Vijaya Sree

Download Go Math Grade 7 Answer Key for Chapter 5 Percent Increase and Decrease pdf for free. Quick and easy learning is possible with Go Math 7th Grade Answer Key Chapter 5 Percent Increase and Decrease. So, we suggest the students of 7th standard to go through the HMH Go Math Grade 7 Key Chapter 5 Percent Increase and Decrease. Our team of Go Math Answer Key will help the Grade 7 students to score the highest marks.

Go Math Grade 7 Answer Key Chapter 5 Percent Increase and Decrease

Get a brief explanation for all the questions in Chapter 5 Percent Increase and Decrease Go Math Answer Key Grade 7. Tap on the links provided below and get the solutions according to the topics. So, utilize the time in the proper way and practice Go Math 7th Grade Solution Key Chapter 5 Percent Increase and Decrease.

Chapter 5 – Percent Increase and Decrease

• Percent Increase and Decrease – Guided Practice – Page No. 144
• Percent Increase and Decrease – Independent Practice – Page No. 145
• Percent Increase and Decrease – Page No. 146

Chapter 5 – Rewriting Percent Expressions

• Rewriting Percent Expressions – Guided Practice – Page No. 150
• Rewriting Percent Expressions – Independent Practice – Page No. 151
• Rewriting Percent Expressions – Page No. 152

Chapter 5 – Applications of Percent

• Applications of Percent – Guided Practice – Page No. 156
• Applications of Percent – Independent Practice – Page No. 157
• Applications of Percent – Page No. 158

Chapter 5

• MODULE QUIZ – 5.1 Percent Increase and Decrease – Page No. 159
• Selected Response – Page No. 160
• Module 5 – Page No. 162
• Unit 2 Performance Tasks – Page No. 163
• Unit 2 Performance Tasks (con’td) – Page No. 164
• Selected Response – Page No. 165
• Page No. 166

Percent Increase and Decrease – Guided Practice – Page No. 144

Find each percent increase. Round to the nearest percent.

Question 1.
From $5 to $8
______ %

Answer: 60%

Explanation:
Percent Charge = Amount of Change/Original Amount
Original amount = 5
Final amount = 8
8 – 5 = 3
Percent change = 3/5 = 0.6 = 60%

Question 2.
From 20 students to 30 students
______ %

Answer: 50%

Explanation:
Percent Charge = Amount of Change/Original Amount
Original amount = 20
Final amount = 30
We find the amount of change
30 – 20 = 10
We determine the percent of the increase
Percent change = 10/20 = 0.5 = 50%

Question 3.
From 86 books to 150 books
______ %

Answer: 74%

Explanation:
Percent Charge = Amount of Change/Original Amount
Original amount = 86
Final amount = 150
We find the amount of change
150 – 86 = 64
We determine the percent of increase and round it to the nearest percent
Percent Change = 64/86 ≈ 0.74 = 74%

Question 4.
From $3.49 to $3.89
______ %

Answer: 11%

Explanation:
Percent Charge = Amount of Change/Original Amount
Original amount = 3.49
Final amount = 3.89
We find the amount of change
3.89 – 3.49 = 0.40
We determine the percent of increase and round it to the nearest percent
Percent Change = 0.40/0.39 ≈ 0.11 = 11%

Question 5.
From 13 friends to 14 friends
______ %

Answer: 8%

Explanation:
Percent Charge = Amount of Change/Original Amount
Original amount = 13
Final amount = 14
We find the amount of change
14 – 13 = 1
We determine the percent of increase and round it to the nearest percent
Percent Change = 1/13 ≈ 0.08 = 8%

Question 6.
From 5 miles to 16 miles
______ %

Answer: 220%

Explanation:
Percent Charge = Amount of Change/Original Amount
Original amount = 5
Final amount = 16
We find the amount of change
16 – 5 = 11
We determine the percent of increase and round it to the nearest percent
Percent Change = 11/5 = 2.2 = 220%

Question 7.
Nathan usually drinks 36 ounces of water per day. He read that he should drink 64 ounces of water per day. If he starts drinking 64 ounces, what is the percent increase? Round to the nearest percent.
______ %

Answer: 78%

Explanation:
Given,
Nathan usually drinks 36 ounces of water per day. He read that he should drink 64 ounces of water per day.
Original Amount: 36
Final Amount: 64
Percent Charge = Amount of Change/Original Amount
We find the amount of change
64 – 36 = 28
We determine the percent of increase and round it to the nearest percent
Percent Change = 28/36 ≈ 0.78 = 78%
Thus the nearest percent is 78%

Find each percent decrease. Round to the nearest percent.

