest common factor is 14.

Question 30.
58 + 28

Answer: 2

Explanation:
The factors of 28 are: 1, 2, 4, 7, 14, 28
The factors of 58 are: 1, 2, 29, 58
Then the greatest common factor is 2.

Question 31.
72 – 39

Answer: 3

Explanation:
The factors of 39 are: 1, 3, 13, 39
The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Then the greatest common factor is 3.

Question 32.
69 + 84

Answer: 3

Explanation:
The factors of 69 are: 1, 3, 23, 69
The factors of 84 are: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Then the greatest common factor is 3.

Question 33.
REASONING
The whole numbers a and b are divisible by c, where b is greater than a. Is a + b divisible by c ? Is b − a divisible by c ? Explain your reasoning.

Answer:
Let the whole numbers a and b be 12 and 54
Let c be 6.
In this case b is greater than a.
Now let us check whether and b are divisible by c.
a + b ÷ c:
12 + 54 ÷ 6
66 ÷ 6 = 11
b – a ÷ c:
54 – 12 ÷ 6
42 ÷ 6 = 7

Question 34.
MULTIPLE CHOICE
Which expression is not equivalent to 81x + 54?
A. 27(3x + 2)
B. 3(37x + 18)
C. 9(9x + 6)
D. 6(13x + 9)

Answer: B. 3(37x + 18), D. 6(13x + 9)

Explanation:
Given the expression 81x + 54
A. 27(3x + 2)
= (27 × 3x) + (27 × 2)
= 81x + 54
B. 3(37x + 18)
= 111x + 54
C. 9(9x + 6)
= 81x + 54
D. 6(13x + 9)
78x + 54
Thus the expression is not equivalent to 81x + 54 are option B and D.

FACTORING ALGEBRAIC EXPRESSIONS
Factor the expression using the GCF.

Question 35.
2x + 10

Answer: 2

Explanation:
Since 2x, 10 contain both numbers and variables, there are two steps to find the GCF.
The factors of 2 are: 1, 2
The factors of 10 are: 1, 2, 5, 10
Then the greatest common factor is 2.

Question 36.
15x + 6

Answer: 3

Explanation:
Since 15x, 6 contain both numbers and variables, there are two steps to find the GCF.
The factors of 6 are: 1, 2, 3, 6
The factors of 15 are: 1, 3, 5, 15
Then the greatest common factor is 3.

Question 37.
26x – 13

Answer: 13

Explanation:
Since 26x, 13 contain both numbers and variables, there are two steps to find the GCF.
The factors of 13 are: 1, 13
The factors of 26 are: 1, 2, 13, 26
Then the greatest common factor is 13

Question 38.
50x – 60

Answer: 10

Explanation:
Since 50x, 60 contain both numbers and variables, there are two steps to find the GCF.
The factors of 50 are: 1, 2, 5, 10, 25, 50
The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Then the greatest common factor is 10.

Question 39.
36x + 9

Answer: 9

Explanation:
Since 36x, 9 contain both numbers and variables, there are two steps to find the GCF.
The factors of 9 are: 1, 3, 9
The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36
Then the greatest common factor is 9

Question 40.
14x – 98

Answer: 14

Explanation:
Since 14x, 98 contain both numbers and variables, there are two steps to find the GCF.
The factors of 14 are: 1, 2, 7, 14
The factors of 98 are: 1, 2, 7, 14, 49, 98
Then the greatest common factor is 14.

Question 41.
18p + 26

Answer: 2

Explanation:
Since 18p, 26 contain both numbers and variables, there are two steps to find the GCF.
The factors of 18 are: 1, 2, 3, 6, 9, 18
The factors of 26 are: 1, 2, 13, 26
Then the greatest common factor is 2.

Question 42.
16m + 40

Answer: 8

Explanation:
Since 16m, 40 contain both numbers and variables, there are two steps to find the GCF.
The factors of 16 are: 1, 2, 4, 8, 16
The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40
Then the greatest common factor is 8.

Question 43.
24 + 72n

Answer: 24

Explanation:
Since 24, 72n contain both numbers and variables, there are two steps to find the GCF.
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Then the greatest common factor is 24.

Question 44.
50 + 65h

Answer: 5

Explanation:
Since 50, 65h contain both numbers and variables, there are two steps to find the GCF.
The factors of 50 are: 1, 2, 5, 10, 25, 50
The factors of 65 are: 1, 5, 13, 65
Then the greatest common factor is 5.

Question 45.
76d – 24

Answer: 4

Explanation:
Since 76d, 24 contain both numbers and variables, there are two steps to find the GCF.
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
The factors of 76 are: 1, 2, 4, 19, 38, 76
Then the greatest common factor is 4.

Question 46.
27 – 45c

Answer: 9

Explanation:
Since 27, 45c contains both numbers and variables, there are two steps to find the GCF.
The factors of 27 are: 1, 3, 9, 27
The factors of 45 are: 1, 3, 5, 9, 15, 45
Then the greatest common factor is 9.

Question 47.
18t + 38x

Answer: 2

Explanation:
Since 18t, 38x contains both numbers and variables, there are two steps to find the GCF.
The factors of 18 are: 1, 2, 3, 6, 9, 18
The factors of 38 are: 1, 2, 19, 38
Then the greatest common factor is 2.

Question 48.
90y + 65z

Answer: 5

Explanation:
Since 90y, 65z contains both numbers and variables, there are two steps to find the GCF.
The factors of 65 are: 1, 5, 13, 65
The factors of 90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Then the greatest common factor is 5.

Question 49.
10x – 25y

Answer: 5

Explanation:
Since 10x, 25y contains both numbers and variables, there are two steps to find the GCF.
The factors of 10 are: 1, 2, 5, 10
The factors of 25 are: 1, 5, 25
Then the greatest common factor is 5.

Question 50.
24y + 88x

Answer: 8

Explanation:
Since 24y, 88x contains both numbers and variables, there are two steps to find the GCF.
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
The factors of 88 are: 1, 2, 4, 8, 11, 22, 44, 88
Then the greatest common factor is 8.

Question 51.
OPEN-ENDED
Use the Distributive Property to write two expressions that are equivalent to 8x + 16.

Answer: 8(x + 2), 4(2x + 4)

Explanation:
By using the Distributive Property we can write 8x + 16 in two ways.
8x + 16
Take 8 as a common factor
8(x + 2)
Next take 4 as a common factor
4(2x + 4)
The expressions 8(x + 2) and 4(2x + 4) are equivalent to 8x + 16

MATCHING
Match the expression with an equivalent expression.

Question 52.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 94

Answer: C

Explanation:
Given the expression 8x + 16y
Let us take 4 as a common factor.
4(2x + 4y)
Thus the equivalent expression is option C.

Question 53.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 95

Answer: B

Explanation:
Given the expression 4x + 8y
Let us take 2 as a common factor.
4x + 8y = 2(4y + 2x)
Thus the equivalent expression is option B.

Question 54.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 96

Answer: D

Explanation:
Given the expression 16x + 8y
Let us take 8 as a common factor.
16x + 8y = 8(2x + y)
This can also be written as 8(y + 2x)
Thus the equivalent expression is option D.

Question 55.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 97

Answer: A

Explanation:
Given the expression 8x + 4y
Let us take 4 as a common factor.
8x + 4y = 4(2x + y)
Thus the equivalent expression is option A.

Question 56.
YOU BE THE TEACHER
Your friend factors the expression 24x + 56. Is your friend correct? Explain your reasoning.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 98

Answer: your friend is incorrect

Explanation:
Given the expression 24x + 56
Take 8 as the common factor from the expression.
24x + 56 = 8(3x + 7)
By this, we can say that your friend is incorrect.

Question 57.
MODELING REAL LIFE
You sell soup mixes for a fundraiser. For each soup mix you sell, the company that makes the soup receives x dollars, and you receive the remaining amount. You sell 16 soup mixes for a total of (16x + 96) dollars. How much money do you receive for each soup mix that you sell?

Answer: $6

Explanation:
Here, the cost price of each soup = x dollars
The cost price of 16 soup = 16 x
The selling price of 16 soup = 16 x + 96
Since, the total money received for 16 soup = The selling price of 16 soup – The cost price of 16 soup
= 16 x + 96 – 16 x
= 96
Thus, the total money received for 16 soup = 96 dollars
⇒ The total money received for 1 soup = 96/16 dollars
⇒ The total money received for 1 soup = 6 dollars
Hence, for each soup 6 dollars is received.

Question 58.
PROBLEM SOLVING
A clothing store is having a sale on holiday socks. Each pair of socks costs x dollars. You leave the store with 6 pairs of socks and spend a total of (6x − 14) dollars. You pay with $40. How much change do you receive? Explain your reasoning.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 99

Answer: $14

Explanation:
Given,
A clothing store is having a sale on holiday socks. Each pair of socks costs x dollars.
You leave the store with 6 pairs of socks and spend a total of (6x − 14) dollars.
You pay with $40.
Since, the cost of 1 pair of socks = x
The cost of 6 pair of socks = 6 x
Total amount spend = $ 40
According to the question,
6 x – 14 = 40
6 x = 40 + 14
6 x = 54
x = 9
Thus, the original price of one pair of socks = $ 9
The original price of 6 pairs of socks = $ 54
Hence, the total change = original price of socks – the price of socks in the sale = 54 – 40 = $ 14

Question 59.
STRUCTURE
You buy 37 concert tickets for $8 each, and then sell all 37 tickets for $11 each. The work below shows two ways you can determine your profit. Describe each solution method. Which do you prefer? Explain your reasoning.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 100

Answer:
Given,
You buy 37 concert tickets for $8 each, and then sell all 37 tickets for $11 each.
I prefer the second method which is simplified using the distributive property.
Number of concert tickets = 37
Actual price = $8
selling price = $11
Profit = Number of tickets (selling price – cost price)
P = 37 (11 – 8)
P = 37(3)
P = $111

Question 60.
NUMBER SENSE
The prime factorizations of two numbers are shown, where a and b represent prime numbers. Write the sum of the two numbers as an expression of the form Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 101. Explain your reasoning.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 101.1

Answer:
Let us consider a and b are 2 and 5
Number 1:
2 × 11 × 5 × a
Number 2:
7 × b × 3 × 3
14 (2 + 5) = 140

Algebraic Expressions and Properties Connecting Concepts

Connecting Concepts
Using the Problem-Solving Plan

Question 1.
A store sells 18 pairs of the wireless earbuds shown. Customers saved a total of $882 on the earbuds. Find the original price of the earbuds.
Understand the problem.
You know the percent discount on a pair of wireless earbuds, the number of pairs of earbuds sold, and the total amount of money that customers saved. You are asked to find the original price of the earbuds.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 102
Make a plan
First, write an expression that represents the total amount of money that customers pay for the earbuds. Then factor the expression to find the discount (in dollars) on each pair of earbuds. Finally, solve a percent problem to find the original price.
Solve and check.
Use the plan to solve the problem. Then check your solution.

Answer:
Number of pairs = 18
Amount saved = $882
Let d be the cost of the wireless earbuds
So, the expression would be 18d + 882

Question 2.
All of the weight plates in a gym are labeled in kilograms. You want to convert the weights to pounds. Write an expression to find the number of pounds in z kilograms. Then find the weight in pounds of a plate that weighs 20.4 kilograms.
Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 103

Answer:
All of the weight plates in a gym are labeled in kilograms. You want to convert the weights to pounds
Convert from kilograms to pounds
1 kg = 2.20 pounds
The expression would be 2.20z
Now we have to find the weight of 20.4 kilograms to pounds.
20.4kg = 2.20 × 20.4
= 44.97 pounds

Question 3.
You buy apple chips and banana chips in the ratio of 2 : 7.
a. How many ounces of banana chips do you buy when you buy n ounces of apple chips? Explain.

Answer:
The ratio of apple chips and banana chips = 2 : 7
Apple chips = 2
Banana chips = 7
2 + 7 = 9
n/2 = 9
n = 18
18 ounces of apple chips
n/7 = 9
n = 9 × 7
n = 63
63 ounces of banana chips for 18 ounces of apple chips.
b. You buy 12 ounces of apple chips. How many ounces of banana chips do you buy?

Answer:
You buy 12 ounces of apple chips.
The ratio of apple chips and banana chips = 2 : 7
Apple chips = 2x
Banana chips = 7x
2 + 7 = 9
n = 12
For 12 ounces of apple chips you buy 42 ounces of banana chips

Performance Task

Describing Change

At the beginning of this chapter, you watched a STEAM video called “Shadow Drawings.” You are now ready to complete the performance task related to this video, available at BigIdeasMath.com. Be sure to use the problem-solving plan as you work through the performance task.
Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 104

Algebraic Expressions and Properties Chapter Review

Review Vocabulary

Write the definition and give an example of each vocabulary term.
Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 105

Graphic Organizers

You can use an Example and Non-Example Chartto list examples and non-examples of a concept. Here is an Example and Non-Example Chart for the CommutativeProperty of Addition.
Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 106

Choose and complete a graphic organizer to help you study the concept.

  1. algebraic expressions
  2. variable
  3. Commutative Property of Multiplication
  4. Associative Property of Addition
  5. Associative Property of Multiplication
  6. Addition Property of Zero
  7. Multiplication Property of Zero
  8. Multiplication Property of One
  9. Distributive Property

Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 107

Chapter Self-Assessment

As you complete the exercises, use the scale below to rate your understanding of the success criteria in your journal.
Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 108

5.1 Algebraic Expressions (pp. 201 – 208)

Identify the terms, coefficients, and constants in the expression.

Question 1.
9x + 2 + 8y

Answer:
2 – constant
9, 8 – coefficient
x, y – variable or term
A term without a variable is called a constant.
The numerical factor of a term that contains a variable is called a coefficient.
A variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.

Question 2.
3x2 + x + 7

Answer:
7 – constant
3, 1 – coefficient
x – variable or term
2 is the exponent
A term without a variable is called a constant.
The numerical factor of a term that contains a variable is called a coefficient.
An exponent refers to the number of times a number is multiplied by itself.
A variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.

Question 3.
Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 109

Answer:
1 – constant
7, 1/4 – coefficient
q – variable or term
A term without a variable is called a constant.
The numerical factor of a term that contains a variable is called a coefficient.
A variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.

Evaluate the expression when x = 20, y = 4, and z = 7.

Question 4.
x ÷ 5

Answer: 4

Explanation:
Given expression is x ÷ 5
Where x = 20
20 ÷ 5 = 4
Thus x ÷ 5 = 4

Question 5.
12 – z

Answer: 5

Explanation:
Given expression is 12 – z
Where z = 7
12 – z
= 12 – 7
= 5
Thus 12 – z = 5

Question 6.
4y

Answer: 16

Explanation:
The given expression is 4y
Where
y = 4
4y = 4(4) = 16

Question 7.
y + x

Answer: 24

Explanation:
Given expression is y + x
Where
y = 4
x = 20
y + x
= 4 + 20 = 24
Thus y + x = 24

Question 8.
x . z

Answer: 80

Explanation:
Given expression is x . z
Where
x = 20
z = 7
x . z = 20 × 7 = 140
Thus x . z = 140

Question 9.
x – y

Answer: 16

Explanation:
Given expression is x – y
Where
y = 4
x = 20
20 – 4 = 16
Thus x – y = 16

Question 10.
3z + 8

Answer: 29

Explanation:
Given expression is 3z + 8
Where
z = 7
3z + 8 = 3(7) + 8
= 21 + 8
= 29
Thus 3z + 8 = 29

Question 11.
8y – x

Answer: 12

Explanation:
Given expression is 8y – x
Where
y = 4
x = 20
8y – x = 8(4) – 20
= 32 – 20
= 12
Thus 8y – x = 12

Question 12.
Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 110

Answer:

Explanation:
Given expression is Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 110
Where
y = 4
x = 20
(20)²/4
= (20 × 20)/4
= 5 × 20
= 100

Question 13.
The amount earned (in dollars) for recycling pounds of copper is 2p. How much do you earn for recycling 28 pounds of copper?

Answer: 56

Explanation:
Given,
The amount earned (in dollars) for recycling pounds of copper is 2p.
Substitute the value of p in the expression.
p = 28
2p = 2(28) = 56

Question 14.
While playing a video game, you score p game points and b triple bonus points. An expression for your score is p + 3b. What is your score when you earn 245 game points and 20 triple bonus points?
Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 111

Answer:
Given,
While playing a video game, you score p game points and b triple bonus points. An expression for your score is p + 3b.
p = 245
b = 20
Substitute the value of p and b in the given expression
p + 3b = 245 + 3(22)
245 + 66 = 311

Question 15.
Tickets for a baseball game cost a dollars for adults and c dollars for children. The expression 2a + 3c represents the cost (in dollars) for a family to go to the game. What is the cost for the family when an adult ticket is $17 and a child ticket is $12?

Answer:
Given,
Tickets for a baseball game cost a dollars for adults and c dollars for children.
The expression 2a + 3c represents the cost (in dollars) for a family to go to the game.
a = 17
c = 12
2a + 3c
Substitute the value of a and c in the given expression
= 2(17) + 3(12)
= 34 + 36
= 70

Question 16.
Add one set of parentheses to the expression 2x2 + 4 − 5 so that the value of the expression is 75 when x = 6.

Answer:
2x2 + 4 − 5
x = 6
2(6)2 + 4 − 5
= 2(36) – 1
= 72 – 1
= 71
Add 4 to the expression to get the value 75
2x2 + 4 − 5 + 4
x = 6
2(6)2 + 4 − 5 + 4
= 2(36) – 1 + 4
= 72 – 1 + 4
= 71 + 4
= 75

5.2 Writing Expressions (pp. 209–214)

Write the phrase as an expression.

Question 17.
9 fewer than 23

Answer: 9 – 23

Explanation:
The phrase “fewer than” represents – symbol
Thus the expression would be 9 – 23

Question 18.
6 more than the quotient of 15 and 3

Answer: 6 + (15 ÷ 3)

Explanation:
The phrase more than represents ‘+’ and quotient represents ‘÷’
Thus the expression would be 6 + (15 ÷ 3)

Question 19.
the product of a number d and 32

Answer: 32d

Explanation:
The phrase product represents ‘×’ symbol.
Thus the expression would be 32d

Question 20.
a number t decreased by 17

Answer: d – 17

Explanation:
The phrase “decreased” represents ‘-‘ symbol.
Thus the expression would be d – 17

Question 21.
Your basketball team scored 4 fewer than twice as many points as the other team.
a. Write an expression that represents the number of points your team scored.

Answer:
Your basketball team scored 4 fewer than twice as many points, x, as the other team.
n = 2x – 4
b. The other team scored 24 points. How many points did your team score?

Answer: 14

Explanation:
The other team scored 24 points i.e. n=24.
24 = 2x – 4
2x = 24 + 4
2x = 28
x = 28/2
x = 14
Thus the team score 14 points.

Question 22.
The boiling temperature (in degrees Celsius) of platinum is 199 more than four times the boiling temperature (in degrees Celsius) of zinc.
a. Write an expression that represents the boiling temperature (in degrees Celsius) of platinum.

Answer: P = 199 + 4z
b. The boiling temperature of zinc is 907 degrees Celsius. What is the boiling temperature of platinum?

Answer:
The boiling temperature of zinc is 907 degrees Celsius.
P = 199 + 4z
P = 199 + 4(907)
P = 3827

Question 23.
Write an algebraic expression with two variables, x and y, that has a value of 50 when x = 3 and y = 5. (pp. 215–220)

Answer: 5x + 7y = 50

Explanation:
Let us assume that the algebraic expression is 5x + 7y = 50
Where x = 3 and y = 5
5(3) + 7(5) = 50
15 + 35 = 50
50 = 50
Our assumption is correct.

5.3 Properties of Addition and Multiplication

Simplify the expression. Explain each step.

Question 24.
10 + (2 + y)

Answer: 12 + y

Explanation:
Given the expression 10 + (2 + y)
Combine the like terms
10 + 2 + y = 12 + y

Question 25.
(21 + b) + 1

Answer: 22 + b

Explanation:
Given the expression (21 + b) + 1
Combine the like terms
21+ 1 + b
22 + b

Question 26.
3(7x)

Answer: 21x

Explanation:
Given the expression 3(7x)
3 × 7x = 21x

Question 27.
1(3.2w)

Answer: 3.2w

Explanation:
Given the expression 1(3.2w)
1 × 3.2w = 3.2w

Question 28.
5.3 + (w + 1.2)

Answer: 6.5 + w

Explanation:
Given the expression 5.3 + (w + 1.2)
Combine the like terms
5.3 + 1.2 + w
= 6.5 + w

Question 29.
(0 + t) + 9

Answer: t + 9

Explanation:
Given the expression (0 + t) + 9
Combine the like terms
(0 + t) + 9 = t + 9

Question 30.
The expression 7 + 3x+ 4 represents the perimeter of the triangle. Simplify the expression.
Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 112

Answer:
Given,
The expression 7 + 3x+ 4 represents the perimeter of the triangle.
Combine the like terms
7 + 3x+ 4 = 11 + 3x

Question 31.
Write an algebraic expression that can be simplified using the Associative Property of Addition.

Answer:
Associative property of addition: Changing the grouping of addends does not change the sum. For example, ( 2 + 3 ) + 4 = 2 + ( 3 + 4 ) (2 + 3) + 4 = 2 + (3 + 4) (2+3)+4=2+(3+4) left parenthesis, 2, plus, 3, right parenthesis, plus, 4, equals, 2, plus, left parenthesis, 3, plus, 4, right parenthesis.

5.4 The Distributive Property

Use the Distributive Property to simplify the expression.

Question 32.
2(x + 12)

Answer:
We can simplify the expression by using the Distributive Property.
The distributive property explains that multiplying two numbers together will result in the same thing as breaking up one factor into two addends, multiplying both addends by the other factor, and adding together both products.
2(x + 12) = 2 × x + 2 × 12
= 2x + 24

Question 33.
11(4b – 3)

Answer:
Given the expression 11(4b – 3)
We can simplify the expression by using the Distributive Property.
The distributive property explains that multiplying two numbers together will result in the same thing as breaking up one factor into two addends, multiplying both addends by the other factor, and adding together both products.
11(4b – 3) = 11 × 4b – 11 × 3
= 44b – 33

Question 34.
8(s – 1)

Answer:
Given the expression 8(s – 1)
We can simplify the expression by using the Distributive Property.
The distributive property explains that multiplying two numbers together will result in the same thing as breaking up one factor into two addends, multiplying both addends by the other factor, and adding together both products.
8(s – 1) = 8 × s – 8 × 1
= 8s – 8

Question 35.
6(6 + y)

Answer:
Given the expression 6(6 + y)
We can simplify the expression by using the Distributive Property.
The distributive property explains that multiplying two numbers together will result in the same thing as breaking up one factor into two addends, multiplying both addends by the other factor, and adding together both products.
6(6 + y) = 6 × 6 + 6 × y
36 + 6y

Simplify the expression.

Question 36.
5(n + 3) + 4n

Answer:
Given the expression 5(n + 3) + 4n
Combine the like terms
5(n + 3) + 4n
= 5 × n + 5 × 3 + 4n
= 5n + 15 + 4n
= 9n + 15

Question 37.
t + 2 + 6t

Answer:
Given the expression t + 2 + 6t
Combine the like terms
t + 2 + 6t
7t + 2

Question 38.
3z + 14 + 5z – 9

Answer:
Given the expression 3z + 14 + 5z – 9
Combine the like terms
3z + 14 + 5z – 9
8z – 5

Question 39.
A family of three goes to a salon. Each person gets a haircut and highlights. The cost of each haircut is $15, and the cost per person for highlights is x dollars. Write and simplify an expression that represents the total cost (in dollars) for the family at the salon.

Answer: 45 + 3(x)

Explanation:
Given,
A family of three goes to a salon. Each person gets a haircut and highlights.
The cost of each haircut is $15, and the cost per person for highlights is x dollars.
The expression would be 45 + 3x
Each person gets a haircut = 3 × 15 = 45

Question 40.
Each day, you take vocal lessons for v minutes and trumpet lessons for 30 minutes. Write and simplify an expression to find how many minutes of lessons you take in 4 days.
Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 113

Answer:
Given,
Minutes of vocal lessons I take each day =
Minutes of trumpet lessons I take each day = 30
To write and simplify how many minutes of lessons I take in 4 days.
Solution:
Total number of minutes of lesson I take each day can be calculated by adding the minutes of lessons taken each day and can be given as:
= v + 30
The expression would be (v + 30)
So in 4 days I will take = 4(v + 30)
= 4v + 120
Thus, total minutes of lessons I take in 4 days = 4v + 120

5.5 Factoring Expressions (pp. 227 – 232)

Factor the expression using the GCF.

Question 41.
42 – 12

Answer: 6

Explanation:
The factors of 12 are: 1, 2, 3, 4, 6, 12
The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42
Then the greatest common factor is 6.

Question 42.
15 + 35

Answer: 5

Explanation:
The factors of 15 are: 1, 3, 5, 15
The factors of 35 are: 1, 5, 7, 35
Then the greatest common factor is 5.

Question 43.
36x – 28

Answer: 4

Explanation:
The factors of 28 are: 1, 2, 4, 7, 14, 28
The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36
Then the greatest common factor is 4.

Question 44.
24 + 64x

Answer: 8

Explanation:
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
The factors of 64 are: 1, 2, 4, 8, 16, 32, 64
Then the greatest common factor is 8.

Question 45.
60 – 150x

Answer: 30

Explanation:
The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The factors of 150 are: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
Then the greatest common factor is 30.

Question 46.
16x + 56y

Answer: 8

Explanation:
The factors of 16 are: 1, 2, 4, 8, 16
The factors of 56 are: 1, 2, 4, 7, 8, 14, 28, 56
Then the greatest common factor is 8.

Question 47.
A soccer team receives a discount on each jersey purchased. The original price of each jersey is x dollars. The team buys 18 jerseys for a total of (18x − 36) dollars. What can you conclude about the discount?

Answer:
Given,
A soccer team receives a discount on each jersey purchased.
The original price of each jersey is x dollars.
The team buys 18 jerseys for a total of (18x − 36) dollars.
Multiply 18 with the original price after that you decrease 36 dollars.
By this, we can conclude that $36 is the discount

Question 48.
You sell apple cider for a fundraiser. For each gallon of cider you sell, the company that makes the cider receives x dollars, and you receive the remaining amount. You sell 15 gallons of cider for (15x + 45) dollars. How much money do you receive for each gallon of cider that you sell?
Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 113.1

Answer:
Given,
You sell apple cider for a fundraiser. For each gallon of cider you sell, the company that makes the cider receives x dollars, and you receive the remaining amount.
You sell 15 gallons of cider for (15x + 45) dollars
Let x = 1
15(1) + 45 = 60
x = 2
15(2) + 45 = 30 + 45 = 75

Algebraic Expressions and Properties Practice Test

Question 1.
Identify the terms, coefficients, and constants of \(\frac{q}{3}\) + 6 + 9q.

Answer:
6 – constant
9,  \(\frac{1}{3}\) – coefficient
q – variable or term
A term without a variable is called a constant.
The exponent tells us how many times the base is used as a factor
The numerical factor of a term that contains a variable is called a coefficient.
A variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.

Question 2.
Evaluate 4b – a when a = 12 and b = 7.

Answer: 16

Explanation:
Given the expression 4b – a
where a = 12 and b = 7
4(7) – 12
28 – 12 = 16
Thus 4b – a = 16

Write the phrase as an expression.

Question 3.
25 more than 50

Answer: The phrase for the expression 25 more than 50 is 25 + 50

Question 4.
6 less than the quotient of 32 and a number y.

Answer: The phrase for the expression 6 less than the quotient of 32 and a number y is 6 – 32 ÷ y

Simplify the expression. Explain each step.

Question 5.
3.1 + (8.6 + m)

Answer:
Given the expression 3.1 + (8.6 + m)
Combine the like terms
3.1 + (8.6 + m)
3.1 + 8.6 + 3
11.7 + m

Question 6.
Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 114

Answer:
Given the expression (\(\frac{2}{3}\) × t) × 1 \(\frac{1}{2}\)
First, convert the mixed fraction to the improper fraction
1 \(\frac{1}{2}\) = \(\frac{3}{2}\)
\(\frac{3}{2}\) × \(\frac{2}{3}\) × t
= t
Thus (\(\frac{2}{3}\) × t) × 1 \(\frac{1}{2}\) = t

Question 7.
4(x + 8)

Answer:
Given the expression 4(x + 8)
= 4 × x + 4 × 8
= 4x + 32

Question 8.
4t + 7 + 2t – 2

Answer: 6t + 5

Explanation:
Combine the like terms
4t + 7 + 2t – 2
6t + 5
Thus 4t + 7 + 2t – 2 = 6t + 5

Factor the expression using the GCF.

Question 9.
18 + 24

Answer:
Find the GCF for 18, 24
The factors of 18 are 1, 2, 3, 6, 9, 18
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
The common factors are 1, 2, 3, 6.
Thus the GCF of 18 + 24 is 6.

Question 10.
15x + 20

Answer:
Since 15x, 20 contain both numbers and variables, there are two steps to find the GCF.
Find the GCF fo the numerical part 15, 20
The factors of 20 are 1, 2, 4, 5, 10, 20
The factors of 15 are 1, 3, 5, 15
The number do not contain any common variable factors.
The greatest common factor is 5

Question 11.
32x – 40y

Answer: 8

Explanation:
Since 32x, 40y contain both numbers and variables, there are two steps to find the GCF.
Find the GCF for the numerical part 32, 40
The factors of 32 are 1, 2, 4, 8, 16, 32
The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40
The number do not contain any common variable factors.
Then the greatest common factor is 8.

Question 12.
Playing time is added at the end of a soccer game to make up for stoppages. An expression for the length (in minutes) of a 90-minute soccer game with minutes of stoppage time is 90 + x. How long is a game with 4 minutes of stoppage time?
Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 114.1

Answer: 94

Explanation:
Given,
Playing time is added at the end of a soccer game to make up for stoppages.
An expression for the length (in minutes) of a 90-minute soccer game with minutes of stoppage time is 90 + x.
x = 4
Substitute the value of x in the expression
90 + 4 = 94

Question 13.
The expression 15 . x . 6 represents the volume of a rectangular prism with a length of 15, a width of x, and a height of 6. Simplify the expression.

Answer:
Given,
The expression 15 . x . 6 represents the volume of a rectangular prism with a length of 15, a width of x, and a height of 6.
The formula for the volume of a rectangular prism is lwh
V = 15 × x × 6
V = 90x

Question 14.
The Coiling Dragon Cliff Skywalk in China is 128 feet longer than the length x (in feet) of the Tianmen Skywalk in China. The world’s longest glass-bottom bridge, located in China’s Zhangjiajie National Park, is about 4.3 times longer than the Coiling Dragon Cliff Skywalk. Write and simplify an expression that represents the length (in feet) of the world’s longest glass-bottom bridge.
Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 115

Answer:
The Coiling Dragon Cliff Skywalk in China is 128 feet longer than the length x (in feet) of the Tianmen Skywalk in China.
128 + x
The world’s longest glass-bottom bridge, located in China’s Zhangjiajie National Park, is about 4.3 times longer than the Coiling Dragon Cliff Skywalk.
(128 + x) × 4.3
128 × 4.3 + 4.3 × x
550.4 + 4.3x
Thus the expression is 4.3x + 550.4ft

Question 15.
A youth group is making and selling sandwiches to raise money. The cost to make each sandwich is dollars. The group sells 150 sandwiches for a total of (150h + 450) dollars. How much profit does the group earn for each sandwich sold?

Answer:
We are given that
Cost to make each sandwich= h dollar
The total selling price of 150 sandwiches=(150h+450 )dollars
We have to find the profit earn by the group on each sandwich sold.
Total cost for making 150 sandwiches= 150 × h
Total cost for making 150 sandwiches=150 h
Now,
Profit made by the group on 150 sandwiches
=150h+450-150h
=450 dollars
Profit earn by group for each sandwich sold= 450/150
Profit earn by group for each sandwich sold=$ 3

Question 16.
You make party favors for an event. You tie 9 inches of ribbon around each party favor. Write an expression for the number of inches of ribbon needed for n party favors. The ribbon costs $3 for each yard. Write an expression for the total cost (in dollars) of the ribbon.

Answer:
Need 9n inches of ribbon Cost is $0.75n
Since you need 9 inches per party favor and you have n party favors, the amount of ribbon you need is 9 times n inches.
So R = 9n inches
Since the ribbon costs $3 per yard and our current equation is inches, we need to do a bit of conversion.
There are 36 inches per yard and 9 inches per ribbon, so each yard of ribbon can make 36/9 = 4 ribbons for the party favors.
So the cost per party favor will be one-fourth of the cost per yard of ribbon per party favor.
So $3.00 / 4 = $0.75, making the cost equation: C = $0.75n

Algebraic Expressions and Properties Cumulative Practice

Question 1.
The student council is organizing a school fair. Council members are making signs to show the prices for admission and for each game a person can play.
Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 116

Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 117

Let x represent the number of games. Which expression can you use to determine the total amount (in dollars) a person pays for admission and playing x games?
A. 2.25
B. 2.25x
C. 2 + 0.25x
D. 2x + 0.25

Answer: 2 + 0.25x

Explanation:
Given the data,
The student council is organizing a school fair. Council members are making signs to show the prices for admission and for each game a person can play.
Admission fee is $2
Price per game is $0.25
Let x represent the number of games.
The expression would be the sum of admission and product of price and number of games
That is 2 + 0.25x
Thus the correct answer is option C.

Question 2.
Which ratio relationship is represented in the graph?
Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 118
F. 2 cups of flour for every cup of sugar \(\frac{1}{2}\) up of sugar
G. 6 cups of flour for every 3 cups of sugar
H. 1 cup of flour for every 4 cups of sugar
I. \(\frac{1}{2}\) cup of flour for every 1 cup of sugar

Answer: 2 cups of flour for every cup of sugar \(\frac{1}{2}\) up of sugar

Explanation:
The graph represents that 2 cups of flour for every cup of sugar.
Thus the correct answer is option F.

Question 3.
At a used bookstore, you can purchase two types of books.
Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 119
You can use the expression 3h + 2p to find the total cost (in dollars) for h hardcover books and p paperback books. What is the total cost (in dollars) for 6 hardcover books and 4 paperback books?
Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 120

Answer:
Given expression 3h + 2p
h represents hardcover books
p represents paperback books
The cost of hardcover books is $3
The cost of paperback books is $2
3h + 2p = 3(3) + 2(2)
= 9 + 4
= 13
We have to find the total cost (in dollars) for 6 hardcover books and 4 paperback books.
The equation will be 6h + 4p
= 6(3) + 4(5)
= 18 + 20
= 38
The total cost (in dollars) for 6 hardcover books and 4 paperback books is $38.

Question 4.
Your friend divided two decimal numbers. Her work is shown in the box below. What should your friend change in order to divide the two decimal numbers correctly?
Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 121

Answer: C

Explanation:
0.07 ÷ 14.56 can be written as
7 ÷ 0.1456
Thus the correct answer is option C.

Question 5.
What is the value of 4.391 + 5.954?
F. 9.12145
G. 9.245
H. 9.345
I. 10.345

Answer: 10.345

Explanation:
Add two decimal numbers 4.391 and 5.954
4.391
+5.954
10.345
Thus the correct answer is option I.

Question 6.
The circle graph shows the eye color of students in a sixth-grade class. Nine students in the class have brown eyes. How many students are in the class?
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 122
A. 4 students
B. 18 students
C. 20 students
D. 405 students

Answer: 20 students

Explanation:
By seeing the above figure we can find the number of students in the class.
The circle graph shows the eye color of students in a sixth-grade class. Nine students in the class have brown eyes.
45/9 = 5
Each student is equal to 5%
35/5 = 7 students
20/5 = 4 students
9 + 7 + 4 = 20 students
Thus the correct answer is option C.

Question 7.
Properties of Addition and Multiplication are used to simplify an expression.
Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 123
What number belongs in place of the x?

Answer:
36 × 23 + 33 × 64 = 36 × 23 + 64 × 33
= 36 × 23 + 64 × (23 + 10)
= 36 × 23 + 64 × 23 + 64 × 10
= 23(36 + 64) + 64 × 10
= 100 × 23 + 64 × 10
x = 100
Thus the number that belong to x is 100.

Question 8.
What is the prime factorization of 1350?
F. 10 . 135
G. 2 . 3 . 5
H. 6 . 225
I. 2 . 33 . 52

Answer:
The prime factorisation of 1350 is
1350 = 2 × 3 × 3 × 3 × 5 × 5
1350 = 2 . 33 . 52
Thus the correct answer is option I.

Question 9.
A horse gallops at a speed of 44 feet per second. What is the speed of the horse in miles per hour?
A. \(\frac{1}{2}\) mile per hour
B. 30 miles per hour
C. 64\(\frac{8}{15}\) miles per hour
D. 158,400 miles per hour

Answer: 30 miles per hour

Explanation:
Given,
A horse gallops at a speed of 44 feet per second.
Convert from feet per second to miles per hour.
1 foot per second = 0.68 miles per hour
44 feet per second = 30 miles per hour
Thus the correct answer is option B.

Question 10.
Which equation correctly demonstrates the Distributive Property?
F. a(b + c) = ab + ac
G. a(b + c) = ab + ac
H. a + (b + c) = (a + b) + (a + c)
I. a + (b + c) = (a + b) . (a + c)

Answer: F

Explanation:
The distributive property explains that multiplying two numbers (factors) together will result in the same thing as breaking up one factor into two addends, multiplying both addends by the other factor, and adding together both products.
a(b + c) = ab + ac
Thus the correct answer is option F.

Question 11.
Which number is equivalent to 2\(\frac{4}{5}\) . 1\(\frac{2}{7}\) ?
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 124

Answer: C

Explanation:
Convert the mixed fraction to the improper fraction.
2\(\frac{4}{5}\) = \(\frac{14}{5}\)
1\(\frac{2}{7}\) = \(\frac{9}{7}\)
Now multiply both the fractions
\(\frac{14}{5}\) × \(\frac{9}{7}\) = \(\frac{126}{35}\)
Now convert from improper fraction to the mixed fractions.
\(\frac{126}{35}\) = 3 \(\frac{3}{5}\)
Thus the correct answer is option C.

Question 12.
Which pair of numbers does not have a least common multiple of 24?
F. 2, 12
G. 3, 8
H. 6, 8
I. 12, 24

Answer: 6, 8
The least common multiple of 24 is 24.
2, 12 is 24
3, 8 is 24
6, 8 is 48
Thus the correct answer is option H.

Question 13.
Use the Properties of Multiplication to simplify the expression in an efficient way. Show your work and explain how you used the Properties of Multiplication.
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 125
Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 126

Answer:
We can use the associative property of multiplication to simplify the expression.
The associative property is a math rule that says that the way in which factors are grouped in a multiplication problem does not change the product.
(25 × 18) × 4 = 25 × (18 × 4)
450 × 4 = 1800

Question 14.
Which number is not a perfect square?
A. 64
B. 81
C. 96
D. 100

Answer: 96

Explanation:
A. 64 = 8 × 8
It is a perfect square.
B. 81 = 9 × 9
It is a perfect square.
C. 96 = 12 × 8
96 is not a perfect square.
D. 100 = 10 × 10
It is a perfect square.
Thus the correct answer is option C.

Conclusion:

Big Ideas Math Answers Grade 6 Chapter 5 Algebraic Expressions and Properties is here along with the solutions. Check all the problems and solutions in the above sections along with the examples. For all the queries, you can question us in the below comment box. Share the above article and pdf links with your friends and peers to overcome all the issues in maths. To clear all your doubts and questions, check all the links given in the above sections.

Big Ideas Math Answers Grade 6 Chapter 6 Equations

Big Ideas Math Answers Grade 6 Chapter 6 Equations

Download Big Ideas Math Answers Grade 6 Chapter 6 Equations Pdf for free of cost. If you are browsing for various questions of equations, then here is the one-stop solution. Know the benefit of referring to Big Ideas Math Book 6th Grade Answer Key Chapter 6 Equations. You can learn the tips and simple methods to solve all the problems. With the below-given material, it acts as a guide to get better marks in the exam. Get a free step-by-step solution from this ultimate guide ie., BIM 6th Grade Solutions Ch 6 Equations. Check the below sections to get various details and information.

Big Ideas Math Book 6th Grade Answer Key Chapter 6 Equations

It is necessary for the candidates to understand the concept in maths. Concept is important than scoring marks in the exam. Therefore relate the questions with real-time problems and understand the concept in depth. With all the factors into consideration, BIM 6th Grade Answer Key or Equations Pdf is prepared. Click on the links in the next sections and start practicing the problems. Follow the various topics, Steam videos and Solved problems available in BIM Equations book and pdf.

Performance Task

Lesson 1: Writing Equations in One Variable

Lesson: 2 Solving Equations Using Addition or Subtraction

Lesson: 3 Solving Equations Using Multiplication or Division

Lesson: 4 Writing Equations in Two Variables

Chapter 6 – Equations

Equations STEAM Video/ Performance Task

STEAM Video

Rock Climbing
Equations can be used to solve many different kinds of problems in real life, such as estimating the amount of time it will take to climb a rock wall. Can you think of any other real-life situations where equations are useful?
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 1
In rock climbing, a pitch is a section of a climbing route between two anchor points. Watch the STEAM Video “Rock Climbing.”en answer the following questions.
1. How can you use pitches to estimate the amount of time it will take to climb a rock wall?
2. Are there any other methods you could use to estimate the amount of time it will take to climb a rock wall? Explain.
3. You know two of the three pieces of information below. Explain how you can find the missing piece of information.
Average climbing speed
Height of rock wall
Time to complete climb

Performance Task

Planning the Climb
After completing this chapter, you will be able to use the concepts you learned to answer the questions in the STEAM Video Performance Task. You will be given information about two rock-climbing routes.
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 2
Route 1: 500 feet, 125 feet per pitch
Route 2: 1200 feet, 8 pitch
You will find the average speed of the climbers on Route 1 and the amount of time it takes to complete Route 2. Will the average speed of the climbers on Route 1 provide accurate predictions for the amount of time it takes to climb other routes? Explain why or why not.

Equations Getting Ready for Chapter 6

Chapter Exploration

Work with a partner. Every equation that has an unknown variable can be written as a question. Write a question that represents the equation. Then answer the question.
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 3

Answer:
Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-3

Work with a partner. Write an equation that represents the question. Then answer the question.
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 4

Answer:
Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-4

Vocabulary
The following vocabulary terms are defined in this chapter. Think about what each term might mean and record your thoughts.
equation
independent variable
inverse operations
dependent variable
equation in two variables.

Lesson 6.1 Writing Equations in One Variable

EXPLORATION 1

Writing Equations
Work with a partner. Customers order sandwiches at a cafe from the menu board shown.
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 1
a. The equation 6.75x =20.25 represents the purchase of one customer from the menu board. What does the equation tell you about the purchase? What cannot be determined from the equation?
b. The four customers in the table buy multiple sandwiches of the same type. For each customer, write an equation that represents the situation. Then determine how many sandwiches each customer buys. Explain your reasoning.
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 2
Answer:

Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 3

An equation
is a mathematical sentence that uses an equal sign, =, to show that two expressions are equal.
Expressions
4 + 8
x + 8
Equations
4 + 8 = 12
x + 8 = 12
To write a word sentence as an equation, look for key words or phrases such as is, the same as, or equals to determine where to place the equal sign.

Try It

Write the word sentence as an equation.
Question 1.
9 less than a number be equals 2.
Answer: 9-x=2

Explanation:
We have to write the equation for the word sentence
The phrase “less than” indicates -.
let the number be x.
9 – x = 2

Question 2.
The product of a number g and 5 is 30.
Answer: 5 × g=30

Explanation:
We have to write the equation for the word sentence
The phrase “product” indicates ‘×’
g × 5 = 30

Question 3.
A number k increased by 10 is the same as 24.
Answer: k + 10 = 24

Explanation:
We have to write the equation for the word sentence
The phrase “increased” indicates ‘+’
The equation is k + 10 = 24

Question 4.
The quotient of a number q and 4 is 12.
Answer: q ÷ 4 = 12

Explanation:
We have to write the equation for the word sentence
The phrase quotient indicates ‘÷’
The equation is q ÷ 4 = 12

Question 5.
2\(\frac{1}{2}\) is the same as the sum of a number w and \(\frac{1}{2}\).
Answer: 2 \(\frac{1}{2}\) = w + \(\frac{1}{2}\)

Explanation:
We have to write the equation for the word sentence
The phrase sum indicates ‘+’
The equation is 2 \(\frac{1}{2}\) = w + \(\frac{1}{2}\)

Question 6.
WHAT IF?
Each server decorates one table. Which equation can you use to find c?
Answer: We can use the multiplication equation to find c.

Self-Assessment for Concepts & Skills
Solve each exercise. Then rate your understanding of the success criteria in your journal.

Question 7.
VOCABULARY
How are expressions and equations different?
Answer: An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An equation is made up of two expressions connected by an equal sign.

Question 8.
DIFFERENT WORDS, SAME QUESTION
Which is different? Write “both” equations.
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 4
Answer: n-4=8
4<8

Question 9.
OPEN-ENDED
Write a word sentence for the equation 28 −n= 5.
Answer: 28 less than a number n is equals to 5.

Question 10.
WRITING
You purchase x items for $4 each. Explain how the variable in the expression 4x and the variable in the equation 4x= 20 are similar. Explain how they are different.
Answer:
You purchase x items for $4 each
4x = 20
x = 20/4
x = 5

Question 11.
After four rounds, 74 teams are eliminated from a robotics competition. There are 18 teams remaining. Write and solve an equation to find the number of teams that started the competition.
Answer:
Given,
After four rounds, 74 teams are eliminated from a robotics competition. There are 18 teams remaining.
Let x be 74 teams
let y be 18 teams
The equation would be
x + y = 92
74 + 18 = 92
Thus the total number of teams are 92.

Question 12.
The mass of the blue copper sulfate crystal is two-thirds the mass of the red fluorite crystal. Write an equation you can use to find the mass (in grams) of the blue copper sulfate crystal.
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 5
Answer: blue copper sulfate crystal = 2/3 (red fluorite crystal)

Question 13.
DIG DEEPER!
You print photographs from a vacation. Find the number of photographs you can print for $3.60.
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 6
Answer: We can print 15 photographs for $3.60

Explanation:
Cost of each print = $0.24
The total cost for photographs is $3.60
3.60/0.24 = 15
Thus We can print 15 photographs for $3.60

Writing Equations in One Variable Homework & Practice 6.1

Review & Refresh

Factor the expression using the GCF.
Question 1.
6 + 27
Answer: 3 (2 + 9)

Explanation:
Given the expression 6 + 27
Take 3 as the common factor
3(2 + 9)

Question 2.
9w + 72
Answer: 9(w + 8)

Explanation:
Given the expression 9w + 72
Take 9 as the common factor
9w + 72 = 9(w + 8)

Question 3.
42 + 24n
Answer: 6(7 + 4n)

Explanation:
Given the expression 42 + 24n
Take 6 as the common factor
42 + 24n = 6(7 + 4n)

Question 4.
18h + 30k
Answer: 6(3h + 5k)

Explanation:
Given the expression 18h + 30k
Take 6 as the common factor
18h + 30k = 6(3h + 5k)

Question 5.
Which number is not equal to 225%?
A. 2\(\frac{1}{4}\)
B. \(\frac{9}{4}\)
C. \(\frac{50}{40}\)
D. \(\frac{45}{20}\)
Answer: C
225% is not equal to \(\frac{50}{40}\)

Evaluate the expression when a = 7.
Question 6.
6 + a
Answer: 13

Explanation:
Given the expression 6 + a
where a = 7
Substitute the value of a in the expression
6 + 7 = 13

Question 7.
a – 4
Answer: 3

Explanation:
Given the expression a – 4
where a = 7
Substitute the value of a in the expression
a – 4
7 – 4 = 3

Question 8.
4a
Answer: 28

Explanation:
Given the expression 4a
where a = 7
Substitute the value of a in the expression
4 × 7 = 28

Question 9.
\(\frac{35}{a}\)
Answer: 5

Explanation:
Given the expression \(\frac{35}{a}\)
where a = 7
Substitute the value of a in the expression
\(\frac{35}{7}\) = 5

Find the perimeter of the rectangle.
Question 10.
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 7
Answer:
l = 8 ft
Area = 40 sq ft
We know that,
Area of rectangle = l × w
40 sq. ft = 8 ft × w
w = 40/8 = 5 ft
Thus the width of the above rectangle is 5 ft.

Question 11.
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 8
Answer:
l = 13 cm
w = ?
A = 52 sq. cm
We know that,
Area of rectangle = l × w
52 sq. cm = 13 cm × w
w = 52/13
w = 4 cm
Thus the width of the above rectangle is 4 cm.

Question 12.
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 9
Answer:
A = 224 sq. miles
l = 14 miles
We know that,
Area of rectangle = l × w
224 sq. miles = 14 × w
w = 224/14
w = 16 miles
Thus the width of the above figure is 16 miles.

Concepts, Skills, & Problem Solving

WRITING EQUATIONS A roast beef sandwich costs $6.75. A customer buys multiple roast beef sandwiches. Write an equation that represents the situation. Then determine how many sandwiches the customer buys. (See Exploration 1, p. 245.)
Question 13.
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 10
Answer:
Given,
A roast beef sandwich costs $6.75.
Amount used for payment = $50.
Change Received = $16.25
The total number of sandwich the customer buys = 5

Question 14.
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 11
Answer:
Given,
A roast beef sandwich costs $6.75.
Amount used for payment = $80.
Change Received = $19.25
Amount used for payment – Change Received
= $ 80 – $19.25
= $60.75
1 sandwich = $6.75
The total number of sandwich the customer buys = 9

WRITING EQUATIONS Write the word sentence as an equation.
Question 15.
A number y decreased by 9 is 8.
Answer: y – 9 = 8

Explanation:
We have to write the word sentence in the equation form.
y – 9 = 8

Question 16.
The sum of a number x and 4 equals 12.
Answer: x + 4 = 12

Explanation:
We have to write the word sentence in the equation form.
x + 4 = 12

Question 17.
9 times a number b is 36.
Answer: 9b = 36

Explanation:
We have to write the word sentence in the equation form.
The phrase times indicates ‘×’
The equation would be 9b = 36

Question 18.
A number w divided by 5 equals 6.
Answer: w ÷ 5 = 6

Explanation:
We have to write the word sentence in the equation form.
The phrase divided by indicates ‘÷’
The equation would be w ÷ 5 = 6

Question 19.
54 equals 9 more than a number t.
Answer: 54 = 9 + t

Explanation:
We have to write the word sentence in the equation form.
The phrase more than indicates ‘+’
The equation would be 54 = 9 + t

Question 20.
5 is one-fourth of a number c.
Answer: 5 = 1/4 c

Explanation:
We have to write the word sentence in the equation form.
The phrase of indicates ‘×’
The equation would be 5 = 1/4 c

Question 21.
9.5 less than a number n equals 27.
Answer: 9.5 – n = 27

Explanation:
We have to write the word sentence in the equation form.
The phrase less than indicates ‘-‘
The equation would be 9.5 – n = 27

Question 22.
11\(\frac{3}{4}\) is the quotient of a number y and 6\(\frac{1}{4}\).
Answer: 11\(\frac{3}{4}\) = y ÷ 6\(\frac{1}{4}\)

Explanation:
We have to write the word sentence in the equation form.
The phrase quotient indicates ‘÷’
The equation would be 11\(\frac{3}{4}\) = y ÷ 6\(\frac{1}{4}\)

Question 23.
YOU BE THE TEACHER
Your friend writes the word sentence as an equation. Is your friend correct? Explain your reasoning.
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 12
Answer:
Given the word sentence, 5 less than a number n is 12.