Question 8.
From $80 to $64
______ %

Answer: 20%

Explanation:
Percent Charge = Amount of Change/Original Amount
Original amount = 80
Final amount = 64
We find the amount of change
Amount of change = Greater value – Lesser value
= 80 – 64 = 16
We determine the percent of increase and round it to the nearest percent
Percent Change = 16/80 = 0.20 = 20%
Thus the nearest percent is 20%

Question 9.
From 95 °F to 68 °F
______ %

Answer: 28%

Explanation:
Percent Charge = Amount of Change/Original Amount
Original amount = 95
Final amount = 68
We find the amount of change
Amount of change = Greater value – Lesser value
= 95 – 68 = 27
We determine the percent of increase and round it to the nearest percent
Percent Change = 27/98 ≈ 0.28 = 28%
Thus the nearest percent is 28%

Question 10.
From 90 points to 45 points
______ %

Answer: 50%

Explanation:
Percent Charge = Amount of Change/Original Amount
Original amount = 90
Final amount = 45
We find the amount of change
Amount of change = Greater value – Lesser value
90 – 45 = 45
We determine the percent of increase and round it to the nearest percent
Percent Change = 45/90 = 0.50 = 50%
Thus the nearest percent is 50%

Question 11.
From 145 pounds to 132 pounds
______ %

Answer: 9%

Explanation:
Percent Charge = Amount of Change/Original Amount
Original amount = 145
Final amount = 132
We find the amount of change
Amount of change = Greater value – Lesser value
145 – 132 = 13
We determine the percent of increase and round it to the nearest percent
Percent Change = 13/145 ≈ 0.09 = 9%
The nearest percent is 9%

Question 12.
From 64 photos to 21 photos
______ %

Answer: 67%

Explanation:
Percent Charge = Amount of Change/Original Amount
Original amount = 64
Final amount = 21
We find the amount of change
Amount of change = Greater value – Lesser value
64 – 21 = 43
We determine the percent of increase and round it to the nearest percent
Percent Change = 43/64 ≈ 0.67 = 67%
Therefore the nearest percent is 67%

Question 13.
From 16 bagels to 0 bagels
______ %

Answer: 100%

Explanation:
Percent Charge = Amount of Change/Original Amount
Original amount = 16
Final amount = 0
We find the amount of change
Amount of change = Greater value – Lesser value
16 – 0 = 16
We determine the percent of increase and round it to the nearest percent
Percent Change = 16/16 = 1.0% = 100%

Question 14.
Over the summer, Jackie played video games 3 hours per day. When school began in the fall, she was only allowed to play video games for half an hour per day. What is the percent decrease? Round to the nearest percent.
______ %

Answer: 83%

Explanation:
Percent Charge = Amount of Change/Original Amount
Original amount = 3
Final amount = 0.5
We find the amount of change
Amount of change = Greater value – Lesser value
3 – 0.5 = 2.5
We determine the percent of increase and round it to the nearest percent
Percent Change = 2.5/3 ≈ 0.83 = 83%
The nearest percent is 83%

Find the new amount given the original amount and the percent of change.

Question 15.
$9; 10% increase
$ ______

Answer: $9.90

Explanation:
Percent Charge = Amount of Change/Original Amount
Original amount = 9
Increase = 10%
We find the amount of change
0.1 × 9 = 0.90
New Amount = Original Amount + Amount of Change
9 + 0.90 = 9.90

Question 16.
48 cookies; 25% decrease
______ cookies

Answer: 36 cookies

Explanation:
Original amount = 48
Decrease = 25%
We find the amount of change
0.25 × 48 = 12
New Amount = Original Amount – Amount of Change
48 – 12 = 36
Thus the answer is 36 cookies.

Question 17.
340 pages; 20% decrease
______ pages

Answer: 272 pages

Explanation:
Original Amount: 340 pages
Decrease: 20%
We find the amount of change
0.20 × 340 = 68
New Amount = Original Amount – Amount of Change
340 – 68 = 272
The answer is 272 pages.