Question 24.
MODELING REAL LIFE
Students and faculty raise $6042 for band uniforms. The faculty raised $1780. Write an equation you can use to find the amount a (in dollars) the students raised.
Answer:
Given,
Students and faculty raise $6042 for band uniforms (x).
The faculty raised $1780 (y)
The students raised be z
z = x – y
z = 6042 – 1780
z = 4262

Question 25.
MODELING REAL LIFE
You hit a golf ball 90 yards. It travels three-fourths of the distance to the hole. Write an equation you can use to find the distance d (in yards) from the tee to the hole.
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 13
Answer:
Given,
You hit a golf ball 90 yards. It travels three-fourths of the distance to the hole.
3/4 × D = 90
D = 360/3
D = 120

GEOMETRY Write an equation you can use to find the value of x.
Question 26.
Perimeter of triangle: 16 in.
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 14
Answer:
side of the triangle = x
Perimeter of triangle 16 in
P = a + b + c
16 in = x + x + x
3x = 16
x = 16/3
x = 5.3
Thus the side of the triangle is 5.3 inches.

Question 27.
Perimeter of square: 30 mm
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 15
Answer:
4x = 30
x = 30/4
x = 7.5 mm

Question 28.
MODELING REAL LIFE
You sell instruments at a Caribbean music festival. You earn $326 by selling 12 sets of maracas,6 sets of claves, and x djembe drums. Find the number of djembe drums you sold.
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 16
Answer:
Let the price of maracas be m
Let the price of claves be c
Let the price of djembe drums be x
Number of maracas = 12 sets
Number of claves = 6 sets
Number of djembe drums = xx
Total earned amount = $326
The equation would be
12m + 6c + dxx = 326
The cost for 1 maracas is $14
For 12 sets = 12 × 14 = $168
The cost for 1 clave = $5
For 6 sets = 6 × 5 = $30
The cost for 1 djembe drums is $16
For x sets = 16x
12m + 6c + dxx = 326
168 + 30 + 16x = 326
16x = 128
x = 128 ÷ 16
x = 8

Question 29.
PROBLEM SOLVING
Neil Armstrong set foot on the Moon 109.4 hours after Apollo 11departed from the Kennedy Space Center. Apollo 11landed on the Moon about 6.6 hours before Armstrong’s first step. How many hours did it take for Apollo 11 to reach the Moon?
Answer:
Given,
Neil Armstrong set foot on the Moon 109.4 hours after Apollo 11 departed from the Kennedy Space Center.
Apollo 11landed on the Moon about 6.6 hours before Armstrong’s first step.
To find how many hours did it take for Apollo 11 to reach the Moon we have to subtract 6.6 hours from 109.4 hours
109.4 – 6.6 = 102.8 hours
Thus it took 102.8 hours for Apollo 11 to reach the Moon.

Question 30.
LOGIC
You buy a basket of 24 strawberries. You eat them as you walk to the beach. It takes the same amount of time to walk each block. When you are halfway there, half of the berries are gone. After walking 3 more blocks, you still have 5 blocks to go. You reach the beach 28 minutes after you began. One-sixth of your strawberries are left.
a. Is there enough information to find the time it takes to walk each block? Explain.

Answer:
Yes, you are given enough information to find the time to walk each block
To find the total number of block you, add
3 + 5 + 8 = 16
Also the time it takes to walk the 16 blocks is given 28 minutes.

b. Is there enough information to find how many strawberries you ate while walking the last block? Explain.
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 17
Answer:
No, there is not enough information to find how many strawberries ate while walking the last block.
You are only given the amount of strawberries you started with 24 and what you have left (1/6) with 5 blocks to go. Therefore you can only be given how many strawberries were eaten walking the last block.

Question 31.
DIG DEEPER!
Find a sales receipt from a store that shows the total price of the items and the total amount paid including sales tax.
a. Write an equation you can use to find the sales tax rate r.
b. Can you use r to find the percent for the sales tax? Explain.
Answer:
Total amount paid = total price + (total price × sales tax rate)
sample equation
14.20 = 13.27 + (13.27 × 0.07)
Yes, you can use r to find the percent for the sales tax.
Multiplying r by 100 gives the percent for the sales tax.

Question 32.
GEOMETRY
A square is cut from a rectangle. The side length of the square is half of the unknown width w. The area of the shaded region is 84 square inches. Write an equation you can use to find the width (in inches).
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 18
Answer:
Given,
A square is cut from a rectangle. The side length of the square is half of the unknown width w.
The area of the shaded region is 84 square inches.
84 square inches divided by 14 inches equals 6
84 divided by 14 = s
84 ÷ 14 = s

Lesson 6.2 Solving Equations Using Addition or Subtraction

EXPLORATION 1

Solving an Equation Using a Tape Diagram
Work with a partner. A student solves an equation using the tape diagrams below.
Big Ideas Math Answers 6th Grade Chapter 6 Equations 6.2 1
a. What equation did the student solve? What is the solution?

Answer: x + 4 = 12

Explanation:
By seeing step 1 we can say that the equation for the above tape diagram x + 4 = 12

b. Explain how the tape diagrams in Steps 2 and 3 relate to the equation and its solution.
Answer:
By seeing the steps 2 and 3 we can say
8 + 4 = 12
x + 4 = 12
x = 12 – 4
x = 8

EXPLORATION 2
Solving an Equation Using a Model
Work with a partner.
Big Ideas Math Answers 6th Grade Chapter 6 Equations 6.2 2
a. How are the two sides of an equation similar to a balanced scale?
b. When you add weight to one side of a balanced scale, what can you do to balance the scale? What if you subtract weight from one side of a balanced scale? How does this relate to solving an equation?
c. Use a model to solve x + 2 = 7. Describe how you can solve the equation algebraically.
Answer:
x + 2 = 7
x = 7 – 2
x = 5

Big Ideas Math Answers 6th Grade Chapter 6 Equations 6.2 3

Try It

Tell whether the given value is a solution of the equation.
Question 1.
a + 6 = 17; a = 9
Answer: not a solution

Explanation:
Given the equation a + 6 = 17
when a = 9
9 + 6 = 17
15 ≠ 17
Thus the equation is not a solution.

Question 2.
9 – g = 5; g = 3
Answer: not a solution

Explanation:
Given the equation 9 – g = 5
where g = 3
9 – 3 = 5
6 ≠ 5
Thus the equation is not a solution.

Question 3.
35 – 7n; n = 5
Answer: solution

Explanation:
Given the equation 35 – 7n
where n = 5
35 – 7(5)
35 – 35 = 0
Thus the equation is a solution.

Question 4.
\(\frac{q}{2}\) = 28; q = 14
Answer: not a solution

Explanation:
Given the equation \(\frac{q}{2}\) = 28
where q = 14
\(\frac{14}{2}\) = 28
7 ≠ 28
Thus the equation is not a solution.

You can use inverse operations to solve equations. Inverse operations “undo” each other. Addition and subtraction are inverse operations.

Solve the equation. Check your solution.
Question 5.
k – 3 = 1
Answer: k = 4

Explanation:
Given the equation k – 3 = 1
k = 1 + 3
k = 4

Question 6.
n – 10 = 4
Answer: n = 14

Explanation:
Given the equation n – 10 = 4
n = 4 + 10
n = 14

Question 7.
15 = r – 6
Answer: r = 21

Explanation:
Given the equation 15 = r – 6
15 + 6 = r
r = 21

Question 8.
s + 8 = 17
Answer: s = 9

Explanation:
Given the equation s + 8 = 17
s = 17 – 8
s = 9

Question 9.
9 = y + 6
Answer: y = 3

Explanation:
Given the equation 9 = y + 6
9 – 6 = y
y = 3

Question 10.
13 + m = 20
Answer: m = 7

Explanation:
Given the equation 13 + m = 20
m = 20 – 13
m = 7

Self-Assessment for Concepts & Skills
Solve each exercise. Then rate your understanding of the success criteria in your journal.

CHECKING SOLUTIONS Tell whether the given value is a solution of the equation.
Question 11.
n + 8 = 42; n = 36
Answer: not a solution

Explanation:
Given the equation n + 8 = 42
where n = 36
36 + 8 = 44
44 ≠ 42
Thus the value is not a solution.

Question 12.
g – 9 = 24; g = 35
Answer: not a solution

Explanation:
Given the equation g – 9 = 24
where g = 35
35 – 9 = 24
26 ≠ 24
Thus the value is not a solution.

SOLVING EQUATIONS Solve the equation. Check your solution.
Question 13.
x – 8 = 12
Answer: 20

Explanation:
Given the equation x – 8 = 12
x = 12 + 8
x = 20

Question 14.
b + 14 = 33
Answer: 19

Explanation:
Given the equation b + 14 = 33
b = 33 – 14
b = 19

Question 15.
WRITING
When solving x + 5 =16, why do you subtract 5 from the left side of the equation? Why do you subtract 5 from the right side of the equation?
Answer:
To solve the equation we have to subtract 5.
x + 5 = 16
x = 16 – 5
x = 11

Question 16.
REASONING
Do the equations have the same solution? Explain your reasoning.
x – 8 = 6
x – 6 = 8
Answer:
i. x – 8 = 6
x = 6 + 8
x = 14
ii. x – 6 = 8
x = 8 + 6
x = 14
Yes both the equations has same solutions.

Question 17.
STRUCTURE
Just by looking at the equation x + 6 + 2x = 2x + 6 + 4, find the value of x. Explain your reasoning.
Answer:
x + 6 + 2x = 2x + 6 + 4
3x + 6 = 2x + 10
3x – 2x = 10 – 6
x = 4

Question 18.
An emperor penguin is 45 inches tall. It is 24 inches taller than a rockhopper penguin. Write and solve an equation to find the height (in inches) of a rockhopper penguin. Is your answer reasonable? Explain.
Big Ideas Math Answers 6th Grade Chapter 6 Equations 6.2 4
Answer:
Given,
An emperor penguin is 45 inches tall. It is 24 inches taller than a rockhopper penguin.
45 inches – 24 inches = 21 inches
Thus the height of the rockhopper penguin is 21 inches.

Question 19.
DIG DEEPER!
You get in an elevator and go up 2 floors and down8 floors before exiting. Then you get back in the elevator and go up 4 floors before exiting on the 12th floor. On what floors did you enter the elevator?
Answer: The answer to your question is 14 floor

Explanation:
To solve this problem start from the end changing the sense if it says up, then consider the action as down, etc.
Last floor = 12
Go down 4 floors = 12 – 4 = 8
Go up 8 floors = 8 + 8 = 16
Go down 2 floors = 16 – 2 = 14

Solving Equations Using Addition or Subtraction Homework & Practice 6.2

Review & Refresh

Write the word sentence as an equation.
Question 1.
Th sum of a number x and 9 is 15.
Answer: x + 9 = 15

Explanation:
We have to write the equation for the word sentence
The phrase sum indicates ‘+’
The equation would be x + 9 = 15

Question 2.
12 less than a number m equals 20.
Answer: 12 – m = 20

Explanation:
We have to write the equation for the word sentence
The phrase less than indicates ‘-‘
The equation would be 12 – m = 20

Question 3.
The product of a number d and 7 is 63.
Answer: d7 = 63

Explanation:
We have to write the equation for the word sentence
The phrase product indicates ‘×’
The equation would be d × 7 = 63

Question 4.
18 divided by a number s equals 3.
Answer: 18 ÷ s = 3

Explanation:
We have to write the equation for the word sentence
The phrase divided by indicates ‘÷’
The equation would be 18 ÷ s = 3

Divide. Write the answer in simplest form.
Question 5.
\(\frac{1}{2}\) ÷ \(\frac{1}{4}\)
Answer: 2

Explanation:
Dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction.
Take the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes
\(\frac{1}{2}\) × \(\frac{4}{1}\) = 2

Question 6.
12 ÷ \(\frac{3}{8}\)
Answer: 32

Explanation:
Dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction.
Take the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes
12 × \(\frac{8}{3}\)
= 4 × 8
= 32

Question 7.
8 ÷ \(\frac{4}{5}\)
Answer: 10

Explanation:
Dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction.
Take the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes
8 × \(\frac{5}{4}\)
= 2 × 5
= 10

Question 8.
\(\frac{7}{9}\) ÷ \(\frac{3}{2}\)
Answer: \(\frac{14}{27}\)

Explanation:
Dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction.
Take the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes
\(\frac{7}{9}\) × \(\frac{2}{3}\) = \(\frac{14}{27}\)

Question 9.
Which ratio is not equivalent to 72 : 18?
A. 36 : 9
B. 18 : 6
C. 4 : 1
D. 288 : 72
Answer: B. 18 : 6

Explanation:
72 : 18 = 36:9, 4 : 1, 288 : 72
18 : 6 is not equivalent to 72 : 18
Thus the correct answer is option B.

Evaluate the expression.
Question 10.
(2 + 52) ÷ 3
Answer: 9

Explanation:
Given the expression (2 + 52) ÷ 3
(2 + 25) ÷ 3
27 ÷ 3 = 9

Question 11.
6 + 23 . 3 – 5
Answer: 25

Explanation:
Given the expression 6 + 23 . 3 – 5
6 + 8 . 3 – 5
6 + 24 – 5
6 + 19
25

Question 12.
4 . [3 + 3(20 – 42 – 2)]
Answer: 36

Explanation:
Given the expression 4 . [3 + 3(20 – 42 – 2)]
4(3 + 3(20 – 16 – 2))
4(3 + 3(2))
4 (3 + 6)
4(9)
36

Question 13.
Find the missing values in the ratio table. Then write the equivalent ratios.
Big Ideas Math Answers 6th Grade Chapter 6 Equations 6.2 5
Answer:
Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-6.2-5

Concepts, Skills, & Problem Solving

CHOOSE TOOLS Use a model to solve the equation. (See Explorations 1 and 2, p. 251.)
Question 14.
n + 7 = 9
Answer: n = 2

Explanation:
n + 7 = 9
n = 9 – 7
n = 2

Question 15.
t + 4 = 5
Answer: t = 1

Explanation:
t + 4 = 5
t = 5 – 4
t = 1

Question 16.
c + 2 = 8
Answer: c = 6

Explanation:
c + 2 = 8
c = 8 – 2
c = 6

CHECKING SOLUTIONS Tell whether the given value is a solution of the equation.
Question 17.
x + 42 = 85; x = 43
Answer: solution

Explanation:
x + 42 = 85
Substitute the value of x in the equation
x = 43
43 + 42 = 85

Question 18.
8b = 48; b = 6
Answer: solution

Explanation:
8b = 48
Substitute the value of b in the equation
b = 6
8(6) = 48
48 = 48

Question 19.
19 – g = 7; g = 15
Answer: not a solution

Explanation:
19 – g = 7
Substitute the value of g in the equation
g = 15
19 – 15 = 7
2 ≠ 7
This is not a solution

Question 20.
\(\frac{m}{4}\) = 16; m = 4
Answer: not a solution

Explanation:
\(\frac{m}{4}\) = 16
Substitute the value of m in the equation
\(\frac{4}{4}\) = 16
1 ≠ 16
This is not a solution

Question 21.
w + 23 = 41; w = 28
Answer: not a solution

Explanation:
w + 23 = 41
Substitute the value of w in the equation
28 + 23 = 41
51 ≠ 41
This is not a solution

Question 22.
s – 68 = 11; s = 79
Answer: solution

Explanation:
Given,
s – 68 = 11
Substitute the value of s in the equation
s = 79
79 – 68 = 11
11 = 11
This is a solution

SOLVING EQUATIONS Solve the equation. Check your solution.
Question 23.
y – 7 = 3
Answer:
Given the equation
y – 7 = 3
y = 3 + 7
y = 10

Question 24.
z – 3 = 13
Answer:
Given the equation
z – 3 = 13
z = 13 +3
z = 16

Question 25.
8 = r – 14
Answer:
Given the equation
8 = r – 14
r = 8 + 14
r = 22

Question 26.
p + 5 = 8
Answer:
Given the equation
p + 5 = 8
p = 8 – 5
p = 3

Question 27.
k + 6 = 18
Answer:
Given the equation
k + 6 = 18
k = 18 – 6
k = 12

Question 28.
64 = h + 30
Answer:
Given the equation
64 = h + 30
h = 64 – 30
h = 34

Question 29.
f – 27 = 19
Answer:
Given the equation
f – 27 = 19
f = 19 +27
f = 46

Question 30.
25 = q + 14
Answer:
Given the equation
25 = q + 14
q = 25 – 14
q = 11

Question 31.
\(\frac{3}{4}\) = j – \(\frac{1}{2}\)
Answer:
Given the equation
\(\frac{3}{4}\) = j – \(\frac{1}{2}\)
\(\frac{3}{4}\) + \(\frac{1}{2}\) = j
j = 1 \(\frac{1}{4}\)

Question 32.
x + \(\frac{2}{3}\) = \(\frac{9}{10}\)
Answer:
Given the equation
x + \(\frac{2}{3}\) = \(\frac{9}{10}\)
x = \(\frac{9}{10}\) – \(\frac{2}{3}\)
x = \(\frac{7}{30}\)

Question 33.
1.2 = m – 2.5
Answer:
Given the equation
1.2 = m – 2.5
m = 1.2 + 2.5
m = 3.7

Question 34.
a + 5.5 = 17.3
Answer:
Given the equation
a + 5.5 = 17.3
a = 17.3 – 5.5
a = 11.8

YOU BE THE TEACHER Your friend solves the equation. Is your friend correct? Explain your reasoning.
Question 35.
Big Ideas Math Answers 6th Grade Chapter 6 Equations 6.2 6
Answer:
x + 7 = 13
x = 13 – 7
x = 4
Your friend is incorrect

Question 36.
Big Ideas Math Answers 6th Grade Chapter 6 Equations 6.2 7
Answer:
34 = y – 12
y – 12 = 34
y = 34 + 12
y = 46

Question 37.
MODELING REAL LIFE
The main span of the Sunshine SkywayBridge is 366 meters long. The bridge’s main span is 30 meters shorter than the main span of the Dames Point Bridge. Write and solve an equation to find the length (in meters) of the main span of the Dames Point Bridge.
Big Ideas Math Answers 6th Grade Chapter 6 Equations 6.2 8
Answer:
Given,
The main span of the Sunshine SkywayBridge is 366 meters long.
The bridge’s main span is 30 meters shorter than the main span of the Dames Point Bridge.
336 – 30 = 306
Let the main span of the Sunshine SkywayBridge be x
Let the main span of the Dames Point Bridge be y
x – y = 306

Question 38.
PROBLEM SOLVING
A park has 22 elm trees. Elm leaf beetles have been attacking the trees. After removing several of the diseased trees, there are 13 healthy elm trees left. Write and solve an equation to find the number of elm trees that were removed.
Answer:
Given,
A park has 22 elm trees. Elm leaf beetles have been attacking the trees.
After removing several of the diseased trees, there are 13 healthy elm trees left.
x – y = 9
22 – 13 = 9
Thus the number of trees removed 9.

Question 39.
PROBLEM SOLVING
The area of Jamaica is 6460 square miles less than the area of Haiti. Find the area (in square miles) of Haiti.
Big Ideas Math Answers 6th Grade Chapter 6 Equations 6.2 9
Answer:
Given,
The area of Jamaica is 6460 square miles less than the area of Haiti.
Y = X – 6460
Y = Haiti
X = area of Jamaica

Question 40.
REASONING
The solution of the equation x+ 3 = 12 is shown. Explain each step. Use a property, if possible.
Big Ideas Math Answers 6th Grade Chapter 6 Equations 6.2 10
Answer:
The sum of a number x and 3 is 12
x + 3 = 12
x = 12 – 3
x = 9

WRITING EQUATIONS Write the word sentence as an equation. Then solve the equation.
Question 41.
13 subtracted from a number w is 15.
Answer: w – 13 = 15

Explanation:
We have to write the equation for the word sentence
The phrase subtracted indicates ‘-‘
The equation would be w – 13 = 15

Question 42.
A number k increased by 7 is 34.
Answer: K + 7 = 34

Explanation:
We have to write the equation for the word sentence
The phrase increased indicates ‘+’
The equation would be K + 7 = 34

Question 43.
9 is the difference of a number n and 7.
Answer: n – 7 = 9

Explanation:
We have to write the equation for the word sentence
The phrase difference indicates ‘-‘
The equation would be n – 7 = 9

Question 44.
93 is the sum of a number g and 58.
Answer: g + 58 = 93

Explanation:
We have to write the equation for the word sentence
The phrase sum indicates ‘+’
The equation would be g + 58 = 93

Question 45.
11 more than a number k equals 29.
Answer: 11 + k = 29

Explanation:
We have to write the equation for the word sentence
The phrase more than indicates ‘+’
The equation would be 11 + k = 29

Question 46.
A number p decreased by 19 is 6.
Answer: p – 19 = 6

Explanation:
We have to write the equation for the word sentence
The phrase decreased indicates ‘-‘
The equation would be p – 19 = 6

Question 47.
46 is the total of 18 and a number d.
Answer: 18 + d = 46

Explanation:
We have to write the equation for the word sentence
The phrase total indicates ‘+’
The equation would be 18 + d = 46

Question 48.
84 is 99 fewer than a number c.
Answer: 84 = 99 – c

Explanation:
We have to write the equation for the word sentence
The phrase fewer than indicates ‘-‘
The equation would be 84 = 99 – c

SOLVING EQUATIONS Solve the equation. Check your solution.
Question 49.
b + 7 + 12 = 30
Answer:
Given the equation
b + 7 + 12 = 30
b = 30 – 19
b = 11

Question 50.
y + 4 − 1 = 18
Answer:
Given the equation
y + 4 − 1 = 18
y + 3 = 18
y = 18 – 3
y = 15

Question 51.
m + 18 + 23 = 71
Answer:
Given the equation
m + 18 + 23 = 71
m + 41 = 71
m = 71 – 41
m = 30

Question 52.
v − 7 = 9 + 12
Answer:
Given the equation
v − 7 = 9 + 12
v – 7 = 21
v = 21 + 7
v = 28

Question 53.
5 + 44 = 2 + r
Answer:
Given the equation
5 + 44 = 2 + r
49 = 2 + r
r = 49 – 2
r = 47

Question 54.
22 + 15 = d− 17
Answer:
Given the equation
22 + 15 = d− 17
37 = d – 17
d = 37 + 17
d = 54

GEOMETRY Solve for x.
Question 55.
Perimeter = 48 ft
Big Ideas Math Answers 6th Grade Chapter 6 Equations 6.2 11
Answer:
P = a + b + c
48 ft = x + 20 + 12
x = 48 – 32
x = 16 ft

Question 56.
Perimeter = 132 in.
Big Ideas Math Answers 6th Grade Chapter 6 Equations 6.2 12
Answer:
P = a + b + c + d
132 = 34 + 16 + 34 + x
132 – 84 = x
x = 50 in

Question 57.
Perimeter = 93 ft
Big Ideas Math Answers 6th Grade Chapter 6 Equations 6.2 13
Answer:
P = 8(a + b + c + d + e)
93 ft = 8(18 + 18 + 15 + d + 15)
d = 93/528
d = 0.17

Question 58.
SIMPLIFYING AND SOLVING Compare and contrast the two problems.
Big Ideas Math Answers 6th Grade Chapter 6 Equations 6.2 14
Answer:
2(x + 3) – 4
= 2x + 6 – 4
= 2x + 2

Question 59.
PUZZLE
In a magic square, the sum of the numbers in each row, column, and diagonal is the same. Find the values of a, b, and c. Justify your answers.
Big Ideas Math Answers 6th Grade Chapter 6 Equations 6.2 15
Answer:
The sum of rows and columns is 53.
a = 22
b = 0
c = 0

Question 60.
REASONING
On Saturday, you spend $33, give $15 to a friend, and receive $20 for mowing your neighbor’s lawn. You have $21 left. Use two methods to find how much money you started with that day.
Answer:
Given,
On Saturday, you spend $33, give $15 to a friend, and receive $20 for mowing your neighbor’s lawn.
You have $21 left.
x = a + b + c – d
x = 33 + 15 + 20 – 21
x = 68 – 21
x = 47

Question 61.
DIG DEEPER!
You have $15.
Big Ideas Math Answers 6th Grade Chapter 6 Equations 6.2 16
a. How much money do you have left if you ride each ride once?
b. Do you have enough money to ride each ride twice? Explain.
Answer:
a. bumper cost : $1.75
super pendulum : $1.25 + $1.50= $2.75
giant slide :  $1.75-$0.50= $1.25
ferris wheels : $1.50+$0.50=$2
total money spent=$7.75
money left=$7.75-$15=$7.25

b. No,
money required to ride once =$7.75
total money required to ride twice=$7.75+$7.75=$15.5

Question 62.
CRITICAL THINKING
Consider the equation 15 − y = 8. Explain how you can solve the equation using the Addition and Subtraction Properties of Equality.
Answer:
15 − y = 8
15 = 8 + y
8 + y = 15
y = 15 – 8
y = 7

Lesson 6.3 Solving Equations Using Multiplication or Division

EXPLORATION 1

Solving an Equation Using a Tape Diagram
Work with a partner. A student solves an equation using the tape diagrams below.
Big Ideas Math Answers Grade 6 Chapter 6 Equations 6.3 1
a. What equation did the student solve? What is the solution?

Answer:
ax = b
4x = 20
x = 20/4
x = 5

b. Explain how the tape diagrams in Steps 2 and 3 relate to the equation and its solution.
Answer:
Step 2 and step 3 shows that x = 5

EXPLORATION 2

Solving an Equation Using a Model
Work with a partner. Three robots go out to lunch. They decide to split the $12 bill evenly. The scale represents the number of robots and the price of the meal.
Big Ideas Math Answers Grade 6 Chapter 6 Equations 6.3 2
a. How much does each robot pay?

Answer:
Three robots go out to lunch.
They decide to split the $12 bill evenly.
12/3 = 4
Thus each robot pay $4.

b. When you triple the weight on one side of a balanced scale, what can you do to balance the scale? What if you divide the weight on one side of a balanced scale in half? How does this relate to solving an equation?
c. Use a model to solve 5x = 15. Describe how you can solve the equation algebraically.
Answer:
5x = 15
x = 15/5
x = 3

Try It

Solve the equation. Check your solution.
Question 1.
\(\frac{a}{8}\) = 6
Answer: a = 48

Explanation:
Given the equation
\(\frac{a}{8}\) = 6
a = 6 × 8
a = 48

Question 2.
14 = \(\frac{2y}{5}\)
Answer: y = 35

Explanation:
Given the equation
14 = \(\frac{2y}{5}\)
14 × 5 = 2y
2y = 70
y = 70/2
y = 35

Question 3.
3z ÷ 2 = 9
Answer: z = 6

Explanation:
Given the equation
3z ÷ 2 = 9
3z = 9 × 2
3z = 18
z = 18/3
z = 6

Question 4.
p . 3 = 18
Answer: p = 6

Explanation:
Given the equation
p . 3 = 18
p = 18/3
p = 6

Question 5.
12q = 60
Answer: q = 5

Explanation:
Given the equation
12q = 60
q = 60/12
q = 5

Question 6.
81 = 9r
Answer: r = 9

Explanation:
Given the equation
81 = 9r
r = 81/9
r = 9

Self-Assessment for Concepts & Skills
Solve each exercise. Then rate your understanding of the success criteria in your journal.

SOLVING EQUATIONS Solve the equation. Check your solution.
Question 7.
6 = \(\frac{2y}{3}\)
Answer: y = 9

Explanation:
Given the equation
6 = \(\frac{2y}{3}\)
6 × 3 = 2y
2y = 18
y = 18/2
y = 9

Question 8.
8s = 56
Answer: s = 7

Explanation:
Given the equation
8s = 56
s = 56/8
s = 7

Question 9.
WHICH ONE DOESN’T BELONG?
Which equation does not belong with the other three? Explain your reasoning.
Big Ideas Math Answers Grade 6 Chapter 6 Equations 6.3 3
Answer: \(\frac{1}{4}\)x = 27 does not belong with the other three.
Because
3x= 36
x = 36/3
x = 12
3/4 x = 9
3x = 36
x = 36/3
x = 12
4x = 48
x = 48/4
x = 12

STRUCTURE Just by looking at the equation, find the value of x. Explain your reasoning.
Question 10.
5x + 3x = 5x + 18
Answer:
Given the equation
x(5+3)=5x+18
8x=5x+18
8x-5x=18
3x=18
x=18/3
x=6

Question 11.
8x + \(\frac{x}{2}\) = 8x + 6
Answer:
Given the equation
8x + \(\frac{x}{2}\) = 8x + 6
x (8 + \(\frac{1}{2}\) ) = 8x + 6
8.5x = 8x + 6
8.5x – 8x = 6
0.5x = 6
x = 6/0.5
x = 12

Question 12.
The area of the screen of the smart watch is shown. What are possible dimensions for the length and the width of the screen? Justify your answer.
Big Ideas Math Answers Grade 6 Chapter 6 Equations 6.3 4
Answer:
Given,
Area = 1625 sq.mm
L = 65 mm
W = 25 mm
We know that,
Area of the rectangle = l × w
1625 = 65 × 25
Thus the length and width of the smart watch is 65 mm and 25 mm.

Question 13.
A rock climber climbs at a rate of 720 feet per hour. Write and solve an equation to find the number of minutes it takes for the rock climber to climb 288 feet.
Answer:
Given,
A rock climber climbs at a rate of 720 feet per hour.
The equation is y = 12x
It takes 24 minutes for the rock climber to get 288 feet
288 = 12x
288/12 = 12x/12
24 = x
Now we have time in minutes that it takes to get 288 feet.

Question 14.
DIG DEEPER!
A gift card stores data using a black, magnetic stripe on the back of the card. Find the width w of the stripe.
Big Ideas Math Answers Grade 6 Chapter 6 Equations 6.3 5
Answer:
Given,
Area = 46 \(\frac{3}{4}\) sq. cm
L = 8 \(\frac{1}{2}\) cm
w = 4 cm + x+ \(\frac{2}{3}\) cm
We know that,
Area of the rectangle = l × w
46 \(\frac{3}{4}\) = 4 cm + x+ \(\frac{2}{3}\) × 8 \(\frac{1}{2}\)
= (4 + 0.6 + x) × 8.5
46.75 = 34 + 5.4 + 8.5x
8.5x = 46.75 – 34 – 5.1
8.5x = 7.6
x = 7.6/8.5
x = 0.89
Thus the width is 0.89 cm

Solving Equations Using Multiplication or Division Homework & Practice 6.3

Review & Refresh
Solve the equation. Check your solution.
Question 1.
y – 5 = 6
Answer: y = 11

Explanation:
Given the equation
y – 5 = 6
y = 6 + 5
y = 11

Question 2.
m + 7 = 8
Answer: 1

Explanation:
Given the equation
m + 7 = 8
m = 8 – 7
m = 1

Question 3.
\(\frac{7}{8}\) = \(\frac{1}{4}\) + 9
Answer:
\(\frac{1}{4}\) + 9 = \(\frac{9}{4}\)
\(\frac{7}{8}\) ≠ \(\frac{9}{4}\)
not a solution

Question 4.
What is the value of a3 when a= 4?
A. 12
B. 43
C. 64
D. 81
Answer: 64

Explanation:
a3 when a= 4
4 × 4 × 4 = 64
Thus the correct answer is option C.

Multiply. Write the answer in simplest form.
Question 5.
\(\frac{1}{5}\) . \(\frac{2}{9}\)
Answer:
For fraction multiplication, multiply the numerators and then multiply the denominators to get
\(\frac{1}{5}\) . \(\frac{2}{9}\) = \(\frac{2}{45}\)

Question 6.
\(\frac{5}{12}\) × \(\frac{4}{7}\)
Answer:
For fraction multiplication, multiply the numerators and then multiply the denominators to get
\(\frac{5}{12}\) × \(\frac{4}{7}\) = \(\frac{5}{21}\)

Question 7.
2\(\frac{1}{3}\) . \(\frac{3}{10}\)
Answer:
For fraction multiplication, multiply the numerators and then multiply the denominators to get
2\(\frac{1}{3}\) = \(\frac{7}{3}\)
\(\frac{7}{3}\) × \(\frac{3}{10}\) = \(\frac{21}{30}\)

Question 8.
1\(\frac{3}{4}\) × 2\(\frac{2}{3}\)
Answer:
1\(\frac{3}{4}\) = \(\frac{7}{4}\)
2\(\frac{2}{3}\) = \(\frac{8}{4}\)
\(\frac{7}{4}\) × \(\frac{8}{4}\) = \(\frac{56}{16}\)

Multiply.
Question 9.
Big Ideas Math Answers Grade 6 Chapter 6 Equations 6.3 6
Answer: 0.36

Explanation:
Multiply the two decimals
0.4 × 0.9 = 0.36

Question 10.
Big Ideas Math Answers Grade 6 Chapter 6 Equations 6.3 7
Answer: 0.39

Explanation:
Multiply the two decimals
0.78 × 0.5 = 0.39

Question 11.
2.63 × 4.31
Answer: 11.3353

Explanation:
Multiply the two decimals
2.63 × 4.31 = 11.3353

Question 12.
1.115 × 3.28
Answer: 69.2

Explanation:
Multiply the two decimals
1.115 × 3.28 = 69.2

Concepts, Skills, &Problem Solving

CHOOSE TOOLS Use a model to solve the equation. (See Explorations 1 and 2, p. 259.)
Question 13.
8x = 8
Answer: 1

Explanation:
Given the equation
8x = 8
x = 8/8
x = 1

Question 14.
9 = 3y
Answer: 3

Explanation:
Given the equation
9 = 3y
y = 9/3
y = 3

Question 15.
2z = 14
Answer: 7

Explanation:
Given the equation
2z = 14
z = 14/2
z = 7

SOLVING EQUATIONS Solve the equation. Check your solution.
Question 16.
\(\frac{s}{10}\) = 7
Answer: 70

Explanation:
Given the equation
\(\frac{s}{10}\) = 7
s = 7 × 10
s = 70

Question 17.
6 = \(\frac{t}{s}\)
Answer: 6s = t

Explanation:
Given the equation
6 = \(\frac{t}{s}\)
t = 6s

Question 18.
5x ÷ 6 = 20
Answer:
Given the equation
5x ÷ 6 = 20
5x = 20 × 6
5x = 120
x = 120/5
x = 24

Question 19.
24 = \(\frac{3}{4}\)r
Answer:
Given the equation
24 = \(\frac{3}{4}\)r
24 × 4 = 3r
96 = 3r
r = 32

Question 20.
3a = 12
Answer: 4

Explanation:
Given the equation
3a = 12
a = 12/3
a = 4

Question 21.
5 . z = 35
Answer: 7

Explanation:
Given the equation
5 . z = 35
z = 35/5
z = 7

Question 22.
40 = 4y
Answer: 10

Explanation:
Given the equation
40 = 4y
40/4 = y
y = 10

Question 23.
42 = 7k
Answer: 6

Explanation:
Given the equation
42 = 7k
7k = 42
k = 42/7

Question 24.
7x = 105
Answer: 15

Explanation:
Given the equation
7x = 105
x = 105/7
x = 15

Question 25.
75 = 6 . w
Answer: 12.5

Explanation:
Given the equation
75 = 6 . w
w = 75/6
w = 12.5

Question 26.
13 = d ÷ 6
Answer: 78

Explanation:
Given the equation
13 = d ÷ 6
d = 13 × 6
d = 78

Question 27.
9 = v ÷ 5
Answer: 45

Explanation:
Given the equation
9 = v ÷ 5
v = 9 × 5
v = 45

Question 28.
\(\frac{5d}{9}\) = 10
Answer: 18

Explanation:
Given the equation
\(\frac{5d}{9}\) = 10
5d = 10 × 9
5d = 90
d = 18

Question 29.
\(\frac{3}{5}\) = 4m
Answer: 0.15

Explanation:
Given the equation
\(\frac{3}{5}\) = 4m
3 = 4m × 5
20m = 3
m = 3/20
m = 0.15

Question 30.
136 = 17b
Answer: 19.4

Explanation:
Given the equation
136 = 17b
b = 136/17
b = 19.4

Question 31.
\(\frac{2}{3}\) = \(\frac{1}{4}\)k
Answer: 2.6

Explanation:
Given the equation
\(\frac{2}{3}\) = \(\frac{1}{4}\)k
k = \(\frac{8}{3}\)
k = 2.6

Question 32.
\(\frac{2c}{15}\) = 8.8
Answer: 66

Explanation:
Given the equation
\(\frac{2c}{15}\) = 8.8
2c = 8.8 × 15
2c = 132
c = 132/2
c = 66

Question 33.
7b ÷ 12 = 4.2
Answer: 7.2

Explanation:
Given the equation
7b ÷ 12 = 4.2
7b = 4.2 × 12
b = 7.2

Question 34.
12.5 . n = 32
Answer: 2.56

Explanation:
Given the equation
12.5 . n = 32
n = 32/12.5
n = 2.56

Question 35.
3.4 m = 20.4
Answer: m = 6

Explanation:
Given the equation
3.4 m = 20.4
m = 20.4/3.4
m = 6

Question 36.
YOU BE THE TEACHER
Your friend solves the equation x ÷ 4 =28. Is your friend correct? Explain your reasoning.
Big Ideas Math Answers Grade 6 Chapter 6 Equations 6.3 8
Answer: Your friend is correct

Explanation:
Your friend solves the equation x ÷ 4 =28.
x ÷ 4 = 28
x = 28/4
x = 7

Question 37.
ANOTHER WAY
Show how you can solve the equation 3x = 9 by multiplying each side by the reciprocal of 3.
Answer:
3x = 9
x = 9 × 1/3
x = 3

Question 38.
MODELING REAL LIFE
Forty-five basketball players participate in a three-on-three tournament. Write and solve an equation to find the number of three-person teams in the tournament.
Big Ideas Math Answers Grade 6 Chapter 6 Equations 6.3 9
Answer: 15

Explanation:
Let the number of teams be x
x × 3 = 45
x = 45/3
x = 15

Question 39.
MODELING REAL LIFE
A theater has 1200 seats. Each row has 20 seats. Write and solve an equation to find the number of rows in the theater.
Answer:
Given,
A theater has 1200 seats. Each row has 20 seats.
Let x be the number of rows.
1200 = 20 × x
x = 1200/20
x = 60

GEOMETRY Solve for x. Check your answer.
Question 40.
Area = 45 square units
Big Ideas Math Answers Grade 6 Chapter 6 Equations 6.3 11
Answer:
l = x
w = 5
Area = 45 square units
We know that,
Area of the Rectangle = l × w
45 = x × 5
x = 45/5
x = 9 units

Question 41.
Area = 176 square units
Big Ideas Math Answers Grade 6 Chapter 6 Equations 6.3 12
Answer:
a = 16
Area = 176 square units
We know that,
Area of the square = a × a
176 = 16 × x
x = 16

Question 42.
LOGIC
Ona test, you earn 92% of the possible points by correctly answering 6 five-point questions and 8 two-point questions. How many points p is the test worth?
Answer:
Given,
Ona test, you earn 92% of the possible points by correctly answering 6 five-point questions and 8 two-point questions.
(6 × 5) + (8 × 2) = 46
92 × 1/100 = 46
0.92x = 46
x = 46/0.92
x = 50

Question 43.
MODELING REAL LIFE
You use index cards to play a homemade game. The object is to be the first to get rid of all your cards. How many cards are in your friend’s stack?
Big Ideas Math Answers Grade 6 Chapter 6 Equations 6.3 13
Answer:
The number of cards in your friend’s stack divided by the height of your’s friends stack equals the number of cards in your stack divided by the height of your stack.
x = the number of cards in your friend’s stack
x ÷ 5 = 48 ÷ 12
x ÷ 5 = 4
x = 4 × 5
x = 20

Question 44.
DIG DEEPER!
A slush drink machine fills 1440 cups in 24 hours.
a. Find the number c of cups each symbol represents.
b. To lower costs, you replace the cups with paper cones that hold 20% less. Find the number n of paper cones that the machine can fill in 24 hours.
Big Ideas Math Answers Grade 6 Chapter 6 Equations 6.3 14
Answer:
The number of symbols times the number of cups per symbol equals the total number of cups filled.
C = The number of cups filled
30 × c = 1440
c = 1440/30
c = 48

Question 45.
NUMBER SENSE
The area of the picture is 100 square inches. The length is 4 times the width. Find the length and width of the picture.
Big Ideas Math Answers Grade 6 Chapter 6 Equations 6.3 15
Answer:
Given,
The area of the picture is 100 square inches.
The length is 4 times the width.
We know that,
Area of Rectangle = l × w
100 sq. in = 4w × w
100 = 4w²
w = √25 = 5
L = 4w
L = 4 × 5
L = 20

Lesson 6.4 Writing Equations in Two Variables

EXPLORATION 1

Writing Equations in Two Variables
Work with a partner. section 3.4 Exploration 1, you used a ratio table to create a graph for an airplane traveling 300 miles per hour. Below is one possible ratio table and graph.
Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 1
a. Describe the relationship between the two quantities. Which quantity depends on the other quantity?

Answer: By seeing the above graph we can say that miles depend on hours (time).

b. Use variables to write an equation that represents the relationship between the time and the distance. What can you do with this equation? Provide an example.
c. Suppose the airplane is 1500 miles away from its destination. Write an equation that represents the relationship between time and distance from the destination. How can you represent this relationship using a graph?
Answer: The relationship between distance and time is distance is inversely proportional to the time.
5x = 1500

An equation in two variables represents two quantities that change in relationship to one another. A solution of an equation in two variables is an ordered pair that makes the equation true.

Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 4

Try It

Tell whether the ordered pair is a solution of the equation.
Question 1.
y = 7x, (2, 21)
Answer: No

Explanation:
Given the equation y = 7x
y = 7 × 2
y = 14
21 ≠ 14
The ordered pair is not the solution.

Question 2.
y = 5x + 1; (3, 16)
Answer: Yes

Explanation:
Given the equation y = 5x + 1
y = 5 × 3 + 1
y = 15 + 1
y = 16
The ordered pair is the solution.

Question 3.
The equation y = 10x + 25 represents the amount y(in dollars) in your savings account after x weeks. Identify the independent and dependent variables. How much is in your savings account after 8 weeks?
Answer:
Because the amount y remaining depends on the number x weeks.
Y is the dependent variable
X is the independent variable
y = 10x + 25
After 8 weeks x = 8
y = 10 (8) + 25
y = 80 + 25
y = 105

Graph the equation.
Question 4.
y = 3x
Answer:
Big Ideas Math Grade 6 Chapter 6 Equations img_2
When x = 0
y = 3(0) = 0
A(x,y) = (0,0)
When x = 1
y = 3(1) = 3
B(x,y) = (3, 1)
When x = 2
y = 3(2) = 6
C(x,y) = (6, 2)
When x = 3
y = 3(3) = 9
D(x,y) = (9, 3)

Question 5.
y = 4x + 1
Answer:
y = 4x + 1
When x = 0
y = 4(0) + 1
y = 1
When x = 1
y = 4(1) + 1
y = 5
When x = 2
y = 4(2) + 1
y = 9
Big Ideas Math Grade 6 Chapter 6 Equations img_3

Question 6.
y = \(\frac{1}{2}\)x + 2
Answer:
Given,
y = \(\frac{1}{2}\)x + 2
when x = 0
y = \(\frac{1}{2}\)0 + 2
y = 2
when x = 1
y = \(\frac{1}{2}\)1 + 2
y = 2\(\frac{1}{2}\)
y = 2.5
when x = 2
y = \(\frac{1}{2}\)2 + 2
y = 1 + 2
y = 3
Big Ideas Math Grade 6 Chapter 6 Equations img_4

Question 7.
It costs $25 to rent a kayak plus $8 for each hour. Write and graph an equation that represents the total cost (in dollars) of renting the kayak.
Answer:
Given,
It costs $25 to rent a kayak plus $8 for each hour.
y = 8x + 25

Self-Assessment for Concepts & Skills
Solve each exercise. Then rate your understanding of the success criteria in your journal.

Question 8.
WRITING
Describe the difference between independent variables and dependent variables.
Answer:
The independent variable is the cause. Its value is independent of other variables in your study. The dependent variable is the effect. Its value depends on changes in the independent variable.

IDENTIFYING SOLUTIONS Tell whether the ordered pair is a solution of the equation.
Question 9.
y = 3x + 8; (4, 20)
Answer:
Given the equation
y = 3x + 8
x = 4
y = 20
20 = 3(4) 8
20 = 12 + 8
20 = 20
The above equation is the solution.

Question 10.
y = 6x – 14; (7, 29)
Answer:
Given the equation
y = 6x – 14
29 = 6(7) – 14
29 = 42 – 14
29 ≠ 28
The above equation is not the solution.

Question 11.
PRECISION
Explain how to graph an equation in two variables.
Answer:

  • Find three points whose coordinates are solutions to the equation. Organize them in a table.
  • Plot the points in a rectangular coordinate system. Check that the points line up. …
  • Draw the line through the three points. Extend the line to fill the grid and put arrows on both ends of the line.

Question 12.
WHICH ONE DOESN’T BELONG?
Which one does not belong with the other three? Explain your reasoning.
Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 5
Answer: n = 4n – 6 does not belong to the other three equations because we can take n has common and we can solve the equation.
Remaining there is not possible to solve the equation.

Question 13.
A sky lantern rises at an average speed of 8 feet per second. Write and graph an equation that represents the relationship between the time and the distance risen. How long does it take the lantern to rise 100 feet?
Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 6
Answer:
Given,
A sky lantern rises at an average speed of 8 feet per second.
the lantern to rise 100 feet = ?
8 feets = 1 sec
100 feets = 8 × x
x = 100/8
x = 12.5 sec

Question 14.
You and a friend start biking in opposite directions from the same point. You travel 108 feet every 8 seconds. Your friend travels 63 feet every 6 seconds. How far apart are you and your friend after 15 minutes?
Answer:
Given,
You and a friend start biking in opposite directions from the same point.
You travel 108 feet every 8 seconds. Your friend travels 63 feet every 6 seconds.
Your distance Y,
Y = 108ft/8 seconds × 60 sec/min × 15 min × 1mile/5280 ft
H is determined similarly
Total distance apart in miles = Y + H
You have only 36 minutes while he travels for all 40.

Writing Equations in Two Variables Homework & Practice 6.4

Review & Refresh
Solve the equation.
Question 1.
4x = 36
Answer: 9

Explanation:
Given the equation 4x = 36
x = 36/4
x = 9

Question 2.
\(\frac{x}{8}\) = 5
Answer: 40

Explanation:
Given the equation \(\frac{x}{8}\) = 5
x = 5 × 8
x = 40

Question 3.
\(\frac{4x}{3}\) = 8
Answer: 6

Explanation:
Given the equation \(\frac{4x}{3}\) = 8
4x = 8 × 3
4x = 24
x = 24/4
x = 6

Question 4.
\(\frac{2}{5}\)x = 6
Answer: 15

Explanation:
Given the equation \(\frac{2}{5}\)x = 6
2x = 5 × 6
2x = 30
x = 30/2
x = 15

Divide. Write the answer in simplest form.
Question 5.
3\(\frac{1}{2}\) ÷ \(\frac{4}{5}\)
Answer: 4 \(\frac{3}{8}\)

Explanation:
Convert any mixed numbers to fractions.
Then your initial equation becomes:
3\(\frac{1}{2}\) = \(\frac{7}{2}\)
\(\frac{7}{2}\) × \(\frac{5}{4}\)
= \(\frac{35}{8}\)
Now convert the improper fraction to the mixed fraction.
\(\frac{35}{8}\) = 4 \(\frac{3}{8}\)

Question 6.
7 ÷ 5\(\frac{1}{4}\)
Answer: 1 \(\frac{1}{3}\)

Explanation:
Convert any mixed numbers to fractions.
Then your initial equation becomes:
7 ÷ 5\(\frac{1}{4}\)
5\(\frac{1}{4}\) = \(\frac{21}{4}\)
\(\frac{7}{1}\) ÷ \(\frac{21}{4}\) = 1 \(\frac{1}{3}\)

Question 7.
\(\frac{3}{11}\) ÷ 1\(\frac{1}{8}\)
Answer: \(\frac{8}{33}\)

Explanation:
Convert any mixed numbers to fractions.
Then your initial equation becomes:
\(\frac{3}{11}\) ÷ 1\(\frac{1}{8}\)
1\(\frac{1}{8}\) = \(\frac{9}{8}\)
\(\frac{3}{11}\) ÷ \(\frac{9}{8}\) = \(\frac{8}{33}\)

Question 8.
7\(\frac{1}{2}\) ÷ 1\(\frac{1}{3}\)
Answer: 5 \(\frac{5}{8}\)

Explanation:
Convert any mixed numbers to fractions.
Then your initial equation becomes:
7\(\frac{1}{2}\) = \(\frac{15}{2}\)
1\(\frac{1}{3}\) = \(\frac{4}{3}\)
\(\frac{15}{2}\) ÷ \(\frac{4}{3}\) = \(\frac{45}{8}\)
Now convert the improper fraction to the mixed fraction.
\(\frac{45}{8}\) = 5 \(\frac{5}{8}\)

Question 9.
Find the area of the carpet tile. Then find the area covered by120 carpet tiles.
Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 7
Answer:
a = 16 in
Area of the square = a × a
A = 16 in × 16 in
A = 256 sq. in
Now we have to find the area covered by120 carpet tiles.
120 × 256 = 30720

Copy and complete the statement. Round to the nearest hundredth if necessary.
Question 10.
Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 8
Answer: 800

Explanation:
convert from meters to centimeters
1 m = 100 cm
8 m = 8 × 100 cm = 800 cm
Thus 8m = 800cm

Question 11.
Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 9
Answer:
Explanation:
Convert from ounces to pounds
88 oz = 5.5 pounds

Question 12.
Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 10
Answer: 709 mL

Explanation:
Convert from cups to milliliters
1 cup = 236.588 mL
3 cups = 709 mL

Question 13.
Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 11
Answer: 9.321 mi

Explanation:
Convert from km to miles
1 km = 0.621 mi
15 km = 15 × 0.621 mi
15 km = 9.321 miles

Divide.
Question 14.
\(\sqrt [ 6 ]{ 34.8 } \)
Answer: 6th root of 34.8 is 1.806

Question 15.
\(\sqrt [ 4 ]{ 12.8 } \)
Answer: 4th root of 12.8 is 1.891

Question 16.
45.92 ÷ 2.8
Answer: 16.2

Explanation:
Multiplying two decimal numbers
45.92 ÷ 2.8 = 16.2

Question 17.
39.525 ÷ 4.25
Answer: 9.3

Explanation:
Multiplying two decimal numbers
39.525 ÷ 4.25 = 9.3

Concepts, Skills, &Problem Solving

WRITING EQUATIONS Use variables to write an equation that represents the relationship between the time and the distance. (See Exploration 1, p. 265.)
Question 18.
An eagle flies 40 miles per hour.
Answer:
y = distance, x = time, rate = 40 miles per minute
distance = rate . time
y = 40 . x

Question 19.
A person runs 175 yards per minute.
Answer:
y = distance, x = time, rate = 175 yards per minute
distance = rate . time
so y = 175 . x

IDENTIFYING SOLUTIONS Tell whether the ordered pair is a solution of the equation.
Question 20.
y = 4x; (0, 4)
Answer:
x = 0
y = 4
4 = 4(0)
4 ≠ 0
The ordered pair is not a solution of the equation.

Question 21.
y = 3x; (2, 6)
Answer:
x = 2
y = 6
y = 3x
6 = 3(2)
6 = 6
The ordered pair is a solution of the equation.