Question 18.
28 members; 50% increase
______ members

Answer: 42 members

Explanation:
Original Amount: 28
Increase: 50%
We find the amount of change
0.5 × 28 = 14
New amount = Original Amount + Amount of Change
28 + 14 = 42
The answer is 42 members

Question 19.
$29,000; 4% decrease
$ ______

Answer: $27,840

Explanation:
Original Amount: 29000
Decrease: 4%
We find the amount of change
0.04 × 29000 = 1160
New Amount = Original Amount – Amount of Change
29000 – 1160 = 27840
The answer is $27,840

Question 20.
810 songs; 130% increase
______ songs

Answer: 1863 songs

Explanation:
Original Amount: 810
Increase: 130%
We find the amount of change
1.3 × 810 = 1053
New amount = Original Amount + Amount of Change
810 + 1053 = 1863 songs

Question 21.
Adam currently runs about 20 miles per week, and he wants to increase his weekly mileage by 30%. How many miles will Adam run per week?
______ miles

Answer: 26 miles

Explanation:
Given,
Adam currently runs about 20 miles per week, and he wants to increase his weekly mileage by 30%.
Original Amount: 20
Increase: 30%
We find the amount of change
0.3 × 20 = 6
New amount = Original Amount + Amount of Change
= 20 + 6 = 26
Therefore Adam run 26 miles per week.

Essential Question Check-In

Question 22.
What process do you use to find the percent change of a quantity?
Type below:
_____________

Answer: In order to find the percent change of a quantity, we determine the amount of change in the quantity and divide it by the original amount.

Percent Increase and Decrease – Independent Practice – Page No. 145

Question 23.
Complete the table.

Type below:
_____________

Answer: bike: 13%, scooter 24%, increase, tennis racket: $83, skis: $435

Explanation:
Since the new price is less than the original price, it is a percent decrease. percent decreases can be found using the equation percent decrease = (original – new)/original
Bike: 110 – 96/110 = 14/110 ≈ 13%
Scooter: 56 – 45/45 = 11/45 ≈ 24%
Use the equation percent increase = new – original/original
let x be the new price
skis: (580 – x)/580 = 0.25
580 – x = 0.25 × 580
580 – x = 145
x = 580 – 145 = 435
The new price is $435

Question 24.
Multiple Representations
The bar graph shows the number of hurricanes in the Atlantic Basin from 2006–2011.

a. Find the amount of change and the percent of decrease in the number of hurricanes from 2008 to 2009 and from 2010 to 2011. Compare the amounts of change and percents of decrease.
Type below:
_____________

Answer: 2008 to 2009 has a smaller amount of change but a larger percent of decrease.

Explanation:
2008 to 2009:
amount of change: 8 – 3 = 5
percent decrease: 5/8 = 0.625 = 62.5%
2010 to 2011:
amount of change: 12 – 7 = 5
percent decrease: 5/12 ≈ 0.416 = 41.6%
The amount of change for 2010 to 2011 was greater than the amount of change for 2008 to 2009 but 2008 to 209 had a greater percent decrease than 2010 to 2011.

Question 24.
b. Between which two years was the percent of change the greatest? What was the percent of change during that period?
_______ %

Answer: 2009 and 2010, 300%

Explanation:
Use the percent change = amount of change/original amount.
The biggest change in heights is between 2009 and 2010.
The percent change is (12-3)/3 = 9/3 = 3 = 300%

Question 25.
Represent Real-World Problems
Cheese sticks that were previously priced at “5 for $1” are now “4 for $1”. Find each percent of change and show your work.
a. Find the percent decrease in the number of cheese sticks you can buy for $1.
_______ %

Answer: 20% decrease

Explanation:
Use the percent change = amount of change/original amount.
(5 – 4)/5 = 1/5 = 0.2 = 20% decrease

Question 25.
b. Find the percent increase in the price per cheese stick.
_______ %

Answer: 25% increase

Explanation:
First, find the price per cheese stick at each price.
Use the percent change = amount of change/original amount.
1.00/5 = 0.20
1/4 = 0.25
(0.25 – 0.20)/0.20 = 0.05/0.20 = 25% increase

Percent Increase and Decrease – Page No. 146

Question 26.
Percent error calculations are used to determine how close to the true values, or how accurate, experimental values really are. The formula is similar to finding percent of change.

chemistry class, Charlie records the volume of a liquid as 13.3 milliliters. The actual volume is 13.6 milliliters. What is his percent error? Round to the nearest percent.
_______ %

Answer: 2%

Explanation:
Use the formula

|13.3 – 13.6|/13.6 = |-0.3|/13.6 ≈ 0.02 = 2%

H.O.T.

Focus on Higher Order Thinking

Question 27.
Look for a Pattern
Leroi and Sylvia both put $100 in a savings account. Leroi decides he will put in an additional $10 each week. Sylvia decides to put in an additional 10% of the amount in the account each week.
a. Who has more money after the first additional deposit? Explain.
___________

Answer: the same

Explanation:
Since 10% of 100 is 100(0.10) = 10, they both make an additional deposit of 10, so they have the same amount of money after the first additional deposit.

Question 27.
b. Who has more money after the second additional deposit? Explain.
___________

Answer: Sylvia

Explanation:
Both Lerio and Sylvia have $110 in their account after their first deposits since they both started with $100 and both deposited $10 for their first deposit.
After the second deposit, Lerio has 110 + 10 = $120.
Sylvia has 110 + 0.10(110) = 110 + 11 = $121
So she has more money after the second deposit.

Question 27.
c. How do you think the amounts in the two accounts will compare after a month? A year?
Type below:
___________

Answer: Sylvia will continue to have more money after a month and a year since 10% of the balance is going to be greater than the 10 deposit that Leroi is making.

Question 28.
Critical Thinking
Suppose an amount increases by 100%, then decreases by 100%. Find the final amount. Would the situation change if the original increase was 150%? Explain your reasoning.
Type below:
___________

Answer: If an amount increases by 100%, then it will double. If it then decreases by 100%, it will become 0.
If you increase a number by 150% and then decrease it by 150%, you will not get to 0. 150% increase of 100 is 100 + 150 = 250.
A decrease of 150% is then 250 – 1.5(250) = 250 – 375 = -125

Question 29.
Look for a Pattern
Ariel deposited $100 into a bank account. Each Friday she will withdraw 10% of the money in the account to spend. Ariel thinks her account will be empty after 10 withdrawals. Do you agree? Explain.
___________

Answer: Ariel is incorrect. Her account balance will decrease as follows for the first 10 withdrawals:
1st withdrawal: 100 – 0.1(100) = 100 – 10 = 90
2nd withdrawal: 90 – 0.1(90) = 90 – 9 = 81
3rd withdrawal: 81 – 0.1(81) = 81 – 8.10 = 72.90
4th withdrawal: 72.90 – 0.1(72.90) = 72.90 – 7.29 = 65.61
5th withdrawal: 65.61 – 0.1(65.61) = 65.61 – 6.56 = 59.05
6th withdrawal: 59.05 – 0.1(59.05) = 59.05 – 5.91 = 53.14
7th withdrawal: 53.14 – 0.1(53.14) = 53.14 – 5.31 = 47.83
8th withdrawal: 47.83 – 0.1(47.83) = 47.83 – 4.78 = 43.05
9th withdrawal: 43.05 – 0.1(43.05) = 43.05 – 4.31 = 38.74
10th withdrawal: 38.74 – 0.1(38.74) = 38.74 – 3.87 = 34.87

Rewriting Percent Expressions – Guided Practice – Page No. 150

Question 1.
Dana buys dress shirts from a clothing manufacturer for s dollars each, and then sells the dress shirts in her retail clothing store at a 35% markup.
a. Write the markup as a decimal.
______

Answer: To convert a percent to a decimal, move the decimal place two places to the left. Therefore, 35% as a decimal is 0.35.

Question 1.
b. Write an expression for the retail price of the dress shirt.
Type below:
___________

Answer:
To write the expression, use the formula
retail price = original place + markup
Since s is the original place, if the markup is 35% = 0.35, then the markup is 0.35s.

Question 1.
c. What is the retail price of a dress shirt that Dana purchased for $32.00?
$ ______

Answer: Plugging in s = 32 into the expression gives a retail price of 1.35 = 1.35(32) = $43.20

Question 1.
d. How much was added to the original price of the dress shirt?
$ ______

Answer: The amount added to the original price is the amount of the markup. Since the amount of the markup is 0.35s and s = 32, then the amount of the markup was 0.35s = 0.35(32) = $11.20.
You can also find the amount of markup by subtracting the retail price and the original price. Since the retail price is $43.20 and the original price is $32, then the markup amount is $43.20 – $32 = $11.20

List the markup and retail price of each item. Round to two decimal places when necessary.