Question 22.
y = 5x – 10; (3, 5)
Answer:
x = 3
y = 5
y = 5x – 10
5 = 5(3) – 10
5 = 15 – 10
5 = 5
The ordered pair is a solution of the equation.

Question 23.
y = x + 7; (1, 6)
Answer:
x = 1
y = 6
y = x + 7
6 = 1 + 7
6 ≠ 8
The ordered pair is not a solution of the equation.

Question 24.
y = x + 4; (2, 4)
Answer:
x = 2
y = 4
4 = 2 + 4
4 ≠ 6
The ordered pair is not a solution of the equation.

Question 25.
y = x – 5; (6, 11)
Answer:
x = 6
y = 11
11 = 6 – 5
11 ≠ 1
The ordered pair is not a solution of the equation.

Question 26.
y = 6x + 1; (2, 13)
Answer:
x = 2
y = 13
13 = 6(2) + 1
13 = 12 + 1
13 = 13
The ordered pair is a solution of the equation.

Question 27.
y = 7x + 2; (2, 0)
Answer:
x = 2
y = 0
0 = 7(2) + 2
0 = 14 + 2
0 ≠ 16
The ordered pair is not a solution of the equation.

Question 28.
y = 2x – 3; (4, 5)
Answer:
x = 4
y = 5
y = 2x – 3
5 = 2(4) – 3
5 = 8 – 3
5 = 5
The ordered pair is a solution of the equation.

Question 29.
y = 3x – 3; (1, 0)
Answer:
x = 1
y = 0
y = 3x – 3
0 = 3(1) – 3
0 = 3 – 3
0 = 0
The ordered pair is a solution of the equation.

Question 30.
7 = y – 5x; (4, 28)
Answer:
x = 4
y = 28
7 = y – 5x
7 = 28 – 5(4)
7 = 28 – 20
7 ≠ 8
The ordered pair is not a solution of the equation.

Question 31.
y + 3 = 6x; (3, 15)
Answer:
x = 3
y = 15
y + 3 = 6x
15 + 3 = 6(3)
18 = 18
The ordered pair is a solution of the equation.

Question 32.
YOU BE THE TEACHER
Your friend determines whether (5, 1) is a solution of y = 3x + 2. Is your friend correct? Explain your reasoning.
Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 12
Answer:
x = 5
y = 1
y = 3x + 2
1 = 3(5) + 2
1 = 15 + 2
1 ≠ 17
Your friend is correct.

IDENTIFYING VARIABLES Identify the independent and dependent variables.
Question 33.
The equation A = 25w represents the area A (in square feet) of a rectangular dance floor with a width of w feet.
Answer:
The area of the dance floor (A) depends on the dance floor
A is the dependent variable
and w is the independent variable

Question 34.
The equation c= 0.09s represents the amount c(in dollars) of commission a salesperson receives for making a sale of s dollars.
Answer:
The commissioner a salesperson receives (c) depends on the sales the salesperson makes
c is dependent variable
s is independent variable

Question 35.
The equation t = 12p+ 12 represents the total cost t (in dollars) of a meal with a tip of p percent (in decimal form).
Answer:
The total cost of a meal depends on the tip of percent
the dependent variable is t
the independent variable is p

Question 36.
The equation h = 60 − 4m represents the height h(in inches) of the water in a tank m minutes after it starts to drain.
Answer:
The height of the water (h) depends on the minutes the tank has been draining
the dependent variable is h
the independent variable is m

OPEN-ENDED Complete the table by describing possible independent or dependent variables.
Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 24
Answer:
37. Independent variable:
The grade you receive on the test dependent variable
38. Independent variable:
The time you reach your destination dependent variable.
39. Dependent variable:
The amount of minutes used to talk independent variable.
40. Dependent variable:
The number of hours you work independent variable.

GRAPHING EQUATIONS Graph the equation.
Question 41.
y = 2x
Answer:
Given,
y = 2x
when x = 0
y = 2(0)
y = 0
when x = 1
y = 2(1)
y = 2
when x = 2
y = 2(2)
y = 4
Big Ideas Math Grade 6 Chapter 6 Equations img_5

Question 42.
y = 5x
Answer:
Given,
y = 5x
when x = 0
y = 5(0)
y = 0
when x = 1
y = 5(1)
y = 5
Big Ideas Math Grade 6 Chapter 6 Equations img_6

Question 43.
y = 6x
Answer:
Big Ideas Math Grade 6 Chapter 6 Equations img_7

Question 44.
y = x + 2
Answer:
Given
y = x + 2
when x = 0
y = 0 + 2
y = 2
(x, y) = (0,2)
when x = 1
y = 1 + 2
y = 3
(x, y) = (1,3)
when x = 2
y = 2 + 2
y = 4
(x, y) = (2,4)
Big Ideas Math Grade 6 Chapter 6 Equations img_8

Question 45.
y = x + 0.5
Answer:
Given,
y = x + 0.5
when x = 0
y = 0 + 0.5
y = 0.5
when x = 1
y = 1 + 0.5
y = 1.5
Big Ideas Math Grade 6 Chapter 6 Equations img_9

Question 46.
y = x + 4
Answer:
Big Ideas Math Grade 6 Chapter 6 Equations img_10

Question 47.
y = x + 10
Answer:
Big Ideas Math Grade 6 Chapter 6 Equations img_11

Question 48.
y = 3x + 2
Answer:
Given,
y = 3x + 2
when x = 0
y = 3(0) + 2
y = 0 + 2
y = 2
(x,y) = (0,2)
when x = 1
y = 3(1) + 2
y = 3 + 2
y = 5
(x,y) = (1,5)
when x = 2
y = 3(2) + 2
y = 6 + 2
y = 8
(x,y) = (2,8)
Big Ideas Math Grade 6 Chapter 6 Equations img_12

Question 49.
y = 2x + 4
Answer:
Given,
y = 2x + 4
when x = 0
y = 2x + 4
y = 2(0) + 4
y = 0 + 4
y = 4
when x = 1
y = 2x + 4
y = 2(1) + 4
y = 2 + 4
y = 6
when x = 2
y = 2x + 4
y = 2(2) + 4
y = 4 + 4
y = 8
Big Ideas Math Grade 6 Chapter 6 Equations img_13

Question 50.
y = \(\frac{2}{3}\)x + 8
Answer:
Big Ideas Math Grade 6 Chapter 6 Equations img_16

Question 51.
y = \(\frac{1}{4}\)x + 6
Answer:
Big Ideas Math Grade 6 Chapter 6 Equations img_15

Question 52.
y = 2.5x + 12
Answer:
Big Ideas Math Grade 6 Chapter 6 Equations img_14

Question 53.
MODELING REAL LIFE
A cheese pizza costs $5. Additional toppings cost $1.50 each. Write and graph an equation that represents the total cost (in dollars) of a pizza.
Answer:
Let x be the total cost of pizza
let x be the number of toppings
Total cost equals the cost of cheese pizza plus the cost of additional toppings times the number of toppings
The equation would be x = 5 + 1.50t
Table & Graph:
Number of toppings                 Total cost, x = 5 + 1.50 t                 Ordered pairs (t, x)

1                                                                6                                           (1, 6.50)
2                                                                9                                           (2, 8)
3                                                                9                                           (3, 9.50)
Big Ideas Math Grade 6 Chapter 6 Equations img_1

Question 54.
MODELING REAL LIFE
It costs $35 for a membership at a wholesale store. The monthly fee is $15. Write and graph an equation that represents the total cost (in dollars) of a membership.
Answer:
The equation is y = 35 + 25x
Table & Graph:
Number of months(x)                 Total cost, y = 35 + 25x                 Ordered pairs (t, x)

1                                                                60                                           (1, 60)
2                                                                85                                           (2, 85)
3                                                                110                                           (3, 110)

Question 55.
PROBLEM SOLVING
The maximum size of a text message is 160 characters. A space counts as one character.
a. Write an equation that represents the number of remaining (unused) characters in a text message as you type.
b. Identify the independent and dependent variables.
c. How many characters remain in the message shown?
Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 14
Answer:
x = the number of characters used
y = the number of characters unused
The equation would be y = 160 – x
The number of unused characters (y) depends on the number of used character (x)
The dependent variable is y
The Independent variable is x
Including space and punctuation, 15 characters were used
y = 160 – x
y = 160 – 15
y = 145

Question 56.
CHOOSE TOOLS
A car averages 60 miles per hour on a road trip. Use a graph to represent the relationship between the time and the distance traveled.
Answer:
Big Ideas Math Grade 6 Chapter 6 Equations img_17

PRECISION Write and graph an equation that represents the relationship between the time and the distance traveled.
Question 57.
Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 15
Answer:
Big Ideas Math Grade 6 Ch 6 Answer Key img_16

Question 58.
Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 16
Answer:
Big Ideas Math Grade 6 Ch 6 Answer Key img_17

Question 59.
Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 17
Answer:
Big Ideas Math Grade 6 Ch 6 Answer Key img_18

Question 60.
Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 18
Answer:
Big Ideas Math Grade 6 Ch 6 Answer Key img_19

IDENTIFYING SOLUTIONS Fill in the blank so that the ordered pair is a solution of the equation.
Question 61.
Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 19
Answer:
y = 8x + 3
x = 1
y = 8(1) + 3
y = 11
Thus the ordered pair (1, 11)

Question 62.
Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 20
Answer:
y = 12x + 2
y = 14
14 = 12x + 2
14 – 2 = 12x
12 = 12x
x = 1
Thus the ordered pair (1, 14)

Question 63.
Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 21
Answer:
y = 9x + 4
y = 22
22 = 9x + 4
22 – 4 = 9x
9x = 18
x = 2

Question 64.
DIG DEEPER!
Can the dependent variable cause a change in the independent variable? Explain.
Answer:
Just like an independent variable, a dependent variable is exactly what it sounds like. It is something that depends on other factors.

Question 65.
OPEN-ENDED
Write an equation that has (3, 4) as a solution.
Answer:
Standard form linear equation
ax + by = c
When a, b and c are constants
We want to make two equations that
i. have that form
ii. do not have all the same solutions and
iii. (3, 4) is a solution to both
a(3) + b(4) = c
3a + 4b = c

Question 66.
MODELING REAL LIFE
You walk 5 city blocks in 12 minutes. How many city blocks can you walk in 2 hours?
Answer:
Given,
You walk 5 city blocks in 12 minutes.
12 min = 5 city
2 hours = 120 minutes
120 minutes = 300 minutes

Question 67.
GEOMETRY
How fast should the ant walk to go around the rectangle in 4 minutes?
Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 22
Answer:
First find the perimeter of the rectangle
P = 2L + 2W
P = 2(16) + 2(12)
P = 32 + 24 = 56 in
r = d/t
r = 56/4
r = 14 in/min

Question 68.
MODELING REAL LIFE
To estimate how far you are from lightning (in miles), count the number of seconds between a lightning flash and the thunder that follows. Then divide the number of seconds by 5. Use two different methods to find the number of seconds between a lightning flash and the thunder that follows when a storm is 2.4 miles away.
Answer:
If you count the number of seconds between the flash of lightning and the sound of thunder, and then divide by 5, you’ll get the distance in miles to the lightning: 5 seconds = 1 mile, 15 seconds = 3 miles, 0 seconds = very close.

Question 69.
REASONING
The graph represents the cost c (in dollars) of buying n tickets to a baseball game.
a. Should the points be connected with a line to show all the solutions? Explain your reasoning.
b. Write an equation that represents the graph.
Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 23
Answer: y = 5x + 0.5

Equations Connecting Concepts

Using the Problem-Solving Plan
Question 1.
A tornado forms 12.25 miles from a weather station. It travels away from the station at an average speed of 440 yards per minute. How far from the station is the tornado after 30 minutes?
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations cc 1
Understand the problem.
You know the initial distance between the tornado and the station, and the average speed the tornado is traveling away from the station. You are asked to determine how far the tornado is from the station after 30 minutes.

Make a plan.
First, convert the average speed to miles per minute. Then write an equation that represents the distance d (in miles) between the tornado and the station after t minutes. Use the equation to find the value of d when t = 30.

Solve and check.
Use the plan to solve the problem. Then check your solution.
Answer:
440 × 30 = 13200

Question 2.
You buy 96 cans of soup to donate to a food bank. The store manager discounts the cost of each case for a total discount of $40. Use an equation in two variables to find the discount for each case of soup. What is the total cost when each can of soup originally costs $1.20?
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations cc 2
Answer:
Given,
You buy 96 cans of soup to donate to a food bank.
The store manager discounts the cost of each case for a total discount of $40.
1 case = 12 cans
x = 96 cans
96 = 12 × x
x = 96/12
x = 8
8 cases
8 × $40 = $320
8 × $1.20 = $9.6

Question 3.
The diagram shows the initial amount raised by an organization for cancer research. A business agrees to donate $2 for every $5 donated by the community during an additional fundraising event. Write an equation that represents the total amount raised (in dollars). How much money does the community need to donate for the organization to reach its fundraising goal?
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations cc 3

Answer: 13,000 – 8000 = 5,000

Performance Task

Planning the Climb
At the beginning of this chapter, you watched a STEAM video called “Rock Climbing.” You are now ready to complete the performance task related to this video, available at BigIdeasMath.com. Be sure to use the problem-solving plan as you work through the performance task.
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations cc 4

Equations Chapter Review

Review Vocabulary

Write the definition and give an example of each vocabulary term.
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations cr 1

Graphic Organizers

You can use an Example and Non-Example Chart to list examples and non-examples of a concept. Here is an Example and Non-Example Chart for the vocabulary term equation.
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations cr 2

Choose and complete a graphic organizer to help you study the concept.
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations cr 3
1. inverse operations
2. solving equations using addition or subtraction
3. solving equations using multiplication or division
4. equations in two variables
5. independent variables
6. dependent variables

Chapter Self-Assessment

As you complete the exercises, use the scale below to rate your understanding of the success criteria in your journal.
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations crr 1

6.1 Writing Equations in One Variable (pp. 245–250)
Learning Target: Write equations in one variable and write equations that represent real-life problems.

Write the word sentence as an equation.
Question 1.
The product of a number m and 2 is 8.
Answer: m × 2 = 8

Explanation:
We have to write the word sentence in the equation.
The phrase product indicates ‘×’
The equation would be m × 2 = 8

Question 2.
6 less than a number t is 7.
Answer: 6 – t = 7

Explanation:
We have to write the word sentence in the equation.
The phrase less than indicates ‘-‘
The equation would be 6 – t = 7

Question 3.
A number m increased by 5 is 7.
Answer: m + 5 = 7

Explanation:
We have to write the word sentence in the equation.
The phrase increased indicates ‘+’
The equation would be m + 5 = 7

Question 4.
8 is the quotient of a number g and 3.
Answer: g ÷ 3 = 8

Explanation:
We have to write the word sentence in the equation.
The phrase quotient indicates ‘÷’
The equation would be g ÷ 3 = 8

Question 5.
The height of the 50-milliliter beaker is one-third the height of the 2000-milliliter beaker. Write an equation you can use to find the height (in centimeters) of the 2000-milliliter beaker.
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations crr 5
Answer: y = 3x

Explanation:
Given,
The height of the 50-milliliter beaker is one-third the height of the 2000-milliliter beaker.
Let the height of 2000 ml beaker = x
Given,
Height of 50 ml beaker, y = 1/3 of x
The equation to find the height of the 2000 ml beaker will be
y = 3x
which means the height of the 2000 ml beaker is three times the height of the 500 ml beaker.
Therefore, the equation is y = 3x.

Question 6.
There are 16 teams in a basketball tournament. After two rounds, 12 teams are eliminated. Write and solve an equation to find the number of teams remaining after two rounds.
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations crr 6
Answer:
Given,
There are 16 teams in a basketball tournament. After two rounds, 12 teams are eliminated.
x = 16
y = 12
Number of teams remaining after two rounds = z
z = x – y
z = 16 – 12
z = 4

Question 7.
Write an equation that has a solution of x = 8.
Answer: 4x = 32

Question 8.
Write a word sentence for the equation y + 3 = 5.
Answer: The sum of the numbers y and 3 is 5.

6.2 Solving Equations Using Addition or Subtraction (pp. 251–258)
Learning Target: Write and solve equations using addition or subtraction.

Question 9.
Tell whether x = 7 is a solution of x + 9 = 16.
Answer: Yes

Explanation:
Given the equation
x + 9 = 16
x = 16 – 9
x = 7

Solve the equation. Check your solution.
Question 10.
x – 1 = 8
Answer: 9

Explanation:
Given the equation
x – 1 = 8
x = 8 + 1
x = 9

Question 11.
m + 7 = 11
Answer: 4

Explanation:
Given the equation
m + 7 = 11
m = 11 – 7
m = 4

Question 12.
21 = p – 12
Answer: 33

Explanation:
Given the equation
21 = p – 12
p – 12 = 21
p = 21 + 12
p = 33

Write the word sentence as an equation. Then solve the equation.
Question 13.
5 more than a number x is 9.
Answer: 5 + x = 9

Explanation:
We have to write the word sentence as an equation
The phrase more than indicates ‘+’
Thus the equation would be 5 + x = 9

Question 14.
82 is the difference of a number b and 24.
Answer: b – 24 = 82

Explanation:
We have to write the word sentence as an equation
The phrase difference indicates ‘-‘
Thus the equation would be b – 24 = 82

Question 15.
A stuntman is running on the roof of a train. His combined speed is the sum of the speed of the train and his running speed. The combined speed is 73 miles per hour, and his running speed is 15 miles per hour. Find the speed of the train.
Answer:
Given,
A stuntman is running on the roof of a train. His combined speed is the sum of the speed of the train and his running speed.
The combined speed is 73 miles per hour, and his running speed is 15 miles per hour.
Speed of the train = ?
Z =  x – y
z = 73 – 15
z = 58

Question 16.
Before swallowing a large rodent, a python weighs 152 pounds. After swallowing the rodent, the python weighs 164 pounds. Find the weight of the rodent.
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations crr 16
Answer:
Given that,
Before swallowing a large rodent, a python weighs 152 pounds.
After swallowing the rodent, the python weighs 164 pounds.
164 – 152 = 12 pounds

6.3 Solving Equations Using Multiplication or Division (pp. 259–264)
Learning Target: Write and solve equations using multiplication or division.

Solve the equation. Check your solution.
Question 17.
6 . q = 54
Answer: 9

Explanation:
Given the equation
6 . q = 54
q = 54/6
q = 9

Question 18.
k ÷ 3 = 21
Answer: 63

Explanation:
Given the equation
k ÷ 3 = 21
k = 21 × 3
k = 63

Question 19.
\(\frac{5}{7}\)a = 25
Answer: 35

Explanation:
Given the equation
\(\frac{5}{7}\)a = 25
5a = 7 × 25
a = 7 × 5
a = 35

Question 20.
The weight of an object on the Moon is about 16.5% of its weight on Earth. The weight of an astronaut on the Moon is 24.75 pounds. How much does the astronaut weigh on Earth?
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations crr 20
Answer: 150 pounds

Explanation:
Given,
The weight of an object on the Moon is about 16.5% of its weight on Earth.
The weight of an astronaut on the Moon is 24.75 pounds.
Let the astronaut weight on Earth be represented by x.
Based on the information given in the question, thus can be formed into an equation as:
16.5% of x = 24.75
16.5% × x = 24.75
16.5/100 × x = 24.75
0.165x = 24.75
x = 24.75/0.165
x = 150 pounds
The astronaut weighs 150 pounds on Earth.

Question 21.
Write an equation that can be solved using multiplication and has a solution of x = 12.
Answer: 3x = 36

Question 22.
At a farmers’ market, you buy 4 pounds of tomatoes and 2 pounds of sweet potatoes. You spend 80% of the money in your wallet. How much money is in your wallet before you pay?
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations crr 22
Answer: The money in your wallet before you pay is 20 dollars

Explanation:
Cost of 1 pound of tomato = 3 dollars
Therefore,
Cost of 4 pound of tomato = 4 x 3 = 12 dollars
Cost of 4 pound of tomato = 12 dollars
Cost of 1 pound of sweet potatoes = 2 dollars
Therefore,
Cost of 2 pound of sweet potatoes = 2 x 2 = 4 dollars
Cost of 2 pounds of sweet potatoes = 4 dollars
The combined cost spend at the market is:
cost spend at market = Cost of 4 pound of tomato + Cost of 2 pound of sweet potatoes
cost spend at market = 12 + 4 = 16 dollars
You spent 80% of the money in your wallet
Therefore, 80% of the money in your wallet is equal to 16 dollars
Let x be the money in your wallet
Then, we get
80 % of x = 16
80/100 × x = 16
0.8 x = 16
x = 16/0.8
x = 20
Thus money in your wallet before you pay is $20.

6.4 Writing Equations in Two Variables (pp. 265-272)
Learning Target: Write equations in two variables and analyze the relationship between the two quantities.

Tell whether the ordered pair is a solution of the equation.
Question 23.
y = 3x + 1; (2, 7)
Answer:
Given the equation
x = 2
y = 7
7 = 3(2) + 1
7 = 6 + 1
7 = 7
Yes, it is the solution of the equation.

Question 24.
y = 7x – 4; (4, 22)
Answer:
Given the equation
x = 4
y = 22
22 = 7(4) – 4
22 = 28 – 4
22 ≠ 24
No, it is not the solution of the equation.

Question 25.
The equation E = 360m represents the kinetic energy E (in joules) of a roller-coaster car with a mass of m kilograms. Identify the independent and dependent variables.
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations crr 25
Answer: E is the dependent variable
m is the independent variable

Graph the equation.
Question 26.
y = x + 1
Answer:
Given,
y = x + 1
when x = 0
y = 0 + 1
y = 1
(x, y)  = (0, 1)
when x = 1
y = 1 + 1
y = 2
(x, y)  = (1, 2)
when x = 2
y = 2 + 1
y = 3
(x, y)  = (2, 3)
Big Ideas Math Grade 6 Chapter 6 Equations img_19

Question 27.
y = 7x
Answer:
Big Ideas Math Grade 6 Chapter 6 Equations img_20

Question 28.
y = 4x + 3
Answer:

Question 29.
y = \(\frac{1}{2}\)x + 5
Answer:
Given,
y = \(\frac{1}{2}\)x + 5
when x = 0
y = \(\frac{1}{2}\)0+ 5
y = 5
when x = 0
y = \(\frac{1}{2}\)1+ 5
y = 5\(\frac{1}{2}\)
Big Ideas Math Grade 6 Chapter 6 Equations img_21

Question 30.
A taxi ride costs $3 plus $2.50 per mile. Write and graph an equation that represents the total cost (in dollars) of a taxi ride. What is the total cost of a five-mile taxi ride?
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations crr 30
Answer:
Given,
A taxi ride costs $3 plus $2.50 per mile.
5 × 2.50 = $25.50

Question 31.
Write and graph an equation that represents the total cost (in dollars) of renting the bounce house. How much does it cost to rent the bounce house for 6 hours?
Big Ideas Math Answer Key Grade 6 Chapter 6 Equations crr 31
Answer:
C= $25 x 6 = $150
25×6=150+100=250

Question 32.
A car averages 50 miles per hour on a trip. Write and graph an equation that represents the relationship between the time and the distance traveled. How long does it take the car to travel 525 miles?
Answer:
Given,
A car averages 50 miles per hour on a trip.
50 miles – 1 hour
525 miles – x
50 × x = 525
x = 525/50
x = 10.50 hours
Thus it takes 10.5 hours to travel 525 miles.

Equations Practice Test

Question 1.
Write “7 times a number is 84” as an equation.
Answer: 7 × n = 84

Explanation:
We have to write the word sentence into the equation
The phrase times indicates ‘×’
Thus the equation would be 7 × n = 84

Solve the equation. Check your solution.
Question 2.
15 = 7 + b
Answer: b = 8

Explanation:
Given,
15 = 7 + b
b = 15 – 7
b = 8

Question 3.
v – 6 = 16
Answer: v = 22

Explanation:
Given,
v – 6 = 16
v = 16 + 6
v = 22

Question 4.
5x = 70
Answer: x = 14

Explanation:
Given,
5x = 70
x = 70/5
x = 14

Question 5.
\(\frac{6m}{7}\) = 30
Answer:
Given,
\(\frac{6m}{7}\) = 30
6m = 30 × 7
6m = 210
m = 210 ÷ 6
m = 35

Question 6.
Tell whether (3, 27) is a solution of y = 9x
Answer: solution

Explanation:
Given,
y = 9x
x = 3
y = 27
27 = 9(3)
27 = 27
Thus the ordered pair is a solution.

Question 7.
Tell whether (8, 36) is a solution of y = 4x + 2.
Answer: not a solution

Explanation:
Given,
y = 4x + 2.
x = 8
y = 36
36 = 4(8) + 2
36 = 32 + 2
36 ≠ 34

Question 8.
The drawbridge shown consists of two identical sections that open to allow boats to pass. Write s an equation you can use to find the length (in feet) of each section of the drawbridge.
Big Ideas Math Answers 6th Grade Chapter 6 Equations pt 8
Answer: 2s = 366ft

Question 9.
Each ticket to a school dance is $4. The total amount collected in ticket sales is $332. Find the number of students attending the dance.
Answer:
Given,
Each ticket to a school dance is $4.
The total amount collected in ticket sales is $332.
The equation would be
4s = 332
s = 83

Question 10.
A soccer team sells T-shirts for a fundraiser. The company that makes the T-shirts charges $10 per shirt plus a $20 shipping fee per order.
a. Write and graph an equation that represents the total cost (in dollars) of ordering the shirts.

Answer:
For this case, the first thing we must do is define variables:
c = total cost
x = x number of shirts.
The equation that adapts to the problem is:
c (x) = 10x + 20

b. Choose an ordered pair that lies on your graph in part(a). Interpret it in the context of the problem.
Big Ideas Math Answers 6th Grade Chapter 6 Equations pt 10
Answer:
Let’s choose the next ordered pair:
(x, c (x)) = (0, 20)
We verify that it is in the graph:
c (20) = 10 (0) + 20
c (20) = 20 (yes, it belongs to the graph).
In the context of the problem, this point means that the cost per shipment is $ 20

Question 11.
You hand in 2 homework pages to your teacher. Your teacher now has 32 homework pages to grade. Find the number of homework pages that your teacher originally had to grade.
Answer:
Given that,
You hand in 2 homework pages to your teacher.
Your teacher now has 32 homework pages to grade.
32 – 2 = 30

Question 12.
Write an equation that represents the total cost (in dollars) of the meal shown with a tip that is a percent of the check total. What is the total cost of the meal when the tip is 15%?
Big Ideas Math Answers 6th Grade Chapter 6 Equations pt 12
Answer: $41.40

Equations Cumulative Practice

Big Ideas Math Answers 6th Grade Chapter 6 Equations cp 1
Question 1.
You buy roses at a flower shop for $3 each. How many roses can you buy with $27?
A. 9
B. 10
C. 24
D. 81
Answer: 9

Explanation:
given,
You buy roses at a flower shop for $3 each.
27/3 = 9
Thus you can buy 9 roses with $27.
Thus the correct answer is option A.

Question 2.
You are making identical fruit baskets using 16 apples, 24 pears, and 32 bananas. What is the greatest number of baskets you can make using all of the fruit?
F. 2
G. 4
H. 8
I. 16
Answer: 8

Explanation:
Given,
You are making identical fruit baskets using 16 apples, 24 pears, and 32 bananas.
8 baskets
MULTIPLES OF 16, 24, and, 32
16: 1, 2, 4, 8, 16
24: 1, 2, 3, 4, 6, 8, 12, 24
32: 1, 2, 4, 8, 16, 32

Question 3.
Which equation represents the word sentence?
Big Ideas Math Answers 6th Grade Chapter 6 Equations cp 3
A. 18 – 5 = 9 – y
B. 18 + 5 = 9 – y
C. 18 + 5 = y – 9
D. 18 – 5 = y – 9
Answer: 18 + 5 = 9 – y

Explanation:
The suitable equation for the above word sentence is
18 + 5 = 9 – y
Thus the correct answer is option B.

Question 4.
The tape diagram shows the ratio of tickets sold by you and your friend. How many more tickets did you sell than your friend?
Big Ideas Math Answers 6th Grade Chapter 6 Equations cp 4
F. 6
G. 12
H. 18
I. 30
Answer: 6

Explanation:
Each rectangle = 6
6 × 5 = 30
6 × 2 = 12
30 + 12 = 42
Thus the correct answer is option A.

Question 5.
What is the value of x that makes the equation true?
Big Ideas Math Answers 6th Grade Chapter 6 Equations cp 5
59 + x = 112
Answer:
Given the equation
59 + x = 112
x = 112 – 59
x = 53
Thus the value of x that makes the equation true is 53

Question 6.
The steps your friend took to divide two mixed numbers are shown.
Big Ideas Math Answers 6th Grade Chapter 6 Equations cp 6
What should your friend change in order to divide the two mixed numbers correctly?
A. Find a common denominator of 5 and 2.
B. Multiply by the reciprocal of \(\frac{18}{5}\).
C. Multiply by the reciprocal of \(\frac{3}{2}\).
D. Rename 3\(\frac{3}{5}\) as 2\(\frac{8}{5}\).
Answer:  Multiply by the reciprocal of \(\frac{3}{2}\).

Question 7.
A company ordering parts receives a charge of $25 for shipping and handling plus cp$20 per part. Which equation represents the cost (in dollars) of ordering parts?
F. c = 25 + 20p
G. c = 20 + 25p
H. p = 25 + 20c
I. p = 20 + 25c
Answer: c = 25 + 20p

Question 8.
Which property is illustrated by the statement?
5(a + 6) = 5(a) + 5(6)
A. Associative Property of Multiplication
B. Commutative Property of Multiplication
C. Commutative Property of Addition
D. Distributive Property
Answer: Distributive Property

Question 9.
What is the value of the expression?
Big Ideas Math Answers 6th Grade Chapter 6 Equations cp 5
46.8 ÷ 0.156
Answer:
Divide the two decimal numbers
we get the answer
300

Question 10.
In the mural below, the squares that are painted red are marked with the letter R.
Big Ideas Math Answers 6th Grade Chapter 6 Equations cp 10
What percent of the mural is painted red?
F. 24%
G. 25%
H. 48%
I. 50%
Answer: 48%

Question 11.
Which expression is equivalent to 28x + 70?
A. 14 (2x + 5)
B. 14 (5x + 2)
C. 2 (14x + 5)
D. 14 (7x)
Answer: 14 (2x + 5)

Explanation:
28x + 70
Taking 14 as the common factor
14(2x + 5)
Thus the correct answer is option A.

Question 12.
What is the first step in evaluating the expression?
3 . (5 + 2)2 ÷ 7
F. Multiply 3 and 5.
G. Add 5 and 2
H. Evaluate 52.
I. Evaluate 22.
Answer: G. Add 5 and 2

Question 13.
Jeff wants to save $4000 to buy a used car. He has already saved $850. He plans to save an additional $150 each week.
Big Ideas Math Answers 6th Grade Chapter 6 Equations cp 13
Part A Write and solve an equation to represent the number of weeks remaining until he can afford the car.
Jeff saves $150 per week by saving \(\frac{3}{4}\) of what he earns at his job each week.
He works 20 hours per week.
Part B Write an equation to represent the amount per hour that Jeff must earn to save $150 per week. Explain your reasoning.
Part C What is the amount per hour that Jeff must earn? Show your work and explain your reasoning.
Answer: 21 weeks

Explanation:
150 × 21 = 3150
3150 + 850 = 4000

Conclusion:

We put all our efforts and experience to prepare Big Ideas Math Book 6th Grade Answer Key Chapter 6 Equations pdf. Hope you are satisfied with the given data and information regarding Big Ideas Math Book 6th Grade Answer Key Chapter 6 Equations. If you have any kind of doubts, clarify with us here. We wish all the very best for all the aspirants preparing for the exam.

Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure

Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure

Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure is given here in a comprehensive manner to help the students for better understanding. Must solve every problem given on the Big Ideas Math Answers Chapter 11 Convert and Display Units of Measure Grade 5. You will become perfect as you practice as many questions as you practice. Practice the problems and cross-check the answer to know your preparation level. If you feel any topic difficult, then concentrate more on those topics. Every topic is important to get a good score in the exam. Download Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure PDF without any cost.

Big Ideas Math Book 5th Grade Chapter 11 Convert and Display Units of Measure Answer Key

The list of concepts covered mainly in Convert and Display Measure are Mass and Capacity in Metric Units, Length in Metric Units, Weight in Customary Units, Length in Customary Units, Capacity in Customary Units, etc. Don’t skip any of the topics from the given chapter. Completely get free access to Big Ideas Math Book 5th Grade Answer Key Chapter 11 Convert and Display Units of Measure PDF. Below attached links help you to find every individual topic.

Lesson: 1 Length in Metric Units

Lesson: 2 Mass and Capacity in Metric Units

Lesson: 3 Length in Customary Units

Lesson: 4 Weight in Customary Units

Lesson: 5 Capacity in Customary Units

Lesson: 6 Make and Interpret Line Plots

Lesson: 7 Problem Solving: Measurement

Chapter – 11: Convert and Display Units of Measure

Lesson 11.1 Length in Metric Units

Explore and Grow

Work with a partner. Find 3 objects in your classroom and use a meter stick to measure them. Record your measurements in the table.
Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure 1
Answer:
1 centimeter is 0.1 times as long as 1 millimeter.
1 meter is 0.01 times as long as 1 centimeter.
1 meter is 0.001 times as long as 1 millimeter.

Structure
How can you convert a metric length from a larger unit to a smaller unit? How can you convert a metric length from a smaller unit to a larger unit?
Answer:
We can convert a metric length from a larger unit to a smaller unit by Multiplying.
Example: There are 1000 meters in one kilometer. Then the answer is  5km = 5000 meters. (5 × 1000)
We can convert a metric length from a smaller unit to a larger unit by Dividing.
Example: one meter is equal to 0.001 km.  1 meter = 0.001 km ( 1m/1000=0.001km)

Think and Grow: Convert Metric Lengths

You can use powers of 10 to find equivalent measures in the metric system.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 2
Key Idea
When finding equivalent metric lengths, multiply to convert from a larger unit to a smaller unit. Divide to convert from a smaller unit to a larger unit.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 3
Example
Convert 6 centimeters to millimeters.
Answer:
There are 10 millimeters in 1 centimeter.

Explanation:
Because you are converting from a larger unit to a smaller unit, multiply.
6 × 10 = 60
So, 6 centimeters is 60 millimeters.

Example
Convert 14,000 meters to kilometers.
Answer: There are 1,000 meters in 1 kilometer.

Explanation:
Because you are converting from a smaller unit to a larger unit, divide.
14,000 ÷ 1000 = 14.
So, 14,000 meters is 14 kilometers.

Show and Grow

Convert the length.

Question 1.
8.5 km = 8500 m.

Answer:
8.5 × 1000 = 8500.

Explanation:
Convert from kilometers to meters.
We know that,
1 km= 1000m
8.5 km = 8.5 × 1000 = 8500 m

Question 2.
180 cm = 1.8 m
Answer: 180/100 = 1.8 m

Explanation:
Convert from centimeters to meters.
1 m = 100 cm
1 cm = 1/100 m
180 cm = 180/100 = 1.8 m

Apply and Grow: Practice

Convert the length.

Question 3.
150 m = 0.15 km
Answer:
150 m = 0.15 km

Explanation:
Convert from meters to kilometers.
(Divide the meter value by 1000)
150m/1000 = 0.15 km

Question 4.
90 cm = 900 mm
Answer: 90 cm = 900 mm

Explanation:
Convert from centimeters to millimeters.
multiply the length value (i.e., cm value) by 10
90cm × 10 = 900 mm

Question 5.
0.03 m = 3 cm.
Answer: 0.03 m = 3 cm

Explanation:
Convert from meter to centimeter
Multiply the length value by (i.e., m value ) by 100
0.03 m × 100 = 3cm

Question 6.
0.6 km = 60,000 cm
Answer: 0.6 km = 60,000 cm

Explanation:
Convert from kilometers to centimeters
multiply the length value (i.e., km value by 100000)
0.6km × 100000 = 60,000 cm

Question 7.
800 mm = 0.8 m
Answer: 800 mm = 0.8 m

Explanation:
Convert from millimeters to meters
Divide the length value(i.e., mm value by 1000)
800/1000 = 0.8 m

Question 8.
700 cm = 0.007 km
Answer: 700 cm = 0.007 km

Explanation:
Convert from centimeters to meters
Divide the length value (i.e., cm value by 100000)
700/100000 = 0.007 km

Compare.

Question 9.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 4

 

 

Answer:
0.02 m = 20 mm
multiply the length value (i.e., m value by 1000)
0.02 × 1000 = 20mm
3mm = 0.003 m
divide the length value(i.e., mm value by 1000)
3/1000 = 0.003 m
0.02 m < 3 mm
Question 10.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 6
Answer:
0.025 km = 25000 mm
multiply the km value by 1e+6
3,500 mm = 0.0035 km
divide the length mm value by 1e+6

Question 12.

The giant anteater has the longest tongue in relation to its body size of any mammal. Its tongue is about 0.6 meter long. How many centimeters long is its tongue?

Answer:
The giant anteater has the longest tongue in relation to its body size of any mammal. Its tongue is about 0.6 meter long. Its tongue is about 60 centimeters long.

Explanation:
(0.6 meter = 60 centimeters) multiply the length value with 100.  i.e., (0.6 × 100 = 60)
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 7

Question 13.
Number Sense
The length of an object can be written as b millimeters or c kilometers. Compare the values of b and c. Explain your reasoning.
Answer:
The length of an object can be written as b millimeters or c kilometers
Let us assume that b = 2mm,  c = 2km
By comparing the b and c values
c value is greater than b
kilometers is greater than millimeters  ( 1km = 1000000 mm , 1mm = 1 × 10 ^ -6 km).

Question 14.
Writing
Why does the decimal point move to the left when converting from a smaller measure to a larger measure?

Answer:
As we move from a smaller unit to a larger unit, the number of larger units required will be less. Therefore the decimal point will always move to the left when you want to make a number smaller. Therefore the decimal point will always move to the right when you want to make the number Bigger.

Think and Grow: Modeling Real Life

Example
The base of Mauna Kea extends about 5.76 kilometers below sea level. What is the total height of the volcano in meters?
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 8
Convert the distance below sea level to meters.
Answer: There are 1000 meters in 1 kilometer.

Explanation:
Given,
The base of Mauna Kea extends about 5.76 kilometers below sea level.
5.76 × 1000 = 5,760
So, the volcano extends 5,760 meters below sea level.
Adding below sea level and above sea level
Given in question distance of above sea level = 4,200
The distance of below sea level = 5,760
Adding both values 4,200 + 5,760 = 9,960
So, the total height of the volcano is about 9,960 meters.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 9

Show and Grow

Question 15.
A pool is 3.65 meters deep. A diving board is 100 centimeters above the surface of the water. What is the distance from the diving board to the bottom of the pool in centimeters?
Answer: Given pool depth = 3.65 meters
Explanation: The diving board is above the surface of water = 100 centimeters
Converting 3.65 meters into centimeters ( Since, 1m = 100 cm )
3.65 meters = 365 centimeters ( Multiply the meters value by 100 )
3.65 × 100 = 365 cm
The distance from the diving board to the bottom of the pool = 365 + 100 = 465 cm

Question 16.
You hike 1.6 kilometers from a cabin to a lookout. You plan to hike the same way back. On your way back, you stop after 1,050 meters to look at a map. How many meters have you hiked so far? How many kilometers are you from the cabin?
Answer: Given, that hike from a cabin toa lookout = 1.6 km

Explanation:
on the way you stopped after = 1,050 meters
so, 1.6 km = 1600 meters
1600 m + 1,050 m = 2,650 meters
Therefore, 2,650 meters have you hiked so far
Therefore , 550 meters from the cabin  ( 1600m – 1050m = 550m )
Converting 550 meters to kilometers = 0.55 km ( divide the meter value by 1000).
Therefore,0.55 km from the cabin.
Question 17.
DIG DEEPER!
You can take one of two routes to school. Which route is longer? How much longer? Write your answer two different ways.

Answer: Here, we are taking one route to school i.e., (Route A)

Explanation: From Route A and Route B the longer route is “Route A”.
So, we are taking “Route A” values.
Here 1.3km = 1300 meters (1.3km × 1000 = 1300 meters)
[Since we know that  1kilometer(km)  = 1000metres] 0.6 km = 600 meters (0.6km × 1000 = 600 meters)
So, we are adding1.3km + 0.6km
= 1300m + 600m
= 1900 meters
(OR)
Method (2): Here, we are having two routes:- Route A and Route B.
From the question, We observed that
We have to find out the longer route from Route A and Route B.
The value of Route A is 1.3km and 0.6km
The value of Route B is  625m and 800m
Now add both the routes A and B
We are converting the Route A value from “Kilometers to Meters”
Here (1.3km = 1300metres and 0.6km = 600metres)
By Adding we get 1300m+600m = 1900m
Now take Route B = 800m + 625m = 1425m
By comparing both Route A and Route B, “Route A is longer than Route B”.

Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 10                          

Length in Metric Units Homework & Practice 11.1

Convert the length

Question 1.
0.8 cm = __ mm
Answer: 0.8 cm = 8 millimeters (mm)

Explanation:
We have to convert from centimeters to millimeters
1 mm = 0.1 cm
Multiply the 0.8 with 10  (0.8 × 10 =8)

Question 2.
7 m = _ km
Answer: 7 m =  0.007 km

Explanation:
Convert from meters to kilometers
1 km = 1000 m
Divide the length value by 1000 ( 7/1000 =  0.007)

Question 3.
6.4 km = ___ m
Answer: 6.4 km = 6400 m

Explanation:
Convert from kilometers to meters
1 km = 1000 m
Multiply the length value by 1000 (6.4 × 1000 = 6400)

Question 4.
1,300 mm = __ cm
Answer: 1,300 mm = 130 cm

Explanation:
Convert from millimeters to centimeters.
1 mm = 0.1 cm
Divide the length value by 10 ( 1300/10 = 130)

Question 5.
91,000 cm = ___ km
Answer: 91,000 cm = 0.91 km

Explanation:
Convert from centimeters to kilometers.
1 cm = 1e – 5
Divide the length value by 100000 ( 91000/100000 = 0.91)

Question 6.
20,000 mm = ___ km
Answer: 20,000 mm = 0.02 km

Explanation:
Convert from millimeters to kilometers
Multiply the value in mm by the conversion factor 1.0E-6.
So, 20000 mm times 1.0E-6 is equal to 0.02 km.

Compare

Question 7.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 11
Answer: 1.6 m is greater than 16 cm

Explanation:
16cm = 0.16 m
16cm/100 = 0.16m
1.6 m = 1.6m × 100 = 160 cm

Question 8.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 12
Answer:
300 mm = 0.3 m
1mm = 0.001 m ( divide the 300mm by 1000 )
0.3 m = 300 mm
1m = 1000mm ( multiply the 0.3m by 1000 )

Question 9.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 13
Answer: 0.045 km = 45,000 mm

Explanation:
Convert from kiometers to millimeters
1km = 1000000 mm
45 mm = 4.5 × 10 ^ -5 km ( it is spelled as 10 to the power of -5)  (or)   4.5 e^-5

Question 10.
Dolphins can hear sounds underwater that are 24 kilometers away. How many meters away can dolphins hear sounds underwater?
Answer:
Given,
Dolphins can hear sounds underwater that are 24 kilometers away.
24000 meters away dolphins can hear sounds underwater.

Question 11.
Reasoning
How can you convert 7.8 meters to kilometers by moving the decimal point? Explain your reasoning.
Answer:
Converting 7.8 meters to kilometers
7.8 meters = 0.0078 kilometers.

Explanation:
7.8 m / 1000 = 0.0078 km ( Divide the meter value by 1000 ) ( 1km = 1000 m )
To convert from meters to kilometers, divide the meter value by 1000
since , 1km = 1000m
divide the whole meter value by 1000, put a decimal point at the end of the number and then move it three places to the left.
(But in question we have the decimal number that is 7.8  so, that is why we have moved the decimal point to the fourth number from left).

Question 12.
YOU BE THE TEACHER
Your friend divides by 100 to convert a length from meters to centimeters. Is your friend correct? Explain.
Answer:
No, it is not correct.

Explanation:
Converting a length from meters to centimeters, We have to multiply the length value by 100.

Question 13.
Which One Doesn’t Belong? Which measurement does not belong with the other three?
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 14

Answer:
5,000 cm measurement does not belong with the other three.

Explanation:
500,000 mm = 500 m
500 m = 0.5km
But, 5000 cm = 50m (Here the value 50 m is didn’t belong with given values in question)

Question 14.
Modeling Real Life
A small chunk of ice called a growler breaks away from an ice burg. The growler sticks out of the water 840 millimeters and is 3.5 meters deep in the water. What is the total height of the growler in meters?
Answer:
Converting 840 millimeters into meters

Explanation:
840 mm = 0.84 meter
( Divide the length value by 1000)
840/1000 = 0.84 meter
Total Height of the growler = 0.84 m × 3.5 m (Multiply 0.84m and 3.5m)
= 2.94 meters.

Question 15.
DIG DEEPER!
A spaceship’s route from Earth to the moon is 384,400 kilometers long. The spaceship travels 500,000 meters. How many kilometers does it have left to travel?
Answer:
The Spaceship has left to travel from Earth to the Moon = 500 kilometers.

Explanation:
According, to the question
We are converting 500,000 meters to Kilometers ( 500,000 meters = 500 kilometers)
So, the spaceship has left to travel is 500 kilometers.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 15

Review & Refresh

Write the fraction in the simplest form.

Question 16.
\(\frac{2}{8}\)
Answer: \(\frac{2}{8}\) = \(\frac{1}{4}\)

Question 17.
\(\frac{10}{100}\)
Answer: \(\frac{10}{100}\) = \(\frac{1}{10}\)

Question 18.
\(\frac{24}{16}\)
Answer: \(\frac{24}{16}\) = \(\frac{3}{2}\)

Lesson 11.2 Mass and Capacity in Metric Units

Explore and Grow

Use a balance and weights to help you complete the statement.
Answer: 1 kilogram is 0.001 times as much as 1 gram.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 16
Structure
How can you convert kilograms to grams? How can you convert grams to kilograms?

Use a 1-liter beaker to help you complete the statement.
Answer: 1 liter is 0.001 times as much as 1 milliliter.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 17

Structure
How can you convert liters to milliliters? How can you convert milliliters to liters?
Answer: Converting liters to milliliters ( 1 liter = 1000 milliliters )

Explanation:
multiply the volume (i.e., liter value by 1000 )
For example :-  0.01 liter = 10 ml
0.1 liter = 100 ml
1 liter = 1000 ml
Converting milliliters to liters ( 1 milliliters = 0.001 liters)
Divide the volume value ( i.e., liter value by 1000)
1/1000 = 0.001 liter .

Think and Grow: Convert Metric Measures

Key Idea
When finding equivalent metric masses or capacities, multiply to convert from a larger unit to a smaller unit. Divide to convert from a smaller unit to a larger unit.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 18
Example
Convert 12.4 grams to milligrams.
Answer: There are 1000 milligrams in 1 gram.

Explanation:
Because you are converting from a larger unit to a smaller unit, multiply.
12.4 × 1000 = 12400
So, 12.4 grams is 12400 milligrams.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 19

Example
Convert 18,000 milliliters to liters.
Answer:
There are 1000 milliliters in 1 liter.
Because you are converting from a smaller unit to a larger unit, divide.
18,000 ÷ 1000 = 18 liters .
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 20
So, 18,000 milliliters is 18 liters.

Show and Grow

Convert the mass.

Question 1.
8 kg = ___ g
Answer: 8 kg = 8000 g (8 × 1000 = 8000g)

Explanation:
Convert from kilograms to grams
1 kg = 1000 g
8 kg = 8 × 1000 g = 8000 g

Question 2.
3,800 mg = __ g
Answer: 3,800 mg = 3.8 g
Explanation:
Convert from milligrams to grams
Divide the mass value ( mg value) by 1000
( 3800/1000 = 3.8 g )

Convert the capacity.

Question 3.
22,000 mL = __ L
Answer: 22,000 mL = 22 L
Explanation:
Convert from milliliters to liters.
Divide the volume value ( mL value) by 1000
( 22000/1000 = 22 L )

Question 4.
4.6 L = __ mL
Answer: 4.6 L = 4600 mL

Explanation:
Convert from liters to milliliters
Multiply the volume value ( L  value) by 1000
4.6 × 1000 = 4600 mL

Apply and Grow: Practice

Convert the mass.

Question 5.
5,000 g = ___ kg
Answer: 5,000 g = 5 kg

Explanation:
Convert from grams to kgs
Divide the mass value ( g value) by 1000
1000 grams = 1 kg
5000/1000 = 5kg

Question 6.
67 g = ___ mg
Answer: 67 g = 67000 mg

Explanation:
Convert from grams to milligrams
1 g = 1000 mg
Multiply the mass value ( g value ) by 1000
67 × 1000 = 67000 mg

Question 7.
0.2 kg = __ mg
Answer: 0.2 kg = 200000 mg

Explanation:
Multiply the mass value ( kg value) by 1e+6

Question 8.
30,000 mg = __ kg
Answer: 30,000 mg = 0.03 kg

Explanation:
Divide the mass value ( mg value ) by 1e+6

Convert the capacity.

Question 9.
8 L = ___ mL
Answer: 8 L = 8000 mL  ( 8 × 1000 = 8000 mL )

Explanation:
Convert from liters to milliliters
1L = 1000 mL
( Multiply the volume ( L ) value by 1000)
8 liters = 8 × 1000 ml = 8000 ml

Question 10.
70 mL = ___ L
Answer: 70 mL = 0.07 L

Explanation:
Convert from milliliters to liters
Divide the volume ( mL ) value by 1000
70/1000 = 0.07 L

Question 11.
1.200 mL = __ L
Answer: 1.200 mL = 0.0012 L

Explanation:
Convert from milliliters to liters
Divide the volume ( mL ) value by 1000
1.200/1000 = 0.0012 L

Question 12.
0.4 L = ___ mL
Answer: 0.4 L = 400 mL

Explanation:
Convert from milliliters to liters
Multiply the volume ( L ) value by 1000
( 0.4 × 1000 = 400 mL )

Question 13.
What is the mass of the pumpkin in kilograms?
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 21

Answer:
Given, the mass of the pumpkin = 6,000 grams
According to the question, we have to find out the mass of pumpkin in kilograms.
Converting the 6,000 grams into kilograms = 6 kilograms

Explanation:
Divide the mass ( grams ) value by 1000
[1 kilogram = 1000 grams] , [ 6 kilogram = 6,000 grams ]
(6000/1000 = 6 kilograms )
So, the mass of pumpkin in kilograms is 6 kilograms.

Question 14.
Which One Doesn’t Belong? Which one does not have the same capacity as the other three?
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 22
Answer:
Here , 2000 ml = 2L
2L = 2000 ml
2 × 10³ ml =2000 ml
But 2 ml = 0.002 L

Explanation:
So, the 2ml does not have the same capacity as the other three

Question 15.
DIG DEEPER!
Order the masses from least to greatest. Explain how you converted the masses.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 23
Answer: Order the masses from least to greatest is
14000 mg , 0.039 kg  ,  56 g , 0.14 kg

Explanation:
0.039 kg = 39 grams
0.14 kg = 140 grams
56 g = 0.056 kg
14,000 mg = 14 grams.

Think and Grow: Modeling Real Life

Example
You have a 5-kilogram bag of dog food. You give your dog 50 grams of food each day. How many days does the bag of food last?
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 24
Answer: Convert the mass of the bag to grams.