Question 2.

Markup: $ ______ Retail Price: $ ______

Answer: Markup: $ 2.70 Retail Price: $ 20.70

Explanation:

Use the formula markup = price(markup%)
18(0.15) = 2.70
Use the retail price formula = price + markup
18 + 2.70 = 20.70

Question 3.

Markup: $ ______ Retail Price: $ ______

Answer:

Use the formula markup = (price)(markup %)
22.50(0.42) = 9.45
Use the retail price formula = price + markup
22.50 + 9.45 = 31.95

Question 4.

Markup: $ ______ Retail Price: $ ______

Answer:

Use the formula markup = (price)(markup %)
= 33.75(0.75) = 25.31
Use the formula retail price = price + markup
33.75 + 25.31 = 59.06

Question 5.

Markup: $ ______ Retail Price: $ ______

Answer:

Use the formula markup = (price)(markup %)
= 74.99(0.33) = 24.75
Use the formula retail price = price + markup
74.99 + 24.75 = 99.74

Question 6.

Markup: $ ______ Retail Price: $ ______

Answer:

Use the formula markup = (price)(markup %)
48.60(1.00) = 48.60
Use the formula retail price = price + markup
48.60 + 48.60 = 97.20

Question 7.

Markup: $ ______ Retail Price: $ ______

Answer:

Use the formula markup = (price)(markup %)
= 185 × 1.25 = 231.25
Use the formula retail price = price + markup
185 + 231.25 = 461.25

Find the sale price of each item. Round to two decimal places when necessary.

Question 8.
Original price: $45.00; Markdown: 22%
$ ______

Answer:
Use the formula markup = (price)(markup %)
45(0.22) = 9.90
Markdown is 9.90
Use the formula retail price = price + markup
45 – 9.90 = 35.10
Sale price is $35.10

Question 9.
Original price: $89.00; Markdown: 33%
$ ______

Answer:
Use the formula markup = (price)(markup %)
89 × 0.33 = 29.37
Use the formula retail price = price – markup
89 – 29.37 = 59.63

Question 10.
Original price: $23.99; Markdown: 44%
$ ______

Answer:
Use the formula markup = (price)(markup %)
23.99 × 0.44 = 10.56
Use the formula retail price = price – markup
23.99 – 10.56 = 13.43

Question 11.
Original price: $279.99, Markdown: 75%
$ ______

Answer:
Use the formula markup = (price)(markup %)
279.99 × 0.75 = 209.99
Use the formula retail price = price – markup
279.99 – 209.99 = 70

Essential Question Check-In

Question 12.
How can you determine the sale price if you are given the regular price and the percent of markdown?
Type below:
____________

Answer:
Use the formula
Sale price = Original Price – Markdown
If the Sale price is S, Original Price p, and x the average reduction, then the formula becomes:|
S = p – x . p

Rewriting Percent Expressions – Independent Practice – Page No. 151

Question 13.
A bookstore manager marks down the price of older hardcover books, which originally sell for b dollars, by 46%.
a. Write the markdown as a decimal.
______

Answer: 0.46

Explanation:
To convert a percent to decimal form, move the decimal point 2 places to the left and don’t write the percent symbol. Therefore, 46% as a decimal is 0.46.

Question 13.
b. Write an expression for the sale price of the hardcover book.
Type below:
____________

Answer: 0.54b

Explanation:
The sale price is the original price minus the discount amount. If the original price is discounted 46% and the original price is b dollars, the amount of the discount is 46% of b = 0.46b.
The sale price is then b – 0.46b = (1 – 0.46)b = 0.54b

Question 13.
c. What is the sale price of a hardcover book for which the original retail price was $29.00?
$ ______

Answer: $15.66

Explanation:
From part (b), the sale price of an item with an original price of b dollars is 0.54b. If the original price is then b = 29 dollars, the sale price is 0.54b = 0.54 × 29 = $15.66

Question 13.
d. If you buy the book in part c, how much do you save by paying the sale price?
$ ______

Answer: $13.34

Explanation:
The amount of savings is the difference between the original price and the sale price. If the original price is $29 and the sale price is $15.66, then the amount of savings is $29.00 – $15.66 = $13.34

Question 14.
Raquela’s coworker made price tags for several items that are to be marked down by 35%. Match each Regular Price to the correct Sale Price, if possible. Not all sales tags match an item.