Explanation:
There are 1000 grams in 1 kilogram.
5 × 1000 = 5000
So, the bag contains 5000 grams of dog food.
Divide the amount of dog food in the bag by the amount you give your dog each day.
5000 ÷ 50 =100
So, the bag lasts for 100 days.

Show and Grow

Question 16.
You have 6 liters of juice to make frozen treats. You pour 30 milliliters of juice into each treat mold. How many treats can you make?
Answer: We can make 200 treats.

Explanation:
We have 6 Liters of juice
6 Liters = 6000 milliliters
From the formula ( 1 liter = 1000 milliliter )
30 milliliters of juice is poured into each treat mold
so , 6000 / 30 = 200
so, we can make 200 treats.

Question 17.
Your goal is to eat no more than 2.3 grams of sodium each day. You record the amounts of sodium you eat. How many more milligrams of sodium can you eat and not exceed your limit?
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 25
Answer: Given 2.3 grams of sodium you have to eat each day

Explanation:
convert 2.3 grams into milligrams
2.3 grams = 2300 milligrams ( multiply the value of the gram by 1000 )
subtract the sodium you eat values
2300 – 210 – 250 – 690 = 1150
so, you can take 1150 more milligrams of sodium.

Question 18.
Which contains more juice, 3 of the bottles, or 32 of the juice boxes? How much more? Write your answer in milliliters.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 26
Answer: 1 bottle of juice contains = 2 L
1 juice box contains = 200 mL

Explanation:
from the question, we have to find 3 juice bottles quantity and 32 juice boxes quantity in milliliters.
1 L = 1000 mL ( from formula )
2L = 2000 mL
for 3 juice bottles = 3 × 2000 = 6000 ml
for 32 juice boxes = 32 × 200 = 6400 ml
so, 6400 – 6000 = 400 ml
400 mL is more
Therefore, 32 juice boxes contain more juice than 3 juice bottles.

Mass and Capacity in Metric Units Homework & Practice 11.2

Convert the mass

Question 1.
9 g = 9000 mg
Answer: 9 g = 9000 mg

Explanation:
Convert from grams to milligrams
1 g = 1000 mg
9 g = 9000 mg ( multiply the g value by 1000 )

Question 2.
78 g = 0.078 kg
Answer: 78 g = 0.078 kg

Explanation:
Convert from grams to kilograms.
1 g = 0.001 kg
78 g = 0.078 kg ( divide the g value by 1000 )

Question 3.
260,000 mg = _0.26_ kg
Answer: 260,000 mg = 0.26 kg

Explanation:
Convert from milligrams to kilograms.
1 mg = 1e + 6
260,000 mg = 0.26 kg

Question 4.
0.148 kg = 148000 mg
Answer: 0.148 kg = 148000 mg

Explanation:
Convert from kilograms to milligrams
1kg = 1000000 mg
0.148 kg = 148000 mg

Convert the capacity

Question 5.
600 mL = 0.6 L
Answer: 600 mL = 0.6 L

Explanation:
Convert from milliliters to liters.
1mL = 0.001 L
600 mL = 0.6 L
divide the mL by 1000

Question 6.
3 L = 3000 mL
Answer: 3 L = 3000 mL

Explanation:
Convert from liters to milliliters.
1 L = 1000 mL
3 L = 3000 mL ( multiply the L value by 1000 )

Question 7.
0.21L = 210 mL
Answer: 0.21 L = 210 mL

Explanation:
Convert from liters to milliliters.
1 L = 1000 mL
0.21 L = 210 mL ( multiply the L value by 1000 )

Question 8.
35 mL = 0.035 L
Answer: 35 mL = 0.035 L

Explanation:
Convert from milliliters to liters.
1 mL = 0.001 L
35 mL = 0.035 L
divide the mL value by 1000

Question 9.
There are 3.2 liters of iced tea in a pitcher. How many milliliters of iced tea are in the pitcher?
Answer: Given that iced tea in a pitcher = 3.2 Liters
we have to find out iced tea in the pitcher in milliliters

Explanation:
Convert from liters to milliliters.
3.2 Liters = 3200 milliliters
1 Liter = 1000 milliliter
3.2 Liters = 3200 milliliters ( multiply the Liters value by 1000 )
so, therefore 3200 milliliters of iced tea are in the pitcher.

Question 10.
YOU BE THE TEACHER
Your friend says that 0.04 kilogram is less than 4 × 105 milligrams. Is your friend correct? Explain.
Answer: 0.04 kilogram = 40,000 mg
4 × 105 mg = 0.4 kg

Explanation:
yes, your friend is correct
0.04 kg is less than 4 × 105 mg
Question 11.
Number Sense
How does the meaning of each prefix relate to the metric units of mass and capacity?
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 27
Answer: The metric system is the system of measurement primarily used in science and in countries outside of the united states.

Explanation:
The metric system includes units of length ( meters ), mass ( grams ), and capacity (liters).
from the given question we have to relate each prefix to the metric units of mass and capacity is:-
metric units of mass of prefix kilo are:-  kilo is the prefix of the kilogram(kg),  kilogram (kg)=1000 grams
Milli is the prefix of milligram(mg) , milligram(mg) = 0.001 gram
metric units of the capacity of prefix kilo is:- kilo is the prefix of Kiloliter(KL), Kiloliter (KL) = 1000 liters
Milli is the prefix of Milliliter(mL), Milliliter (mL) = 0.001 liters

Question 12.
Modeling Real Life
You have 9 kilograms of corn kernels. You put 450 grams of corn kernels in each bag. How many bags can you make?
Answer: we can make 20 bags.

Explanation:
Given that you have 9 kilograms of corn kernels
convert 9 kilograms to grams = 9 kilograms = 9000grams
you put 450 grams of corn kernels in each bag.
we have to find out the how many bags we can make
so, divide the 9000 grams by 450 grams = 9000/450 = 20
so, we can make 20 bags.

Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 28

Question 13.
DIG DEEPER!
Your teacher has one of each of the beakers shown. You need to measure exactly 2 liters of liquid for an experiment. What are three different ways you can do this?
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 29
Answer: We have 3 beakers as shown in figure with 400ml , 600ml , 1L

Explanation:
We have to measure exactly 2 Liters of liquid for each beaker  ( 2L = 2000 ml )
The three different ways we can do this is :-
for first beaker = 400ml × 5 = 2000ml
for second beaker = 600ml × 2 + 400ml × 2
= 1200ml + 800ml = 2000ml
for third beaker = 1 L + 1 L = 2 L

Review & Refresh

Question 14.
Newton rides to the store in a taxi. He owes the driver $12. He calculates the driver’s tip by multiplying $12 by 0.15. How much money does he pay the driver, including the tip?
Answer:
Given that newton rides to the store in a taxi.
He owes the driver $12.
so, he multiplies the drivers tip by $12 by 0.15
$12 × 0.15 + $12 = 13.8
so, newton paid the driver including a tip is 13.8

Lesson 11.3 Length in Customary Units

Explore and Grow

Work with a partner. Use a yardstick to draw 3 lines on a whiteboard that are 1 yard, 2 yards, and 3 yards in length. Then measure the lengths of the lines in feet and in inches. Record your measurements in the table:-
Table values are:-
1  Length(yards) = 3 (feet) ,  36(inches)
2  Length(yards) = 6 (feet) , 72(inches)
3  Length(yards) = 9 (feet) , 108(inches)

Answer:
1 foot is 12 times as long as 1 inch.
1 yard is 3 times as long as 1 foot.
1 yard is 3 × 12 times as long as 1 inch.

Structure
How can you convert a customary length from a larger unit to a smaller unit? How can you convert a customary length from a smaller unit to a larger unit?
Answer:
When converting customary units of measure from a larger unit to a smaller unit, multiply the larger unit by its smaller equivalent unit.
when converting customary units of measure from a smaller unit to a larger unit, divide the smaller unit by its larger equivalent unit.

Think and Grow: Convert Customary Lengths

Key Idea
When finding equivalent customary lengths, multiply to convert from a larger unit to a smaller unit. Divide to convert from a smaller unit to a larger unit.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 31
Example
Convert 3 miles to yards.
Answer: There are 1760 yards in 1 mile.

Explanation:
Because you are converting from a larger unit to a smaller unit, multiply.
3 × 1760 = 5280
So, 3 miles is 5280 yards.

Example
Convert 42 inches to feet and inches.
Answer: There are 12 inches in 1 foot.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 32
Because you are converting from a smaller unit to a larger unit, divide.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 33
Answer:
There are 12 inches in 1 foot
so, 42 inches is 3 feet 6 inches ( 42 / 12 = 3.5 )

Show and Grow

Convert the length.

Question 1.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 34
Answer:
6 1/2 ft = 78 inches

Explanation:
Convert from feet to inches
1 foot = 12 inches
6 feet = 6 × 12 = 72 inches
1/2 ft = 6 inches
72 + 6 = 78 inches
multiply the ft value by 12
6 1/2 ft = 78 inches

Question 2.
94 in. = ft in.
Answer: 94 in = 7 ft 10 in

Explanation: divide the inch value by 12

Apply and Grow: Practice

Convert the length.

Question 3.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 35
Answer:  3 × 3/4 ft = 45 in.

Explanation: multiply the ft value by 12

Question 4.
60 in. = _5_ ft
Answer:- 60 in = 5 f

Explanation:
divide the in value by 12

Question 5.
375 ft = __ yd
Answer: 375 ft = 125 yd

Explanation: divide the ft value by 3

Question 6.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 36
Answer: 12 × 2/3 yd = 38 feet

Explanation:
Convert from yards to feet.
1 yard = 3 feet
multiply the yd value by 3

Question 7.
51 in. = __ ft___in.
Answer: 51 in = 4 feet 3 inches

Explanation:
Convert from inches to feet.
divide the 51-inch value by 12

Question 8.
5 yd = __ in.
Answer: 5 yd = 180 inches

Explanation:
Convert from yards to inches.
1 yard = 36 inches
multiply the yd value by 36
5 yards = 5 × 36 = 180 inches

Compare.

Question 9.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 37
Answer: 7 × 1/3 yd = 22 ft

Explanation:
Convert from yards to feet.
multiply the yd value by 3
22 ft = 7.333 yd
divide the ft value by 3

Question 10.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 38
Answer: 54 in = 4 feet 6 inches

Explanation:
Convert from inches to feet.
divide the inch value by 12
4 ft 8 in = 56 inches
multiply the length value by 12

Question 11.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 39
Answer: 216 in = 6 yards

Explanation:
Convert from inches to yards.
divide the in value by 36
6 yd = 216 inches
multiply the  yd value by 36

Question 12.
A dugong is 8\(\frac{1}{3}\) feet long. How many inches long is the dugong?
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 40
Answer: A dugong is 8 × 1/3 feet long
8 × \(\frac{1}{3}\) feet = 32 inches

Explanation:
Therefore 32 inches long is the dugong.

Question 13.
DIG DEEPER!
Order the lengths from shortest to longest. Explain how you converted the lengths.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 41

Answer:
1)  5 × \(\frac{1}{2}\) =\(\frac{5}{2}\) feet
5/2 feet = 30 inches
multiply the feet value by 12
2) 5 feet 3 inches = 63 inches
multiply the 5 feet 3 inches value by 12
3) 5 × \(\frac{2}{3}\) feet = 40 inches
multiply the feet value by 12
4)  5 × \(\frac{3}{4}\) feet = 45 inches
multiply the feet value by 12
So, order from shortest to longest = 5 × 1/2 , 5 × 2/3 , 5 × 3/4 , 5 feet 3 inches .

Think and Grow: Modeling Real Life

Example
A golfer uses a device to determine that his golf ball is 265 feet from a hole. After his next shot, his ball is 15 feet short of the hole. How many yards did the golfer hit his ball?
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 42
Because the golfer’s ball is 15 feet short of the hole after his next shot, subtract 265 from 15 to find how many feet the golfer hit his ball.
265 – 15 = _250_ feet
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 43
Answer: 265 – 15 = 250 feet

Explanation:
There are 3 feet in 1 yard.
250/3 = 83.33 yards
= 83 × \(\frac{1}{3}\) yards.

Show and Grow

Question 14.
A tree is 27 feet tall. After the tree is struck by lightning, it is 96 inches shorter. How many feet tall is the tree after it is struck by lightning?
Answer:
Given a tree is 27 feet tall. After the tree is struck by lightning, it is 96 inches shorter
we have to find the feet of the tree after it is struck by lightning.
27 feet = 324 inches
Subtract 324 – 96 = 228 inches
converting 228 inches to feet ( i.e., 228 inches = 19 feet )
So, therefore after the tree is struck by lightning its feet tall = 19 feet

Question 15.
DIG DEEPER!
The rope ladder is 2\(\frac{1}{2}\) yards tall. Each knot is made using 16 inches of rope. How many feet of rope are used to make the ladder? Explain.
Answer: 22 feet of rope are used to make the ladder.

Explanation:
2 yards = 6 feet
1 knot is 16 inches
Total 12 knots
12 × 16 = 16 feet ,  16 + 16 = 22 feet.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 44

Question 16.
DIG DEEPER!
The Chesapeake Bay Bridge is 4\(\frac{3}{10}\) miles long. Road work begins 1,200 yards from one end of the bridge and ends 2 miles from the other end of the bridge. How many yards long is the road work?
Answer: 11760 yards

Explanation:
Given,
The Chesapeake Bay Bridge is 4\(\frac{3}{10}\) miles long.
Road work begins 1,200 yards from one end of the bridge and ends 2 miles from the other end of the bridge.
1760 × 4 = 7,040
1760 × 2 = 3,520
given 1200 yards
so, 7040 + 3520 + 1200 = 11760 yards  ( since 1 mile = 1760 yards )

Length in Customary Units Homework & Practice 11.3

Convert the length.

Question 1.
2\(\frac{1}{3}\) yd = __ in.
Answer:- 2 × \(\frac{1}{3}\) yd = 84 in

Explanation:-
Convert from yards to inches
1 yard = 36 inches
Multiply the yd value by 36

Question 2.
5 mi = __ yd.
Answer: 5 mi = 8800 yards

Explanation:
Convert from miles to yards
1 mile = 1760 yards
multiply  the mi value by 1760
5 miles = 5 × 1760 yards
5 mi = 8800 yards

Question 3.
3\(\frac{1}{3}\) yd = __ ft
Answer:
Convert from yards to feet.
multiply the yd value by 3
3 × 1/3 yd = 1 yd
1 yd = 3 feet

Question 4.
27 in. = __ ft __ in.
Answer: 27 in = 2 feet 3 inches

Explanation:
Convert from inches to feet.
divide the 27 inches value by 12

Question 5.
108 in. = __ yd
Answer: 108 in = 3 yards

Explanation:
Convert from inches to yards
1 yard = 36 inches
divide the in value by 36

Question 6.
34 in. = __ ft
Answer: 34 in = 2 feet 10 inches

Explanation:
Convert from inches to feet
1 foot = 12 inches
Divide the in value by 12

Compare.

Question 7.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 45
Answer:
5 × 3/4 ft = 45 inches
65 in = 5 feet 5 inches ( divide the in value by 12 )

Question 8.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 46
Answer:
19 in = 1 feet 7 inches
1 ft 5 in = 17 inches

Question 9.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 47
Answer:
2 mi = 10560 feet
10,650 ft = 2.017 miles

Question 10.
A football player runs 93 yards. How many feet does he run?
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 48
Answer:
Given a football player runs 93 yards
we have to find how many feet does he run
convert 93 yards to feet
93 yards = 279 feet
So, therefore a football player runs 279 feet

Question 11.
Precision
Write whether you would use multiplication or division for each conversion.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 49
Answer:
yards to feet:- 1 yard = 3 feet ( multiply the yard value by 3 )
miles to inches:- 1 mile = 63360 inches ( multiply the mile value by 63360 )
feet to miles:- 1 feet = 0.000189 mile ( divide the feet value by 5280 )
inches to feet :- 1 inch = 0.0833 feet ( divide the inch value by 12 )
miles to yards:- 1 mile = 1760 yards ( multiply the mile value by 1760 ).

Question 12.
Reasoning
Match each measurement with the best customary unit of measure.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 50
Answer:
the height of jump = feet
length of a crayon = inches
length of river = miles
length of football field = yards.

Question 13.
Modeling Real Life
How long is the velociraptor in yards?
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 51
Answer: we have to find the value of velociraptor in yards

Explanation:
Given velociraptor in ft = 28 ft
Converting 28 ft into yards = 28 ft = 9.333 yards
Divide the ft value by 3.

Question 14.
DIG DEEPER!
You wrap a cube-shaped box with ribbon as shown. The ribbon is wrapped around all of the faces of the cube. You use 9 inches of ribbon for the bow. How many inches of ribbon do you use altogether? Explain.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 52
Answer: Cube sides = 6

Explanation:
one side height = 1 feet 9 inches
so, 12 + 9 = 21 inches
6 × 21 inches = 126 inches
9 inches for the bow
so, 126 + 9 = 135 inches
Therefore 135 inches of ribbon is used altogether.

Review & Refresh

Find the quotient.

Question 15.
3,200 ÷ 40 = 80
Answer: 3,200 ÷ 40 = 80

Question 16.
5,400 ÷ 9 = _600__
Answer: 5,400 ÷ 9 = 600

Question 17.
600 ÷ 20 = _30_
Answer: 600 ÷ 20 = 30

Lesson 11.4 Weight in Customary Units

Explore and Grow

Work with a partner. Use the number line to help you complete each statement.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 53
The vehicle weighs _2000_ pounds.
Answer: 2000 pounds

Explanation:
1 US ton = 2000 pounds
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 54
The whale shark weighs _15 US_ tons.
Answer: 15 US tons
Explanation: divide the 30,000 by 2000

Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 55
Structure
How can you convert tons to pounds? How can you convert pounds to tons?
Answer:
we can convert tons to pounds by multiply the ton value by 2000 (i.e., 1 US ton = 2000)
we can convert pounds to tons by dividing the pound value by 2000 (i.e., 1 pound = 0.0005 us ton)

Think and Grow: Convert Customary Weights

Key Idea
When finding equivalent customary weights, multiply to convert from a larger unit to a smaller unit. Divide to convert from a smaller unit to a larger unit.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 56
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 57A
Answer: 4 × 1/4 tons = 2000 pounds

Explanation:
There are 2000 pounds in 1 ton.
so, 4 × 1/4 tons = 2000 pounds.

Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 58A
Answer: 40 ounces = 2.5 pounds

Explanation:
Convert from ounces to pounds
divide the ounces value by 16
40 / 16 = 2.5
so, 40 ounces is 2.5 pounds.

Show and Grow

Convert the weight.

Question 1.
9 T = __ lb
Answer: 9 T = 19841.604 lb

Explanation:
Convert from tonns to pounds.
multiply the T value by 2205.

Question 2.
6\(\frac{1}{2}\) lb = __ oz
Answer: 6 × \(\frac{1}{2}\) lb = \(\frac{6}{2}\) = 3

Explanation:
Convert from pounds to ounces
3 lb = 48 oz
multiply the lb value by 16

Question 3.
6,000 lb = __ T
Answer: 6,000 lb = 3 US tons

Explanation:
Convert from pounds to tonn
divide the lb value by 2000

Question 4.
80 oz = __ lb
Answer: 80 oz = 5 lb

Explanation:
Convert from ounces to pounds.
divide the oz value by 16

Apply and Grow: Practice

Convert the weight.

Question 5.
10,000 lb = __ T
Answer: 10,000 lb = 4.536 T

Explanation:
divide the lb value by 2205.

Question 6.
8 lb = __ oz
Answer: 8 lb = 128 oz

Explanation:
Convert from pounds to ounces.
multiply the lb value by 16

Question 7.
240 oz = __ lb
Answer: 240 oz = 15 lb

Explanation:
Convert from ounces to pounds
divide the oz value by 16

Question 8.
7\(\frac{1}{4}\) T = ___ lb
Answer: 7 × \(\frac{1}{4}\) = 1.75
1.75 T = 3858.09 lb

Explanation:
Convert from tonnes to pounds
multiply the T value by 2205.

Question 9.
150 oz = ___ lb __ oz
Answer: 150 oz = 9.375 lb  150 oz

Explanation:
Convert from pounds to ounces
divide the oz value by 16

Question 10.
32,000 oz = __ T
Answer: 32,000 oz = 1 US ton

Explanation:
Convert from pounds to tonn
divide the oz value by 32000

Compare.

Question 11.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 59
Answer: 30 T = 60000 lb

Explanation:
multiply the T value by 2000
6,000 lb = 3 US tons
divide the lb value by 2000

Question 12.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 60
Answer: 53 oz = 3.312 lb

Explanation:
divide the oz value by 16
3 × 1/2 lb = 1.5 lb
1.5 lb = 0.00068 t
divide the lb value by 2205

Question 13.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 61
Answer:
8 T = 256000 oz

Explanation:
multiply the oz value by 32000
224,000 oz = 7 US tons
divide the oz value by 32000

Question 14.
What is the weight of the hippopotamus in tons?
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 62
Answer:
Given the weight of hippopotamus = 4000 pounds
convert 4000 pounds to tons
4000 pounds = 2 US tons
divide the pound’s value by 2000
so, the weight of hippopotamus in tons = 2 US tons

Question 15.
Reasoning
Compare 10 pounds and 165 ounces using mental math. Explain.

Answer:
0 pounds = 160 ounces
multiply the value of the pound by 16
165 ounces = 10.3125 pounds
divide the value of the ounce by 16
By comparing both the values 165 ounces is greater than 10 pounds.

Question 16.
Number Sense
Which measurements are equivalent to 60 ounces?
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 63
Answer:
3 × 3/4 lb = 36 oz
3 × 1/2 lb = 56 oz
3 lb 12 oz = 60 oz
3 lb 4 oz = 52 oz

Explanation:
3 lb 12 oz measurement is equivalent to 60 ounces (oz)

Think and Grow: Modeling Real Life

Example
A newborn baby boy weighs 122 ounces. A newborn baby girl weighs 6 pounds 4 ounces. Which baby weighs more? How much more?
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 64
Convert the weight of the boy to pounds and ounces.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 65
Answer: There are 16 ounces in 1 pound.

Explanation:
Given boy weighs = 122 ounces
122 / 16 = 7.625
= 2 – 6 × 16 + 4 = 100 ounces
so, 122 >100
Boy weigh is more than girl weigh = 22 ounces more

Show and Grow

Question 17.
Which box of cereal weighs more? How much more?
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 66
Answer:
1/2 pounds = 8 ounces
17 ounces = 1.062 pounds

Explanation:
17 ounces box of cereal weighs more
0.562 much more

Question 18.
A male rhinoceros weighs 2\(\frac{1}{4}\) tons. Which rhinoceros weighs more? How much more? Write your answer as a fraction in simplest form.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 67
Answer: male rhinoceros = 2 × 1/4 = 2/4 = 1/2 tons

Explanation:
1/2 tons = 1000 pounds ( converting tons to pounds)
Given in figure female rhinoceros = 3,500 lb
3,500 lb = 1.75 US tons ( converting pounds to tons )
Female rhinoceros weigh more than male rhinoceros
1.75 tons – 1/2 tons => 1.75 – 0.5 = 1.25 tons
1.25 tons weigh is more
we can write 1.25 in simplest form as, we have 2 digits after the decimal point so multiply both numerator and denominator by 100, so that there is no decimal point in the numerator.
1.25 × 1001 × 100 = 125100
125 / 25100 / 25 = 54
simplest form of 1.25 = 5/4

Question 19.
DIG DEEPER!
Can all of the passengers listed in the table ride the boat at once? Explain.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 68

Answer: Yes, all passengers who are listed on the table can ride the boat at once.

Explanation:
Add all the passenger weights 91+184+150+248+170+215+132+145+265+126+259+175  = 2260 pounds
we have to convert 2260 pounds to tons
2260 pounds = 1.13 US tons  ( divide the pounds value by 2000 ).
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 69

Weight in Customary Units Homework & Practice 11.4

Convert the weight.

Question 1.
10 T = __ lb
Answer: 10 T = 20000 lb

Explanation:
Convert from tonn to pounds
1 tonn = 2000 pounds
multiply the T value by 2000

Question 2.
32 oz = ___ lb
Answer: 32 oz = 2 pounds

Explanation:
Convert from ounces to pounds
divide the oz value by 16

Question 3.
48,000 lb = __ T
Answer:  48,000 lb = 24 US tons

Explanation:
Convert from pounds to tons
divide the lb value by 2000

Question 4.
50 lb = __ oz
Answer: 50 lb = 800 oz

Explanation:
Convert from pounds to ounces.
multiply the mass value by 16

Question 5.
5\(\frac{3}{4}\)T = __ lb
Answer: 5 × \(\frac{3}{4}\) = 15/4 =3.75 T
3.75 t = 8267.1957671958 lb

Question 6.
8\(\frac{1}{2}\) lb = __ oz
Answer: 8 × \(\frac{1}{2}\) = 8/2 = 4 lb
4 lb = 64 ounces

Explanation:
Convert from pounds to ounces.
multiply the lb value by 16

Question 7.
168 oz = __ lb __ oz
Answer: 168 oz = 10.5 lb 168 oz

Explanation:
Convert from ounces to pounds.
divide the oz value by 16

Question 8.
96,000 oz = __ T
Answer: 96,000 0z = 2.7216 T

Explanation:
Convert from ounces to the ton.
96,000 0z = 2.7216 T

Compare

Question 9.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 70
Answer: 16 lb = 0.01 T
32,000 T = 64000000 lb

Question 10.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 71
Answer: 128 oz = 8 lb

Explanation:
divide the oz value by 16
8 × 1/4 lb = 8/4 = 2 lb
2 lb = 32 oz
multiply the lb value by 16

Question 11.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 72
Answer:
11 T = 388013.581 oz
multiply the T value by 35274
384,000 oz = 10.886 T
divide the oz value by 35274

Question 12.
A newborn puppy weighs 3 pounds 5 ounces. What is the weight of the puppy in ounces?
Answer:
Given a new born puppy weighs 3 pounds 5 ounces
we have to find the weight of the puppy in ounces
3 pounds 5 ounces = 1500 grams
convert 1500 grams to ounces
1500 grams = 52.911 ounces
divide the value of the gram by 28.35
The weight of puppy in ounces = 28.35

Question 13.
Number Sense
How many tons are equal to 500 pounds? Write your answer as a fraction in simplest form.

Answer: 500 pounds = 0.25 US tons

Explanation:
divide the value of the pound by 2000
when 0.25 reduced to the simplest form is (25/25)(100/25) = 14

Open-Ended
Complete the statement.

Question 14.
__ pounds > 72 ounces

Answer: 4.6 pounds > 72 ounces

Explanation:
4.6 pounds = 73.6 ounces
multiply the pound’s value by 16

Question 15.
13 tons < __ pounds
Answer: 13 tons < 27000 pounds

Explanation:
Convert from tons to pounds
1 ton = 2000 pounds
divide the value of the pound by 2000.

Question 16.
Modeling Real Life
An employee at a juice cafe uses 10 ounces of kale and \(\frac{3}{4}\) pound of apples to make a drink. Does the employee use more kale or apples? How much more?
Answer: Given that an employee at a juice cafe uses of kale = 10 ounces
and he uses pound of apples to make a drink = 3/4 pounds

Explanation:
converting 10 ounces to pounds = 0.625 pound
divide the value of the ounce by 16
converting 3/4 pounds to ounces = 12 ounces
12 ounces  is greater than 0.625 pounds
The employee uses more apples than kale
0.125 is more.

Question 17.
Modeling Real Life
You have a 3-pound bag of clay. You use 8 ounces of clay to make an ornament. How many ornaments can you make using all of the clay?
Answer:
Given that you have a 3 pound bag of clay
you use 8 ounces of clay to make an ornament.
we have to find out the how many ornaments you can make using all of the clay
Converting 3 pounds to ounces is
3 pounds = 48 ounces ( multiply the pounds value by 16 )
you have used the 8 ounces of clay to make an ornament
so, divide the 48 / 8 = 6
Therefore, we can make 6 ornaments by using all of the clay.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 73

Review & Refresh

Find the product. Check whether your answer is reasonable.

Question 18.
Big Ideas Math Answers 5th Grade Chapter 11 Convert and Display Units of Measure 74
Answer: Multiply the value 145 × 12 = 1740

Question 19.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 75
Answer: multiply the value 561 × 87 = 48,807

Question 20.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 76
Answer: multiply the value 823 × 65 = 53,495

Lesson 11.5 Capacity in Customary Units

Explore and Grow

Describe the relationship between cups and fluid ounces (fl oz). Then complete the table.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 77
1 cup is _8 US_ times as much as 1 fluid ounce.
Answer:
Relationship between cups and fluid ounces is :-
A cup of water happens to equal both 8 fluid ounces ( in volume ) and 8 ounces( in weight) ,
so you might naturally assume that 1 cup equals to 8 ounces of weight universally in recipes.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 78
Explanation:
About table values
1 capacity (cups ) = 8 US fluid ounces    ( multiply the cups value by 8 )
2 capacity ( cups ) = 16 US fluid ounces
3 capacity ( cups ) = 24 US fluid ounces
4 capacity ( cups ) = 32 US fluid ounces
Structure
How can you convert cups to fluid ounces? How can you convert fluid ounces to cups?

Answer:
We can convert cups to fluid ounces by multiplying the value of the cup by 8
1 cup = 8 fluid ounces
We can convert fluid ounces to cups by dividing the value of the fluid ounce by 8
1 fluid ounce = 0.125 US cup .

Think and Grow: Convert Customary Capacities

Key Idea
When finding equivalent customary capacities, multiply to convert from a larger unit to a smaller unit. Divide to convert from a smaller unit to a larger unit.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 79
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 80Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 81.1

Show and Grow

Convert the capacity

Question 1.
9 gal = __ qt
Answer: 9 gal = 36 Us liquid qt

Explanation:
Convert from gal to quart
1 gal = 4 quart
multiply the gal value by 4

Question 2.
20 pt = __ c.
Answer: 20 pt = 48.038 c

Explanation:
Convert from pints to cups
multiply the pt value by 2.402

Question 3.
42 pt = __ qt
Answer: 42 pt = 25.2199 qt

Explanation:
Convert from pints to quarts
divide the pt value by 1.665

Question 4.
68 qt = __ gal
Answer: 68 qt = 17 gal

Explanation:
Convert from quarts to gal
divide the qt value by 4

Apply and Grow: Practice

Convert the capacity.

Question 5.
7 c = fl oz
Answer: 7 c = 56 US fl oz

Explanation:
Convert from cups to fluid ounces
multiply the c value by 8

Question 6.
6 pt = __ qt
Answer: 6 pt = 3.60285 qt

Explanation:
Convert from pints to quarts
1 pint = 0.5 quart
divide the pt value by 1.665

Question 7.
16 qt = __ gal
Answer: 16 qt = 4 US liquid gal

Explanation:
Convert from quarts to gal
1 quart = 0.25 gal
divide the qt value by 4

Question 8.
15 pt = __ c
Answer: 15 pt = 36.0285 US c

Explanation:
Convert from pints to cups.
multiply the pt value by 2.402

Question 9.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 82
Answer: 2 1/4 c = 2/4 = 1/2 c
1/2 c = 4 fl oz

Compare.

Question 11.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 83
Answer:
14 c = 7 US liquid  pt
divide the c value by 2
10 pt = 24.019 US c
multiply the pt value by 2.402

Question 12.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 84
Answer:
38 qt = 9.5 US liquid gal
divide the qt value by 4
8 × 1/2 = 8/2 = 4
4 gal = 16 US liquid qt
Multiply the gal value by 4

Question 13.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 85
Answer:
4 gal = 26.6456pt
multiply the gal value by 6.661
32 pt = 4.8038 US liquid gal
divide the pt value by 6.661

Question 14.
You fill your turtle’s aquarium with 40 pints of water. How many gallons of water do you use?
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 86
Answer:
Given turtles, aquarium fill with water = 40 pints
we have to find the 40 pints of water into gallons
converting 40 pints to gallons
40 pints = 5 US liquid gallons
Divide the pints value by 8
so, therefore 5 gallons of water is used.

Question 15.
Number Sense
Newton’s water cooler contains 1\(\frac{1}{2}\) gallons of water. How many times can he fill his 16-fluid ounce canteen with water from the water cooler? Explain.
Answer:- Given newton’s water cooler contains 1 × 1/2 = 1/2 = 0.5 gallons
Explanation:-  converting 0.5 gallons = 64 US fluid ounces ( multiply the gallons value by 128 )
Given 16 fluid ounce
He can fill 4 times his 16 fluid ounce canteen with water from the water cooler
( i.e., 16 × 4 = 64 fluid ounce ) .

Question 16.
DIG DEEPER!
Order the capacities from least to greatest. Explain how you converted the capacities.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 87
Answer:
i. 8 × 1/2 c => 8/2 = 4 c
4 c = 32 fl oz ( multiply the c value by 8 )
ii. 72 fl oz = 9 US c
divide the fl oz value by 8
iii. 7 × 3/4 c => 21/4 = 5.25 c
5.25 c = 42 fl oz
iv. 56 fl oz = 7 c
divide the fl oz value by 8
Order of capacities from least to greatest = 8 × 1/2 c , 7 × 3/4c , 56 fl oz , 72 fl oz .

Think and Grow: Modeling Real Life

Example
A car’s engine contains 4\(\frac{1}{2}\) quarts of oil. Can a mechanic use a 24-cup container to drain all of the oil?
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 88
First, convert the quarts of oil to pints.
There are __2pints in 1 quart.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 89
Answer:
Given car engine contains = 4 × 1/2 quarts = 4/2 = 2 quarts

Explanation:
2 quarts = 4 pints
multiply the quarts value by 2
1 pint = 2 cups
converting 2 quarts to cups
2 quarts = 8 cups
multiply the quarts value by 4
So, a mechanic can use just 8 cups
8 cups are enough to drain engine oil.
Show and Grow

Question 17.
An adult has 192 fluid ounces of blood in his body. How many pints of blood are in his body?
Answer: Given an adult has 192 fluid ounces of blood in his body
we have to find the pints of blood in his body
Converting 192 fluid ounces to pints
192 fluid ounces = 12 US liquid pints
divide the value of the fluid ounce by 16
Therefore, 12 pints of blood are in his body.

Question 18.
DIG DEEPER!
You make 4\(\frac{1}{2}\) cups of soup. One serving is 12 fluid ounces. How many servings of soup do you make?
Answer:
Given 4 × 1/2 cups of soup
4 × 1/2 = 4/2 = 2 cups of soup
2 cups of soup converting to fluid ounces
2 US cups = 16 US fluid ounces
Given that serving = 12 fluid ounces
Subtract  16 fluid ounces – 12 fluid ounces = 4 fluid ounces
so, therefore you can make servings of soup in 4 fluid ounces.

Question 19.
DIG DEEPER!
A scientist has two beakers of a solution, one containing 5 cups and the other containing 1\(\frac{1}{2}\) pints. How many gallons of the solution does the scientist have? Write your answer as a fraction in simplest form.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 90
Answer:
Given that scientist has two beakers of solution one contains 5 cups and other contains
1 × 1/2 pints.
we have to find gallons of solution
Converting 5 cups to gallons
5 cups = 0.312 US gallons
Converting 1 × 1/2 pints to gallons
1 × 1/2 => 1/2 = 0.5 pints
0.5 pints = 0.0625 US gallons
By adding both the solutions ( i.e., )
5 cups + 0.5 pints
0.312 gallons + 0.0625 gallons = 0.3745 gallons
So, the scientist has 0.3745 gallons of solution.
0.3745 in simplest form we can write as  749 / 2000.

Capacity in Customary Units Homework & Practice 11.5

Convert the capacity

Question 1.
9 pt = __ c
Answer: 9 pt = 18 c

Explanation: multiply the pt value by 2

Question 2.
72 fl oz = ___ c
Answer: 72 fl oz = 9 c

Explanation:
Convert from fluid ounces to cups.
1 fl oz = 0.125 c
divide the fl oz value by 8

Question 3.
6 c = __ fl oz
Answer: 6 c = 48 fl oz

Explanation:
Convert from cups to fluid ounces
1 cup = 6 fluid ounces
6 cups = 6 × 8 fluid ounces
multiply the c value by 8
Thus 6 c = 48 fl oz

Question 4.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 91
Answer: 3 3/4 gal = 15 qt

Explanation:
Convert from gal to quart
1 gal = 4 quart
4  × 15/4 gal = 15 qt
multiply the gal value by 4

Question 5.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 92
Answer: 5 1/2 qt = 11 pt

Explanation:
Convert from quarts to pints
1 quart = 2 pints

multiply the qt value by 2
5 1/2 = 11/2
11/2 × 2 = 11 pints

Question 6.
40 pt = __ gal
Answer: 40 pt = 5 gal

Explanation:
Convert from pints to gal
1 pint = 0.125 gal
40 pint = 40 × 0.125 = 5 gal
Thus 40 pt = 5 gal

Question 7.
64 qt = __ c
Answer: 64 qt = 256 c
Explanation:
Convert from quarts to cup
1 quart = 4 cups
multiply the qt value by 4

Question 8.
112 fl oz = __ pt
Answer: 112 fl oz = 7 US liquid pt
Explanation: divide the fl oz value by 16

Compare.

Question 9.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 93
Answer:
48 qt = 12 gal
divide the qt value by 4
12 gal = 48 qt
multiply the gal value by 4
Therefore 48 qt = 12 gal

Question 10.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 94
Answer: 24 fl oz = 3 c
divide the fl oz value by 8
3 × 1/4 c = 3/4 c = 6 fl oz
multiply the 3/4 c value by 8
Therefore 24 fl oz is greater than 3 × 1/4 c

Question 11.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 95
Answer:
10 qt = 40 c
multiply the qt value by 4
24 c = 6 qt
divide the c value by 4
So, therefore 10 qt is greater than 24 c.

Question 12.
You buy 2 gallons of apple cider. How many cups of apple cider do you buy?

Answer:
Given that 2 gallons of apple cider
we have to find the cups of apple cider
Converting 2 gallons to Cups
2 gallons = 32 cups
multiply the gallons value by 16
So, you buy the 32 cups of apple cider.

Question 13.
Logic
Your friend makes a table of equivalent capacities. Write two pairs of customary units represented by the chart.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 96
Answer:
We can relate the numbers as they are resembling quarts to cups relation and gallons to quarts relation.
Two pairs of the customary unit represented by the chart are :-
1 quart = 4 cups     1 gallon = 4 quarts
2 quart = 8 cups      2 gallon = 8 quarts
Question 14.
DIG DEEPER!
Which measurements are greater than 16 pints?
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 97
Answer:
Converting fluid ounces to pints
300 fluid ounces = 18.75  pints ( divide the value of the fluid ounce by 16 )
Converting cups to pints
28 cups = 14 pints ( divide the value of the cup by 2 )
Converting quarts to pints
10 quarts = 20 pints ( multiply the quarts value by 2 )
Converting gallon to pints
1 gallon = 8 pints ( multiply the gallon value by 8 )
Converting fluid ounces to pints
275 fluid ounces = 17.188 pints ( divide the value of the fluid ounce by 16 )
Converting cups to pints
35 cups = 17.5 pints ( divide the value of the cup by 2 )
Therefore, 300 fluid ounces, 10 quarts, 275 fluid ounces, 35 cups measurements are greater than 16 pints

Question 15.
Modeling Real Life
Your friend buys 8 quarts of frozen yogurt. How many cups of frozen yogurt does she buy?
Answer: Given that quart of frozen yogurt = 8

Explanation:
we have to find cups of frozen yogurt
converting 8 quarts to cups
8 quarts = 32 cups ( multiply the quarts value by 4 )
Therefore, she buys 32 cups of frozen yogurt

Question 16.
Modeling Real Life
A recipe calls for 2\(\frac{1}{4}\) cups of milk. You want to make 2 batches of the recipe. Should you buy a pint, quart, or half gallon of milk?
Answer: Given 2 × 1/4 => 2/4 = 1/2 cups of milk

Explanation: we want to make 2 batches of recipe (i.e., 2 × 1/2 = 1 cup )
1 pint = 2 cups
1 cup = 1/2 pint

Review & Refresh

Question 17.
0.5 × 0.7 = _0.35_
Answer:
multiply the 0.5 × 0.7 = 0.35

Question 18.
46.2 × 0.68 = _31.416_
Answer:
multiply the 46.2 × 0.68 = 31.416

Question 19.
1.4 × 0.3 = _0.42_
Answer:
multiply the 1.4 × 0.3 = 0.42

Lesson 11.6 Make and Interpret Line Plots

Explore and Grow
Measure and record your height to the nearest quarter of a foot. Collect the heights of all the students in your class and create a line plot of the results.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 98
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 99
Construct Arguments
Make two conclusions from the line plot.

Think and Grow: Make Line Plots

Example
The table shows the amounts of water that 10 students use for a science experiment. Make a line plot to display the data. How many students use more than \(\frac{1}{2}\) cup?
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 100
Step 1: Write the data values as fractions with a common denominator.
The denominators of the data values are 2, 4, and 8. Because 2 and 4 are factors of 8, use a denominator of 8.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 101
Step 2: Use a scale on a number line that shows all of the data values.
Step 3: Mark an X for each data value.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 101.1

Show and Grow

Question 1.
The table shows the distance your friend swims each day for 10 days. Make a line plot to display the data.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 102
How many days does your friend swim \(\frac{3}{4}\) mile or more?
Answer:- From the table we observed that your friend swim 3/4 miles or more than 3/4 miles in  6 days.

Apply and Grow: Practice

Question 2.
The table shows the amounts of mulch a landscaping company orders on 10 different days. Make a line plot to display the data.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 103
What do you notice about the data?
Answer:
From the table we observed that except 1/4 and 1/2 the remaining days like 7/8 and 3/4 company use more than 1/2 ton of mulch .

Question 3.
DIG DEEPER!
Your teacher has the three packages of seeds shown. She divides the first package into bags weighing \(\frac{1}{2}\) ounce each. She divides the second package into bags weighing \(\frac{1}{4}\) ounce each. She divides the third package into bags weighing \(\frac{1}{8}\) ounce each. Find the total number of bags of seeds. Use a line plot to display the results.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 104
Answer:
Given that we observed from figures each bag is 2 ounces
Explanation:
given 1st bag = 1/2 ounce each
2 ounces = 1/2 + 1/2 +1/2 + 1/2 = 4(1/2) = 2
4 bags
2nd bag = 1/4 ounce each
2 ounces = 1/4 + 1/4 +1/4 +1/4 + 1/4 + 1/4 + 1/4 + 1/4
= 8 (1/4) = 2
8 bags
3rd bag = 1/8 ounce each
2 ounces = 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8
= 16 (1/8) = 2
16 bags
Total number of bags of seeds = 4 bags + 8 bags + 16 bags = 28 bags
Think and Grow: Modeling Real Life

Example
You record the amounts of time you skateboard each day for 8 days. Your friend skateboards the same total amount of time, but for an equal number of hours each day. How long does your friend skateboard each day?
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 105
Step 1: You and your friend skateboard the same total amount of time. Use the line graph to find the number of hours you each skateboard.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 105.1
Step 2: Divide the number of hours by the number of days.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 106

Show and Grow

Question 4.
You record the amounts of trail mix you pour into 12 bags. Your friend has the same total amount of trail mix, but equally divides it among 12 bags. How much trail mix does your friend pour into each bag?
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 107
Answer:- your friend pour trail mix into each bag is equal to the amount of trail mix you pour into the bag.

Make and Interpret Line Plots Homework & Practice 11.6

Question 1.
The table shows the amounts of time that 10 students take to land three balls in a row in a game. Make a line plot to display the data. How many pygmy marmosets weigh more than \(\frac{1}{2}\) ounce?
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 108
Answer: Here 1/2 = 0.5 ounce
Except 1/2 ounce
5/8 , 7/8 , 3/4 ounces pygmy weighs more than 1/2 ounce.

Use the table.

Question 2.
The table shows the amounts of berries required to make 10 different smoothie recipes. Make a line plot to display the data.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 109
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 110
Answer: The most common amount of berries required is 3/4
Six times as many recipes use 3/4 cup of berries as 1/4 cup of berries
from table 4 × (3/4) = 12/4 = 3
2 × (1/4) = 2/4 = 1/2
= 3/(1/2) = 6

Question 3.
DIG DEEPER!
How many total cups of berries are needed to make one of each smoothie?
Answer: Total 2 to 3 cups of berries are needed to make one of each smoothie.

Use the line plot.

Question 4.
Modeling Real Life
The line plot shows the number of miles you run each day for 10 days. Your friend runs the same total number of miles, but runs an equal number of miles each day. How far does your friend run each day?
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 111
Answer: Your friend runs 4/5 miles each day for 10 days

Explanation: 0 + 0 + 0.5 + 0.5 + 0.5 + 1 + 1 + 1 + 1.5+ 2 = 8
He runs same miles each day = 8/10 = 0.8
0.8 = 4/5
Question 5.
DIG DEEPER!
Your cousin runs a total amount that is 6 times as far as your friend runs in one day. How far does your cousin run?
Answer: Let us assume that, If the friend runs 0.8 per day

Explanation: 0.8 = 4/5
so, cousin run 6 times more than a friend
so, 6 × 0.8 = 4.8 ( cousin runs per day is 4.8 )

Review & Refresh

Question 6.
561 ÷ 7 = 80.142
Answer: divide the 561 ÷ 7 = 80.142

Question 7.
3,029 ÷ 4 = 757.25
Answer: divide the 3,029 ÷ 4 = 757.25

Question 8.
2,814 ÷ 9 = 312.6
Answer: divide the 2,814 ÷ 9 = 312.6

Lesson 11.7 Problem Solving: Measurement

Explore and Grow

Make a plan to solve the problem.
A fruit vendor sells fruit by the pound. You have a tote that can hold up to 4 pounds. A bag of oranges weighs 2\(\frac{1}{4}\) pounds. A bag of apples weighs 28 ounces. Can your tote hold both bags of fruit? Explain.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 112.1
Answer: Given that vendor sells fruit by the pound.

Explanation:
The tote can hold up to 4 pounds
A bag of oranges weighs = 2 × 1/4 = 2/4 = 1/2 pounds
A bag of apples weighs = 28 ounces
we have to find that can tote to hold both bags
Convert 28 ounces to pounds
28 ounces = 1.75 pounds ( divide the value of the ounce by 16 )
Given in question that tote can hold up to 4 pounds
so, adding 1/2 pounds and 1.75 pounds
= 1/2 pounds = 0.5
0.5 pounds + 1.75 pounds = 2.25 pounds
Therefore tote holds both the bags of fruit.

Precision
Which bag of fruit is heavier? Explain.
Answer: Bag of apple is heavier ( i.e., a bag of apple weighs 28 ounces )

Explanation:
28 ounces = 1.75 pounds
bag of orange is 0.5 pounds
1.74 > 0.5  (So, apple bag weigh is heavier)

Think and Grow: Problem Solving: Measurement

Example
A recipe calls for 2\(\frac{1}{4}\) cups of milk. You have \(\frac{1}{4}\) pint of whole milk and 1\(\frac{1}{2}\) cups of skim milk. Do you have enough milk for the recipe?
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 112.2
Answer: Given that , a recipe calls for 2 × 1/4 cups of milk
Explanation: 2 × 1/4 => 1/2 = 0.5 cups of milk
you have 1/4 pint of milk = 0.25 pints
0.25 pints = 0.5 cups
and 1 × 1/2 cups of skim milk => 1/2 = 0.5 cups
Recipe calls for 0.5 cups of milk
Yes, we have enough milk for the recipe.

Understand the Problem

What do you know?

  • The recipe calls for 2 cups of milk.
  • You have \(\frac{1}{4}\) pint of whole milk and 1\(\frac{1}{2}\) cups of skim milk.

What do you need to find?

You need to find whether you have enough milk for the recipe.
Answer: Given that recipe calls for 2 cups of milk
you have 1/4 pint of whole milk => 1/4 pint = 0.25 pint
0.25 pint = 0.5 cups
and 1 × 1/2 cups of skim milk => 1/2 cups = 0.5 cups
adding cups values => 0.5 + 0.5 = 1
So, you don’t have enough milk for the recipe .

Make a Plan
How will you solve?

  • Convert \(\frac{1}{4}\) pint of whole milk to cups.
  • Add the amounts of whole milk and skim milk.
  • Compare the amount of milk you have to the amount needed.

Solve
Step 1: Convert \(\frac{1}{4}\) pint to cups.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 112.3
Step 2: Add the amounts of whole milk and skim milk.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 113
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 114
Answer: So, you _1.5_cups have enough milk for the recipe.
2/4 cups = 1/2
1/2 = 0.5 cups

Show and Grow

Question 1.
Explain how you can check whether the answer above is reasonable.
Answer:  By calculating we get whole milk = 0.5 cups
By calculating we get skim milk =  0.5 cups
By adding whole milk and skim milk => 0.5 + 0.5 = 1 cup

Apply and Grow: Practice

Understand the problem. What do you know? What do you need to find? Explain.

Question 2.
Your friend buys 1 pound of walnuts, 16 ounces of peanuts, and \(\frac{1}{2}\) pound of cashews. How many ounces do the nuts weigh in all?
Answer: Given walnuts = 1 pounds
peanuts = 16 ounces
cashews = 1/2 pounds
we have to find weight of all nuts in ounces
Explanation: walnuts = 1pounds
converting pounds to ounces
1 pounds = 16 ounces
peanuts = 16 ounces
cashews = 1/2 pounds
converting pounds to ounces
1/2 pounds = 8 ounces
Adding peanuts , cashews , walnuts weight = 16 + 8 + 16 = 40 ounces
The nuts weigh in all = 40 ounces

Question 3.
A bottle of orange juice contains 64 fluid ounces. How many cups of orange juice are in 3 bottles?

Understand the problem. Then make a plan. How will you solve? Explain.
Answer:
Given that a bottle of orange juice contains = 64 fluid ounces.
Converting 64 fluid ounces to cups
64 fluid ounces = 8 cups
8cups × 3 bottles = 8 × 3 = 24 cups

Question 4.
Your friend wants to buy curtains that hang from the top of the window to the floor. Curtain lengths are typically measured in inches. What length curtains should he buy?
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 115
Answer:
Given the length ( ft ) values in figure
we have to measure ft value in inches
5 ft = 60 inches
3 ft = 36 inches  ( He should by 60 inches and 30 inches length curtains ).

Question 5.
Your friend runs a total distance of 1 kilometer at track practice by running 100-meter hurdles. How many times does he run the hurdles?
Answer: Given your friend runs a total distance = 1 km
Convert 1 km to meters
1 km = 1000 meters
your friend practice 100 meter hurdles by running
so 100 × 10 = 1000
so , 10 times he run the hurdles

Question 6.
A trailer can carry 13\(\frac{1}{2}\) tons. It has room to carry 6 cars at once. Can the trailer carry 6 cars that each weigh 3,800 pounds? Explain.

Answer: Convert tons to pounds
13 × 1/2 tons = 13000 pounds
Given total 6 cars
each car weigh 3,800 pounds
so, 6 cars × 3,800 pounds = 6 × 3,800 = 22,800 pounds
so, the trailer cannot carry 6 cars at once

Question 7.
DIG DEEPER!
You walk your dog 4 laps around the block each day. Each block is 400 meters. How many total kilometers do you walk your dog around the block after 35 weeks?
Answer: Given, you walk your dog around the block each day = 4 laps
Each block = 400 meters

Explanation: There are 7 days in a week
given 35 weeks
4 × 400 × 7 × 35 = 392000 meters
Convert 392000 meters to km
392000 meters = 392 km
Therefore, 392 km you walk your dog around the block after 35 weeks

Think and Grow: Modeling Real Life

Example
A crew member needs to put a temporary fence around the perimeter of the rectangular football field. How many feet of temporary fencing does the crew member need?
Think: What do you know? What do you need to find? How will you solve?
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 116
Step 1: Convert the length of the field to feet.
There are __ feet in 1 yard.
120 × __ = __
The length of the field is __ feet.
Step 2: Use a formula to find the perimeter of the field.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 117

Show and Grow

Question 8.
An artist puts a wood border around the perimeter of the rectangular mural. How many feet of wood does the artist need?
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 118
Answer: 1 yard = 3 feet
Given 10/3 yd = 3.33 yd
3.33 yd × 3 = 9.99 feet
perimeter of rectangular mural
p = ( 2 × L ) + ( 2 × W )
=  2 ×  8 + 2 × 9.99
= 16 + 19.98
= 35 feet
Artist need 35 feet of wood .

Question 9.
DIG DEEPER!
The sports jug contains 5 gallons of water. The paper cup holds 8 fluid ounces of water. How many paper cups can 3 sports jugs fill? Justify your answer.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 119
Answer: Convert 5 gallons of water to fluid ounces

Explanation:
5 gallons = 640 fluid ounces
Given paper, cup holds = 8 fluid ounces of water
1 sport jug = 5 gallons
3 sport jugs = 3 × 5 = 15 gallons
15 gallons = 1920 fluid ounces
8 × 240 = 1920
240 paper cups can fill 3 sports jug .

Problem Solving: Measurement Homework & Practice 11.7

Understand the problem. Then make a plan. How will you solve? Explain.

Question 1.
A robotic insect has a mass of 80 milligrams. The mass of a quarter is 5.67 grams. How many more grams is the mass of a quarter than the mass of the robotic insect?
Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure 120
Answer: Given robotic insect mass = 80 milligrams
The mass of quarter = 5.67 grams
Convert 80 milligrams to grams
80 milligrams = 0.008 grams
subtract 5.67 grams – 0.008 grams = 5.662
Therefore the mass of quarter  5.662 grams is more than the mass of robotic insect

Question 2.
Newton pours water out of a filled 2-liter beaker. Now it only has 1,025 milliliters of water in it. How many milliliters of water did Newton pour out?
Answer: Given newton pours water out of a filled beaker = 2 Liters

Explanation:
Now it has water = 1,025 milliliters
Convert 2 Liters to millimeters
2 liters = 2000 milliliters
2000 – 975 = 1,025
Newton pour out  975 millimeters of water

Question 3.
You run 5 laps around a track. Each lap is 400 meters. How many total kilometers do you run?
Answer: Given you run 5 laps around a track
Each lap = 400 meters

Explanation:
5 × 400 = 2000 meters
convert meters to kilometers
2000 meters = 2 kilometers
Therefore you run 2 kilometers

Question 4.
Two hotel workers have a total of 30 bags of luggage each weighing 50 pounds. One worker weighs 150 pounds, and the other weighs 210 pounds. Can they transfer themselves and all of the bags in the elevator at once? Explain.
Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure 120.1
Answer:
Given in figure elevator weight limits = 2.5 tons

Explanation:
Convert 2.5 tons to pounds
2.5 tons = 5000 pounds
Given works have total 30 bags
1 bag weight = 50 pounds
30 bags weight = 50 × 30 = 1500 pounds
Given one worker weight = 150 pounds
second worker weight = 210 pounds
By adding all the values 1500 + 150 + 210 = 1860 pounds
Yes, they can transfer themselves and all of the bags in the elevator once.
Question 5.
DIG DEEPER!
You have 84 feet of streamers. You cut 24 pieces that are \(\frac{1}{2}\) each yard long. How many feet of streamers do you have left?
Answer:
Given steamers = 84 feet
24 pieces are 1/2 = 0.5 each yard long
24 × 0.5 = 12 yard long
12 yards = 36 feet
84 – 36 = 48 feet of streamers you have left .

Question 6.
Writing
Write and solve a two-step word problem involving units of measure.

Question 7.
Modeling Real Life
You want to hang a wallpaper border around the perimeter of the rectangular bathroom shown. How many yards of wallpaper border do you need?
Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure 121
Answer:
Given length = 6 ft , width = 1 y

Explanation:
Convert 6 ft to yd
6 ft = 2 yd
perimeter of rectangle = 2 (L + W)
= 2(2 + 1 )
= 2(3) = 6 yd
6 yd of wallpaper border you need

Question 8.
DIG DEEPER!
You need Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure 122 gallon of fertilizer to cover a lawn. What is the least amount of money that you can pay and have enough fertilizer?
Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure 122.1
Answer: Given one lawn fertilizer is 128 fluid ounces

Explanation:
Take 2 gallons = $ 40 × 2 = 80
Given another lawn fertilizer 16 fluid ounces
2 gallons = $ 11 × 16 = 176
80 is the least amount of money that you can pay and have enough fertilizer
128 fluid ounces is cheap when compared to 16 fluid ounces.

Review & Refresh

Divide. Then check your answer.

Question 9.
Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure 123
Answer: 5,343 divide by 25
5,343 ÷ 25 = 213.72

Question 10.
Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure 124
Answer: 2,064 divide by 24
2,064 / 24 = 86

Convert and Display Units of Measure Performance Task 11

Passenger airliners come in many different sizes. Plane A and Plane B are two different types of wide-body jet airliners.

Question 1.
The table shows some facts about Plane A.
a. The length of Plane B is 80 yards. Which is longer, Plane A or Plane B? How much longer?
Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure 125
Answer:- Given, length of plane B = 80 yards
We observed from the table that the length of plane A = 250 ft 2 in
Convert 250 ft 2 into yards
250 ft 2 in = 83.389 yards
So, Length of plane A = 83.389 yards
Length of plane B = 80 yards
Plane A is longer than Plane B
3.389  is longer.
b. The wingspan of Plane B is 37\(\frac{1}{12}\) feet longer than the Wingspan of Plane A. What is the wingspan of Plane B?
Answer: The wingspan of plane B = 37 × 1/2 = 36.852  inches
Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure 126

Question 2.
Before an airliner can take off, the pilot has to make sure it weighs less than the maximum takeoff weight.
a. Plane A weighs 404,600 pounds and can carry at most 422,000 pounds of fuel. How many pounds can the airliner hold in passengers and cargo?
b. The maximum landing weight of Plane A is 300,000 pounds less than the maximum takeoff weight. Why does an airliner weigh less at the end of a flight than at the beginning?
c. Plane A uses 20 quarts of fuel for each mile it flies. How many gallons of fuel does the plane use during a 3,200-mile flight?

Question 3.
Plane B can hold 544 passengers. Plane A can hold \(\frac{3}{4}\) of passengers that Plane B can hold.
a. How many passengers can Plane A hold?
Answer: Plane A hold 3/4 = 0.75 passengers
Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure 127
b. An airline estimates that each passenger weighs about 200 pounds, including carry-on baggage. How much passenger and carry-on weight does the airline estimate for Plane B?
Answer: 408 passenger and carry on weight does the airline estimate for plane B

Convert and Display Units of Measure Activity

Directions:

  1. Players take turns.
  2. On your turn, place a counter on a yellow hexagon.
  3. Solve for the missing measurement and cover the answer with another counter. If you surround a monster, then put a counter on the monster. If you do not surround a monster, then your turn is over.
  4. Continue playing until all measurements are covered.
  5. The player who captures the most monsters wins!

Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure 128

Convert and Display Units of Measure Chapter Practice

11.1 Length in Metric Units

Convert the length.

Question 1.
4 cm = __ mm
Answer: 4 cm = 40 mm

Explanation:
Convert from centimeter to millimeter
1 cm = 10 mm
4 cm = 4 × 10 mm = 40 mm
multiply the cm value by 10

Question 2.
81 m = _8100__ cm
Answer: 81 m = 8100 cm

Explanation:
Convert from meter to centimeter.
1 m = 100 cm
multiply the m value by 100
81 m = 81 × 100 cm = 8100 cm

Question 3.
0.56 km = _56000_ cm
Answer: 0.56 km = 56000 cm

Explanation:
Convert from kilometer to centimeter.
Multiply the km value by 100000

Question 4.
9 mm = 0.009__ m
Answer: 9 mm = 0.009 m
Explanation:-
Convert millimeter to meter.
divide the mm value by 1000

Compare.

Question 5.
Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure 129
Answer:- 73 m = 0.073 kilometer
Explanation:- divide the m value by 1000
Answer:- 7.3 km = 7300 m
Explanation:- multiply the km value by 1000

Question 6.
Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure 130
Answer:
0.6 cm = 0.006 m
divide the cm value by 100
0.06 m = 6 cm
multiply the m value by 100

Question 7.
Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure 131
Answer:
2mm = 0.2 cm
divide the mm value by 10
0.2 cm = 2mm
multiply the cm value by 10

11.2 Mass and Capacity in Metric Units

Convert the mass.

Question 8.
3 kg = _3000__ g
Answer:
3 kg = 3000 g
Explanation:
Convert from kg to gram
1 kg = 1000 grams
multiply the kg value by 1000
3 kg = 3 × 1000 gram = 3000 gram

Question 9.
0.006g = _6__ mg
Answer: 0.006 g = 6 mg

Explanation:
Convert from grams to milligrams
multiply the g value by 1000

Question 10.
70 g = _0.07_ kg
Answer: 70 g = 0.07 kg

Explanation:
Convert from grams to kilograms
divide the g value by1000

Question 11.
29,000 mg = _0.029_ kg
Answer: 29,000 mg = 0.029 kg

Explanation:
Convert from milligrams to kilograms
divide the mg value by 1e + 6
29,000 mg = 0.029 kg

Convert the capacity.

Question 12.
400 mL = _0.4_ L
Answer: 400 mL = 0.4 L

Explanation:
Convert from milliliters to liters
divide the mL value by 1000

Question 13.
10 L = 10000 mL
Answer: 10 L = 10000 mL

Explanation:
Convert from liters to milliliters
1 L = 1000 ml
10 L = 10 × 1000 = 10000 mL
multiply the L value by 1000

Question 14.
7 mL =0.007 L
Answer: 7 mL = 0.007 L

Explanation:
Convert from milliliters to liters
divide the mL value by 1000
7 mL = 0.007 L

Question 15.
0.65 L = 650mL
Answer: 0.65 L = 650 mL

Explanation:
Convert from liters to milliliters
1 L = 1000 mL
multiply the L value by 1000
0.65 L = 0.65 × 1000 = 650 mL
So, 0.65 L = 650 mL

11.3 Length in Customary Units

Convert the length.

Question 16.
2 mi = ___ yd
Answer: 2 mi = 3520 yards

Explanation:
Convert from miles to yards
1 mi = 1760 yards
multiply the mi value by 1760
2 mi = 2 × 1760 yards = 3520 yards

Question 17.
14\(\frac{2}{3}\) yd = ___ ft
Answer: 14 × 2/3 yd = 28 ft

Question 18.
103 in. = __ ft __ in.
Answer: 103 in = 8 ft 7 in

Explanation:
Convert from inches from feet.
divide the 103 in value by 12

Question 19.
2,340 in. = yd
Answer: 2,340 in = 65 yd

Explanation:
Convert from inches to yards
divide the 2,340 in value by 36

Compare.

Question 20.
Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure 132
Answer: 5 × 2/3 yd = 10 ft
17 ft = 5.667 yd

Explanation:
Convert yards to feet.
divide the 17 ft value by 3

Question 21.
Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure 133
Answer: 67 in = 5 feet 7 inches

Explanation:
divide the in value by 12
5 ft 10 in = 70 in
multiply the 5 ft 10 in value by 12

Question 22.
Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure 134
Answer:
16 mi = 84480 ft
multiply the mi value by 5280
84,000 ft = 15.909 mi
divide the ft value by 5280

Weight in Customary Units

Convert the weight.

Question 23.
Big Ideas Math Solutions Grade 5 Chapter 11 Convert and Display Units of Measure 135
Answer: 4/2 T = 2 (By solving 4/2 we get 2)
so we take 4/2 as 2
1 T = 2000 lb
2 T = 4000 lb

Question 24.
100,000 lb = ___ T
Answer: 100,000 lb = 45.359237 T

Explanation:
100,000 lb × 0.00045359237 = 45.359237 T

Convert the weight.

Question 25.
217 oz = __ lb __ oz
Answer: 217 oz = 13 lb 9 oz

Question 26.
956 oz = __ lb
Answer:  956 oz = 59 lb

Compare.

Question 27.
Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure 136
Answer: 5×1/4 T = 2755 lb
15,000 lb = 6.696 T

Question 28.
Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure 137
Answer: 258 oz = 16.125 lb
divide the oz value by 16
17 lb 12 oz = 284 oz
multiply the lb oz value by 16

Question 29.
Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure 138
Answer: 192,000 oz = 6 T
7 T = 250,880 oz

Question 30.
Number Sense
Which measurements are equivalent to 52 ounces?
Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure 139
Answer: 3 lb 4 oz measurement is equivalent to 52 ounces.

11.5 Capacity in Customary Units

Convert the capacity.

Question 31.
18 qt = __ pt
Answer: 18 qt = 29.9762706 pt

Explanation:
1qt equals to 1.6653484 pt
1.6653484 × 18pt = 29.9762706 pt

Question 32.
Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure 140
Answer: 24 fl oz

Explanation:
4 × 3/4c , by solving this we get 12/4c=3c
from formula= 1c = 8 floz
3c = 8 fl oz × 3c = 24 floz

Question 33.
72 pt = __ gal
Answer: 72 pt = 9 gal

Explanation:
1 pt = 0.125 gal
72 pt = 0.125 × 72 = 9 gal

Question 34.
81 qt = __ gal
Answer: 81 qt = 20.25 gal

Explanation:
1 qt = 0.25 gallons
81 qt = 81 × 0.25 = 20.25 gal

Compare.

Question 35.
Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure 140.1
Answer:
5/4 gal = 5 US qt
multiply the gal value by 4
21 qt = 5.25 US gal
divide the qt value by 4

Question 36.
Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure 141
Answer:
Convert from pints to cups
7/2 pt = 7 c
9 c > 7 c
3 1/2 pt < 9 c

Question 37.
Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure 142
Answer:
Convert from quart to cups.
1 quart = 4 cups
4 qt = 16 c
4 qt < 20 c

Question 38.
Modeling Real Life
You have 2\(\frac{1}{4}\) gallons of apple juice. How many pints of apple juice do you have?
Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure 143
Answer: Given 2 × 1/4 (gallons of apple juice)
By solving 2 × 1/4 we get 1/2=>0.5 gallons
so, we have 4 pints of apple juice

Explanation:
we have to find out pints of apple juice
0.5 gallons is equal to 4 pints
from the formula multiply the gallon value (i.e., 0.5 with 8 = 0.5 × 8 = 4 pints)
11.6 Make and Interpret Line Plots

Question 39.
The table shows the amounts of clay made by 10 students. Make a line plot to display the data.
Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure 144
How many students made more than \(\frac{3}{4}\) cup of clay?
Answer:  3/4 = 0.75
only one student ( 7/8 )made more than 3/4 cup of clay ( i.e., 7/8 = 0.875 )

What is the most common amount of clay made?
Answer: The most common amount of clay made is 3/4

11.7 Problem Solving: Measurement

Question 40.
A recipe calls for 2\(\frac{3}{4}\) cups of fava beans. You have 1\(\frac{1}{4}\)– pint can of fava beans and \(\frac{1}{2}\) cup of cooked fava beans. Do you have enough fava beans for the recipe?
Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure 145
Answer: Yes, you have enough fava beans for the recipe

Explanation:
Given that a recipe calls for 2 × 3/4 = 0.5 cups of fava beans
you have 1 × 1/4 pints = 0.5 cups of fava beans ( convert 1/4 pints to cups )
and 1/2 = 0.5 cups of cooked fava beans
So, the recipe calls 0.5 cups of fava beans are equal to you have 0.5 cups of fava beans.

Convert and Display Units of Measure Practice 1-11

Question 1.
Your friend estimates that a bookcase is 2\(\frac{1}{2}\) feet wide. The actual width is \(\frac{2}{3}\) foot longer. What is the width of the bookcase?
Answer: 2 × 1/2 = 1 estimation feet
2/3 = 0.667 actual width feet
1 – 0.667 = 0.34

Question 2.
What is the product of 845 and 237?
Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure 147
Answer: Option C
product (Multiply) the 845 and 237 = 200,265

Explanation:  845 × 237 = 200,265

Question 3.
How many milliliters are equal to 0.6 liter?
Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure 148
Answer:-  Option D  (600 mL)

Explanation: 1 liter = 1000 mL
0.6 liter = 0.6L × 1000mL
= 600mL

Question 4.
Which are equivalent to Big Ideas Math Answers 5th Grade Chapter 11 Convert and Display Units of Measure 149?
Big Ideas Math Answers 5th Grade Chapter 11 Convert and Display Units of Measure 149.1
Answer:  6 × 3/10  is equivalent to 18 × 1/10

Explanation:
6 × 3/10 = multiply 6 with 3 we  get 18, denominator remains same
so the answer is 18 × 1/10.

Question 5.
To find 34 + (16 + 23), your friend adds 34 and 16. Then she adds 23 to the sum. Which property did she use?
Big Ideas Math Answers 5th Grade Chapter 11 Convert and Display Units of Measure 150
Answer:-  Option B
She used the Associative property of addition.

Question 6.
An Eastern Hognose Snake is 2\(\frac{1}{2}\) feet long. It grows another foot. What is the new length of the snake in inches?
Big Ideas Math Answers 5th Grade Chapter 11 Convert and Display Units of Measure 151
Answer: 2 × 1/2 = 1 feet

Explanation:
It grows another foot = 1
so, 1 + 1 = 2 feet
convert 2 feet to inches
2 feet = 24 inches
So, the new length of the snake is 24 inches.

Question 7.
What common factor should you divide the numerator and denominator of \(\frac{16}{24}\) by so that it is in the simplest form?
Big Ideas Math Answers 5th Grade Chapter 11 Convert and Display Units of Measure 152
Answer: 8 is the common factor that divides the numerator and denominator of 16/24 in simplest form

Explanation:
The simplest form is nothing but if the top and bottom(i.e., numerator and denominator) have no common factors other than 1.
16/24 = solve it by 8
By solving we get 2/3.

Question 8.
A salesperson at a fabric store has 30 yards of fabric. He puts the same number of yards of fabric on each of 4 rolls for a display. How many yards of fabric does the salesperson put on each roll?
Big Ideas Math Answers 5th Grade Chapter 11 Convert and Display Units of Measure 153
Answer:
Option B
2/15 yard

Explanation:
Given 30 yards of fabric
rolls= 4
rolls/yards = 4/30 = 2/15yard

Question 9.
Descartes estimates 96.3 × 42 by rounding each number to the nearest ten. What is Descartes’s estimate?
Big Ideas Math Answers 5th Grade Chapter 11 Convert and Display Units of Measure 154
Answer: Option D (4,000)

Explanation: Here we have to multiply the given number 96.3 × 42
96.3 ~ 100 (96.3 is the nearest value to 100)
42~40 (42 is the nearest value to 40)
so, multiply both the values 100 × 40 = 4000

Question 10.
The fifth-grade classes are making a mural to hang in the front hallway of the school.
Big Ideas Math Answers 5th Grade Chapter 11 Convert and Display Units of Measure 155
Part A Each class creates a square for the mural that has side lengths of \(\frac{1}{2}\) meter. What is the area of each square?

Answer: area of square =s×s
1/2 × 1/2 = 0.5 × 0.5 = 0.25 meters
Part B
There are 12 classes. What is the area of the entire mural? Explain.
12 × 0.25 = 3 meters

Question 11.
Which expressions have a quotient of 4.6?
Big Ideas Math Answers 5th Grade Chapter 11 Convert and Display Units of Measure 156
Answer: All expressions have a quotient of 4.6 except 15.64÷34 does not have a quotient of 4.6

Explanation: we can find out the quotient value by this method
quotient = Dividend ÷ divisor  (i.e., from the above question we are taking one value                                                                                      124.2 ÷ 27 = 4.6)

Question 12.
What is the quotient of 5 and \(\frac{1}{8}\) ?
Big Ideas Math Answers 5th Grade Chapter 11 Convert and Display Units of Measure 157
Answer:- The quotient of 5 and 1/8 = 40
Explanation:- Divide the 5 and 1/8

Question 13.
You need thirty 5-foot pieces of string for a project. A store sells string by the yard. How many yards of string will you need to buy?
Answer:- 11.655

Explanation: Given foot pieces = 35
1 foot = 0.333 yard
1 yard = 3 foot or 3 feet
we have to find yards of string.
foot pieces × yards = 35 × 0.333
= 11.655

Big Ideas Math Answers 5th Grade Chapter 11 Convert and Display Units of Measure 158

Question 14.
In which equations does k = \(\frac{3}{4}\) ?
Big Ideas Math Answers 5th Grade Chapter 11 Convert and Display Units of Measure 159
Answer:  Option D
3/6 × 3/2 =k

Explanation:
we have equated k value as 3/4
so, by solving 3/6 × 3/2 we get 3/4

Question 15.
Newton brings 3 bags of popcorn that are all the same size to a club. There are 12 people at the club. Each person eats the same amount of popcorn and all of the popcorn is eaten. What fraction of a bag of popcorn does each person eat?
Big Ideas Math Answers 5th Grade Chapter 11 Convert and Display Units of Measure 160
Big Ideas Math Answers 5th Grade Chapter 11 Convert and Display Units of Measure 161
Answer: Bags = 3 ,  People = 12
so, divide 3/12 = 1/4
Option A is the answer

Question 16.
Evaluate
Big Ideas Math Answers 5th Grade Chapter 11 Convert and Display Units of Measure 162
Answer:
Convert the decimal values to fractions
4.5 = 9/2
13.68 = 342/25
13.70 = 137/10
15.70 = 157/10

Question 17.
What is the sum of \(\frac{5}{6}\) and \(\frac{1}{4}\) ? Big Ideas Math Answers 5th Grade Chapter 11 Convert and Display Units of Measure 163
Answer: Option D
5/6 + 1/4 = 13/12

Question 18.
What is 40,071 written in word form?
A. four thousand, seventy-one
B. four hundred, seventy-one
C. forty thousand, seventy-one
D. forty thousand, seven hundred ten
Answer: Option C

Forty thousand, seventy-one

Convert and Display Units of Measure STEAM Performance Task

Sound is created from vibrations in the air called sound waves. In music, when you hear different pitches, it is because the sound waves are traveling at different speeds. The frequency of a pitch measures the number of sound waves per second. Higher pitches have higher frequencies, and lower pitches have lower frequencies. Frequencies are measured in Hertz.
Big Ideas Math Answers 5th Grade Chapter 11 Convert and Display Units of Measure 164

Question 1.
A4 is the musical note commonly used to tune instruments. The frequency of A4 is 440 Hertz, because the sound vibrates 440 times per second.
a. The frequency of A3 is \(\frac{1}{2}\) the frequency of A4. The frequency of A2 is \(\frac{1}{2}\) the frequency of A3. What is the frequency of A2?
Answer: frequency of A2 = 110
b. Is the pitch of A2 higher or lower than the pitch of A4? Explain.
c. How can you use the frequency of A4 to find the frequency of A5? Explain.
d. The frequency of B4 is 493.88 Hertz. What is the frequency of B3?
e. A computer software program can correct the frequency of a sound so it has perfect pitch. A violin plays a note that has a frequency of 255.1 Hertz. Explain how to change the frequency so it has the pitch of B3.

Question 2.
Use the Internet or some other resource to learn about how audio processors can help to correct a singer’s pitch, or to alter the way a song sounds. Write one interesting thing you learn.
Answer:
Auto-Tune is an audio processor introduced in 1997 by and registered trademark of Antares Audio Technologies, which uses a proprietary device to measure and alter pitch in vocal and instrumental music recording and performances. It was originally intended to correct off-key inaccuracies, allowing vocal tracks to be perfectly tuned despite originally being slightly off-pitch.
Pitch correction is an electronic effects unit or audio software that changes the highness and lowness in pitch of an audio signal so that all pitches will be notes from the equally tempered system(i.e., like the pitches on a piano). Pitch correction first detects the pitch of an audio signal (using a live pitch detection algorithm), then calculates the desired change and modifies the audio signal accordingly. The widest use of pitch corrector devices is in western popular music on vocal lines.

Question 3.
You borrow a guitar to learn how to play. Use the Guitar table to decide which guitar you should borrow.
Big Ideas Math Answers 5th Grade Chapter 11 Convert and Display Units of Measure 165
a. Based on your height, you need a guitar that is close to 1 yard long. Which guitar is closer?
Answer: 1 yard = 36 inches
Guitar A is 37 inches
So, Guitar A is closer
b. You also need a guitar that is close to 8 pounds. Which guitar do you think you should borrow? Explain.
Answer: Guitar B you should borrow
176 ounces = 11 pounds which is closer to 8 pounds .
c. Guitar B is called a full-size guitar and Guitar A is called a \(\frac{7}{8}\)-size guitar. Is the length of Guitar A \(\frac{7}{8}\) the length of Guitar B? Explain
Answer: From the table Length of Guitar B = 40 inches
Given guitar A = 7/8 = 10.5 inches
No, the length of Guitar A is not equal to Guitar B
d. The scale length on a guitar affects the pitch. To find the scale length of a guitar, multiply the distance between the nut and the 12th fret by 2. On your guitar, that distance is 12\(\frac{3}{4}\) inches. What is the scale length of your guitar?
Answer: 9 × 12 × 2 = 216
The scale of the length of the guitar is 216
Big Ideas Math Answers 5th Grade Chapter 11 Convert and Display Units of Measure 166
e. The strings on your guitar are \(\frac{3}{8}\) inch longer than the scale length to allow you to tune the strings to correct pitch. What are the string lengths on your guitar?
Answer:- The string length on your guitar = 3/8
3/8 = 4.5 inches
f. When you tune a string, you adjust it tighter to make the pitch higher, or looser to make pitch lower. You use a tuning instrument to help you string has a tune your guitar. It says that your A4 string has a frequency of 436.2 Hertz. How should you adjust the string to get the pitch in tune?
Answer:- we have to adjust the string to get the pitch in tune = 440 Hertz
its  wavelength (cm) = 78.41

Conclusion:

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Big Ideas Math Answers Grade 8 | Big Ideas Math Book 8th Grade Answer Key

The Big Ideas Math Modeling Real Life helps students in learning and engaging innovative programs. Students of Grade 8 can cover all the middle school content with the help of Big Ideas Math Grade 8 Answers. BIM Grade 8 Answer Key is prepared by mathematical experts. Hence go through the Big Ideas Math Answers 8th Grade Chapterwise and finish your homework or assignments. The solutions for all the chapters are provided in pdf format. Thus Download BIM Textbook Grade Answer Key Pdf and start your preparation.

Big Ideas Math Book 8th Grade Answer Key | Big Ideas Math Answers 8th Grade Solutions Pdf

The solutions for Bigideas Math Grade are prepared from the Common Core 2019 Student edition. Students who feel difficulty in solve the problems can quickly understand the concepts with the help of Big Ideas Math 8th Grade Answer Key. Keep these solutions pdf aside and kickstart your preparation for the exams. This will enhance your performance in chapter tests, practice tests, assessments, and assignments. Go through the table of contents shown in the below section.

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Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume

go-math-grade-6-chapter-11-surface-area-and-volume-answer-key

Go Math solutions for Class 6 Maths Provide detailed explanations for all the questions provided in the HMH Go Math. We provide topic wise Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume to help the students clear their doubts by offering an understanding of concepts in depth. You can practice different types of questions in Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume. 

Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume

Download HMH Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume and learn offline. With the help of these Go Math 6th Grade Solution Key Chapter 11 Surface Area and Volume, you can score good marks in the exams. The topics include 3-D figures and Nets, Explore Surface Area Using Nets, Surface Area of Prisms, and so on. This will also help to build a strong foundation of all these concepts for secondary level classes.

Lesson 1: Three-Dimensional Figures and Nets

Lesson 2: Investigate • Explore Surface Area Using Nets

Lesson 3: Algebra • Surface Area of Prisms

Lesson 4: Algebra • Surface Area of Pyramids

 Mid-Chapter Checkpoint

Lesson 5: Investigate • Fractions and Volume

Lesson 6: Algebra • Volume of Rectangular Prisms

Lesson 7: Problem Solving • Geometric Measurements

Chapter 11 Review/Test

Share and Show – Page No. 599

Identify and draw a net for the solid figure.

Question 1.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 1

Answer: The base Square or Rectangle, and lateral faces are Triangle and the figure is a Square pyramid or Rectangular pyramid.

Explanation:
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume

Question 2.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 2
Answer: Cube or Rectangular prism.

Explanation: The base is a square or rectangle and lateral faces are squares are rectangle. The figure is a Cube or Rectangular prism.

Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume

Identify and sketch the solid figure that could be formed by the net.

Question 3.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 3

Answer: Triangular pyramid.

Explanation: The net has four triangles, so it is a triangular pyramid.

Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume

Question 4.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 4
Answer: Cube

Explanation: The net has six squares.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume

On Your Own

Identify and draw a net for the solid figure.

Question 5.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 5

Answer: Triangular prism.

Explanation: The base is a rectangle and the lateral faces are triangle and rectangles, so it is a triangular prism.

Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume

Question 6.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 6

Answer:  Rectangular Prism.

Explanation: The base is a rectangle and the lateral faces are squares and rectangles. And it is a Rectangular prism.

Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume

Problem Solving + Applications – Page No. 600

Solve.

Question 7.
The lateral faces and bases of crystals of the mineral galena are congruent squares. Identify the shape of a galena crystal.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 7
Answer: Cube

Explanation: The shape of the galena is Cube.

Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume

Question 8.
Rhianon draws the net below and labels each square. Can Rhianon fold her net into a cube that has letters A through G on its faces? Explain.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 8

Answer: No, she cannot fold her net into a cube. Rhianon’s net has seven squares but there are only six squares in a net of a cube.

Question 9.
Describe A diamond crystal is shown. Describe the figure in terms of the solid figures you have seen in this lesson.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 9

Answer: We can see that Diamond crystal consists of two square pyramids with congruent bases and the pyramids are reversed and placed base to base.

Question 10.
Sasha makes a triangular prism from paper.
The bases are _____.
The lateral faces are _____.

Answer:
The bases are Triangle
The lateral faces are Rectangle

Three-Dimensional Figures and Nets – Page No. 601

Identify and draw a net for the solid figure.

Question 1.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 10

Answer: Rectangular Prism

Explanation:
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume

Question 2.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 11

Answer: Cube, Rectangular prism

Explanation:
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume

Question 3.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 12

Answer: Square Pyramid

Explanation:
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume

Question 4.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 13

Answer: Triangular Prism

Explanation:
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume

Problem Solving

Question 5.
Hobie’s Candies are sold in triangular-pyramidshaped boxes. How many triangles are needed to make one box?

Answer: 4

Explanation: As triangled pyramids have four faces.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume

Question 6.
Nina used plastic rectangles to make 6 rectangular prisms. How many rectangles did she use?

Answer: 36

Explanation:
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume

Question 7.
Describe how you could draw more than one net to represent the same three-dimensional figure. Give examples.

Answer:

Explanation:

Lesson Check – Page No. 602

Question 1.
How many vertices does a square pyramid have?

Answer: 5

Explanation:
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume

Question 2.
Each box of Fred’s Fudge is constructed from 2 triangles and 3 rectangles. What is the shape of each box?

Answer: Triangular Prism

Explanation:
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume

Spiral Review

Question 3.
Bryan jogged the same distance each day for 7 days. He ran a total of 22.4 miles. The equation 7d = 22.4 can be used to find the distance d in miles he jogged each day. How far did Bryan jog each day?

Answer: 3.2 miles

Explanation: As given equation 7d= 22.4,
d= 22.4÷7
= 3.2 miles.

Question 4.
A hot-air balloon is at an altitude of 240 feet. The balloon descends 30 feet per minute. What equation gives the altitude y, in feet, of the hot-air balloon after x minutes?

Answer: Y= 240- 30X.

Explanation: Given altitude Y, and the ballon was descended 30 feet per minute. So the equation is Y= 240- 30X.

Question 5.
A regular heptagon has sides measuring 26 mm and is divided into 7 congruent triangles. Each triangle has a height of 27 mm. What is the area of the heptagon?

Answer: 351 mm2

Explanation: Area of heptagon= 1/2 b×h
= 1/2 (26)×(27)
= 13×27
= 351 mm2

Question 6.
Alexis draws quadrilateral STUV with vertices S(1, 3), T(2, 2), U(2, –3), and V(1, –2). What name best classifies the quadrilateral?

Answer: Parallelogram

Explanation:
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume

Share and Show – Page No. 605

Use the net to find the surface area of the prism.

Question 1.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 14

Answer:

Explanation: First we must find the area of each face
A= 4×3= 12
B= 4×3= 12
C= 5×4= 20
D= 5×4= 20
E= 5×3= 15
F= 5×3= 15
So, the surface area is 12+12+20+20+15+15= 94 cm2

Find the surface area of the rectangular prism.

Question 2.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 15

Answer: 222 cm2

Explanation: Area of a rectangular prism is 2(wl+hl+hw) = 2(7×9+ 3×9+ 3×7)
= 2(63+27+21)
= 2(111)
= 222 cm2

Question 3.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 16

Answer:

Explanation: Area of a rectangular prism is 2(wl+hl+hw) = 2(10×10+ 10×10+ 10×10)
= 2(100+100+100)
= 2(300)
= 600 cm2

Question 4.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 17

Answer: 350 cm2

Explanation: Area of a rectangular prism is 2(wl+hl+hw) = 2(15×5+ 5×5+ 15×5)
= 2(75+25+75)
= 2(175)
= 350 cm2

Problem Solving + Applications

Question 5.
A cereal box is shaped like a rectangular prism. The box is 20 cm long by 5 cm wide by 30 cm high. What is the surface area of the cereal box?

Answer: 1700 cm2

Explanation: The length of the box is 20 cm, the wide is 5 cm and the height is 30 cm. So surface area of the cereal box is 2(wl+hl+hw)= 2(20×5+30×20+30×5)
= 2(100+600+150)
= 2(850)
= 1700 cm2

Question 6.
Darren is painting a wooden block as part of his art project. The block is a rectangular prism that is 12 cm long by 9 cm wide by 5 cm high. Describe the rectangles that make up the net for the prism.

Answer:

Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume

Question 7.
In Exercise 6, what is the surface area, in square meters, that Darren has to paint?

Answer: 416 cm2

Explanation: Surface area = 2(wl+hl+hw)
= 2(9×12+5×12+ 5×9)
= 2(108+60+45)
= 2(213)
= 416 cm2

What’s the Error? – Page No. 606

Question 8.
Emilio is designing the packaging for a new MP3 player. The box for the MP3 player is 5 cm by 3 cm by 2 cm. Emilio needs to find the surface area of the box.
Look at how Emilio solved the problem. Find his error.
STEP 1: Draw a net.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 18
STEP 2: Find the areas of all the faces and add them.
Face A: 3 × 2 = 6 cm2.
Face B: 3 × 5 = 15 cm2.
Face C: 3 × 2 = 6 cm2.
Face D: 3 × 5 = 15 cm2.
Face E: 3 × 5 = 15 cm2.
Face F: 3 × 5 = 15 cm2.
The surface area is 6 + 15 + 6 + 15 + 15 + 15 = 72 cm2.
Correct the error. Find the surface area of the prism.

Answer: Emilio drew the net incorrectly Face D and F should have been 2 cm by 5 cm, not 3 cm by 5 cm

Explanation:
Face A: 3×2= 6 cm2
Face B: 3×5= 15 cm2
Face C: 3×2= 6 cm2
Face D: 2×5= 10 cm2
Face E: 3×5= 15 cm2
Face F: 2×5= 10 cm2
So, the surface area of the prism area is 6+15+6+10+15+10= 62 cm2.

Question 9.
For numbers 9a–9d, select True or False for each statement.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 19
9a. The area of face A is 10 cm2.
9b. The area of face B is 10 cm2.
9c. The area of face C is 40 cm2.
9d. The surface area of the prism is 66 cm2.

9a. The area of face A is 10 cm2.

Answer: True

Explanation: The area of face A is 2×5= 10 cm2.

9b. The area of face B is 10 cm2.

Answer: False

Explanation: The area of face B is 2×8= 16  cm2.

9c. The area of face C is 40 cm2.

Answer: The area of face C is 8×5= 40 cm2.

9d. The surface area of the prism is 66 cm2.

Answer: 160 cm2.

Explanation: The surface area of the prism is
= 2×10+2×10+2×40
= 20+20+80
= 160 cm2.

Explore Surface Area Using Nets – Page No. 607

Use the net to find the surface area of the rectangular prism.

Question 1.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 20
_______ square units

Answer: 52 square units.

Explanation:
The area of face A is 6 squares.
The area of face B is 8 squares.
The area of face C is 6 squares.
The area of face D is 12 squares.
The area of face E is 8 squares.
The area of face F is 12 squares.
The surface area is 6+8+6+12+8+12= 52 square units.

Question 2.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 21
_______ square units

Answer: 112 square units.

Explanation:
The area of face A is 16 squares.
The area of face B is 8 squares.
The area of face C is 32 squares.
The area of face D is 16 squares.
The area of face E is 32 squares.
The area of face F is 8 squares.
The surface area is 112 square units.

Question 3.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 22

Answer: 102 mm2

Explanation: Area= 2(wl+hl+hw)
= 2(3×7+3×7+3×3)
= 2(21+21+9)
= 2(51)
= 102 mm2

Question 4.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 23
_______ in.2

Answer: 58 in.2

Explanation: Area= 2(wl+hl+hw)
= 2(5×1+ 4×1+ 4×5)
= 2(5+4+20)
= 2(29)
= 58 in.2

Question 5.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 24
_______ ft2

Answer: 77 ft2

Explanation: Area= 2(wl+hl+hw)
= 2(6.5×2+3×2+3×6.5)
= 2(13+6+19.5)
= 2(38.5)
= 77 ft2

Problem Solving

Question 6.
Jeremiah is covering a cereal box with fabric for a school project. If the box is 6 inches long by 2 inches wide by 14 inches high, how much surface area does Jeremiah have to cover?
_______ in.2

Answer: 248 in.2

Explanation: Surface area of a cereal box is 2(wl+hl+hw)
= 2(2×6+14×6+14×2)
= 2(12+84+28)
= 2(124)
= 248 in.2
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume

Question 7.
Tia is making a case for her calculator. It is a rectangular prism that will be 3.5 inches long by 1 inch wide by 10 inches high. How much material (surface area) will she need to make the case?
_______ in.2

Answer: 97 in.2

Explanation: Surface Area= 2(wl+hl+hw)
= 2(1×3.5+ 10×3.5+ 10×1)
= 2(3.5+35+10)
= 2(48.5)
= 97 in.2

Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume

Question 8.
Explain in your own words how to find the surface area of a rectangular prism.

Answer: To find the surface area we must know the width, length, and height of the prism and then we can apply the formula which is
Surface area= 2(width ×length)+ 2(length×height)+ 2(height×width)
= 2(width ×length+ length×height+ 2(height×width)

Lesson Check – Page No. 608

Question 1.
Gabriela drew a net of a rectangular prism on centimeter grid paper. If the prism is 7 cm long by 10 cm wide by 8 cm high, how many grid squares does the net cover?
_______ cm2

Answer: 412 cm2.

Explanation: Surface area is 2(wl+hl+hw)
= 2(10×7+8×7+8×10)
= 2(70+56+80)
= 2(206)
= 412 cm2.

Question 2.
Ben bought a cell phone that came in a box shaped like a rectangular prism. The box is 5 inches long by 3 inches wide by 2 inches high. What is the surface area of the box?
_______ in.2

Answer: 62 in.2

Explanation: Surface area is 2(wl+hl+hw)
= 2(3×5+2×5+2×3)
= 2(15+10+6)
= 2(31)
= 62 in.2

Spiral Review

Question 3.
Katrin wrote the inequality x + 56 < 533. What is the solution of the inequality?

Answer: X<477.

Explanation: X+56<533
= X<533-56
= X<477.

Question 4.
The table shows the number of mixed CDs y that Jason makes in x hours.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 25
Which equation describes the pattern in the table?

Answer: y= 5x

Explanation:
y/x = 10/2= 15/4= 3
y= 5x
The pattern is y is x multipled by 5.

Question 5.
A square measuring 9 inches by 9 inches is cut from a corner of a square measuring 15 inches by 15 inches. What is the area of the L-shaped figure that is formed?
_______ in.2

Answer: 144 in.2

Explanation: The area of a square A= a2, so we will find the area of each square.
Area= 92
= 9×9
= 81 in.2
And the area of another square is
A= 152
= 15×15
= 225 in.2
So the area of L shaped figure is 225-81= 144 in.2

Question 6.
Boxes of Clancy’s Energy Bars are rectangular prisms. How many lateral faces does each box have?

Answer: 4

Explanation: As Lateral faces are not included in the bases, so rectangular prism has 4.

Share and Show – Page No. 611

Use a net to find the surface area.

Question 1.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 26
_______ ft2

Answer: 24 ft2

Explanation: The area of each face is 2 ft×2 ft= 4 ft and the number of faces is 6, so surface area is 6×4= 24 ft2

Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume

Question 2.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 27

Answer: 432 cm2

Explanation:
The area of face A is 16×6= 96 cm2
The area of face B is 16×8= 128 cm2
The area of face C and D is 1/2 × 6×8= 24 cm2
The area of face E is 16×10= 160 cm2
The surface 96+128+2×24+160= 432 cm2

Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume

Question 3.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 28
_______ in.2

Answer: 155.5 in.2

Explanation:

Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume
The area of face A and E is  8 ½ × 3½
= 17/2 × 7/2
= 119/4
= 29.75 in.2
The area of face B and F is 8 ½×4
= 17 ½ × 4
= 34 in.2
The area of face C and D is 3 ½×4
7/2 × 4= 14 in.2
The surface area is 2×29.75+2×34+2×14
= 59.5+68+28
= 155.5 in.2

On Your Own

Use a net to find the surface area.

Question 4.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 29
_______ m2

Answer:

Explanation:
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume
The area of face A and E is 8×3= 24 m2
The area of face B and F is 8×5= 40 m2
The area of face C and D is 3×5= 15 m2
The surface area is 2×24+2×40+2×15
= 48+80+30
= 158 m2

Question 5.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 30
_______ \(\frac{□}{□}\) in.2

Answer:

Explanation:

Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume

The area of each face is 7 1/2 × 7 1/2
= 15/2 × 15/2
= 225/4 in.2
The no.of faces are 6 and the surface area is 6× 225/4
= 675/4
= 337 1/2 in.2

Question 6.
Attend to Precision Calculate the surface area of the cube in Exercise 5 using the formula S = 6s2. Show your work.

Answer: 337 1/2 in.2

Explanation: As S= s2
= 6(7 1/2)2
= 6(15/2)2
= 6(225/4)
= 675/2
= 337 1/2 in.2

Unlock the Problem – Page No. 612

Question 7.
The Vehicle Assembly Building at Kennedy Space Center is a rectangular prism. It is 218 m long, 158 m wide, and 160 m tall. There are four 139 m tall doors in the building, averaging 29 m in width. What is the building’s outside surface area when the doors are open?
a. Draw each face of the building, not including the floor.

Answer:

Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume

Question 7.
b. What are the dimensions of the 4 walls?

Answer: The 2 walls measure 218 m ×160 m and 2 walls measure by 158 m×160 m.

Question 7.
c. What are the dimensions of the roof?

Answer: The dimensions of the roof are 218 m×158 m.

Question 7.
d. Find the building’s surface area (not including the floor) when the doors are closed.
_______ m2

Answer: 1,54,764 m2

Explanation:
The area of two walls is 218×160= 34,880 m2
The area of the other two walls is 158×160= 25,280 m2
The area of the roof 158×218= 34,444 m2
The surface area is 2× 34,880+ 2× 25,280+ 34,444
= 69,760+ 50,560+ 34,444
= 1,54,764 m2

Question 7.
e. Find the area of the four doors.
_______ m2

Answer: 16,124 m2

Explanation: Area of a door is 139×29 = 4031 m2
And the area of 4 doors is 4×4031= 16,124 m2

Question 7.
f. Find the building’s surface area (not including the floor) when the doors are open.
_______ m2

Answer: 1,38,640 m2

Explanation: The building’s surface area (not including the floor) when the doors are open is
1,54,764 – 16,124= 1,38,640 m2

Question 8.
A rectangular prism is 1 \(\frac{1}{2}\) ft long, \(\frac{2}{3}\) ft wide, and \(\frac{5}{6}\) ft high. What is the surface area of the prism in square inches?
_______ in.2

Answer: 808 in.2

Explanation: The area of two faces is 1 1/2× 5/6
= 3/2 × 5/6
= 5/4 cm2
The area of two faces is 2/3 × 5/6
= 5/9 ft2
The area of two faces is 1 1/2× 2/3
= 3/2 × 2/3
= 1 ft2
The surface area of the prism is 2(wl+hl+hw)
= 2(5/4 + 5/9 + 1)
= 2( 1.25+0.55+1)
= 2.5+1.1+2
= 5.61 ft2
As 1 square foot = 144 square inches
so 5.61×144 = 807.84
= 808 in.2

Question 9.
A gift box is a rectangular prism. The box measures 8 inches by 10 inches by 3 inches. What is its surface area?
_______ in.2

Answer: 268 in.2

Explanation:
The area of face A and Face E is 8×10= 80 in.2
The area of face B and Face F is 8×3= 24 in.2
The area of face C and Face D is 10×3= 30 in.2
The surface area is 2×80+2×24+2×30
= 160+48+60
= 268 in.2

Surface Area of Prisms – Page No. 613

Use a net to find the surface area.

Question 1.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 31
_______ cm2

Answer: 104 cm2

Explanation: Surface area= 2(wl+hl+hw)
= 2(6×5+2×5+2×6)
= 2(30+10+12)
= 2(52)
= 104 cm2

Question 2.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 32
_______ in.2

Answer: 118 in.2

Explanation: Surface area= 2(wl+hl+hw)
= 2(3.5×4+6×4+6×3.5)
= 2(59)
= 118 in.2

Question 3.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 33
_______ ft2

Answer: 486 ft2

Explanation: Surface area= 2(wl+hl+hw)
= 2(9×9+9×9+9×9)
= 2(81+81+81)
= 2(243)
= 486 ft2

Question 4.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 34
_______ cm2

Answer: 336 cm2.

Explanation: Area = 1/2 bh
= 1/2 (6)(8)
= 3×8
= 24.
As there are 2 triangles, so 2×24= 48.
Surface Area= (wl+hl+hw)
= (6×12+8×12+12×10)
= 228
Total Surface area = 228+48
= 336 cm2

Problem Solving

Question 5.
A shoe box measures 15 in. by 7 in. by 4 \(\frac{1}{2}\) in. What is the surface area of the box?
_______ in.2

Answer: 408 in.2

Explanation:
The area of two faces is 15×7= 105 in.2
The area of two faces is 15× 4 1/2
= 15 × 9/2
= 15 × 4.5
= 67.5 in.2
The area of two faces is 7× 4 1/2
= 7× 9/2
= 7× 4.5
= 31.5 in.2
The surface area is 2×105+ 2×67.5+ 2×31.5
= 210+ 135+ 63
= 408 in.2

Question 6.
Vivian is working with a styrofoam cube for art class. The length of one side is 5 inches. How much surface area does Vivian have to work with?
_______ in.2

Answer: 150 in.2

Explanation:
The area of each face is 5×5= 25 in.2
The number of faces that styrofoam cube has is 6
So the surface area is 6×25= 150 in.2

Question 7.
Explain why a two-dimensional net is useful for finding the surface area of a three-dimensional figure.

Answer: Two-dimensional net is useful because by using a two-dimensional net you can calculate the surface area of each face and add them up to find the surface area of the three-dimensional figure.

Lesson Check – Page No. 614

Question 1.
What is the surface area of a cubic box that contains a baseball that has a diameter of 3 inches?
_______ in.2

Answer: 54 in.2

Explanation:
The area of each face is 3×3= 9 in.2
The number of faces for a cubic box is 6 in.2
The surface area of box that contains a baseball is 6×9= 54 in.2

Question 2.
A piece of wood used for construction is 2 inches by 4 inches by 24 inches. What is the surface area of the wood?
_______ in.2

Answer: 304 in.2

Explanation:
The area of two faces is 4×2= 8 in.2
The area of two faces is 2×24= 48 in.2
The area of two faces is 24×4= 96 in.2
So the surface area is 2×8+ 2×48+ 2×96
= 16+96+192
= 304 in.2

Spiral Review

Question 3.
Detergent costs $4 per box. Kendra graphs the equation that gives the cost y of buying x boxes of detergent. What is the equation?

Answer: Y= 4X.

Explanation: The total price Y and the price is equal to 4 × X, and X is the number of boxes that Kendra buys. So the equation is Y=4X.

Question 4.
A trapezoid with bases that measure 8 inches and 11 inches has a height of 3 inches. What is the area of the trapezoid?
_______ in.2

Answer: 28.5 in.2

Explanation:
Area of a trapezoid is 1/2(b1+b2)h
= 1/2(8+11)3
= 1/2(19)3
= 1/2 (57)
= 28.5 in.2

Question 5.
City Park is a right triangle with a base of 40 yd and a height of 25 yd. On a map, the park has a base of 40 in. and a height of 25 in. What is the ratio of the area of the triangle on the map to the area of City Park?

Answer: 1296:1.

Explanation:
Area= 1/2 bh
= 1/2 (40)(25)
= (20)(25)
= 500 yd2
So area of city park is 500 yd2
Area= 1/2 bh
= 1/2 (40)(25)
= (20)(25)
= 500 in2
So area on the map is 500 in
as 1 yd2= 1296 in2
So 500 in2 = 500×1296
= 648,000
So, the ratio of the area of the triangle on the map to the area of City Park is 648,000:500
= 1296:1.

Question 6.
What is the surface area of the prism shown by the net?
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 35
Answer: 72 square units.

Explanation:
The area of two faces is 18 squares
The area of two faces is 6 squares
The area of two faces is 12 squares
So the surface area is 2×18+ 2×6+ 2×12
= 72 square units.

Share and Show – Page No. 617

Question 1.
Use a net to find the surface area of the square pyramid.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 36
_______ cm2

Answer: 105 cm2

Explanation:

Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume
Area of the base 5×5= 25 ,
and area of one face is 1/2 × 5 × 8
= 5× 4
= 20 cm2
The surface area of a pyramid is 25+ 4×20
= 25+80
= 105 cm2

Question 2.
A triangular pyramid has a base with an area of 43 cm2 and lateral faces with bases of 10 cm and heights of 8.6 cm. What is the surface area of the pyramid?
_______ cm2

Answer: 172 cm2

Explanation:
The area of one face is 1/2×10×8.6
= 5×8.6
= 43 cm2
The surface area of the pyramid is 43+3×43
= 43+ 129
= 172 cm2

Question 3.
A square pyramid has a base with a side length of 3 ft and lateral faces with heights of 2 ft. What is the lateral area of the pyramid?
_______ ft2

Answer: 12 ft2

Explanation:
The area of one face is 1/2×3×2= 3 ft2
The lateral area of the pyramid is 4×3= 12 ft2

On Your Own

Use a net to find the surface area of the square pyramid.

Question 4.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 37
_______ ft2

Answer: 208 ft2

Explanation:
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume
The area of the base is 8×8= 64
The area of one face is 1/2 ×8×9
= 36 ft2
The surface area of the pyramid is 64+4×36
= 64+144
= 208 ft2

Question 5.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 38
_______ cm2

Answer: 220 cm2

Explanation:

Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume
The area of base is 10×10= 100
The area of one place is 1/2×10×6
= 10×3
= 30
The surface area of the pyramid is 100+4×30
= 100+120
= 220 cm2

Question 6.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 39
_______ in.2

Answer: 264 in.2

Explanation:

Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume
The area of the base is 8×8= 64
The area of one face is 1/2×8×12.5
= 4×12.5
= 50 in.2
The surface area of the pyramid is 64+ 4×50
= 64+200
= 264 in.2

Question 7.
The Pyramid Arena is located in Memphis, Tennessee. It is in the shape of a square pyramid, and the lateral faces are made almost completely of glass. The base has a side length of about 600 ft and the lateral faces have a height of about 440 ft. What is the total area of the glass in the Pyramid Arena?
_______ ft2

Answer: 5,28,000 ft2

Explanation:
The area of one face is 1/2×600×440= 1,32,000 ft2
The surface of tha lateral faces is 4× 1,32,000= 5,28,000 ft2
So, the total area of the glass in the arena is 5,28,000 ft2

Problem Solving + Applications – Page No. 618

Use the table for 8–9.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 40

Question 8.
The Great Pyramids are located near Cairo, Egypt. They are all square pyramids, and their dimensions are shown in the table. What is the lateral area of the Pyramid of Cheops?
_______ m2

Answer: 82,800 m2

Explanation:
The area of one face is 1/2×230×180
= 230×90
= 20,700 m2
The lateral area of the pyramid of Cheops is 4×20,700= 82,800 m2

Question 9.
What is the difference between the surface areas of the Pyramid of Khafre and the Pyramid of Menkaure?
_______ m2

Answer: 93,338 m2

Explanation:
The area of the base is 215×215= 46,225
The area of one face is 1/2×215×174
= 215× 87
18,705 m2
The surface area of Pyramid Khafre is= 46,225+4×18,705
= 46,225+ 74820
= 121,045 m2
The area of the base 103×103= 10,609
The area of one face is 1/2×103×83
= 8549÷2
= 4274.4 m2
The surface area of the Pyramid of Menkaure is 10,609+4×4274.5
= 10,609+ 17,098
= 27,707 m2

The difference between the surface areas of the Pyramid of Khafre and the Pyramid of Menkaure
= 121,405-27,707
= 93,338 m2

Question 10.
Write an expression for the surface area of the square pyramid shown.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 41

Answer: 6x+9 ft2.

Explanation: The expression for the surface area of the square pyramid is 6x+9 ft2.

Question 11.
Make Arguments A square pyramid has a base with a side length of 4 cm and triangular faces with a height of 7 cm. Esther calculated the surface area as (4 × 4) + 4(4 × 7) = 128 cm2. Explain Esther’s error and find the correct surface area

Answer: 72 cm2.

Explanation: Esther didn’t apply the formula correctly, she forgot to include 1/2 in the calculated surface area.
The correct surface area is (4×4)+4(1/2 ×4×7)
= 16+4(14)
= 16+56
= 72 cm2.

Question 12.
Jose says the lateral area of the square pyramid is 260 in.2. Do you agree or disagree with Jose? Use numbers and words to support your answer.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 42

Answer: 160 in.2

Explanation: No, I disagree with Jose as he found surface area instead of the lateral area, so the lateral area is
4×1/2×10×8
= 2×10×8
= 160 in.2

Surface Area of Pyramids – Page No. 619

Use a net to find the surface area of the square pyramid.

Question 1.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 43
_______ mm2

Answer: 95 mm2

Explanation:

Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume
The area of the base is 5×5= 25 mm2
The area of one face is 1/2×5×7
= 35/2
= 17.5 mm2
The surface area is 25+4×17.5
= 25+4×17.5
= 25+70
= 95 mm2

Question 2.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 44
_______ cm2

Answer: 612 cm2

Explanation:
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume

The area of the base is 18×18= 324 cm2
The area of one face is 1/2×18×8
= 18×4
=  72 cm2
The surface area is 324+4×72
= 25+4×17.5
= 25+70
= 612 cm2

Question 3.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 45
_______ yd2

Answer: 51.25 yd2

Explanation:
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume

The area of the base is 2.5×2.5= 6.25  mm2
The area of one face is 1/2×2.5×9
= 22.5/2
= 11.25 yd2
The surface area is 25+4×17.5
= 6.25+4×11.25
= 6.25+45
= 51.25 yd2

Question 4.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 46
_______ in.2

Answer: 180 in2

Explanation:

Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume

The area of the base is 10×10= 100 in2
The area of one face is 1/2×4×10
= 2×10
= 20 in2
The surface area is 100+4×20
= 100+4×20
= 100+80
= 180 in2

Problem Solving

Question 5.
Cho is building a sandcastle in the shape of a triangular pyramid. The area of the base is 7 square feet. Each side of the base has a length of 4 feet and the height of each face is 2 feet. What is the surface area of the pyramid?
_______ ft2

Answer: 19 ft2

Explanation:
The area of one face is 1/2×4×2= 4 ft2
The surface area of the triangular pyramid is 7+3×4
= 7+12
= 19 ft2

Question 6.
The top of a skyscraper is shaped like a square pyramid. Each side of the base has a length of 60 meters and the height of each triangle is 20 meters. What is the lateral area of the pyramid?
_______ m2

Answer: 2400 m2

Explanation:
The area of the one face is 1/2×60×20
= 600 m2
The lateral area of the pyramid is 4×600= 2400 m2

Question 7.
Write and solve a problem finding the lateral area of an object shaped like a square pyramid.

Answer: Mary has a triangular pyramid with a base of 10cm and a height of 15cm. What is the lateral area of the pyramid?

Explanation:
The area of one face is 1/2×10×15
= 5×15
= 75 cm2
The lateral area of the triangular pyramid is 3×75
= 225 cm2

Lesson Check – Page No. 620

Question 1.
A square pyramid has a base with a side length of 12 in. Each face has a height of 7 in. What is the surface area of the pyramid?
_______ in.2

Answer: 312 in.2

Explanation:
The area of the base is 12×12= 144 in.2
The area of one face is 1/2×12×7
= 6×7
= 42 in.2
The surface area of the square pyramid is 144+4×42
= 144+ 168
= 312 in.2

Question 2.
The faces of a triangular pyramid have a base of 5 cm and a height of 11 cm. What is the lateral area of the pyramid?
_______ cm2

Answer: 82.5 cm2

Explanation:
The area of one face is 1/2×5×11
= 55/2
= 27.5 cm2
The lateral area of the triangular pyramid is 3×27.5= 82.5 cm2

Spiral Review

Question 3.
What is the linear equation represented by the graph?
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 47

Answer: y=x+1.

Explanation: As the figure represents that every y value is 1 more than the corresponding x value, so the linear equation is y=x+1.

Question 4.
A regular octagon has sides measuring about 4 cm. If the octagon is divided into 8 congruent triangles, each has a height of 5 cm. What is the area of the octagon?
_______ cm2

Answer:

Explanation:
Area is 1/2bh
= 1/2× 4×5
= 2×5
= 10 cm2
So the area of each triangle is 10 cm2
and the area of the octagon is 8×10= 80 cm2

Question 5.
Carly draws quadrilateral JKLM with vertices J(−3, 3), K(3, 3), L(2, −1), and M(−2, −1). What is the best way to classify the quadrilateral?

Answer: It is a Trapezoid.

Explanation: It is a Trapezoid.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume

Question 6.
A rectangular prism has the dimensions 8 feet by 3 feet by 5 feet. What is the surface area of the prism?
_______ ft2

Answer: 158 ft2

Explanation:
The area of the two faces of the rectangular prism is 8×3= 24 ft2
The area of the two faces of the rectangular prism is 8×5= 40 ft2
The area of the two faces of the rectangular prism is 3×5= 15 ft2
The surface area of the rectangular prism is 2×24+2×40+2×15
= 48+80+30
= 158 ft2

Mid-Chapter Checkpoint – Vocabulary – Page No. 621

Choose the best term from the box to complete the sentence.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 48

Question 1.
_____ is the sum of the areas of all the faces, or surfaces, of a solid figure.

Answer: Surface area is the sum of the areas of all the faces, or surfaces, of a solid figure.

Question 2.
A three-dimensional figure having length, width, and height is called a(n) _____.

Answer: A three-dimensional figure having length, width, and height is called a(n) solid figure.

Question 3.
The _____ of a solid figure is the sum of the areas of its lateral faces.

Answer: The lateral area of a solid figure is the sum of the areas of its lateral faces.

Concepts and Skills

Question 4.
Identify and draw a net for the solid figure.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 49

Answer: Triangular prism

Explanation:

Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume

Question 5.
Use a net to find the lateral area of the square pyramid.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 50
_______ in.2

Answer: 216 in.2

Explanation:

Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume
The area of one face is 1/2×9×12
= 9×6
= 54 in.2
The lateral area of the square pyramid is 4×54= 216 in.2

Question 6.
Use a net to find the surface area of the prism.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 51
_______ cm2

Answer: 310 cm2

Explanation:

Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume
The area of face A and E is 10×5= 50 cm2
The area of face B and F is 10×7= 70 cm2
The area of face C and D is 7×5= 35 cm2
The surface area of the prism is 2×50+2×70+2×35
= 100+140+70
= 310 cm2

Page No. 622

Question 7.
A machine cuts nets from flat pieces of cardboard. The nets can be folded into triangular pyramids used as pieces in a board game. What shapes appear in the net? How many of each shape are there?

Answer: 4 triangles.

Explanation: There are 4 triangles.

Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume

Question 8.
Fran’s filing cabinet is 6 feet tall, 1 \(\frac{1}{3}\) feet wide, and 3 feet deep. She plans to paint all sides except the bottom of the cabinet. Find the area of the sides she intends to paint.
_______ ft2

Answer: 56 ft2

Explanation:
The two lateral face area is 6×1 1/3
= 6× 4/3
= 2×4
= 8 ft2
The area of the other two lateral faces is 6×3= 18
The area of the top and bottom is 3× 1 1/3
= 3× 4/3
= 4 ft2
The area of the sides she intends to paint is 2×8+2×18+4
= 16+36+4
= 56 ft2

Question 9.
A triangular pyramid has lateral faces with bases of 6 meters and heights of 9 meters. The area of the base of the pyramid is 15.6 square meters. What is the surface area of the pyramid?

Answer: 96.6 m2

Explanation:
The area of one face is 1/2× 6× 9
= 3×9
= 27 m2
The surface area of the triangular pyramid is 15.6+3×27
= 15.6+ 81
= 96.6 m2

Question 10.
What is the surface area of a storage box that measures 15 centimeters by 12 centimeters by 10 centimeters?
_______ cm2

Answer: 900 cm2

Explanation:
The area of two faces is 15×12= 180 cm2
The area of another two faces is 15×10= 150 cm2
The area of the other two faces is 10×12= 120 cm2
So surface area of the storage box is 2×180+2×150+2×120 cm2
= 360+300+240
= 900 cm2

Question 11.
A small refrigerator is a cube with a side length of 16 inches. Use the formula S = 6s2 to find the surface area of the cube.
_______ in.2

Answer: 1,536 in.2

Explanation:
Area = s2
= 6×(16)2
= 6× 256
= 1,536 in.2

Share and Show – Page No. 625

Question 1.
A prism is filled with 38 cubes with a side length of \(\frac{1}{2}\) unit. What is the volume of the prism in cubic units?
_______ \(\frac{□}{□}\) cubic units

Answer: 4.75 cubic units

Explanation:
The volume of the cube is S3
The volume of a cube with S= (1/2)3
= 1/2×1/2×1/2
= 1/8
= 0.125 cubic units
As there are 38 cubes so 38×0.125= 4.75 cubic units.

Question 2.
A prism is filled with 58 cubes with a side length of \(\frac{1}{2}\) unit. What is the volume of the prism in cubic units?
_______ \(\frac{□}{□}\) cubic units

Answer: 7.25 cubic units.

Explanation:
The volume of the cube is S3
The volume of a cube with S= (1/2)3
= 1/2×1/2×1/2
= 1/8
= 0.125 cubic units
As there are 58 cubes so 58×0.125= 7.25 cubic units.

Find the volume of the rectangular prism.

Question 3.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 52
_______ cubic units

Answer: 33 cubic units.

Explanation:
The volume of the rectangular prism is= Width×Height×Length
= 5 1/2 ×3×2
= 11/2 ×3×2
= 33 cubic units.

Question 4.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 53
_______ \(\frac{□}{□}\) cubic units

Answer: 91 1/8 cubic units.

Explanation:
The volume of the rectangular prism is= Width×Height×Length
= 4 1/2 ×4 1/2×4 1/2
= 9/2 ×9/2×9/2
= 729/8
= 91 1/8 cubic units.

Question 5.
Theodore wants to put three flowering plants in his window box. The window box is shaped like a rectangular prism that is 30.5 in. long, 6 in. wide, and 6 in. deep. The three plants need a total of 1,200 in.3 of potting soil to grow well. Is the box large enough? Explain.

Answer: No, the box is not large enough as the three plants need a total of 1,200 in.3 and here volume is 1,098 in.3

Explanation:
Volume= Width×Height×Length
= 30.5×6×6
= 1,098 in.3

Question 6.
Explain how use the formula V = l × w × h to verify that a cube with a side length of \(\frac{1}{2}\) unit has a volume of \(\frac{1}{8}\) of a cubic unit.

Answer: 1/8 cubic units

Explanation:
As length, width and height is 1/2′ so
Volume = Width×Height×Length
= 1/2 × 1/2 × 1/2
= 1/8 cubic units

Problem Solving + Applications – Page No. 626

Use the diagram for 7–10.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 54

Question 7.
Karyn is using a set of building blocks shaped like rectangular prisms to make a model. The three types of blocks she has are shown at right. What is the volume of an A block? (Do not include the pegs on top.)
\(\frac{□}{□}\) cubic units

Answer: 1/2 cubic units

Explanation: Volume = Width×Height×Length
= 1× 1/2 ×1
= 1/2 cubic units

Question 8.
How many A blocks would you need to take up the same amount of space as a C block?
_______ A blocks

Answer: No of blocks required to take up the same amount of space as a C block is 4 A blocks.

Explanation: Volume = Width×Height×Length
= 1×2×1
= 2 cubic unit
No of blocks required to take up the same amount of space as a C block is 1/2 ÷2
= 2×2
= 4 A blocks

Question 9.
Karyn puts a B block, two C blocks, and three A blocks together. What is the total volume of these blocks?
_______ \(\frac{□}{□}\) cubic units

Answer: 6 1/2 cubic units

Explanation: The volume of A block is
Volume = Width×Height×Length
= 1×1 ×1/2
= 1/2 cubic units.
As Karyn puts three A blocks together, so 3× 1/2= 3/2 cubic units.
The volume of B block is
Volume = Width×Height×Length
= 1×1 × 1
= 1 cubic units.
As Karyn puts only one B, so 1 cubic unit.
The volume of C block is
Volume = Width×Height×Length
= 2×1×1
= 2 cubic units.
As Karyn puts two C blocks together, so 2× 2= 4 cubic units.
So, the total volume of these blocks is 3/2 + 1+ 4
= 3/2+5
= 13/2
= 6 1/2 cubic units

Question 10.
Karyn uses the blocks to make a prism that is 2 units long, 3 units wide, and 1 \(\frac{1}{2}\) units high. The prism is made of two C blocks, two B blocks, and some A blocks. What is the total volume of A blocks used?
_______ cubic units

Answer: 3 cubic units.

Explanation:
Volume = Width×Height×Length
= 2×3×1 1/2
= 2×3× 3/2
= 9 cubic units.
The total volume of A block used is 9-(2×2)-(2×1)
= 9- 4- 2
= 9-6
= 3 cubic units.

Question 11.
Verify the Reasoning of Others Jo says that you can use V = l × w × h or V = h × w × l to find the volume of a rectangular prism. Does Jo’s statement make sense? Explain.

Answer: Yes

Explanation: Yes, Jo’s statement makes sense because by the commutative property we can change the order of the variables of length, width, height and both will produce the same result.

Question 12.
A box measures 5 units by 3 units by 2 \(\frac{1}{2}\) units. For numbers 12a–12b, select True or False for the statement.
12a. The greatest number of cubes with a side length of \(\frac{1}{2}\) unit that can be packed inside the box is 300.
12b. The volume of the box is 37 \(\frac{1}{2}\) cubic units.
12a. __________
12b. __________

Answer:
12a True.
12b True.

Explanation: The volume of the cube is S3
The volume of a cube with S= (1/2)3
= 1/2×1/2×1/2
= 1/8 cubic units
As there are 300 cubes so 300× 1/8= 75/2
= 37 1/2 cubic units.

Fractions and Volume – Page No. 627

Find the volume of the rectangular prism.

Question 1.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 55
_______ \(\frac{□}{□}\) cubic units

Answer: 6 3/4 cubic units

Explanation: Volume = Width×Height×Length
= 3× 1 1/2× 1 1/2
= 3× 3/2 × 3/2
= 27/4
= 6 3/4 cubic units

Question 2.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 56
_______ \(\frac{□}{□}\) cubic units

Answer: 22 1/2 cubic units

Explanation: Volume = Width×Height×Length
= 5×1× 4 1/2
= 5× 9/2
= 45/2
= 22 1/2 cubic units

Question 3.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 57
_______ \(\frac{□}{□}\) cubic units

Answer: 16 1/2 cubic units.

Explanation: Volume = Width×Height×Length
= 5 1/2× 1 1/2× 2
= 11/2×3/2×2
= 33/2
= 16 1/2 cubic units.

Question 4.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 58
_______ \(\frac{□}{□}\) cubic units

Answer: 28 1/8 cubic units.

Explanation: Volume = Width×Height×Length
= 2 1/2× 2 1/2 × 4 1/2
= 5/2 × 5/2 × 9/2
= 225/8
= 28 1/8 cubic units.

Problem Solving

Question 5.
Miguel is pouring liquid into a container that is 4 \(\frac{1}{2}\) inches long by 3 \(\frac{1}{2}\) inches wide by 2 inches high. How many cubic inches of liquid will fit in the container?
_______ \(\frac{□}{□}\) in.3

Answer: 31 1/2 cubic units

Explanation: Volume = Width×Height×Length
= 4 1/2 × 3 1/2 ×2
= 9/2 × 7/2 × 2
= 63/2
= 31 1/2 cubic units

Question 6.
A shipping crate is shaped like a rectangular prism. It is 5 \(\frac{1}{2}\) feet long by 3 feet wide by 3 feet high. What is the volume of the crate?
_______ \(\frac{□}{□}\) ft3

Answer: 49 1/2 ft3

Explanation: Volume = Width×Height×Length
= 5 1/2 × 3 × 3
= 11/2 ×9
= 99/2
= 49 1/2 ft3

Question 7.
How many cubes with a side length of \(\frac{1}{4}\) unit would it take to make a unit cube? Explain how you determined your answer.

Answer: There will be 4×4×4= 64 cubes and 1/4 unit in the unit cube.

Explanation:
As the unit cube has a 1 unit length, 1 unit wide, and 1 unit height
So length 4 cubes = 4× 1/4= 1 unit
width 4 cubes = 4× 1/4= 1 unit
height 4 cubes = 4× 1/4= 1 unit
So there will be 4×4×4= 64 cubes and 1/4 unit in the unit cube.

Lesson Check – Page No. 628

Question 1.
A rectangular prism is 4 units by 2 \(\frac{1}{2}\) units by 1 \(\frac{1}{2}\) units. How many cubes with a side length of \(\frac{1}{2}\) unit will completely fill the prism?

Answer: 120 cubes

Explanation:
No of cubes with a side length of 1/2 unit is
Length 8 cubes= 8× 1/2= 4 units
Width 5 cubes= 5× 1/2= 5/2= 2 1/2 units
Height 3 cubes= 3× 1/2= 3/2= 1 1/2 units
So there are 8×5×3= 120 cubes in the prism.

Question 2.
A rectangular prism is filled with 196 cubes with \(\frac{1}{2}\)-unit side lengths. What is the volume of the prism in cubic units?
_______ \(\frac{□}{□}\) cubic units

Answer: 24 1/2 cubic units.

Explanation: As it takes 8 cubes with a side length of 1/2 to form a unit cube, so the volume of the prism in the cubic units is 196÷8= 24 1/2 cubic units.

Spiral Review

Question 3.
A parallelogram-shaped piece of stained glass has a base measuring 2 \(\frac{1}{2}\) inches and a height of 1 \(\frac{1}{4}\) inches. What is the area of the piece of stained glass?
_______ \(\frac{□}{□}\) in.2

Answer: 3 1/8 in.2

Explanation: Area of a parallelogram = base×height
= 2 1/2 × 1 1/4
= 5/2 × 5/4
= 25/8
= 3 1/8 in.2

Question 4.
A flag for the sports club is a rectangle measuring 20 inches by 32 inches. Within the rectangle is a yellow square with a side length of 6 inches. What is the area of the flag that is not part of the yellow square?
_______ in.2

Answer: 604 in.2

Explanation: Area of a flag= Length×width
= 20×32
= 640 in.2
Area of the yellow square= S2
= 6
= 36 in.2
So the area of the flag that is not a part of the yellow square is 640-36= 604 in.2

Question 5.
What is the surface area of the rectangular prism shown by the net?
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 59
_______ square units

Answer: 80 square units

Explanation:
Area of two faces is 12 squares
Area of other two faces is 16 squares
Area of another two faces is 12 squares
So the surface area is 2×12+2×16+2×12
= 24+32+24
= 80 square units

Question 6.
What is the surface area of the square pyramid?
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 60
_______ cm2

Answer: 161 cm2

Explanation: The area of the base is 7×7= 49 cm2
And the area of one face is 1/2 × 7× 8
= 7×4
= 28 cm2
The surface area of the square pyramid is 49+4×28
= 49+112
= 161 cm2

Share and Show – Page No. 631

Find the volume.

Question 1.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 61
_______ \(\frac{□}{□}\) in.3

Answer: 3,937 1/2 in.3

Explanation: Volume= Length× wide× heght
= 10 1/2 ×15 × 25
= 11/2 × 15 × 25
= 4,125/2
= 3,937 1/2 in.3

Question 2.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 62
_______ \(\frac{□}{□}\) in.3

Answer: 27/512 in.3

Explanation: Volume= Length× wide× height
=3/8 ×3/8 × 3/8
= 27/512 in.3

On Your Own

Find the volume of the prism.

Question 3.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 63
_______ \(\frac{□}{□}\) in.3

Answer: 690 5/8in.3

Explanation: Volume= Length× wide× height
= 8 1/2 × 6 1/2 × 12 1/2
= 17/2 × 13/2× 25/2
= 5525/2
= 690 5/8in.3

Question 4.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 64
_______ \(\frac{□}{□}\) in.3

Answer: 125/4096 in.3

Explanation: Volume= Length× wide× height
= 5/16 ×5/16 × 5/16
= 125/4096 in.3

Question 5.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 65
_______ yd3

Answer: 20 yd3

Explanation:
Area= 3 1/3 yd2
So Area= wide×height
3 1/3= w × 1 1/3
10/3= w× 4/3
w= 10/3 × 3/4
w= 5/2
w= 2.5 yd
Volume= Length×width×height
= 6× 2.5× 1 1/3
= 6×2.5× 4/3
= 2×2.5×4
= 20 yd3

Question 6.
Wayne’s gym locker is a rectangular prism with a width and height of 14 \(\frac{1}{2}\) inches. The length is 8 inches greater than the width. What is the volume of the locker?
_______ \(\frac{□}{□}\) in.3

Answer: 4,730 5/8 in.3

Explanation: As length is 8 inches greater than width, so 14 1/2+ 8
= 29/2+8
= 45/2
= 22 1/2 in
Then volume= Length×width×height
= 22 1/2 × 14 1/2 × 14 1/2
= 45/2× 29/2× 29/2
= 37845/8
= 4,730 5/8 in.3

Question 7.
Abraham has a toy box that is in the shape of a rectangular prism.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 66
The volume is _____.
_______ \(\frac{□}{□}\) ft3

Answer: 33 3/4 ft3

Explanation: Volume of rectangular prism is= Length×width×height
= 4 1/2× 2 1/2× 3
= 9/2 × 5/2× 3
= 135/3
= 33 3/4 ft3

Aquariums – Page No. 632

Large public aquariums like the Tennessee Aquarium in Chattanooga have a wide variety of freshwater and saltwater fish species from around the world. The fish are kept in tanks of various sizes.
The table shows information about several tanks in the aquarium. Each tank is a rectangular prism.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 67
Find the length of Tank 1.
V = l w h
52,500 = l × 30 × 35
\(\frac{52,500}{1,050}\) = l
50 = l
So, the length of Tank 1 is 50 cm.

Solve.

Question 8.
Find the width of Tank 2 and the height of Tank 3.

Answer: Width of Tank 2= 8m, Height of the Tank 3= 10 m

Explanation:
The volume of Tank 2= 384 m3
so V= LWH
384=  12×W×4
W= 384/48
W= 8 m
So the width of Tank 2= 8m
The volume of Tank 3= 2160 m
So V= LWH
2160= 18×12×H
H= 2160/216
H= 10 m
So the height of the Tank 3= 10 m

Question 9.
To keep the fish healthy, there should be the correct ratio of water to fish in the tank. One recommended ratio is 9 L of water for every 2 fish. Find the volume of Tank 4. Then use the equivalencies 1 cm3 = 1 mL and 1,000 mL = 1 L to find how many fish can be safely kept in Tank 4.

Answer: 35 Fishes

Explanation:
Volume of Tank 4 = LWH
= 72×55×40
= 1,58,400 cm3
As 1 cm3 = 1 mL and 1,000 mL = 1 L
1,58,400 cm3 = 1,58,400 mL and 1,58,400 mL = 158.4 L
So tank can keep safely (158.4÷ 9)×2
= (17.6)× 2 = 35.2
= 35 Fishes

Question 10.
Use Reasoning Give another set of dimensions for a tank that would have the same volume as Tank 2. Explain how you found your answer.

Answer: Another set of dimensions for a tank that would have the same volume as Tank 2 is 8m by 8m by 6m.
So when we multiply the product will be 384

Volume of Rectangular Prisms – Page No. 633

Find the volume.

Question 1.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 68
_______ \(\frac{□}{□}\) m3

Answer: 150 5/16 m3

Explanation: Volume= Length×width×height
= 5× 3 1/4× 9 1/4
= 5× 13/4 × 37/4
= 2405/16
= 150 5/16 m3

Question 2.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 69
_______ \(\frac{□}{□}\) in.3

Answer: 27 1/2 in.3

Explanation: Volume= Length×width×height
= 5 1/2 × 2 1/2 × 2
= 11/2 × 5/2 × 2
= 55/2
= 27 1/2 in.3

Question 3.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 70
_______ \(\frac{□}{□}\) mm3

Answer: 91 1/8 mm3

Explanation: Volume= Length×width×height
= 4 1/2 × 4 1/2 × 4 1/2
= 9/2 × 9/2 × 9/2
= 729/8
= 91 1/8 mm3

Question 4.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 71
_______ \(\frac{□}{□}\) ft3

Answer: 112 1/2 ft3

Explanation: Volume= Length×width×height
= 7 1/2 × 2 1/2 × 6
= 15/2 × 5/2 × 6
= 225/2
= 112 1/2 ft3

Question 5.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 72
_______ m3

Answer: 36 m3

Explanation:
The area of shaded face is Length × width= 8 m2
Volume of the prism= Length×width×height
= 8 × 4 1/2
= 8 × 9/2
= 4 × 9
= 36 m3

Question 6.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 73
_______ \(\frac{□}{□}\) ft3

Answer: 30 3/8 ft3

Explanation: Volume of the prism= Length×width×height
= 2 1/4 × 6 × 2 1/4
= 9/4 × 6 × 9/4
= 243/8
= 30 3/8 ft3

Problem Solving

Question 7.
A cereal box is a rectangular prism that is 8 inches long and 2 \(\frac{1}{2}\) inches wide. The volume of the box is 200 in.3. What is the height of the box?
_______ in.

Answer: H= 10 in

Explanation: As volume = 200 in.3. So
V= LWH
200= 8 × 2 1/2 × H
200= 8 × 5/2 × H
200= 20 × H
H= 10 in

Question 8.
A stack of paper is 8 \(\frac{1}{2}\) in. long by 11 in. wide by 4 in. high. What is the volume of the stack of paper?
_______ in.3

Answer: 374 in.3

Explanation: The volume of the stack of paper= LWH
= 8 1/2 × 11 × 4
= 17/2 × 11 × 4
= 374 in.3

Question 9.
Explain how you can find the side length of a rectangular prism if you are given the volume and the two other measurements. Does this process change if one of the measurements includes a fraction?

Answer: We can find the side length of a rectangular prism if you are given the volume and the two other measurements by dividing the value of the volume by the product of the values of width and height of the prism. And the process doesn’t change if one of the measurements include a fraction.

Lesson Check – Page No. 634

Question 1.
A kitchen sink is a rectangular prism with a length of 19 \(\frac{7}{8}\) inches, a width of 14 \(\frac{3}{4}\) inches, and height of 10 inches. Estimate the volume of the sink.

Answer: 3,000 in.3

Explanation: Length = 19 7/8 as the number was close to 20 and width 14 3/4 which is close to 15 and height is 10
So Volume= LBH
= 20 × 15 × 10
= 3,000 in.3

Question 2.
A storage container is a rectangular prism that is 65 centimeters long and 40 centimeters wide. The volume of the container is 62,400 cubic centimeters. What is the height of the container?

Answer: H= 24 cm

Explanation: Volume of container= LBH
Volume= 62,400 cubic centimeters
62,400 = 65× 40 × H
62,400 = 2600 × H
H= 62,400/ 2600
H= 24 cm

Spiral Review

Question 3.
Carrie started at the southeast corner of Franklin Park, walked north 240 yards, turned and walked west 80 yards, and then turned and walked diagonally back to where she started. What is the area of the triangle enclosed by the path she walked?
_______ yd2

Answer: 9,600 yd2

Explanation:
Area of triangle= 1/2 bh
= 1/2 × 240 × 80
= 240 × 40
= 9,600 yd2

Question 4.
The dimensions of a rectangular garage are 100 times the dimensions of a floor plan of the garage. The area of the floor plan is 8 square inches. What is the area of the garage?

Answer: 80,000 in2

Explanation: As 1 in2= 10,000 in2, so area of the floor plan 8 in
= 8×10000
= 80,000 in2

Question 5.
Shiloh wants to create a paper-mâché box shaped like a rectangular prism. If the box will be 4 inches by 5 inches by 8 inches, how much paper does she need to cover the box?

Answer: 184 in2

Explanation: Area of the rectangular prism= 2(wl+hl+hw)
= 2(4×5 + 5×8 + 8×4)
= 2(20+40+32)
= 2(92)
= 184 in2

Question 6.
A box is filled with 220 cubes with a side length of \(\frac{1}{2}\) unit. What is the volume of the box in cubic units?
_______ \(\frac{□}{□}\) cubic units

Answer: 27.5 cubic units.

Explanation: The volume of a cube side is (1/2)3 = 1/8
So 220 cubes= 220× 1/8
= 27.5 cubic units.

Share and Show – Page No. 637

Question 1.
An aquarium tank in the shape of a rectangular prism is 60 cm long, 30 cm wide, and 24 cm high. The top of the tank is open, and the glass used to make the tank is 1 cm thick. How much water can the tank hold?
_______ cm3

Answer: So tank can hold 37,352 cm3

Explanation: As Volume= LBH
Let’s find the inner dimensions of the tank, so 60-2 × 30-2 × 24-1
= 58×28×23
= 37,352 cm3

Question 2.
What if, to provide greater strength, the glass bottom were increased to a thickness of 4 cm? How much less water would the tank hold?
_______ cm3

Answer: 4,872 cm3

Explanation: As the glass bottom was increased to a thickness of 4 cm, 60-2 × 30-2 × 24-4
= 58×28×20
= 32,480 cm3
So the tank can hold 37,352- 32,480= 4,872 cm3

Question 3.
An aquarium tank in the shape of a rectangular prism is 40 cm long, 26 cm wide, and 24 cm high. If the top of the tank is open, how much tinting is needed to cover the glass on the tank? Identify the measure you used to solve the problem.
_______ cm3

Answer: 4,208 cm3  tinting needed to cover the glass on the tank.

Explanation:
The lateral area of the two faces is 26×24= 624 cm2
The lateral area of the other two faces is 40×24= 960 cm2
And the area of the top and bottom is 40×26= 1040 cm2
So the surface area of the tank without the top is 2×624 + 2×960 + 1040
= 1,248+1,920+1,040
= 4,208 cm3

Question 4.
The Louvre Museum in Paris, France, has a square pyramid made of glass in its central courtyard. The four triangular faces of the pyramid have bases of 35 meters and heights of 27.8 meters. What is the area of glass used for the four triangular faces of the pyramid?

Answer: 1946 m2

Explanation: The area of one face is 1/2 × 35 × 27.8= 486.5 m2
And the area of glass used for the four triangular faces of the pyramid is 4×486.5= 1946 m2

On Your Own – Page No. 638

Question 5.
A rectangular prism-shaped block of wood measures 3 m by 1 \(\frac{1}{2}\) m by 1 \(\frac{1}{2}\) m. How much of the block must a carpenter carve away to obtain a prism that measures 2 m by \(\frac{1}{2}\) m by \(\frac{1}{2}\) m?
_______ \(\frac{□}{□}\) m3

Answer: 6 1/4 m3

Explanation: The volume of the original block= LWH
= 3 × 1 1/2 × 1 1/2
= 3× 3/2 × 3/2
= 27/4
= 6 3/4 m2
And volume of carpenter carve is 2× 1/2 × 1/2
= 1/2 m2
So, the carpenter must carve 27/4 – 1/2
= 25/2
= 6 1/4 m3

Question 6.
The carpenter (Problem 5) varnished the outside of the smaller piece of wood, all except for the bottom, which measures \(\frac{1}{2}\) m by \(\frac{1}{2}\) m. Varnish costs $2.00 per square meter. What was the cost of varnishing the wood?
$ _______

Answer: $8.50

Explanation: The area of two lateral faces are 2×1/2= 1 m2
The area of the other two lateral faces are 2×1/2= 1 m2
The area of the top and bottom is 1/2×1/2= 1/4 m2
And the surface area is 2×1 + 2×1 + 1/4
= 2+2+1/4
= 17/4
= 4.25 m2
And the cost of vanishing the wood is $2.00× 4.25= $8.50

Question 7.
A wax candle is in the shape of a cube with a side length of 2 \(\frac{1}{2}\) in. What volume of wax is needed to make the candle?
_______ \(\frac{□}{□}\) in.3

Answer:

Explanation: The Volume of wax is needed to make the candle is= LWH
= 2 1/2 × 2 1/2 × 2 1/2
= 5/2 × 5/2 × 5/2
= 125/8
= 15 5/8 in.3

Question 8.
Describe A rectangular prism-shaped box measures 6 cm by 5 cm by 4 cm. A cube-shaped box has a side length of 2 cm. How many of the cube-shaped boxes will fit into the rectangular prismshaped box? Describe how you found your answer.

Answer: 12 cube-shaped boxes

Explanation: As 6 small boxes can fit on the base i.e 6 cm by 5 cm, as height is 4cm there can be a second layer of 6 small boxes. So, there will be a total of 12 cube-shaped boxes and will fit into a rectangular prism-shaped box

Question 9.
Justin is covering the outside of an open shoe box with colorful paper for a class project. The shoe box is 30 cm long, 20 cm wide, and 13 cm high. How many square centimeters of paper are needed to cover the outside of the open shoe box? Explain your strategy
_______ cm2

Answer: 1,900 cm2

Explanation:
The area of the two lateral faces of the shoebox is 20×13= 260 cm2
The area of another two lateral faces of the shoebox is 30×13= 390 cm2
The area of the top and bottom is 30×20= 600 cm2
So, the surface area of the shoebox without the top is 2×260 + 2× 390 + 600
= 520+780+600
= 1,900 cm2

Problem Solving Geometric Measurements – Page No. 639

Read each problem and solve.

Question 1.
The outside of an aquarium tank is 50 cm long, 50 cm wide, and 30 cm high. It is open at the top. The glass used to make the tank is 1 cm thick. How much water can the tank hold?
_______ cm3

Answer: So water tank can hold 66,816 cm3

Explanation: The volume of inner dimensions of the aquarium is 50-2 × 50-2 × 30-1
= 48×48×29
= 66,816 cm3
So water tank can hold 66,816 cm3

Question 2.
Arnie keeps his pet snake in an open-topped glass cage. The outside of the cage is 73 cm long, 60 cm wide, and 38 cm high. The glass used to make the cage is 0.5 cm thick. What is the inside volume of the cage?
_______ cm3

Answer: The volume of the cage is 1,59,300 cm3

Explanation: The volume of inner dimensions is 73-1 × 60-1 × 38-0.5
= 72×59×37.5
= 1,59,300 cm3
So, the volume of the cage is 1,59,300 cm3

Question 3.
A display number cube measures 20 in. on a side. The sides are numbered 1–6. The odd-numbered sides are covered in blue fabric and the even-numbered sides are covered in red fabric. How much red fabric was used?
_______ in.2

Answer: 1200 in.2

Explanation: The area of each side of a cube is 20×20= 400 in.2, as there are 3 even-numbered sides on the cube. So there will be
3×400= 1200 in.2

Question 4.
The caps on the tops of staircase posts are shaped like square pyramids. The side length of the base of each cap is 4 inches. The height of the face of each cap is 5 inches. What is the surface area of the caps for two posts?
_______ in.2

Answer: 112 in.2

Explanation: The area of the base is 4×4= 16 in.2
The area of one face is 1/2×5×4= 10 in.2
The surface area of one cap is 16+4×10
= 16+40
= 56 in.2
And the surface area of the caps for two posts is 2×56= 112 in.2

Question 5.
A water irrigation tank is shaped like a cube and has a side length of 2 \(\frac{1}{2}\) feet. How many cubic feet of water are needed to completely fill the tank?
_______ \(\frac{□}{□}\) ft3

Answer: 15 5/8 ft3

Explanation: Volume= LWH
= 2 1/2 × 2 1/2 × 2 1/2
= 5/2 × 5/2 × 5/2
= 125/8
= 15 5/8 ft3

Question 6.
Write and solve a problem for which you use part of the formula for the surface area of a triangular prism.

Answer: In a triangular prism, the triangular end has a base of 5cm and the height is 8 cm. The length of each side is 4 cm and the height of the prism is 10 cm. What is the lateral area of this triangular prism?

Explanation: The area of two triangular faces is 1/2 × 5 × 8
= 5×4
= 20 cm2
The area of two rectangular faces is 4×10= 40 cm2
The lateral area is 2×20+2×40
= 40+80
= 120 cm2

Lesson Check – Page No. 640

Question 1.
Maria wants to know how much wax she will need to fill a candle mold shaped like a rectangular prism. What measure should she find?

Answer: Maria needs to find the volume of the mold.

Question 2.
The outside of a closed glass display case measures 22 inches by 15 inches by \(\frac{1}{2}\) inches. The glass is 12 inch thick. How much air is contained in the case?
_______ in.3

Answer: 3381 in.3

Explanation: The inner dimensions are 22-1× 15-1 × 12- 1/2
= 21 ×14×23/2
= 3381 in.3

Spiral Review

Question 3.
A trapezoid with bases that measure 5 centimeters and 7 centimeters has a height of 4.5 centimeters. What is the area of the trapezoid?
_______ cm2

Answer: 27 cm2

Explanation: Area of trapezoid= 1/2 ×(7+5)×4.5
= 6×4.5
= 27 cm2

Question 4.
Sierra has plotted two vertices of a rectangle at (3, 2) and (8, 2). What is the length of the side of the rectangle?
_______ units

Answer: 5 units.

Explanation: The length of the side of the rectangle is 8-3= 5 units.

Question 5.
What is the surface area of the square pyramid?
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 74
_______ m2

Answer: 104 m2

Explanation: The area of the base 4×4= 16
The area of the one face is 1/2 × 4 × 11
= 2×11
= 22 m2
The surface area of the square pyramid is 16+4×22
= 16+88
= 104 m2

Question 6.
A shipping company has a rule that all packages must be rectangular prisms with a volume of no more than 9 cubic feet. What is the maximum measure for the height of a box that has a width of 1.5 feet and a length of 3 feet?
_______ feet

Answer: 2 feet.

Explanation: As given volume = 9 cubic feet
So 1.5×3×H < 9
4.5×H < 9
H< 9/4.5
and H<2
So maximum measure for the height of the box is 2 feet.

Chapter 11 Review/Test – Page No. 641

Question 1.
Elaine makes a rectangular pyramid from paper.
The base is a _____. The lateral faces are _____.
The base is a ___________ .
The lateral faces are ___________ .

Answer:
The base is a rectangle.
The lateral faces are triangles.

Question 2.
Darrell paints all sides except the bottom of the box shown below.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 75
Select the expressions that show how to find the surface area that Darrell painted. Mark all that apply.
Options:
a. 240 + 240 + 180 + 180 + 300 + 300
b. 2(20 × 12) + 2(15 × 12) + (20 × 15)
c. (20 × 12) + (20 × 12) + (15 × 12) + (15 × 12) + (20 × 15)
d. 20 × 15 × 12

Answer: b,c

Explanation: The expressions that show how to find the surface area is 2(20 × 12) + 2(15 × 12) + (20 × 15), (20 × 12) + (20 × 12) + (15 × 12) + (15 × 12) + (20 × 15)

Question 3.
A prism is filled with 44 cubes with \(\frac{1}{2}\)-unit side lengths. What is the volume of the prism in cubic units?
_______ \(\frac{□}{□}\) cubic unit

Answer:

Explanation:
The volume of a cube with S= (1/2)3
= 1/2×1/2×1/2
= 1/8
= 0.125 cubic units
As there are 44 cubes so 44×0.125=5.5 cubic units.

Question 4.
A triangular pyramid has a base with an area of 11.3 square meters, and lateral faces with bases of 5.1 meters and heights of 9 meters. Write an expression that can be used to find the surface area of the triangular pyramid.

Answer: 11.3+ 3 × 1/2+ 5.1×9

Explanation: The expression that can be used to find the surface area of the triangular pyramid is 11.3+ 3 × 1/2+ 5.1×9

Page No. 642

Question 5.
Jeremy makes a paperweight for his mother in the shape of a square pyramid. The base of the pyramid has a side length of 4 centimeters, and the lateral faces have heights of 5 centimeters. After he finishes, he realizes that the paperweight is too small and decides to make another one. To make the second pyramid, he doubles the length of the base in the first pyramid.
For numbers 5a–5c, choose Yes or No to indicate whether the statement is correct.
5a. The surface area of the second pyramid is 144 cm2.
5b. The surface area doubled from the first pyramid to the second pyramid.
5c. The lateral area doubled from the first pyramid to the second pyramid.
5a. ___________
5b. ___________
5c. ___________

Answer:
5a. True.
5b. False
5c. True.

Explanation:
The area of the base is 4×4= 16 cm2.
The area of one face is 1/2×4×5
= 2×5
= 10 cm2.
The surface area of the First pyramid is 16+ 4×10
= 16+40
= 56 cm2.
The area of the base is 8×8= 64
The area of one face is 1/2×8×5
= 4×5
= 20 cm2.
The surface area od the second pyramid is 64+ 4×20
= 64+80
= 144 cm2.

Question 6.
Identify the figure shown and find its surface area. Explain how you found your answer.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 76

Answer: 369 in2

Explanation:
The area of the base is 9×9= 81 in2
The area of one face is 1//2 × 16× 9
= 8×9
= 72 in2
The surface area of a square pyramid is 81+ 4× 72
= 81+ 288
= 369 in2

Question 7.
Dominique has a box of sewing buttons that is in the shape of a rectangular prism.
The volume of the box is 2 \(\frac{1}{2}\) in. × 3 \(\frac{1}{2}\) in. × _____ = _____.

Answer: 17.5 in3

Explanation: The volume of the box is 2 1/2 × 3 1/2 × 2
= 5/2 × 7/2 × 2
= 5/2 × 7
= 35/2
= 17.5 in3

Page No. 643

Question 8.
Emily has a decorative box that is shaped like a cube with a height of 5 inches. What is the surface area of the box?
_______ in.2

Answer: 150 in.2

Explanation: Surface area of the box is 6 a2
So 6 × 52
= 6×5×52
= 150 in.2

Question 9.
Albert recently purchased a fish tank for his home. Match each question with the geometric measure that would be most appropriate for each scenario.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 77

Answer:
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume

Question 10.
Select the expressions that show the volume of the rectangular prism. Mark all that apply.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 78Options:
a. 2(2 units × 2 \(\frac{1}{2 }\) units) + 2(2 units × \(\frac{1}{2}\) unit) + 2(\(\frac{1}{2}\) unit × 2 \(\frac{1}{2}\) units)
b. 2(2 units × \(\frac{1}{2}\) unit) + 4(2 units × 2 \(\frac{1}{2}\) units)
c. 2 units × \(\frac{1}{2}\) unit × 2 \(\frac{1}{2}\) units
d. 2.5 cubic units

Answer: c, d

Explanation: 2 units ×1/2 unit × 2 1/2 units and 2.5 cubic units

Page No. 644

Question 11.
For numbers 11a–11d, select True or False for the statement.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 79
11a. The area of face A is 8 square units.
11b. The area of face B is 10 square units.
11c. The area of face C is 8 square units.
11d. The surface area of the prism is 56 square units.
11a. ___________
11b. ___________
11c. ___________
11d. ___________

Answer:
11a. True.
11b. True.
11c. False.
11d. False.

Explanation:
The area of the face A is 4×2= 8 square units
The area of the face B is 5×2= 10 square units
The area of the face C is 5×4= 20 square units
So the surface area is 2×8+2×10+2×20
= 16+20+40
= 76 square units

Question 12.
Stella received a package in the shape of a rectangular prism. The box has a length of 2 \(\frac{1}{2}\) feet, a width of 1 \(\frac{1}{2}\) feet, and a height of 4 feet.
Part A
Stella wants to cover the box with wrapping paper. How much paper will she need? Explain how you found your answer

Answer: 39.5 ft2

Explanation:
The area of two lateral faces is 4 × 2 1/2
= 4 × 5/2
= 2×5
= 10 ft2
The area of another two lateral faces is 4 × 1 1/2
= 4 × 3/2
= 2×3
= 6 ft2
The area of the top and bottom is 2 1/2 × 1 1/2
= 5/2 × 3/2
= 15/4
= 3 3/4 ft2
So Stella need 2×10+ 2×6 + 2 × 15/4
= 20+ 12+15/2
= 20+12+7.5
= 39.5 ft2

Question 12.
Part B
Can the box hold 16 cubic feet of packing peanuts? Explain how you know

Answer: The box cannot hold 16 cubic feet of the packing peanuts

Explanation: Volume = LWH
= 2 1/2 ×1 1/2 × 4
= 5/2 × 3/2 ×4
= 5×3
= 15 ft3
So the box cannot hold 16 cubic feet of the packing peanuts.

Page No. 645

Question 13.
A box measures 6 units by \(\frac{1}{2}\) unit by 2 \(\frac{1}{2}\) units.
For numbers 13a–13b, select True or False for the statement.
13a. The greatest number of cubes with a side length of \(\frac{1}{2}\) unit that can be packed inside the box is 60.
13b. The volume of the box is 7 \(\frac{1}{2}\) cubic units.
13a. ___________
13b. ___________

Answer:
13a. True
13b. True.

Explanation:
Length is 12 × 1/2= 6 units
Width is 1× 1/2= 1/2 units
Height is 5× 1/2= 5/2 units
So, the greatest number of cubes with a side length of 1/2 unit that can be packed inside the box is 12×1×5= 60
The volume of the cube is S3
The volume of a cube with S= (1/2)3
= 1/2×1/2×1/2
= 1/8
= 0.125 cubic units
As there are 60 cubes so 60×0.125= 7.5cubic units.

Question 14.
Bella says the lateral area of the square pyramid is 1,224 in.2. Do you agree or disagree with Bella? Use numbers and words to support your answer. If you disagree with Bella, find the correct answer.

Answer: 900 in2

Explanation:
Area= 4× 1/2 bh
= 4× 1/2 × 18 × 25
= 2× 18 × 25
=  900 in2
So lateral area is 900 in2, so I disagree

Question 15.
Lourdes is decorating a toy box for her sister. She will use self-adhesive paper to cover all of the exterior sides except for the bottom of the box. The toy box is 4 feet long, 3 feet wide, and 2 feet high. How many square feet of adhesive paper will Lourdes use to cover the box?
_______ ft2

Answer: 40 ft2

Explanation:
The area of two lateral faces is 4×2= 8 ft2
The area of another two lateral faces is 3×2= 6 ft2
The area of the top and bottom is 4×3= 12 ft2
So Lourdes uses to cover the box is 2×8 + 2×6 + 12
= 16+12+12
= 40 ft2

Question 16.
Gary wants to build a shed shaped like a rectangular prism in his backyard. He goes to the store and looks at several different options. The table shows the dimensions and volumes of four different sheds. Use the formula V = l × w × h to complete the table.
Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 80

Answer:
Length of shed 1= 12 ft
Width of shed 2= 12 ft
Height of shed 3= 6 ft
Volume of shed 4= 1200 ft3

Explanation: Volume= LWH
Volume of shed1= 960 ft
So 960= L×10×8
960= 80×L
L= 960/80
L= 12 ft
Volume of shed2= 2160 ft
So 2160= 18×W×10
960= 180×W
W= 2160/180
W= 12 ft
Volume of shed3= 288 ft
So 288= 12×4×H
288= 48×H
H= 288/48
W= 6 ft
Volume of shed2= 10×12×10
So V= 10×12×10
V= 1200 ft3

Page No. 646

Question 17.
Tina cut open a cube-shaped microwave box to see the net. How many square faces does this box have?
_______ square faces

Answer: The box has 6 square faces.

Question 18.
Charles is painting a treasure box in the shape of a rectangular prism.
Which nets can be used to represent Charles’ treasure box? Mark all that apply.
Options:
a. Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 81
b. Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 82
c. Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 83
d. Go Math Grade 6 Answer Key Chapter 11 Surface Area and Volume img 84

Answer: a and b can be used to represent Charle’s treasure box.

Question 19.
Julianna is lining the inside of a basket with fabric. The basket is in the shape of a rectangular prism that is 29 cm long, 19 cm wide, and 10 cm high. How much fabric is needed to line the inside of the basket if the basket does not have a top? Explain your strategy.
_______ cm2

Answer: 1511 cm2

Explanation: The surface area= 2(WL+HL+HW)
The surface area of the entire basket= 2(19×29)+2(10×29)+2(10×19)
= 2(551)+2(290)+2(190)
= 1102+580+380
= 2,062 cm2
The surface area of the top is 29×19= 551
So Julianna needs 2062-551= 1511 cm2

Conclusion

Click on the related links and begin your preparation. Make your preparation perfect by practicing the problems a number of times. We wish the info provided in the Go Math 6th Standard Answer Key Chapter 11 Surface Area and Volume is satisfactory for all of you. Keep in touch with us to get the latest updates regarding the HMH Go Math Grade 6 Answer Key.

Go Math Grade 4 Answer Key Homework Practice FL Chapter 7 Add and Subtract Fractions

go-math-grade-4-chapter-7-add-and-subtract-fractions-review-test-answer-key

Hello Kids!!! What you are waiting for? Here is the Answer Key for Go Math HMH Grade 4 Chapter 7? Just make use of these Go Math Grade 4 Answer Key Homework Practice FL Chapter 7 Add and Subtract Fractions and practice well. Students who are preparing for the grade 4 maths exam can get this Go Math Grade 4 Answer Key Homework Practice FL Chapter 7 Add and Subtract Fractions pdf from here to access and download for free.

Go Math Grade 4 Answer Key Homework Practice FL Chapter 7 Add and Subtract Fractions

Download Go Math Grade 4 Solution Key Homework Practice FL Chapter 7 Add and Subtract Fractions in pdf format and aid your preparation. First of all, begin your practice session with textbook solutions and then jump into this Go Math Grade 4 Answer Key Homework Practice FL Chapter 7 Add and Subtract Fractions for gaining better subject knowledge. These solutions are written by subject experts in a comprehend manner. So, you all can easily understand and practice more concepts.

Lesson: 1 – Add and Subtract Parts of a Whole

Lesson: 2 – Write Fractions as Sums

Lesson: 3 – Add Fractions Using Models

Lesson: 4 – Subtract Fractions Using Models

Lesson: 5 – Add and Subtract Fractions

Lesson: 6 – Rename Fractions and Mixed Numbers

Lesson: 7 – Add and Subtract Mixed Numbers

Lesson: 8 – Record Subtraction with

Lesson: 9 – Fractions and Properties of Addition

Lesson: 10 – Read each problem and solve.

Lesson 7.1

Common Core – Add and Subtract Fractions – Page No. 133

Add and Subtract Parts of a Whole

Use the model to write an equation.

Question 1.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 7 Add and Subtract Fractions Common Core - Add and Subtract Fractions img 1

Explanation:
By seeing the above 3 figures we can say that the fraction of the shaded part of the first circle is 3/8, the fraction of the second figure is 2/8
By adding the 2 fractions we get the fraction of the third circle.
3/8 + 2/8 = 5/8

Question 2.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 7 Add and Subtract Fractions Common Core - Add and Subtract Fractions img 2
Type below:
_________

Answer: 4/5 – 3/5 = 1/5

Explanation:
The fraction of the shaded part for the above rectangle is 4/5
The fraction of the box is 3/5
The equation for the above figure is 4/5 – 3/5 = 1/5

Question 3.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 7 Add and Subtract Fractions Common Core - Add and Subtract Fractions img 3
Type below:
_________

Answer: 1/4 + 2/4 = 3/4

Explanation:
The name of the fraction for the shaded part of first figure is 1/4
The name of the fraction for the shaded part of second figure is 1/4
The name of the fraction for the shaded part of third figure is 3/4
So, The equation for the above figure is 1/4 + 2/4 = 3/4

Use the model to solve the equation.

Question 4.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 7 Add and Subtract Fractions Common Core - Add and Subtract Fractions img 4
\(\frac{2}{6}+\frac{3}{6}\) = \(\frac{□}{□}\)

Answer: \(\frac { 2 }{ 6 } +\frac { 3 }{ 6 } =\frac { 5 }{ 6 } \)

Explanation:
The name of the fraction for the shaded part of first figure is 2/6
The name of the fraction for the shaded part of second figure is 3/6
The name of the fraction for the shaded part of third figure is 5/6
So, The equation for the above figure is \(\frac { 2 }{ 6 } +\frac { 3 }{ 6 } =\frac { 5 }{ 6 } \)

Question 5.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 7 Add and Subtract Fractions Common Core - Add and Subtract Fractions img 5
\(\frac{3}{5}-\frac{2}{5}\) = \(\frac{□}{□}\)

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

Explanation:
The name of the fraction for the shaded part of figure is 3/5
The name of the fraction for the shaded part of closed box is 2/5
So, The equation for the above figure is \(\frac { 3 }{ 5 } -\frac { 2 }{ 5 } =\frac { 1 }{ 5 } \)

Problem Solving

Question 6.
Jake ate \(\frac{4}{8}\) of a pizza. Millie ate \(\frac{3}{8}\) of the same pizza. How much of the pizza was eaten by Jake and Millie?
\(\frac{□}{□}\)

Answer: 7/8 of pizza

Explanation:
Given that,
Jake ate \(\frac { 4 }{ 8 } \) of a pizza.
Millie ate \(\frac { 3}{ 8 } \) of the same pizza.
To find how much of the pizza was eaten by Jake and Millie
We have to add both the fractions
\(\frac { 4 }{ 8 } \) + \(\frac { 3 }{ 8 } \) = \(\frac { 7 }{ 8 } \)
Thus the fraction of the pizza eaten by Jake and Millie is \(\frac { 7 }{ 8 } \)

Question 7.
Kate ate \(\frac{1}{4}\) of her orange. Ben ate \(\frac{2}{4}\) of his banana. Did Kate and Ben eat \(\frac{1}{4}+\frac{2}{4}=\frac{3}{4}\) of their fruit?
Explain.
Type below:
__________

Answer: No, one whole refers to orange and the other whole to a banana.

Common Core – Add and Subtract Fractions – Page No. 134

Lesson Check

Question 1.
A whole pie is cut into 8 equal slices. Three of the slices are served. How much of the pie is left?
Options:
a. \(\frac{1}{8}\)
b. \(\frac{3}{8}\)
c. \(\frac{5}{8}\)
d. \(\frac{7}{8}\)

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

Explanation:
Given,
A whole pie is cut into 8 equal slices. Three of the slices are served.
The fraction of 8 slices is 8/8.
Out of which 3/8 are served.
8/8 – 3/8 = 5/8
Therefore \(\frac { 5 }{ 8} \) of the pie is left.
Thus the correct answer is option c.

Question 2.
An orange is divided into 6 equal wedges. Jody eats 1 wedge. Then she eats 3 more wedges. How much of the orange did Jody eat?
Options:
a. \(\frac{1}{6}\)
b. \(\frac{4}{6}\)
c. \(\frac{5}{6}\)
d. \(\frac{6}{6}\)

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

Explanation:
Given,
An orange is divided into 6 equal wedges.
Jody eats 1 wedge.
Then she eats 3 more wedges.
The fraction of orange that Jody eat is \(\frac { 4}{ 6 } \).
Thus the correct answer is option b.

Spiral Review

Question 3.
Which list of distances is in order from least to greatest?
Options:
a. \(\frac{1}{8} mile, \frac{3}{16} mile, \frac{3}{4} mile\)
b. \(\frac{3}{4} mile, \frac{1}{8} mile, \frac{3}{16} mile\)
c. \(\frac{1}{8} mile, \frac{3}{4} mile, \frac{3}{16} mile\)
d. \(\frac{3}{16} mile, \frac{1}{8} mile, \frac{3}{4} mile\)

Answer: \(\frac { 1 }{ 8 } \) Mile, \(\frac { 3 }{ 16 } \) Mile, \(\frac { 3 }{ 4 } \) Mile

Explantion:
Compare the three fractions 1/8, 3/4 and 3/16
Make the common denominators.
1/8 × 2/2 = 2/16
3/4 × 4/4 = 12/16
The fractions are 2/16, 12/16 and 3/16
The numerator with the highest number will be the greatest.
The fractions from least to greatest is \(\frac { 1 }{ 8 } \) Mile, \(\frac { 3 }{ 16 } \) Mile, \(\frac { 3 }{ 4 } \) Mile.
Thus the correct answer is option d.

Question 4.
Jeremy walked \(\frac{6}{8}\) of the way to school and ran the rest of the way. What fraction, in simplest form, shows the part of the way that Jeremy walked?
Options:
a. \(\frac{1}{4}\)
b. \(\frac{3}{8}\)
c. \(\frac{1}{2}\)
d. \(\frac{3}{4}\)

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

Explanation:
Given,
Jeremy walked 6/8 of the way to school and ran the rest of the way.
The simplest form of 6/8 is 3/8.
The simplest form of part of the way that Jeremy walked is 3/8.
Thus the correct answer is option b.

Question 5.
An elevator starts on the 100th floor of a building. It descends 4 floors every 10 seconds. At what floor will the elevator be 60 seconds after it starts?
Options:
a. 60th floor
b. 66th floor
c. 72nd floor
d. 76th floor

Answer: 76th floor

Explanation:
Given,
An elevator starts on the 100th floor of a building.
It descends 4 floors every 10 seconds.
4 floors – 10 seconds
? – 60 seconds
60 × 4/10 = 240/10 = 24 floors
100 – 24 = 76th floor
Thus the correct answer is option d.

Question 6.
For a school play, the teacher asked the class to set up chairs in 20 rows with 25 chairs in each row. After setting up all the chairs, they were 5 chairs short. How many chairs did the class set up?
Options:
a. 400
b. 450
c. 495
d. 500

Answer: 495

Explanation:
Given,
For a school play, the teacher asked the class to set up chairs in 20 rows with 25 chairs in each row.
After setting up all the chairs, they were 5 chairs short.
20 × 25 = 500
500 – 5 = 495
Therefore the class set up 495 chairs.
Thus the correct answer is c.

Common Core – Add and Subtract Fractions – Page No. 135

Write Fractions as Sums

Write the fraction as a sum of unit fractions.

Question 1.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 7 Add and Subtract Fractions Common Core - Add and Subtract Fractions img 6

Answer: 1/5 + 1/5 + 1/5 + 1/5

Explanation:
The sum of the unit fractions for 4/5 is 1/5 + 1/5 + 1/5 + 1/5.

Question 2.
\(\frac{3}{8}\) =
Type below:
__________

Answer: 1/8 + 1/8 + 1/8

Explanation:
The sum of the unit fractions for 3/8 is 1/8 + 1/8 + 1/8

Question 3.
\(\frac{6}{12}\) =
Type below:
__________

Answer: 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12

Explanation:
The sum of the unit fractions for 6/12 is 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12

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

Answer: 1/4 + 1/4 + 1/4 + 1/4

Explanation:
The sum of the unit fractions for 4/4 is 1/4 + 1/4 + 1/4 + 1/4

Write the fraction as a sum of fractions three different ways.

Question 5.
\(\frac{7}{10}\)
Type below:
__________

Answer: 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10

Explanation:
The sum of the unit fractions for 7/10 is 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10

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

Answer: 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6

Explanation:
The sum of the unit fractions for 6/6 is 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6

Problem Solving

Question 7.
Miguel’s teacher asks him to color \(\frac{4}{8}\) of his grid. He must use 3 colors: red, blue, and green. There must be more green sections than red sections. How can Miguel color the sections of his grid to follow all the rules?
Type below:
__________

Answer: 1/8 red, 1/8 blue, and 2/8 green

Explanation:
If there are 8 tiles, coloring \(\frac { 4 }{ 8 }\) means coloring 4 tiles. Using those three colors, we could use each 1 time with 1 leftover. Since we must have more green, we would use it twice; this would give us 2 green, 1 red and 1 blue.
Since the grid is not necessarily 8 squares, we must account for this by saying 2/8 green, 1/8 red, and 1/8 blue

Question 8.
Petra is asked to color \(\frac{6}{6}\) of her grid. She must use 3 colors: blue, red, and pink. There must be more blue sections than red sections or pink sections. What are the different ways Petra can color the sections of her grid and follow all the rules?
Type below:
__________

Answer: 3/6 blue, 2/6 red, 1/6 pink

Explanation:
1. 3 blues, 2 red, 1 pink.
2. 3 blues, 2 pink, 1 red.
3. 4 blues, 1 red, 1 pink
The different ways in which Petra can color the sections of her grid and follow the rules are;
1. 3 blues, 2 red, 1 pink.
2. 3 blues, 2 pink, 1 red.
3. 4 blues, 1 red, 1 pink
All these three ways follows the rules that; there must be three colors an also Blue sections are more than red sections or pink sections.

Common Core – Add and Subtract Fractions – Page No. 136

Lesson Check

Question 1.
Jorge wants to write \(\frac{4}{5}\) as a sum of unit fractions. Which of the following should he write?
Options:
a. \(\frac{3}{5}+\frac{1}{5}\)
b. \(\frac{2}{5}+\frac{2}{5}\)
c. \(\frac{1}{5}+\frac{1}{5}+\frac{2}{5}\)
d. \(\frac{1}{5}+\frac{1}{5}+\frac{1}{5}+\frac{1}{5}\)

Answer: \(\frac { 1 }{ 5 } +\frac { 1 }{ 5 } +\frac { 1 }{ 5 } +\frac { 1 }{ 5 } \)

Explanation:
Given,
Jorge wants to write \(\frac { 4 }{ 5 } \) as a sum of unit fractions.
The sum of the unit fraction for \(\frac { 4 }{ 5 } \) is \(\frac { 1 }{ 5 } +\frac { 1 }{ 5 } +\frac { 1 }{ 5 } +\frac { 1 }{ 5 } \)
Thus the correct answer is option d.

Question 2.
Which expression is equivalent to \(\frac{7}{8}\)?
Options:
a. \(\frac{5}{8}+\frac{2}{8}+\frac{1}{8}\)
b. \(\frac{3}{8}+\frac{3}{8}+\frac{1}{8}+\frac{1}{8}\)
c. \(\frac{4}{8}+\frac{2}{8}+\frac{1}{8}\)
d. \(\frac{4}{8}+\frac{2}{8}+\frac{2}{8}\)

Answer: \(\frac { 4 }{ 8 } +\frac { 2 }{ 8 }+\frac { 1 }{ 8 } \)

Explanation:
The fraction equivalent to \(\frac { 7 }{ 8 } \) is \(\frac { 4 }{ 8 } +\frac { 2 }{ 8 }+\frac { 1 }{ 8 } \).
Thus the correct answer is option c.

Spiral Review

Question 3.
An apple is cut into 6 equal slices. Nancy eats 2 of the slices. What fraction of the apple is left?
Options:
a. \(\frac{1}{6}\)
b. \(\frac{2}{6}\)
c. \(\frac{3}{6}\)
d. \(\frac{4}{6}\)

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

Explanation:
Given,
An apple is cut into 6 equal slices. Nancy eats 2 of the slices.
6 – 2 = 4
\(\frac { 6 }{ 6 } \) – \(\frac { 2 }{ 6 } \) = \(\frac { 4 }{ 6 } \)
Thus the correct answer is option d.

Question 4.
Which of the following numbers is a prime number?
Options:
a. 1
b. 11
c. 21
d. 51

Answer: 11

Explanation:
A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers.
11 is a multiple of 1 and itself.
Thus the correct answer is option b.

Question 5.
A teacher has a bag of 100 unit cubes. She gives an equal number of cubes to each of the 7 groups in her class. She gives each group as many cubes as she
can. How many unit cubes are left over?
Options:
a. 1
b. 2
c. 3
d. 6

Answer: 2

Explanation:
Given,
A teacher has a bag of 100 unit cubes. She gives an equal number of cubes to each of the 7 groups in her class.
She gives each group as many cubes as she can.
100 divided by 7 is 14 r 2, so there are 2 leftover.
Thus the correct answer is option b.

Question 6.
Jessie sorted the coins in her bank. She made 7 stacks of 6 dimes and 8 stacks of 5 nickels. She then found 1 dime and 1 nickel. How many dimes and nickels does Jessie have in all?
Options:
a. 84
b. 82
c. 80
d. 28

Answer: 84

Explanation:
Given,
Jessie sorted the coins in her bank. She made 7 stacks of 6 dimes and 8 stacks of 5 nickels.
She then found 1 dime and 1 nickel.
43 dimes and 41 nickles
43 + 41 = 84
Jessie has 84 dimes and nickels in all.
Thus the correct answer is option a.

Common Core – Add and Subtract Fractions – Page No. 137

Add Fractions Using Models

Find the sum. Use fraction strips to help.

Question 1.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 7 Add and Subtract Fractions Common Core - Add and Subtract Fractions img 7

Answer: 3/6

Question 2.
\(\frac{4}{10}+\frac{5}{10}\) = \(\frac{□}{□}\)

Answer: 9/10
HMH Go Math Grade 4 Answer Key Chapter 7 Add and Subtract Fractions Img_6

Question 3.
\(\frac{1}{3}+\frac{2}{3}\) = \(\frac{□}{□}\)

Answer: 3/3
HMH Go Math Grade 4 Answer Key Chapter Add & Subtract Fractions Img_7

Question 4.
\(\frac{2}{4}+\frac{1}{4}\) = \(\frac{□}{□}\)

Answer: 3/4
HMH Go Math Grade 4 Key Chapter 7 Add and Subtract Fractions Img_8

Question 5.
\(\frac{2}{12}+\frac{4}{12}\) = \(\frac{□}{□}\)

Answer: 6/12
HMH Go Math Grade 4 Key Chapter 7 Add & Subtract Fractions Img_9

Question 6.
\(\frac{1}{6}+\frac{2}{6}\) = \(\frac{□}{□}\)

Answer: 3/6
Go Math Grade 4 Key Chapter 7 Add & Subtract Fractions Img_10

Question 7.
\(\frac{3}{12}+\frac{9}{12}\) = \(\frac{□}{□}\)

Answer: 12/12

Go Math Grade 4 Answer Key Chapter 7 Add & Subtract Fractions Img_11

Question 8.
\(\frac{3}{8}+\frac{4}{8}\) = \(\frac{□}{□}\)

Answer: 7/8

Go Math 4th Grade Key Chapter 7 Add & Subtract Fractions Img_12

Question 9.
\(\frac{3}{4}+\frac{1}{4}\) = \(\frac{□}{□}\)

Answer: 4/4
Go Math 4th Grade Answer Key Chapter 7 Add & Subtract Fractions Img_13

Question 10.
\(\frac{1}{5}+\frac{2}{5}\) = \(\frac{□}{□}\)

Answer: 3/5

Explanation:
Go Math Grade 4 Answer Key Chapter Img_14

Problem Solving

Question 11.
Lola walks \(\frac{4}{10}\) mile to her friend’s house. Then she walks \(\frac{5}{10}\) mile to the store. How far does she walk in all?
\(\frac{□}{□}\) mile

Answer: \(\frac { 9 }{ 10 } \) mile

Explanation:
Given,
Lola walks \(\frac { 4 }{ 10} \) mile to her friend’s house.
Then she walks \(\frac { 5 }{ 10 } \) mile to the store.
\(\frac { 4 }{ 10} \) + \(\frac { 5 }{ 10 } \) = \(\frac { 9 }{ 10 } \)
Therefore she walked \(\frac { 9 }{ 10 } \) mile in all.

Question 12.
Evan eats \(\frac{1}{8}\) of a pan of lasagna and his brother eats \(\frac{2}{8}\) of it. What fraction of the pan of lasagna do they eat in all?
\(\frac{□}{□}\)

Answer: \(\frac { 3 }{ 8 } \) of the pan

Explanation:
Given,
Evan eats \(\frac { 1 }{ 8 } \) of a pan of lasagna and his brother eats \(\frac { 2 }{ 8 } \) of it.
\(\frac { 1 }{ 8 } \) + \(\frac { 2 }{ 8 } \)
= \(\frac { 3 }{ 8 } \)

Question 13.
Jacqueline buys \(\frac{2}{4}\) yard of green ribbon and \(\frac{1}{4}\) yard of pink ribbon. How many yards of ribbon does she buy in all?
\(\frac{□}{□}\) yard

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

Explanation:
Given,
Jacqueline buys \(\frac { 2 }{ 4 } \) yard of green ribbon and \(\frac { 1 }{ 4 } \) yard of pink ribbon.
\(\frac { 2 }{ 4 } \) + \(\frac { 1 }{ 4 } \)
= \(\frac { 3 }{ 4 } \)
Thus Jacqueline bought \(\frac { 3 }{ 4 } \) yards of ribbon in all.

Question 14.
Shu mixes \(\frac{2}{3}\) pound of peanuts with \(\frac{1}{3}\) pound of almonds. How many pounds of nuts does Shu mix in all?
\(\frac{□}{□}\) pound

Answer: 3/3 pound

Explanation:
Given,
Shu mixes \(\frac { 2 }{ 3 } \) pound of peanuts with \(\frac { 1 }{ 3 } \) pound of almonds.
\(\frac { 2 }{ 3 } \) + \(\frac { 1 }{ 3 } \)
= \(\frac { 3 }{ 3 } \)
Therefore Shu mix \(\frac { 3 }{ 3 } \) pounds of nuts in all.

Common Core – Add and Subtract Fractions – Page No. 138

Lesson Check

Question 1.
Mary Jane has \(\frac{3}{8}\) of a medium pizza left. Hector has \(\frac{2}{8}\) of another medium pizza left. How much pizza do they have altogether?
Options:
a. \(\frac{1}{8}\)
b. \(\frac{4}{8}\)
c. \(\frac{5}{8}\)
d. \(\frac{6}{8}\)

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

Explanation:
Given,
Mary Jane has \(\frac { 3 }{ 8 } \) of a medium pizza left.
Hector has \(\frac { 2 }{ 8 } \) of another medium pizza left.
To find how much pizza do they have altogether we have to add both the fractions.
\(\frac { 3 }{ 8 } \) + \(\frac { 2 }{ 8 } \) = \(\frac { 5 }{ 8 } \)
Therefore Mary Jane and Hector has \(\frac { 5 }{ 8 } \) pizza altogether.
Thus the correct answer is option c.

Question 2.
Jeannie ate \(\frac{1}{4}\) of an apple. Kelly ate \(\frac{2}{4}\) of the apple. How much did they eat in all?
Options:
a. \(\frac{1}{4}\)
b. \(\frac{2}{8}\)
c. \(\frac{3}{8}\)
d. \(\frac{3}{4}\)

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

Explanation:
Given,
Jeannie ate \(\frac { 1 }{ 4 } \) of an apple.
Kelly ate \(\frac { 2 }{ 4 } \) of the apple.
\(\frac { 1 }{ 4 } \) + \(\frac { 2 }{ 4 } \) = \(\frac { 3 }{ 4 } \)
Thus the correct answer is option d.

Spiral Review

Question 3.
Karen is making 14 different kinds of greeting cards. She is making 12 of each kind. How many greeting cards is she making?
Options:
a. 120
b. 132
c. 156
d. 168

Answer: 168

Explanation:
Given,
Karen is making 14 different kinds of greeting cards.
She is making 12 of each kind.
To find how many greeting cards she is making we have to multiply 14 and 12.
14 × 12 = 168.
Thus the correct answer is option d.

Question 4.
Jefferson works part time and earns $1,520 in four weeks. How much does he earn each week?
Options:
a. $305
b. $350
c. $380
d. $385

Answer: $380

Explanation:
Jefferson works part-time and earns $1,520 in four weeks.
1520 – 4 weeks
? – 1 week
1520/4 = $380
Thus the correct answer is option c

Question 5.
By installing efficient water fixtures, the average American can reduce water use to about 45 gallons of water per day. Using such water fixtures, about how many gallons of water would the average American use in December?
Options:
a. about 1,200 gallons
b. about 1,500 gallons
c. about 1,600 gallons
d. about 2,000 gallons

Answer: about 1,500 gallons

Explanation:
Given,
By installing efficient water fixtures, the average American can reduce water use to about 45 gallons of water per day.
1 day – 45 gallons
31 days – ?
45 × 31 = 1395 gallons
The number near to 1395 is 1500 gallons.
Thus the correct answer is option b.

Question 6.
Collin is making a bulletin board and note center. He is using square cork tiles and square dry-erase tiles. One of every 3 squares will be a cork square. If he uses 12 squares for the center, how many will be cork squares?
Options:
a. 3
b. 4
c. 6
d. 8

Answer: 4

Explanation:
Given that,
Collin is making a bulletin board and note center.
He is using square cork tiles and square dry-erase tiles.
One of every 3 squares will be a cork square.
12/3 = 4
Thus the correct answer is option b.

Common Core – Add and Subtract Fractions – Page No. 139

Subtract Fractions Using Models

Subtract. Use fraction strips to help.

Question 1.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 7 Add and Subtract Fractions Common Core - Add and Subtract Fractions img 8

Answer: 3/5

Explanation:
Given the fraction, 4/5 and 1/5
The denominators of both the fractions are the same so subtract the numerators.
4/5 – 1/5 = 3/5

Question 2.
\(\frac{3}{4}-\frac{1}{4}\) = \(\frac{□}{□}\)

Answer: 2/4

Explanation:
Given the fractions \(\frac { 3}{ 4 } \) and [/latex] \frac { 1}{ 4 } [/latex]
The denominators of both the fractions are the same so subtract the numerators.
\(\frac { 3}{ 4 } – \frac { 1}{ 4 } = \frac { 2 }{ 4 } \)

Question 3.
\(\frac{5}{6}-\frac{1}{6}\) = \(\frac{□}{□}\)

Answer: 4/6

Explanation:
Given the fractions \(\frac { 5 }{ 6 } \) and [/latex] \frac { 1 }{ 6 } [/latex]
The denominators of both the fractions are the same so subtract the numerators.
\(\frac { 5}{ 6 } – \frac { 1}{ 6 } = \frac { 4 }{ 6 } \)

Question 4.
\(\frac{7}{8}-\frac{1}{8}\) = \(\frac{□}{□}\)

Answer: 6/8

Explanation:
Given the fractions \(\frac { 7 }{ 8 } \) and [/latex] \frac { 1 }{ 8 } [/latex]
The denominators of both the fractions are the same so subtract the numerators.
\(\frac { 7}{ 8 } – \frac { 1}{ 8 } = \frac { 6 }{ 8 } \)

Question 5.
1 – \(\frac{2}{3}\) = \(\frac{□}{□}\)

Answer: 1/3

Explanation:
Given the fractions \(\frac { 1 }{ 3 } \) and [/latex] \frac { 2 }{ 3 } [/latex]
The denominators of both the fractions are the same so subtract the numerators.
\(\frac { 1}{ 3 } – \frac { 2}{ 3 } = \frac { 1}{ 3 } \)

Question 6.
\(\frac{8}{10}-\frac{2}{10}\) = \(\frac{□}{□}\)

Answer: 6/10

Explanation:
Given the fractions \(\frac { 8 }{ 10 } \) and [/latex] \frac { 2 }{ 10 } [/latex]
The denominators of both the fractions are the same so subtract the numerators.
\(\frac { 8}{ 10 } – \frac { 2}{ 10 } = \frac { 6 }{ 10 } \)

Question 7.
\(\frac{3}{4}-\frac{1}{4}\) = \(\frac{□}{□}\)

Answer: 2/4

Explanation:
Given the fractions \(\frac { 3 }{ 4 } \) and [/latex] \frac { 1 }{ 4 } [/latex]
The denominators of both the fractions are the same so subtract the numerators.
\(\frac { 3}{ 4 } – \frac { 1}{ 4 } = \frac { 2 }{ 4 } \)

Question 8.
\(\frac{7}{6}-\frac{5}{6}\) = \(\frac{□}{□}\)

Answer: 2/6

Explanation:
Given the fractions \(\frac { 7 }{ 6 } \) and [/latex] \frac { 5 }{ 6 } [/latex]
The denominators of both the fractions are the same so subtract the numerators.
\(\frac { 7}{ 6 } – \frac {5}{ 6 } = \frac { 2 }{ 6 } \)

Problem Solving

Use the table for 9 and 10.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 7 Add and Subtract Fractions Common Core - Add and Subtract Fractions img 9

Question 9.
Ena is making trail mix. She buys the items shown in the table. How many more pounds of pretzels than raisins does she buy?
\(\frac{□}{□}\)

Answer: 5/8 pound

Explanation:
Given that,
Ena is making trail mix.
pretzels = 7/8
Raisins = 2/8
To find the number of more pounds of pretzels than raisins she buy
we have to subtract both the fractions.
7/8 – 2/8 = 5/8

Question 10.
How many more pounds of granola than banana chips does she buy?
\(\frac{□}{□}\)

Answer: 2/8 pound

Explanation:
Granola = 5/8
Banana Chips = 3/8
To find How many more pounds of granola than banana chips does she buy we have to subtract both the fractions.
5/8 – 3/8 = 2/8 pounds

Common Core – Add and Subtract Fractions – Page No. 140

Lesson Check

Question 1.
Lee reads for \(\frac{3}{4}\) hour in the morning and \(\frac{2}{4}\) hour in the afternoon. How much longer does Lee read in the morning than in the afternoon?
Options:
a. 5 hours
b. \(\frac{5}{4}\) hours
c. \(\frac{4}{4}\) hour
d. \(\frac{1}{4}\) hour

Answer: \(\frac { 1}{ 4} \)

Explanation:
Given,
Lee reads for \(\frac { 3}{ 4} \) hour in the morning and \(\frac {2}{ 4} \) hour in the afternoon.
\(\frac { 3}{ 4} \) – \(\frac {2}{ 4} \) = \(\frac { 1}{ 4} \)
Lee read \(\frac { 1}{ 4} \) hour in the morning than in the afternoon.
Thus the correct answer is option d.

Question 2.
Which equation does the model below represent?
Go Math Grade 4 Answer Key Homework Practice FL Chapter 7 Add and Subtract Fractions Common Core - Add and Subtract Fractions img 10
Options:
a. \(\frac{3}{6}-\frac{2}{6}=\frac{1}{6}\)
b. \(\frac{2}{6}-\frac{1}{6}=\frac{1}{6}\)
c. \(\frac{5}{6}-\frac{3}{6}=\frac{2}{6}\)
d. 1 – \(\frac{3}{6}\) = \(\frac{3}{6}\)

Answer: \(\frac { 5}{ 6} – \frac { 3}{ 6} = \frac { 2}{ 6} \)

Explanation:
From the above figure we can say that \(\frac { 5}{ 6} – \frac { 3}{ 6} = \frac { 2}{ 6} \)
Thus the correct answer is option c.

Spiral Review

Question 3.
A city received 2 inches of rain each day for 3 days. The meteorologist said that if the rain had been snow, each inch of rain would have been 10 inches of snow. How much snow would that city have received in the 3 days?
Options:
a. 20 inches
b. 30 inches
c. 50 inches
d. 60 inches

Answer: 60 inches

Explanation:
Given,
A city received 2 inches of rain each day for 3 days.
2 × 3 inches = 6 inches
The meteorologist said that if the rain had been snow, each inch of rain would have been 10 inches of snow.
6 × 10 inches = 60 inches
Therefore the city has received 60 inches of snow in 3 days.
Thus the correct answer is option d.

Question 4.
At a party there were four large submarine sandwiches, all the same size. During the party, \(\frac{2}{3}\) of the chicken sandwich, \(\frac{3}{4}\) of the tuna sandwich, \(\frac{7}{12}\) of the roast beef sandwich, and \(\frac{5}{6}\) of the veggie sandwich were eaten. Which sandwich had the least amount left?
Options:
a. chicken
b. tuna
c. roast beef
d. veggie

Answer: veggie

Explanation:
Given,
At a party there were four large submarine sandwiches, all the same size. During the party, \(\frac { 2}{ 3} \) of the chicken sandwich, \(\frac { 3}{ 4} \) of the tuna sandwich, \(\frac { 7}{ 12} \) of the roast beef sandwich, and \(\frac { 5}{ 6} \) of the veggie sandwich were eaten.
Compare the fractions \(\frac { 2}{ 3} \), \(\frac { 3}{ 4} \) , \(\frac { 7}{ 12} \) and \(\frac { 5}{ 6} \).
Among all the fractions veggie has the least fraction.
Thus the correct answer is option d.

Question 5.
Deena uses \(\frac{3}{8}\) cup milk and \(\frac{2}{8}\) cup oil in a recipe. How much liquid does she use in all?
Options:
a. \(\frac{1}{8}\) cup
b. \(\frac{5}{8}\) cup
c. \(\frac{6}{8}\) cup
d. 5 cups

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

Explanation:
Given,
Deena uses \(\frac { 3}{ 8} \) cup milk and \(\frac { 2}{ 8} \) cup oil in a recipe.
\(\frac { 3}{ 8} \) + \(\frac { 2}{ 8} \) = \(\frac {5}{ 8} \) cup
Therefore she used \(\frac {5}{ 8} \) cup of milk in all.
Thus the correct answer is option b.

Question 6.
In the car lot, \(\frac{4}{12}\) of the cars are white and \(\frac{3}{12}\) of the cars are blue. What fraction of the cars in the lot are either white or blue?
Options:
a. \(\frac{1}{12}\)
b. \(\frac{7}{24}\)
c. \(\frac{7}{12}\)
d. 7

Answer: \(\frac { 7}{ 12} \)

Explanation:
Given,
In the car lot, \(\frac { 4}{ 12} \) of the cars are white and \(\frac { 3}{ 12} \) of the cars are blue.
\(\frac { 4}{ 12} \) + \(\frac { 3}{ 12} \) = \(\frac { 7}{ 12} \)
Thus the correct answer is option c.

Common Core – Add and Subtract Fractions – Page No. 141

Add and Subtract Fractions

Find the sum or difference.

Question 1.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 7 Add and Subtract Fractions Common Core - Add and Subtract Fractions img 11

Answer: 12/12

Explanation:
The denominators of both the fractions are the same so add the numerators.
\(\frac{4}{12}\) + \(\frac{8}{12}\)
= \(\frac{12}{12}\)

Question 2.
\(\frac{3}{6}-\frac{1}{6}\) = \(\frac{□}{□}\)

Answer: 2/6

Explanation:
The denominators of both the fractions are the same so Subtract the numerators.
\(\frac{3}{6}\) – \(\frac{1}{6}\)
= \(\frac{2}{6}\)

Question 3.
\(\frac{4}{5}-\frac{3}{5}\) = \(\frac{□}{□}\)

Answer: 1/5

Explanation:
The denominators of both the fractions are the same so Subtract the numerators.
\(\frac{4}{5}\) – \(\frac{3}{5}\)
= \(\frac{1}{5}\)

Question 4.
\(\frac{6}{10}+\frac{3}{10}\) = \(\frac{□}{□}\)

Answer: 9/10

Explanation:
The denominators of both the fractions are the same so add the numerators.
\(\frac{6}{10}+\frac{3}{10}\) = \(\frac{9}{10}\)

Question 5.
1 – \(\frac{3}{8}\) = \(\frac{□}{□}\)

Answer: 5/8

Explanation:
The denominators of both the fractions are the same so Subtract the numerators.
1 – \(\frac{3}{8}\)
= \(\frac{8}{8}\) – \(\frac{3}{8}\)
= \(\frac{5}{8}\)

Question 6.
\(\frac{1}{4}+\frac{2}{4}\) = \(\frac{□}{□}\)

Answer: 3/4

Explanation:
The denominators of both the fractions are the same so add the numerators.
\(\frac{1}{4}+\frac{2}{4}\) = \(\frac{3}{4}\)

Question 7.
\(\frac{9}{12}-\frac{5}{12}\) = \(\frac{□}{□}\)

Answer: 4/12

Explanation:
The denominators of both the fractions are the same so Subtract the numerators.
\(\frac{9}{12}-\frac{5}{12}\) = \(\frac{4}{12}\)

Question 8.
\(\frac{5}{6}-\frac{2}{6}\) = \(\frac{□}{□}\)

Answer: 3/6

Explanation:
The denominators of both the fractions are the same so Subtract the numerators.
\(\frac{5}{6}-\frac{2}{6}\) = \(\frac{3}{6}\)

Question 9.
\(\frac{2}{3}+\frac{1}{3}\) = \(\frac{□}{□}\)

Answer: 3/3 = 1

Explanation:
The denominators of both the fractions are the same so add the numerators.
\(\frac{2}{3}+\frac{1}{3}\) = \(\frac{3}{3}\) = 1

Problem Solving

Use the table for 10 and 11. Go Math Grade 4 Answer Key Homework Practice FL Chapter 7 Add and Subtract Fractions Common Core - Add and Subtract Fractions img 12

Question 10.
Guy finds how far his house is from several locations and makes the table shown. How much farther away from Guy’s house is the library than the cafe?
\(\frac{□}{□}\)

Answer: \(\frac{5}{10}\) mile

Explanation:
The distance from Guy’s house to the library is \(\frac{9}{10}\) mile
The distance from Guy’s house to the cafe is \(\frac{4}{10}\) mile
To find how much farther away from Guy’s house is the library than the cafe subtract both the fractions.
\(\frac{9}{10}\) – \(\frac{4}{10}\) = \(\frac{5}{10}\) mile

Question 11.
If Guy walks from his house to school and back, how far does he walk?
\(\frac{□}{□}\)

Answer: 10/10 mile

Explanation:
The distance from Guy’s house to school = \(\frac{5}{10}\) mile
From school to house \(\frac{5}{10}\) mile
\(\frac{5}{10}\) + \(\frac{5}{10}\) = \(\frac{10}{10}\) mile

Common Core – Add and Subtract Fractions – Page No. 142

Lesson Check

Question 1.
Mr. Angulo buys \(\frac{5}{8}\) pound of red grapes and \(\frac{3}{8}\) pound of green grapes. How many pounds of grapes did Mr. Angulo buy in all?
Options:
a. \(\frac{1}{8}\) pound
b. \(\frac{2}{8}\) pound
c. 1 pound
d. 2 pounds

Answer: 1 pound

Explanation:
Given that,
Mr. Angulo buys \(\frac{5}{8}\) pound of red grapes and \(\frac{3}{8}\)pound of green grapes.
\(\frac{5}{8}\) + \(\frac{3}{8}\)
= \(\frac{8}{8}\)
= 1
Thus the correct answer is option c.

Question 2.
Which equation does the model below represent?
Go Math Grade 4 Answer Key Homework Practice FL Chapter 7 Add and Subtract Fractions Common Core - Add and Subtract Fractions img 13
Options:
a. \(\frac{7}{8}+\frac{2}{8}=\frac{9}{8}\)
b. \(\frac{5}{8}-\frac{2}{8}=\frac{3}{8}\)
c. \(\frac{8}{8}-\frac{5}{8}=\frac{3}{8}\)
d. \(\frac{7}{8}-\frac{2}{8}=\frac{5}{8}\)

Answer: \(\frac{7}{8}\) – \(\frac{2}{8}\) = \(\frac{5}{8}\)

Explanation:
By seeing the above figure we can say that, the equation of the model is
\(\frac{7}{8}\) – \(\frac{2}{8}\) = \(\frac{5}{8}\)
Thus the correct answer is option d.

Spiral Review

Question 3.
There are 6 muffins in a package. How many packages will be needed to feed 48 people if each person has 2 muffins?
Options:
a. 4
b. 8
c. 16
d. 24

Answer: 16

Explanation:
There are 6 muffins in a package.
Number of people = 48
48/6 = 8
Also given that each person gets 2 muffins.
8 × 2 = 16
Thus the correct answer is option c.

Question 4.
Camp Oaks gets 32 boxes of orange juice and 56 boxes of apple juice. Each shelf in the cupboard can hold 8 boxes of juice. What is the least number of shelves
needed for all the juice boxes?
Options:
a. 4
b. 7
c. 11
d. 88

Answer: 11

Explanation:
Given,
Camp Oaks gets 32 boxes of orange juice and 56 boxes of apple juice.
Each shelf in the cupboard can hold 8 boxes of juice.
First, add the boxes of orange juice and apple juice.
32 + 56 = 88 boxes of juice
Now divide 88 by 8
88/8 = 11
Thus the correct answer is option c.

Question 5.
A machine makes 18 parts each hour. If the machine operates 24 hours a day, how many parts can it make in one day
Options:
a. 302
b. 332
c. 362
d. 432

Answer: 432

Explanation:
Given,
A machine makes 18 parts each hour.
Multiply the number of parts with the number of hours.
18 × 24 = 432 parts in a day.
Thus the correct answer is option d.

Question 6.
Which equation does the model below represent?
Go Math Grade 4 Answer Key Homework Practice FL Chapter 7 Add and Subtract Fractions Common Core - Add and Subtract Fractions img 14
Options:
a. \(\frac{5}{6}-\frac{4}{6}=\frac{1}{6}\)
b. \(\frac{4}{5}-\frac{1}{5}=\frac{3}{5}\)
c. \(\frac{5}{5}-\frac{4}{5}=\frac{1}{5}\)
d. \(\frac{6}{6}-\frac{4}{6}=\frac{2}{6}\)

Answer: \(\frac{5}{6}\) – \(\frac{4}{6}\) = \(\frac{1}{6}\)

Explanation:
By observing the figure we can say that the equation is \(\frac{5}{6}\) – \(\frac{4}{6}\) = \(\frac{1}{6}\).
Thus the correct answer is option a.

Common Core – Add and Subtract Fractions – Page No. 143

Rename Fractions and Mixed Numbers

Write the mixed number as a fraction.

Question 1.
2 \(\frac{3}{5}\)
Go Math Grade 4 Answer Key Homework Practice FL Chapter 7 Add and Subtract Fractions Common Core - Add and Subtract Fractions img 15

 

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

Answer: \(\frac{13}{3}\)

Explanation:
\(\frac{3}{3}\) + \(\frac{3}{3}\) + \(\frac{3}{3}\) + \(\frac{3}{3}\) + \(\frac{1}{3}\) = \(\frac{13}{3}\)

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

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

Explanation:
\(\frac{5}{5}\) + \(\frac{2}{5}\) = \(\frac{7}{5}\)

Question 4.
3 \(\frac{3}{2}\)
\(\frac{□}{□}\)

Answer: \(\frac{9}{2}\)

Explanation:
\(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{1}{2}\) = \(\frac{9}{2}\)

Question 5.
4 \(\frac{1}{8}\)
\(\frac{□}{□}\)

Answer: \(\frac{33}{8}\)

Explanation:
\(\frac{8}{8}\) + \(\frac{8}{8}\) + \(\frac{8}{8}\) + \(\frac{8}{8}\) + \(\frac{1}{8}\) = \(\frac{33}{8}\)

Question 6.
1 \(\frac{7}{10}\)
\(\frac{□}{□}\)

Answer: \(\frac{17}{10}\)

Explanation:
\(\frac{10}{10}\) + \(\frac{7}{10}\) = \(\frac{17}{10}\)

Question 7.
5 \(\frac{1}{2}\)
\(\frac{□}{□}\)

Answer: \(\frac{11}{2}\)

Explanation:
\(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{1}{2}\) = \(\frac{11}{2}\)

Question 8.
2 \(\frac{3}{8}\)
\(\frac{□}{□}\)

Answer: \(\frac{19}{8}\)

Explanation:
\(\frac{8}{8}\) + \(\frac{8}{8}\) + \(\frac{3}{8}\)

Write the fraction as a mixed number.

Question 9.
\(\frac{31}{6}\)
______ \(\frac{□}{□}\)

Answer: 5 \(\frac{1}{6}\)

Explanation:
\(\frac{6}{6}\) + \(\frac{6}{6}\) + \(\frac{6}{6}\) + \(\frac{6}{6}\) + \(\frac{6}{6}\) + \(\frac{1}{6}\)
1 + 1 + 1 + 1 + 1 + \(\frac{1}{6}\) = 5 \(\frac{1}{6}\)

Question 10.
\(\frac{20}{10}\)
______ \(\frac{□}{□}\)

Answer: 2

Explanation:
\(\frac{10}{10}\) + \(\frac{10}{10}\) = 1 + 1 = 2

Question 11.
\(\frac{15}{8}\)
______ \(\frac{□}{□}\)

Answer: 1 \(\frac{7}{8}\)

Explanation:
\(\frac{8}{8}\) + \(\frac{7}{8}\)
1 + \(\frac{7}{8}\) = 1 \(\frac{7}{8}\)

Question 12.
\(\frac{13}{6}\)
______ \(\frac{□}{□}\)

Answer: 2 \(\frac{1}{6}\)

Explanation:
\(\frac{6}{6}\) + \(\frac{6}{6}\) + \(\frac{1}{6}\)
= 1 + 1 + \(\frac{1}{6}\) = 2 \(\frac{1}{6}\)

Question 13.
\(\frac{23}{10}\)
______ \(\frac{□}{□}\)

Answer: 2 \(\frac{3}{10}\)

Explanation:
\(\frac{10}{10}\) + \(\frac{10}{10}\) + \(\frac{3}{10}\)
1 + 1 + \(\frac{3}{10}\) = 2 \(\frac{3}{10}\)

Question 14.
\(\frac{19}{5}\)
______ \(\frac{□}{□}\)

Answer: 3 \(\frac{4}{5}\)

Explanation:
\(\frac{5}{5}\) + \(\frac{5}{5}\) + \(\frac{5}{5}\) + \(\frac{4}{5}\)
1 + 1 + 1 + \(\frac{4}{5}\) = 3 \(\frac{4}{5}\)

Question 15.
\(\frac{11}{3}\)
______ \(\frac{□}{□}\)

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

Explanation:
\(\frac{3}{3}\) + \(\frac{3}{3}\) + \(\frac{3}{3}\) + \(\frac{2}{3}\)
= 1 + 1 + 1 \(\frac{2}{3}\)
= 3 \(\frac{2}{3}\)

Question 16.
\(\frac{9}{2}\)
______ \(\frac{□}{□}\)

Answer: 4 \(\frac{1}{2}\)

Explanation:
\(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{1}{2}\)
= 1 + 1 + 1 + 1 + \(\frac{1}{2}\)
= 4 \(\frac{1}{2}\)

Question 17.
A recipe calls for 2 \(\frac{2}{4}\) cups of raisins, but Julie only has a \(\frac{1}{4}\) -cup measuring cup. How many \(\frac{1}{4}\) cups does Julie need to measure out 2 \(\frac{2}{4}\) cups of raisins?
She needs ______ \(\frac{1}{4}\) cups

Answer: 10 \(\frac{1}{4}\) cups

Explanation:
Given,
A recipe calls for 2 \(\frac{2}{4}\) cups of raisins, but Julie only has a \(\frac{1}{4}\) -cup measuring cup.
\(\frac{4}{4}\) + \(\frac{4}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\)
= 10 \(\frac{1}{4}\) cups

Question 18.
If Julie needs 3 \(\frac{1}{4}\) cups of oatmeal, how many 14 cups of oatmeal will she use?
She will use ______ \(\frac{1}{4}\) cups of oatmeal

Answer: 13 \(\frac{1}{4}\) cups of oatmeal

Explanation:
\(\frac{4}{4}\) + \(\frac{4}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\)
= 13 \(\frac{1}{4}\)
Therefore Julie needs 13 \(\frac{1}{4}\) cups of oatmeal.

Common Core – Add and Subtract Fractions – Page No. 144

Lesson Check

Question 1.
Which of the following is equivalent to \(\frac{16}{3}\)?
Options:
a. 3 \(\frac{1}{5}\)
b. 3 \(\frac{2}{5}\)
c. 5 \(\frac{1}{3}\)
d. 5 \(\frac{6}{3}\)

Answer: 5 \(\frac{1}{3}\)

Explanation:
Convert from improper fraction to the mixed fraction.
\(\frac{16}{3}\) = \(\frac{3}{3}\) + \(\frac{3}{3}\) + \(\frac{3}{3}\) + \(\frac{3}{3}\) + \(\frac{3}{3}\) + \(\frac{1}{3}\)
= 5 \(\frac{1}{3}\)
Thus the correct answer is option c.

Question 2.
Stacey filled her \(\frac{1}{2}\) cup measuring cup seven times to have enough flour for a cake recipe. How much flour does the cake recipe call for?
Options:
a. 3 cups
b. 3 \(\frac{1}{2}\) cups
c. 4 cups
d. 4 \(\frac{1}{2}\) cups

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

Explanation:
Given,
Stacey filled her \(\frac{1}{2}\)cup measuring cup seven times to have enough flour for a cake recipe.
\(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{1}{2}\)
1 + 1 + 1 + \(\frac{1}{2}\)
= 3 \(\frac{1}{2}\) cups
Thus the correct answer is option b.

Spiral Review

Question 3.
Becki put some stamps into her stamp collection book. She put 14 stamps on each page. If she completely filled 16 pages, how many stamps did she put in the book?
Options:
a. 224
b. 240
c. 272
d. 275

Answer: 224

Explanation:
Becki put some stamps into her stamp collection book.
She put 14 stamps on each page.
If she completely filled 16 pages
Multiply 14 with 16 pages.
14 × 16 = 224 pages
Thus the correct answer is option a.

Question 4.
Brian is driving 324 miles to visit some friends. He wants to get there in 6 hours. How many miles does he need to drive each hour?
Options:
a. 48 miles
b. 50 miles
c. 52 miles
d. 54 miles

Answer: 54 miles

Explanation:
Brian is driving 324 miles to visit some friends. He wants to get there in 6 hours.
Divide the number of miles by hours.
324/6 = 54 miles
Thus the correct answer is option d.

Question 5.
During a bike challenge, riders have to collect various colored ribbons. Each \(\frac{1}{2}\) mile they collect a red ribbon, each \(\frac{1}{8}\) mile they collect a green ribbon, and each \(\frac{1}{4}\) mile they collect a blue ribbon. Which colors of ribbons will be collected at the \(\frac{3}{4}\) mile marker?
Options:
a. red and green
b. red and blue
c. green and blue
d. red, green, and blue

Answer: green and blue

Explanation:
Given,
During a bike challenge, riders have to collect various colored ribbons.
Each \(\frac{1}{2}\) mile they collect a red ribbon, each \(\frac{1}{8}\) mile they collect a green ribbon, and each \(\frac{1}{4}\) mile they collect a blue ribbon.
Green and Blue colors of ribbons will be collected at the \(\frac{3}{4}\) mile marker.
Thus the correct answer is option c.

Question 6.
Stephanie had \(\frac{7}{8}\) pound of bird seed. She used \(\frac{3}{8}\) pound to fill a bird feeder. How much bird seed does Stephanie have left?
Options:
a. \(\frac{3}{8}\) pound
b. \(\frac{4}{8}\) pound
c. 1 pound
d. \(\frac{10}{8}\) pound

Answer: \(\frac{4}{8}\) pound

Explanation:
Given,
Stephanie had \(\frac{7}{8}\) pound of bird seed.
She used \(\frac{3}{8}\) pound to fill a bird feeder.
\(\frac{7}{8}\) – \(\frac{3}{8}\) = \(\frac{4}{8}\) pound
Thus the correct answer is option b.

Common Core – Add and Subtract Fractions – Page No. 145

Add and Subtract Mixed Numbers

Find the sum. Write the sum as a mixed number, so the fractional part is less than 1.

Question 1.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 7 Add and Subtract Fractions Common Core - Add and Subtract Fractions img 16

Question 2.
4 \(\frac{1}{2}\)
+ 2 \(\frac{1}{2}\)
_______ \(\frac{□}{□}\)

Answer: 7

4 \(\frac{1}{2}\)
+2 \(\frac{1}{2}\)
6 \(\frac{2}{2}\) = 6 + 1 = 7

Question 3.
2 \(\frac{2}{3}\)
+ 3 \(\frac{2}{3}\)
_______ \(\frac{□}{□}\)

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

Explanation:
2 \(\frac{2}{3}\)
+3 \(\frac{2}{3}\)
5 \(\frac{4}{3}\)
= 5 + 1 \(\frac{1}{3}\)
= 6 \(\frac{1}{3}\)

Question 4.
6 \(\frac{4}{5}\)
+ 7 \(\frac{4}{5}\)
_______ \(\frac{□}{□}\)

Answer: 14 \(\frac{3}{5}\)

Explanation:
6 \(\frac{4}{5}\)
+7 \(\frac{4}{5}\)
13 \(\frac{8}{5}\)
13 + 1 \(\frac{3}{5}\)
= 14 \(\frac{3}{5}\)

Question 5.
9 \(\frac{3}{6}\)
+ 2 \(\frac{2}{6}\)
_______ \(\frac{□}{□}\)

Answer: 11 \(\frac{5}{6}\)

Explanation:
9 \(\frac{3}{6}\)
+2 \(\frac{2}{6}\)
11 \(\frac{5}{6}\)

Question 6.
8 \(\frac{4}{12}\)
+ 3 \(\frac{6}{12}\)
_______ \(\frac{□}{□}\)

Answer: 11 \(\frac{10}{12}\)

Explanation:
8 \(\frac{4}{12}\)
+3 \(\frac{6}{12}\)
11 \(\frac{10}{12}\)

Question 7.
4 \(\frac{3}{8}\)
+ 1 \(\frac{5}{8}\)
_______ \(\frac{□}{□}\)

Answer: 6

Explanation:
4 \(\frac{3}{8}\)
+1 \(\frac{5}{8}\)
5 \(\frac{8}{8}\)
= 5 + 1 = 6

Question 8.
9 \(\frac{5}{10}\)
+ 6 \(\frac{3}{10}\)
_______ \(\frac{□}{□}\)

Answer: 15 \(\frac{8}{10}\)

Explanation:
9 \(\frac{5}{10}\)
+6 \(\frac{3}{10}\)
15 \(\frac{8}{10}\)

Find the difference.

Question 9.
6 \(\frac{7}{8}\)
– 4 \(\frac{3}{8}\)
_______ \(\frac{□}{□}\)

Answer: 2 \(\frac{4}{8}\)

Explanation:
6 \(\frac{7}{8}\)
-4 \(\frac{3}{8}\)
2 \(\frac{4}{8}\)

Question 10.
4 \(\frac{2}{3}\)
– 3 \(\frac{1}{3}\)
_______ \(\frac{□}{□}\)

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

Explanation:
4 \(\frac{2}{3}\)
-3 \(\frac{1}{3}\)
1 \(\frac{1}{3}\)

Question 11.
6 \(\frac{4}{5}\)
– 3 \(\frac{3}{5}\)
_______ \(\frac{□}{□}\)

Answer: 3 \(\frac{1}{5}\)

Explanation:
6 \(\frac{4}{5}\)
-3 \(\frac{3}{5}\)
3 \(\frac{1}{5}\)

Question 12.
7 \(\frac{3}{4}\)
– 2 \(\frac{1}{4}\)
_______ \(\frac{□}{□}\)

Answer: 5 \(\frac{1}{2}\)

Explanation:
7 \(\frac{3}{4}\)
-2 \(\frac{1}{4}\)
5 \(\frac{2}{4}\) = 5 \(\frac{1}{2}\)

Problem Solving

Question 13.
James wants to send two gifts by mail. One package weighs 2 \(\frac{3}{4}\) pounds. The other package weighs 1 \(\frac{3}{4}\) pounds. What is the total weight of the packages?
_______ \(\frac{□}{□}\)

Answer: 4 \(\frac{1}{2}\)

Explanation:
2 \(\frac{3}{4}\)
+ 1 \(\frac{3}{4}\)
4 \(\frac{1}{2}\)

Question 14.
Tierra bought 4 \(\frac{3}{8}\) yards blue ribbon and 2 \(\frac{1}{8}\) yards yellow ribbon for a craft project. How much more blue ribbon than yellow ribbon did Tierra buy?
_______ \(\frac{□}{□}\)

Answer: 2 \(\frac{1}{4}\)

Explanation:
Given,
4 \(\frac{3}{8}\)
-2 \(\frac{1}{8}\) 
2 \(\frac{1}{4}\)

Common Core – Add and Subtract Fractions – Page No. 146

Lesson Check

Question 1.
Brad has two lengths of copper pipe to fit together. One has a length of 2 \(\frac{5}{12}\) feet and the other has a length of 3 \(\frac{7}{12}\) feet. How many feet of pipe does he have in all?
Options:
a. 5 feet
b. 5 \(\frac{6}{12}\) feet
c. 5 \(\frac{10}{12}\)
d. 6 feet

Answer: 5 feet

Explanation:
Given,
Brad has two lengths of copper pipe to fit together. One has a length of 2 \(\frac{5}{12}\) feet and the other has a length of 3 \(\frac{7}{12}\) feet.
Add both the lengths
2 \(\frac{5}{12}\) + 3 \(\frac{7}{12}\)
= 5 \(\frac{12}{12}\) = 5 feet
Thus the correct answer is option a.

Question 2.
A pattern calls for 2 \(\frac{1}{4}\)yards of material and 1 \(\frac{1}{4}\)yards of lining. How much total fabric is needed?
Options:
a. 2 \(\frac{2}{4}\) yards
b. 3 yards
c. 3 \(\frac{1}{4}\) yards
d. 3 \(\frac{2}{4}\) yards

Answer: 3 \(\frac{2}{4}\) yards

Explanation:
Given,
A pattern calls for 2 \(\frac{1}{4}\) yards of material and 1 \(\frac{1}{4}\) yards of lining.
2 \(\frac{1}{4}\) + 1 \(\frac{1}{4}\)
= 3 + \(\frac{1}{4}\) + \(\frac{1}{4}\)
= 3 \(\frac{2}{4}\) yards
Thus the correct answer is option d.

Spiral Review

Question 3.
Shanice has 23 baseball trading cards of star players. She agrees to sell them for $16 each. How much will she get for the cards?
Options:
a. $258
b. $358
c. $368
d. $468

Answer: $368

Explanation:
Given,
Shanice has 23 baseball trading cards of star players. She agrees to sell them for $16 each.
To find how much will she get for the cards
23 × 16 = 368
Therefore she will get $368 for the cards.
Thus the correct answer is option c.

Question 4.
Nanci is volunteering at the animal shelter. She wants to spend an equal amount of time playing with each dog. She has 145 minutes to play with all 7 dogs. About how much time can she spend with each dog?
Options:
a. about 10 minutes
b. about 20 minutes
c. about 25 minutes
d. about 26 minutes

Answer: about 20 minutes

Explanation:
Given,
Nanci is volunteering at the animal shelter. She wants to spend an equal amount of time playing with each dog. She has 145 minutes to play with all 7 dogs.
145/7 = 20.7
Therefore she can spend about 20 minutes with each dog.
Thus the correct answer is option b.

Question 5.
Frieda has 12 red apples and 15 green apples. She is going to share the apples equally among 8 people and keep any extra apples for herself. How many apples
will Frieda keep for herself?
Options:
a. 3
b. 4
c. 6
d. 7

Answer: 3

Explanation:
Given,
Frieda has 12 red apples and 15 green apples.
She is going to share the apples equally among 8 people and keep any extra apples for herself.
12 + 15 = 27
27/8
27 – 24 = 3
Thus Frieda keep for herself 3 apples.
Thus the correct answer is option a.

Question 6.
The Lynch family bought a house for $75,300. A few years later, they sold the house for $80,250. How much greater was the selling price than the purchase price?
Options:
a. $4,950
b. $5,050
c. $5,150
d. $5,950

Answer: $4,950

Explanation:
Given,
The Lynch family bought a house for $75,300.
A few years later, they sold the house for $80,250.
$80,250 – $75,300 = $4,950
Thus the correct answer is option a.

Common Core – Add and Subtract Fractions – Page No. 147

Record Subtraction with

Find the difference.

Question 1.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 7 Add and Subtract Fractions Common Core - Add and Subtract Fractions img 17

Question 2.
6
– 3 \(\frac{2}{5}\)
_______ \(\frac{□}{□}\)

Answer: 2 \(\frac{3}{5}\)

Explanation:
First subtract the whole numbers
6 – 3 = 3
Next subtract the fractions,
3 – \(\frac{2}{5}\) = 2 \(\frac{3}{5}\)

Question 3.
5 \(\frac{1}{4}\)
– 2 \(\frac{3}{4}\)
_______ \(\frac{□}{□}\)

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

Explanation:
First subtract the whole numbers
5 – 2 = 3
Next subtract the fractions,
\(\frac{1}{4}\) – \(\frac{3}{4}\) = – \(\frac{1}{2}\)
3 – \(\frac{1}{2}\)
= 2 \(\frac{1}{2}\)

Question 4.
9 \(\frac{3}{8}\)
– 8 \(\frac{7}{8}\)
_______ \(\frac{□}{□}\)

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

Explanation:
First subtract the whole numbers
9 – 8 = 1
Next subtract the fractions,
\(\frac{3}{8}\) – \(\frac{7}{8}\)
= – \(\frac{4}{8}\)
= – \(\frac{1}{2}\)
= 1 – \(\frac{1}{2}\)
= \(\frac{1}{2}\)

Question 5.
12 \(\frac{3}{10}\)
– 7 \(\frac{7}{10}\)
_______ \(\frac{□}{□}\)

Answer: 4 \(\frac{3}{5}\)

Explanation:
First subtract the whole numbers
12 – 7 = 5
Next subtract the fractions,
\(\frac{3}{10}\) – \(\frac{7}{10}\) = – \(\frac{4}{10}\)
5 – \(\frac{4}{10}\)
5 – \(\frac{2}{5}\) = 4 \(\frac{3}{5}\)

Question 6.
8 \(\frac{1}{6}\)
– 3 \(\frac{5}{6}\)
_______ \(\frac{□}{□}\)

Answer: 4 \(\frac{1}{3}\)

Explanation:
First subtract the whole numbers
8 – 3 = 5
Next subtract the fractions,
\(\frac{1}{6}\) – \(\frac{5}{6}\) = – \(\frac{2}{3}\)
5 – \(\frac{2}{3}\) = 4 \(\frac{1}{3}\)

Question 7.
7 \(\frac{3}{5}\)
– 4 \(\frac{4}{5}\)
_______ \(\frac{□}{□}\)

Answer: 2 \(\frac{4}{5}\)

Explanation:
First subtract the whole numbers
7 – 4 = 3
Next subtract the fractions,
\(\frac{3}{5}\) – \(\frac{4}{5}\) = – \(\frac{1}{5}\)
3 – \(\frac{1}{5}\) = 2 \(\frac{4}{5}\)

Question 8.
10 \(\frac{1}{2}\)
– 8 \(\frac{1}{2}\)
_______ \(\frac{□}{□}\)

Answer: 2

Explanation:
First subtract the whole numbers
10 – 8 = 2
\(\frac{1}{2}\) – \(\frac{1}{2}\) = 0

Question 9.
7 \(\frac{1}{6}\)
– 2 \(\frac{5}{6}\)
_______ \(\frac{□}{□}\)

Answer: 4 \(\frac{1}{3}\)

Explanation:
First subtract the whole numbers
7 – 2 = 5
Next subtract the fractions,
\(\frac{1}{6}\) – \(\frac{5}{6}\) = – \(\frac{4}{6}\)
5 – \(\frac{4}{6}\) = 4 \(\frac{1}{3}\)

Question 10.
9 \(\frac{3}{12}\)
– 4 \(\frac{7}{12}\)
_______ \(\frac{□}{□}\)

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

Explanation:
First subtract the whole numbers
9 – 4 = 5
Next subtract the fractions,
\(\frac{3}{12}\) – \(\frac{7}{12}\) = – \(\frac{4}{12}\) = – \(\frac{1}{3}\)
5 – \(\frac{1}{3}\) = 2 \(\frac{2}{3}\)

Question 11.
9 \(\frac{1}{10}\)
– 8 \(\frac{7}{10}\)
_______ \(\frac{□}{□}\)

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

Explanation:
First subtract the whole numbers
9 – 8 = 1
Next subtract the fractions,
\(\frac{1}{10}\) – \(\frac{7}{10}\) = – \(\frac{6}{10}\)
1 – \(\frac{3}{5}\) = \(\frac{2}{5}\)

Question 12.
9 \(\frac{1}{3}\)
– \(\frac{2}{3}\)
_______ \(\frac{□}{□}\)

Answer: 8 \(\frac{2}{3}\)

Explanation:
9 \(\frac{1}{3}\)
– \(\frac{2}{3}\)
8 \(\frac{2}{3}\)

Question 13.
3 \(\frac{1}{4}\)
– 1 \(\frac{3}{4}\)
_______ \(\frac{□}{□}\)

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

3 \(\frac{1}{4}\)
– 1 \(\frac{3}{4}\)
1 \(\frac{1}{2}\)

Question 14.
4 \(\frac{5}{8}\)
– 1 \(\frac{7}{8}\)
_______ \(\frac{□}{□}\)

Answer: 2 \(\frac{3}{4}\)

Explanation:
First subtract the whole numbers
4 – 1 = 3
Next subtract the fractions,
\(\frac{5}{8}\) – \(\frac{7}{8}\) = – \(\frac{1}{4}\)
3 – \(\frac{1}{4}\) = 2 \(\frac{3}{4}\)

Question 15.
5 \(\frac{1}{12}\)
– 3 \(\frac{8}{12}\)
_______ \(\frac{□}{□}\)

Answer: 1 \(\frac{5}{12}\)

Explanation:
First subtract the whole numbers
5 – 3 = 2
Next subtract the fractions,
\(\frac{1}{12}\) – \(\frac{8}{12}\) = – \(\frac{7}{12}\)
2 – \(\frac{7}{12}\) = 1 \(\frac{5}{12}\)

Question 16.
7
– 1 \(\frac{3}{5}\)
_______ \(\frac{□}{□}\)

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

Explanation:
7
– 1 \(\frac{3}{5}\)
5 \(\frac{2}{5}\)

Problem Solving

Question 17.
Alicia buys a 5-pound bag of rocks for a fish tank. She uses 1 \(\frac{1}{8}\) pounds for a small fish bowl. How much is left?
_______ \(\frac{□}{□}\)

Answer: 3 \(\frac{7}{8}\)

Explanation:
Given,
Alicia buys a 5-pound bag of rocks for a fish tank. She uses 1 \(\frac{1}{8}\) pounds for a small fish bowl.
First subtract the whole numbers
5 – 1 = 4
4 – 1 \(\frac{1}{8}\)
= 3 \(\frac{7}{8}\)

Question 18.
Xavier made 25 pounds of roasted almonds for a fair. He has 3 \(\frac{1}{2}\) pounds left at the end of the fair. How many pounds of roasted almonds did he sell at the fair?
_______ \(\frac{□}{□}\)

Answer: 21 \(\frac{1}{2}\)

Explanation:
Given,
Xavier made 25 pounds of roasted almonds for a fair.
He has 3 \(\frac{1}{2}\) pounds left at the end of the fair.
First subtract the whole numbers
25 – 3 = 22
22 – \(\frac{1}{2}\) = 21 \(\frac{1}{2}\)

Common Core – Add and Subtract Fractions – Page No. 148

Lesson Check

Question 1.
Reggie is making a double-layer cake. The recipe for the first layer calls for 2 \(\frac{1}{4}\) cups sugar. The recipe for the second layer calls for 1 \(\frac{1}{4}\) cups sugar. Reggie has 5 cups of sugar. How much will he have left after making both recipes?
Options:
a. 1 \(\frac{1}{4}\) cups
b. 1 \(\frac{2}{4}\) cups
c. 2 \(\frac{1}{4}\) cups
d. 2 \(\frac{2}{4}\) cups

Answer: 1 \(\frac{2}{4}\) cups

Explanation:
Given,
Reggie is making a double-layer cake. The recipe for the first layer calls for 2 \(\frac{1}{4}\) cups sugar.
The recipe for the second layer calls for 1 \(\frac{1}{4}\) cups sugar.
Reggie has 5 cups of sugar.
2 \(\frac{1}{4}\) + 1 \(\frac{1}{4}\) = 3 \(\frac{1}{2}\)
5 – 3 \(\frac{1}{2}\) = 1 \(\frac{2}{4}\) cups
Thus the correct answer is option b.

Question 2.
Kate has 4 \(\frac{3}{8}\) yards of fabric and needs 2 \(\frac{7}{8}\) yards to make a skirt. How much extra fabric will she have left after making the skirt?
Options:
a. 2 \(\frac{4}{8}\) yards
b. 2 \(\frac{2}{8}\) yards
c. 1 \(\frac{4}{8}\) yards
d. 1 \(\frac{2}{8}\) yards

Answer: 1 \(\frac{4}{8}\) yards

Explanation:
Given,
Kate has 4 \(\frac{3}{8}\) yards of fabric and needs 2 \(\frac{7}{8}\) yards to make a skirt.
First, subtract the whole numbers
4 – 2 = 2
Next, subtract the fractions,
\(\frac{3}{8}\) – \(\frac{7}{8}\) = – \(\frac{4}{8}\)
2 – \(\frac{4}{8}\) = 1 \(\frac{4}{8}\) yards
Thus the correct answer is option c.

Spiral Review

Question 3.
Paulo has 128 glass beads to use to decorate picture frames. He wants to use the same number of beads on each frame. If he decorates 8 picture frames, how many beads will he put on each frame?
Options:
a. 6
b. 7
c. 14
d. 16

Answer: 16

Explanation:
Given,
Paulo has 128 glass beads to use to decorate picture frames. He wants to use the same number of beads on each frame
128/8 = 16
Thus the correct answer is option d.

Question 4.
Madison is making party favors. She wants to make enough favors so each guest gets the same number of favors. She knows there will be 6 or 8 guests at the party. What is the least number of party favors Madison should make?
Options:
a. 18
b. 24
c. 30
d. 32

Answer: 24

Explanation:
Given,
Madison is making party favors. She wants to make enough favors so each guest gets the same number of favors.
She knows there will be 6 or 8 guests at the party.
To find the least number of party favors, we have to consider the number of guests.
In this case, there are two possibilities—6 or 8.
For 6: 6, 12, 18, 24 (Add 6 to each number)
For 8: 8, 16, 24 (Add 8 to each number)
Now in both series, the least number (that is in common) is 24. Hence, Madison should make at least 24 party favors.
Thus the correct answer is option b.

Question 5.
A shuttle bus makes 4 round-trips between two shopping centers each day. The bus holds 24 people. If the bus is full on each one-way trip, how many passengers are carried by the bus each day?
Options:
a. 96
b. 162
c. 182
d. 192

Answer: 96

Explanation:
Given,
A shuttle bus makes 4 round-trips between two shopping centers each day. The bus holds 24 people.
4 × 24 = 96
Thus the correct answer is option a.

Question 6.
To make a fruit salad, Marvin mixes 1 \(\frac{3}{4}\) cups of diced peaches with 2 \(\frac{1}{4}\) cups of diced pears. How many cups of peaches and pears are in the fruit salad?
Options:
a. 4 cups
b. 3 \(\frac{2}{4}\) cups
c. 3 \(\frac{1}{4}\) cups
d. 3 cups

Answer: 4 cups

Explanation:
Given,
To make a fruit salad, Marvin mixes 1 \(\frac{3}{4}\) cups of diced peaches with 2 \(\frac{1}{4}\) cups of diced pears.
1 \(\frac{3}{4}\) + 2 \(\frac{1}{4}\)
= 4 cups
Thus the correct answer is option a.

Common Core – Add and Subtract Fractions – Page No. 149

Fractions and Properties of Addition

Use the properties and mental math to find the sum.

Question 1.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 7 Add and Subtract Fractions Common Core - Add and Subtract Fractions img 18

Question 2.
\(10 \frac{1}{8}+\left(3 \frac{5}{8}+2 \frac{7}{8}\right)\)
_______ \(\frac{□}{□}\)

Answer: 16 \(\frac{5}{8}\)

Explanation:
Given,
\(10 \frac{1}{8}+\left(3 \frac{5}{8}+2 \frac{7}{8}\right)\)
First add the whole numbers in the bracket.
3 + 2 = 5
10 \(\frac{1}{8}\) + 5 + \(\frac{5}{8}\) + \(\frac{7}{8}\)
10 \(\frac{1}{8}\) + 5 + \(\frac{12}{8}\)
10 + 5 = 15
15 + \(\frac{1}{8}\) + \(\frac{12}{8}\)
15 + \(\frac{13}{8}\)
16 \(\frac{5}{8}\)
\(10 \frac{1}{8}+\left(3 \frac{5}{8}+2 \frac{7}{8}\right)\) = 16 \(\frac{5}{8}\)

Question 3.
\(8 \frac{1}{5}+\left(3 \frac{2}{5}+5 \frac{4}{5}\right)\)
_______ \(\frac{□}{□}\)

Answer: 17 \(\frac{2}{5}\)

Explanation:
\(8 \frac{1}{5}+\left(3 \frac{2}{5}+5 \frac{4}{5}\right)\)
8 \(\frac{1}{5}\) + 3 \(\frac{2}{5}\) + 5 \(\frac{4}{5}\)
3 + 5 = 8
8 \(\frac{1}{5}\) + 8 + \(\frac{2}{5}\) + \(\frac{4}{5}\)
8 \(\frac{1}{5}\) + 8 + \(\frac{6}{5}\)
8 + 8 = 16
16 + \(\frac{1}{5}\) + \(\frac{6}{5}\)
16 + \(\frac{7}{5}\)
17 \(\frac{2}{5}\)
\(8 \frac{1}{5}+\left(3 \frac{2}{5}+5 \frac{4}{5}\right)\) = 17 \(\frac{2}{5}\)

Question 4.
\(6 \frac{3}{4}+\left(4 \frac{2}{4}+5 \frac{1}{4}\right)\)
_______ \(\frac{□}{□}\)

Answer: 16 \(\frac{1}{2}\)

Explanation:
\(6 \frac{3}{4}+\left(4 \frac{2}{4}+5 \frac{1}{4}\right)\)
First add the whole numbers in the bracket.
6 \(\frac{3}{4}\) + 4 \(\frac{2}{4}\) + 5 \(\frac{1}{4}\)
4 + 5 = 9
6 \(\frac{3}{4}\) + 9 \(\frac{3}{4}\)
6 + 9 = 15
15 + \(\frac{3}{4}\) + \(\frac{3}{4}\)
16 \(\frac{1}{2}\)
\(6 \frac{3}{4}+\left(4 \frac{2}{4}+5 \frac{1}{4}\right)\) = 16 \(\frac{1}{2}\)

Question 5.
\(\left(6 \frac{3}{6}+10 \frac{4}{6}\right)+9 \frac{2}{6}\)
_______ \(\frac{□}{□}\)

Answer: 26 \(\frac{3}{6}\)

Explanation:
\(\left(6 \frac{3}{6}+10 \frac{4}{6}\right)+9 \frac{2}{6}\)
6 \(\frac{3}{6}\) + 10 \(\frac{4}{6}\) + 9 \(\frac{2}{6}\)
First add the whole numbers in the bracket.
6 + 10 = 16
16 + \(\frac{3}{6}\) + \(\frac{4}{6}\) + 9 \(\frac{2}{6}\)
16 + \(\frac{7}{6}\) + 9 \(\frac{2}{6}\)
16 + 9 = 25
25 + \(\frac{7}{6}\) + \(\frac{2}{6}\)
25 + \(\frac{9}{6}\)
= 26 \(\frac{3}{6}\)
\(\left(6 \frac{3}{6}+10 \frac{4}{6}\right)+9 \frac{2}{6}\) = 26 \(\frac{3}{6}\)

Question 6.
\(\left(6 \frac{2}{5}+1 \frac{4}{5}\right)+3 \frac{1}{5}\)
_______ \(\frac{□}{□}\)

Answer: 11 \(\frac{2}{5}\)

Explanation:
\(\left(6 \frac{2}{5}+1 \frac{4}{5}\right)+3 \frac{1}{5}\)
6 \(\frac{2}{5}\) + 1 \(\frac{4}{5}\) + 3 \(\frac{1}{5}\)
First add the whole numbers in the bracket.
6 + 1 = 7
7 \(\frac{2}{5}\) + \(\frac{4}{5}\) + 3 \(\frac{1}{5}\)
7 + \(\frac{6}{5}\) + 3 \(\frac{1}{5}\)
7 + 3 = 10
10 + \(\frac{6}{5}\) + \(\frac{1}{5}\)
10 + \(\frac{7}{5}\) = 11 \(\frac{2}{5}\)
Therefore \(\left(6 \frac{2}{5}+1 \frac{4}{5}\right)+3 \frac{1}{5}\) = 11 \(\frac{2}{5}\)

Question 7.
\(7 \frac{7}{8}+\left(3 \frac{1}{8}+1 \frac{1}{8}\right)\)
_______ \(\frac{□}{□}\)

Answer: 12 \(\frac{1}{8}\)

Explanation:
\(7 \frac{7}{8}+\left(3 \frac{1}{8}+1 \frac{1}{8}\right)\)
7 \(\frac{7}{8}\) + 3 \(\frac{1}{8}\) + 1 \(\frac{1}{8}\)
First add the whole numbers in the bracket.
3 + 1 = 4
7 \(\frac{7}{8}\) + 4 + \(\frac{1}{8}\) + \(\frac{1}{8}\)
7 \(\frac{7}{8}\) + 4 +\(\frac{2}{8}\)
7 + 4 = 11
11 + \(\frac{7}{8}\) + \(\frac{2}{8}\)
11 + \(\frac{9}{8}\) = 12 \(\frac{1}{8}\)
Thus \(7 \frac{7}{8}+\left(3 \frac{1}{8}+1 \frac{1}{8}\right)\) = 12 \(\frac{1}{8}\)

Question 8.
\(14 \frac{1}{10}+\left(20 \frac{2}{10}+15 \frac{7}{10}\right)\)
_______ \(\frac{□}{□}\)

Answer: 50

Explanation:
\(14 \frac{1}{10}+\left(20 \frac{2}{10}+15 \frac{7}{10}\right)\)
First add the whole numbers in the bracket.
14 \(\frac{1}{10}\) + 20 \(\frac{2}{10}\) + 15 \(\frac{7}{10}\)
20 + 15 = 35
14 \(\frac{1}{10}\) + 35 + \(\frac{2}{10}\) + \(\frac{7}{10}\)
14 \(\frac{1}{10}\) + 35 \(\frac{9}{10}\)
49 \(\frac{1}{10}\) + \(\frac{9}{10}\)
49 + 1 = 50
Thus \(14 \frac{1}{10}+\left(20 \frac{2}{10}+15 \frac{7}{10}\right)\) = 50

Question 9.
\(\left(13 \frac{2}{12}+8 \frac{7}{12}\right)+9 \frac{5}{12}\)
_______ \(\frac{□}{□}\)

Answer: 31 \(\frac{2}{12}\)

Explanation:
\(\left(13 \frac{2}{12}+8 \frac{7}{12}\right)+9 \frac{5}{12}\)
13 \(\frac{2}{12}\) + 8 \(\frac{7}{12}\) + 9 \(\frac{5}{12}\)
First add the whole numbers in the bracket.
13 + 8 = 21
21 + \(\frac{2}{12}\) + \(\frac{7}{12}\) + 9 \(\frac{5}{12}\)
21 + \(\frac{9}{12}\) + 9 \(\frac{5}{12}\)
30 + \(\frac{9}{12}\) + \(\frac{5}{12}\) = 31 \(\frac{2}{12}\)
Thus \(\left(13 \frac{2}{12}+8 \frac{7}{12}\right)+9 \frac{5}{12}\) = 31 \(\frac{2}{12}\)

Problem Solving

Question 10.
Nate’s classroom has three tables of different lengths. One has a length of 4 \(\frac{1}{2}\) feet, another has a length of 4 feet, and a third has a length of 2 \(\frac{1}{2}\) feet. What is the length of all three tables when pushed end to end?
_______ \(\frac{□}{□}\)

Answer: 11

Explanation:
Given,
Nate’s classroom has three tables of different lengths. One has a length of 4 \(\frac{1}{2}\) feet, another has a length of 4 feet, and a third has a length of 2 \(\frac{1}{2}\) feet.
4 \(\frac{1}{2}\) + 4 + 2 \(\frac{1}{2}\)
4 + 4 + 2 = 10
\(\frac{1}{2}\) + \(\frac{1}{2}\) = 1
10 + 1 = 11
Therefore the length of all three tables when pushed end to end is 11 feet.

Question 11.
Mr. Warren uses 2 \(\frac{1}{4}\) bags of mulch for his garden and another 4 \(\frac{1}{4}\) bags for his front yard. He also uses \(\frac{3}{4}\) bag around a fountain. How many total bags of mulch does Mr. Warren use?
_______ \(\frac{□}{□}\)

Answer: 7 \(\frac{1}{4}\)

Explanation:
Given,
Mr. Warren uses 2 \(\frac{1}{4}\) bags of mulch for his garden and another 4 \(\frac{1}{4}\) bags for his front yard.
He also uses \(\frac{3}{4}\) bag around a fountain.
2 \(\frac{1}{4}\) + 4 \(\frac{1}{4}\) + \(\frac{3}{4}\)
2 + 4 = 6
6 + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{3}{4}\)
= 7 \(\frac{1}{4}\)

Common Core – Add and Subtract Fractions – Page No. 150

Lesson Check

Question 1.
A carpenter cut a board into three pieces. One piece was 2 \(\frac{5}{6}\) feet long. The second piece was 3 \(\frac{1}{6}\) feet long. The third piece was 1 \(\frac{5}{6}\) feet long. How long was the board?
Options:
a. 6 \(\frac{5}{6}\) feet
b. 7 \(\frac{1}{6}\) feet
c. 7 \(\frac{5}{6}\) feet
d. 8 \(\frac{1}{6}\) feet

Answer: c. 7 \(\frac{5}{6}\) feet

Explanation:
Given,
A carpenter cut a board into three pieces. One piece was 2 \(\frac{5}{6}\) feet long. The second piece was 3 \(\frac{1}{6}\) feet long.
The third piece was 1 \(\frac{5}{6}\) feet long.
Add three pieces.
2 \(\frac{5}{6}\) + 3 \(\frac{1}{6}\)
= 5 + \(\frac{6}{6}\)
= 5 + 1 = 6
6 + 1 \(\frac{5}{6}\)
= 7 \(\frac{5}{6}\) feet
Thus the correct answer is option c.

Question 2.
Harry works at an apple orchard. He picked 45 \(\frac{7}{8}\) pounds of apples on Monday. He picked 42 \(\frac{3}{8}\) pounds of apples on Wednesday. He picked 54 \(\frac{1}{8}\) pounds of apples on Friday. How many pounds of apples did Harry pick those three days?
Options:
a. 132 \(\frac{3}{8}\) pounds
b. 141 \(\frac{3}{8}\) pounds
c. 142 \(\frac{1}{8}\) pounds
d. 142 \(\frac{3}{8}\) pounds

Answer: 142 \(\frac{3}{8}\) pounds

Explanation:
Given,
Harry works at an apple orchard. He picked 45 \(\frac{7}{8}\) pounds of apples on Monday.
He picked 42 \(\frac{3}{8}\) pounds of apples on Wednesday.
He picked 54 \(\frac{1}{8}\) pounds of apples on Friday.
45 \(\frac{7}{8}\) + 42 \(\frac{3}{8}\) + 54 \(\frac{1}{8}\)
Add the whole numbers first
45 + 42 + 54 = 141
141 + \(\frac{7}{8}\) + \(\frac{3}{8}\) + \(\frac{1}{8}\)
141 + 1 \(\frac{3}{8}\)
= 142 \(\frac{3}{8}\) pounds
Thus the correct answer is option d.

Spiral Review

Question 3.
There were 6 oranges in the refrigerator. Joey and his friends ate 3 \(\frac{2}{3}\) oranges. How many oranges were left?
Options:
a. 2 \(\frac{1}{3}\) oranges
b. 2 \(\frac{2}{3}\) oranges
c. 3 \(\frac{1}{3}\) oranges
d. 9 \(\frac{2}{3}\) oranges

Answer: 9 \(\frac{2}{3}\) oranges

Explanation:
Given,
There were 6 oranges in the refrigerator.
Joey and his friends ate 3 \(\frac{2}{3}\) oranges.
6 + 3 \(\frac{2}{3}\)
= 9 \(\frac{2}{3}\) oranges
Thus the correct answer is option d.

Question 4.
Darlene was asked to identify which of the following numbers is prime. Which number should she choose?
Options:
a. 2
b. 12
c. 21
d. 39

Answer: 2

Explanation:
A prime number is an integer, or whole number, that has only two factors 1 and itself.
In the above options, all are composite numbers except 2.
Therefore 2 is a prime number.
Thus the correct answer is option a.

Question 5.
A teacher has 100 chairs to arrange for an assembly. Which of the following is NOT a way the teacher could arrange the chairs?
Options:
a. 10 rows of 10 chairs
b. 8 rows of 15 chairs
c. 5 rows of 20 chairs
d. 4 rows of 25 chairs

Answer: 8 rows of 15 chairs

Explanation:
A teacher has 100 chairs to arrange for an assembly.
15 × 8 = 120
So, 8 rows of 15 chairs are not the way to arrange the chairs.
Thus the correct answer is option b.

Question 6.
Nic bought 28 folding chairs for $16 each. How much money did Nic spend on chairs?
Options:
a. $196
b. $348
c. $448
d. $600

Answer: c. $448

Explanation:
Given,
Nic bought 28 folding chairs for $16 each.
28 × 16 = 448
Thus the correct answer is option c.

Common Core – Add and Subtract Fractions – Page No. 151

Read each problem and solve.

Question 1.
Each child in the Smith family was given an orange cut into 8 equal sections. Each child ate \(\frac{5}{8}\) of the orange. After combining the leftover sections, Mrs. Smith noted that there were exactly 3 full oranges left. How many children are in the Smith family?
Go Math Grade 4 Answer Key Homework Practice FL Chapter 7 Add and Subtract Fractions Common Core - Add and Subtract Fractions img 19

Question 2.
Val walks 2 \(\frac{3}{5}\) miles each day. Bill runs 10 miles once every 4 days. In 4 days, who covers the greater distance?
_________

Answer: Val

Explanation:
Given,
Val walks 2 \(\frac{3}{5}\) miles each day. Bill runs 10 miles once every 4 days.
2 \(\frac{3}{5}\) × 4
Convert from mixed fraction to the improper fraction.
2 \(\frac{3}{5}\) = \(\frac{13}{5}\) × 4 = 10.4
10.4 > 10
Thus Val covers the greater distance.

Question 3.
Chad buys peanuts in 2-pound bags. He repackages them into bags that hold \(\frac{5}{6}\) pound of peanuts. How many 2-pound bags of peanuts should Chad buy so that he can fill the \(\frac{5}{6}\) -pound bags without having any peanuts left over?
_________ 2-pound bags

Answer: 5

Explanation:
Given,
Chad buys peanuts in 2-pound bags. He repackages them into bags that hold \(\frac{5}{6}\) pound of peanuts.
\(\frac{5}{6}\) + \(\frac{5}{6}\) + \(\frac{5}{6}\) + \(\frac{5}{6}\) + \(\frac{5}{6}\)
Thus 5 2-pound bags of peanuts are left.

Question 4.
A carpenter has several boards of equal length. He cuts \(\frac{3}{5}\) of each board. After cutting the boards, the carpenter notices that he has enough pieces left over to make up the same length as 4 of the original boards. How many boards did the carpenter start with?
_________

Answer: 10

Explanation:
Given,
A carpenter has several boards of equal length. He cuts \(\frac{3}{5}\) of each board. After cutting the boards, the carpenter notices that he has enough pieces left over to make up the same length as 4 of the original boards.
4 of the original boards have a summed length of 20 units. 5 x 4 = 20.
Since 2/5 is left from each board, you simply add them until the 2’s add to 20.
So, 2 x 10 = 20. Hence, there are 10 2/5 boards.
That’s just 4 of the boards that the 2/5 make up, but that should also mean that there are 10 3/5 boards as well.
30/5 + 20/5 = 50/5 = 10

Common Core – Add and Subtract Fractions – Page No. 152

Lesson Check

Question 1.
Karyn cuts a length of ribbon into 4 equal pieces, each 1 \(\frac{1}{4}\) feet long. How long was the ribbon?
Options:
a. 4 feet
b. 4 \(\frac{1}{4}\) feet
c. 5 feet
d. 5 \(\frac{1}{4}\) feet

Answer: 5 feet

Explanation:
Given,
Karyn cuts a length of ribbon into 4 equal pieces, each 1 \(\frac{1}{4}\) feet long.
1 \(\frac{1}{4}\) × 4
Convert from the mixed fraction to the improper fraction.
1 \(\frac{1}{4}\) = \(\frac{5}{4}\)
\(\frac{5}{4}\) × 4 = 5 feet
Thus the correct answer is option c.

Question 2.
Several friends each had \(\frac{2}{5}\) of a bag of peanuts left over from the baseball game. They realized that they could have bought 2 fewer bags of peanuts between them. How many friends went to the game?
Options:
a. 6
b. 5
c. 4
d. 2

Answer: 5

Explanation:
Given,
Several friends each had \(\frac{2}{5}\) of a bag of peanuts left over from the baseball game.
They realized that they could have bought 2 fewer bags of peanuts between them
2 ÷ \(\frac{2}{5}\) = 5
Thus the correct answer is option b.

Spiral Review

Question 3.
A frog made three jumps. The first was 12 \(\frac{5}{6}\) inches. The second jump was 8 \(\frac{3}{6}\) inches. The third jump was 15 \(\frac{1}{6}\) inches. What was the total distance the frog jumped?
Options:
a. 35 \(\frac{3}{6}\) inches
b. 36 \(\frac{1}{6}\) inches
c. 36 \(\frac{3}{6}\) inches
d. 38 \(\frac{1}{6}\) inches

Answer: 36 \(\frac{3}{6}\) inches

Explanation:
Given,
A frog made three jumps. The first was 12 \(\frac{5}{6}\) inches. The second jump was 8 \(\frac{3}{6}\) inches. The third jump was 15 \(\frac{1}{6}\) inches.
First add the whole numbers
12 + 8 + 15 = 35
Next add the fractions,
\(\frac{5}{6}\) + \(\frac{3}{6}\) + \(\frac{1}{6}\) = 1 \(\frac{3}{6}\)
35 + \(\frac{3}{6}\) = 36 \(\frac{3}{6}\) inches
Thus the correct answer is option c.

Question 4.
LaDanian wants to write the fraction \(\frac{4}{6}\) as a sum of unit fractions. Which expression should he write?
Options:
a. \(\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}\)
b. \(\frac{2}{6}+\frac{2}{6}\)
c. \(\frac{3}{6}+\frac{1}{6}\)
d. \(\frac{1}{6}+\frac{1}{6}+\frac{2}{6}\)

Answer: \(\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}\)

Explanation:
Given,
LaDanian wants to write the fraction \(\frac{4}{6}\) as a sum of unit fractions.
The unit fraction for \(\frac{4}{6}\) is \(\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}\)
Thus the correct answer is option a.

Question 5.
Greta made a design with squares. She colored 8 out of the 12 squares blue. What fraction of the squares did she color blue?
Options:
a. \(\frac{1}{4}\)
b. \(\frac{1}{3}\)
c. \(\frac{2}{3}\)
d. \(\frac{3}{4}latex]

Answer: [latex]\frac{2}{3}\)

Explanation:
Given,
Greta made a design with squares. She colored 8 out of the 12 squares blue.
\(\frac{8}{12}\)
= \(\frac{2}{3}\)
Thus the correct answer is option c.

Question 6.
The teacher gave this pattern to the class: the first term is 5 and the rule is add 4, subtract 1. Each student says one number. The first student says 5. Victor is tenth in line. What number should Victor say?
Options:
a. 17
b. 19
c. 20
d. 21

Answer:
given
a=5
d=4-1=3
to find t10
tn=a + (n-1) d
t10=5 + (10-1) 3
t10=5 + 27
t10 = 32
victor is tenth in line,therefore he should say the number 32

Common Core – Add and Subtract Fractions – Page No. 153

Lesson 7.1

Use the model to write an equation.

Question 1.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 7 Add and Subtract Fractions Common Core - Add and Subtract Fractions img 20
Type below:
_________

Answer: 1/6 + 3/6 = 4/6

Explanation:
From the figure, we can see that the shaded fraction of the first circle is 1/6.
The shaded fraction of the second circle is 3/6
The shaded fraction of the third circle is 4/6.

Question 2.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 7 Add and Subtract Fractions Common Core - Add and Subtract Fractions img 21
Type below:
_________

Answer: 5/8

Explanation:
From the above figure, we can say that the fraction of the shaded part is 5/8.

Use the model to solve the equation.

Question 3.
\(\frac{3}{10}+\frac{5}{10}\) =
Go Math Grade 4 Answer Key Homework Practice FL Chapter 7 Add and Subtract Fractions Common Core - Add and Subtract Fractions img 22
\(\frac{□}{□}\)

Answer: \(\frac{8}{10}\)

Explanation:
The shaded part of the first figure is 3/10
The shaded part of the second figure is 5/10
\(\frac{3}{10}+\frac{5}{10}\) = \(\frac{8}{10}\)

Question 4.
\(\frac{7}{12}-\frac{6}{12}\) =
Go Math Grade 4 Answer Key Homework Practice FL Chapter 7 Add and Subtract Fractions Common Core - Add and Subtract Fractions img 23
\(\frac{□}{□}\)

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

Explanation:
The shaded part of the above figure is 7/12. Out of which 6/12 are subtracted.
\(\frac{7}{12}-\frac{6}{12}\) = \(\frac{1}{12}\)

Lesson 7.2

Write the fraction as a sum of unit fractions.

Question 5.
\(\frac{2}{3}\) =
Type below:
_________

Answer: The unit fraction of \(\frac{2}{3}\) is \(\frac{1}{3}\) + \(\frac{1}{3}\)

Question 6.
\(\frac{3}{10}\) =
Type below:
_________

Answer: The unit fraction of \(\frac{3}{10}\) is \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\)

Question 7.
\(\frac{4}{6}\) =
Type below:
_________

Answer: The unit fraction of \(\frac{4}{6}\) is \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\)

Question 8.
\(\frac{5}{12}\) =
Type below:
_________

Answer: The unit fraction of \(\frac{5}{12}\) is \(\frac{1}{12}\) + \(\frac{1}{12}\) + \(\frac{1}{12}\) + \(\frac{1}{12}\) + \(\frac{1}{12}\)

Lessons 7.3–7.5

Find the sum or difference. Use fraction strips to help.

Question 9.
\(\frac{3}{8}+\frac{2}{8}\) =
\(\frac{□}{□}\)

Answer: \(\frac{5}{8}\)
HMH Go Math grade 4 Key Chapter 7 add & subtract fractions img_1

Question 10.
\(\frac{4}{5}+\frac{1}{5}\) =
\(\frac{□}{□}\)

Answer: 1
HMH Go Math Grade 4 key ch-7 add & subtract fractions img_2

Question 11.
\(\frac{6}{10}+\frac{1}{10}\) =
\(\frac{□}{□}\)

Answer: \(\frac{7}{10}\)

Go Math Grade 4 Answer Key ch-7 img-3

Question 12.
\(\frac{5}{6}-\frac{4}{6}\) =
\(\frac{□}{□}\)

Answer: \(\frac{1}{6}\)
HMH Go Math Grade 4 Key ch-7 add and subtract fractions img-5

Question 13.
\(\frac{3}{4}-\frac{1}{4}\) =
\(\frac{□}{□}\)

Answer: \(\frac{1}{2}\)
Go Math grade 4 solution key ch-7 img_6

Question 14.
1 – \(\frac{7}{12}\) =
\(\frac{□}{□}\)

Answer: \(\frac{5}{12}\)
Go Math Grade 4 Solution Key Chapter 7 add & subtract fractions img_7

Question 15.
\(\frac{7}{10}-\frac{3}{10}\) =
\(\frac{□}{□}\)

Answer: \(\frac{4}{10}\)
Go Math Grade 4 Key ch-7 add & subtract fractions img_4

Question 16.
\(\frac{2}{6}+\frac{4}{6}\) =
\(\frac{□}{□}\)

Answer: 1
Go Math 4th Grade key chapter 7 img_7

Question 17.
\(\frac{5}{8}-\frac{4}{8}\) =
\(\frac{□}{□}\)

Answer: \(\frac{1}{8}\)
HMH Go Math 4th Grade add & subtract fractions img_8

Common Core – Add and Subtract Fractions – Page No. 154

Lesson 7.6

Write each mixed number as a fraction and each fraction as a mixed number.

Question 1.
4 \(\frac{2}{3}\) =
\(\frac{□}{□}\)

Answer: \(\frac{14}{3}\)

Explanation:
First multiply 4 and 3
4 × 3 = 12
And then add 2 to 12
12 + 2 = 14
Thus the fraction of the mixed fraction is \(\frac{14}{3}\).

Question 2.
6 \(\frac{1}{4}\) =
\(\frac{□}{□}\)

Answer: \(\frac{25}{4}\)

Explanation:
First multiply 6 and 4
6 × 4 = 24
And then add 1 to 24
24 + 1 = 25
Thus the fraction of the mixed fraction is \(\frac{25}{4}\)

Question 3.
\(\frac{11}{3}\) =
_______ \(\frac{□}{□}\)

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

Explanation:
Convert from improper fraction to the mixed fraction.
3 × 3 = 9
9 + 2 = 11
\(\frac{11}{3}\) = 3 \(\frac{2}{3}\)

Question 4.
\(\frac{16}{15}\) =
_______ \(\frac{□}{□}\)

Answer: 1 \(\frac{1}{15}\)

Explanation:
Given,
Convert from improper fraction to the mixed fraction.
15 × 1 = 15
15 + 1 = 16
\(\frac{16}{15}\) = 1 \(\frac{1}{15}\)

Lessons 7.7–7.8

Find the sum or difference.

Question 5.
\(3 \frac{1}{4}+2 \frac{3}{4}\) =
_______ \(\frac{□}{□}\)

Answer: 6

Explanation:
Given,
\(3 \frac{1}{4}+2 \frac{3}{4}\)
First add the whole numbers
3 + 2 = 5
\(\frac{1}{4}\) + \(\frac{3}{4}\) = 1
5 + 1 = 6
\(3 \frac{1}{4}+2 \frac{3}{4}\) = 6

Question 6.
\(1 \frac{5}{12}+2 \frac{1}{12}\) =
_______ \(\frac{□}{□}\)

Answer: 3 \(\frac{6}{12}\)

Explanation:
Given,
\(1 \frac{5}{12}+2 \frac{1}{12}\)
First add the whole numbers
1 + 2 = 3
3 \(\frac{5}{12}\) + \(\frac{1}{12}\) = 3 \(\frac{6}{12}\)

Question 7.

\(9 \frac{5}{6}-7 \frac{1}{6}\) =
_______ \(\frac{□}{□}\)

Answer: 2 \(\frac{4}{6}\)

Explanation:
Given,
\(9 \frac{5}{6}-7 \frac{1}{6}\)
First subtract the whole numbers
9 – 7 = 2
5/6 – 1/6 = \(\frac{4}{6}\)
2 + \(\frac{4}{6}\) = 2 \(\frac{4}{6}\)
Thus \(9 \frac{5}{6}-7 \frac{1}{6}\) = 2 \(\frac{4}{6}\)

Question 8.

\(9 \frac{3}{10}-1 \frac{7}{10}\) =
_______ \(\frac{□}{□}\)

Answer: 7 \(\frac{6}{10}\)

Explanation:
Given,
\(9 \frac{3}{10}-1 \frac{7}{10}\)
First subtract the whole numbers
9 – 1 = 8
3/10 – 7/10 = – 4/10
8 – 4/10 = 7 \(\frac{6}{10}\)

Lesson 7.9

Use the properties and mental math to find the sum.

Question 9.
\(\left(1 \frac{1}{4}+4\right)+2 \frac{3}{4}\)
_______ \(\frac{□}{□}\)

Answer: 8

Explanation:
Given,
\(\left(1 \frac{1}{4}+4\right)+2 \frac{3}{4}\)
1 \(\frac{1}{4}\) + 4 + 2 \(\frac{3}{4}\)
Add the whole numbers
1 + 4 = 5
5 \(\frac{1}{4}\) + 2 \(\frac{3}{4}\)
5 + 2 = 7
\(\frac{1}{4}\) + \(\frac{3}{4}\) = 1
7 + 1 = 8

Question 10.
\(\frac{3}{5}+\left(90 \frac{2}{5}+10\right)\)
_______ \(\frac{□}{□}\)

Answer: 101

Explanation:
Given,
\(\frac{3}{5}+\left(90 \frac{2}{5}+10\right)\)
Add the whole numbers
90 + 10 = 100
3/5 + 2/5 = 5/5 = 1
100 + 1 = 101

Question 11.
\(3 \frac{2}{6}+\left(2 \frac{1}{6}+\frac{4}{6}\right)\)
_______ \(\frac{□}{□}\)

Answer: 6 \(\frac{1}{6}\)

Explanation:
Given,
\(3 \frac{2}{6}+\left(2 \frac{1}{6}+\frac{4}{6}\right)\)
1/6 + 4/6 = 5/6
3 \(\frac{2}{6}\) + 2 \(\frac{5}{6}\) = 6 \(\frac{1}{6}\)

Question 12.
\(\left(\frac{5}{8}+2 \frac{3}{8}\right)+1 \frac{3}{8}\)
_______ \(\frac{□}{□}\)

Answer: 4 \(\frac{3}{8}\)

Explanation:
Given,
\(\left(\frac{5}{8}+2 \frac{3}{8}\right)+1 \frac{3}{8}\)
5/8 + 3/8 = 8/8 = 1
2 + 1 = 3
3 + 1 3/8 = 4 \(\frac{3}{8}\)

Lesson 7.10

Question 13.
Adrian jogs \(\frac{3}{4}\) mile each morning. How many days will it take him to jog 3 miles?
____ days

Answer: 4 days

Explanation:
Given,
Adrian jogs \(\frac{3}{4}\) mile each morning.
\(\frac{3}{4}\)/3 = 4
Thus it will take 4 days for him to jog 3 miles.

Question 14.
Trail mix is sold in 1-pound bags. Mary will buy some trail mix and re-package it so that each of the 15 members of her hiking club gets one \(\frac{2}{5}\) -pound bag. How many 1-pound bags of trail mix should Mary buy to have enough trail mix without leftovers?
____ 1-pound bags

Answer: 6 1-pound bags

Explanation:
Given,
Trail mix is sold in 1-pound bags. Mary will buy some trail mix and re-package it so that each of the 15 members of her hiking club gets one \(\frac{2}{5}\) -pound bag.
15 × \(\frac{2}{5}\) = 6
Therefore Mary should buy 6 1-pound bags to have enough trail mix without leftovers.

Conclusion:

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Go Math Grade 4 Answer Key Homework Practice FL Chapter 13: Algebra: Perimeter and Area

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Are you viewing for Go Math Grade 4 Answer Key Homework Practice FL Chapter 13 Algebra: Perimeter and Area? This is the correct page for you. We have listed chapterwise Go math grade 4 practice FL Answer key along with homework practice FL solution Key on our site. So, you can learn the concepts in an understanding manner & score maximum scores in the assessments and standardized tests. Hence, download the HMH Go Math 4th Grade Chapter 13 Perimeter and Area Answer key to find out the area & perimeter of the rectangle & square quickly & easily.

Go Math Grade 4 Answer Key Homework Practice FL Chapter 13: Algebra: Perimeter and Area

Go Math Grade 4 Ch 13 Answer Key includes topics covered in Algebra: Perimeter and Area. Students who are pursuing 4th grade can find the HMH Go Math Grade 4 Solution Key Chapter 13 Algebra: Perimeter and Area extremely useful. Simply identify your preparation level and weak areas by practicing and solving the questions from 4th Grade Go Math Answer Key Chapter 13 Algebra: Perimeter and Area. Tap on the below provided links and check the detailed explanation for each and every question covered here.

Lesson: 1 – Perimeter

Lesson: 2 – Area

Lesson: 3 – Area of Combined Rectangles

Lesson: 4 – Find Unknown Measures

Lesson: 5 – Problem Solving Find the Area

Lesson: 6 

Common Core – Algebra: Perimeter and Area –