Type below:
_____________

Answer:
35% markdown means the expression for the sales price is p – 0.35p = 0.65p. Plug in the regular prices for p to find the sale prices. Remember the directions stated not all sales tags will match a regular price so you won’t be able to match every regular price ticket with a sale price ticket.
0.65(3.29) = 2.14
0.65(4.19) = 2.72
0.65(2.79) = 1.81
0.65(3.09) = 2.01
0.65(3.77) = 2.45

Question 15.
Communicate Mathematical Ideas
For each situation, give an example that includes the original price and final price after markup or markdown.
a. A markdown that is greater than 99% but less than 100%
Type below:
_____________

Answer:
A markdown that is greater than 99% but less than 100% could be 99.5%. If the original price is $100, then the final price is 100 – 100(0.995) = 100 – 99.50 = 0.50

Question 15.
b. A markdown that is less than 1%
Type below:
_____________

Answer:
A markdown that is less then 1% could be 0.5%. If the original price is $100, then the final price would be 100 – 0.005(100) = 100 – 0.50 = 99.50

Question 15.
c. A markup that is more than 200%
Type below:
_____________

Answer:
A markup that is more than 200% could be 300%. If the original price is $100, then the final price would be 100 + 100 (3.00) = 100 + 300 = 400

Rewriting Percent Expressions – Page No. 152

Question 16.
Represent Real-World Problems
Harold works at a men’s clothing store, which marks up its retail clothing by 27%. The store purchases pants for $74.00, suit jackets for $325.00, and dress shirts for $48.00. How much will Harold charge a customer for two pairs of pants, three dress shirts, and a suit jacket?
$ __________

Answer: $783.59

Explanation:
Given,
Harold works at a men’s clothing store, which marks up its retail clothing by 27%.
The store purchases pants for $74.00, suit jackets for $325.00, and dress shirts for $48.00.
If the markup is 27%, then the expression for the retail price is p + 0.27p = 1.27p
where p is the original price.
The retail price of the pants is then 1.27(74) = 93.98.
The retail price of the suit jackets is 1.27(325) = 412.75
The retail price of the dress shirts is 1.27(48) = 60.96
The total for two pants, three dress shirts, and one suit jacket would then be 2(93.98) + 3(60.96) + 412.75
= 187.96 + 182.88 + 412.75 = 783.59

Question 17.
Analyze Relationships
Your family needs a set of 4 tires. Which of the following deals would you prefer? Explain.

Type below:
____________

Answer: I and III

Explanation:
The percent discount for buying 3 tires and getting one free is 25% since you are getting 1/4 of the tires for free and 1/4 off = 25%.
This means deal (I) and deal (III) are the same. They are greater than a 20% discount so deals (I) and (III) are preferable.

H.O.T.

Focus on Higher Order Thinking

Question 18.
Critique Reasoning
Margo purchases bulk teas from a warehouse and marks up those prices by 20% for retail sale. When teas go unsold for more than two months, Margo marks down the retail price by 20%. She says that she is breaking even, that is, she is getting the same price for the tea that she paid for it. Is she correct? Explain.
_______

Answer:
She is not correct. If she originally purchases the teas for $100 and then marks the price up 20%, the retail price would then be 100 + 0.20(100) = 100 + 20 = 120.
The sales price would then be 120 – 0.2(120) = 120 – 24 = 96.
This less than the purchase price so she is losing money, not breaking even.

Question 19.
Problem Solving
Grady marks down some $2.49 pens to $1.99 for a week and then marks them back up to $2.49. Find the percent of increase and the percent of decrease to the nearest tenth. Are the percents of change the same for both price changes? If not, which is a greater change?
_______

Answer: The percent decrease is found by using the formula (original price – new price)/(original price). The percent decrease is then (2.49 – 1.99)/2.49 = 0.20 = 20%.
A percent increase is found by using the formula (new price – original price)/original price.
The percent increase is then (2.49 – 1.99)/1.99 = 0.25 = 25%
The percents of change are not the same. The percent increase is greater.

Question 20.
Persevere in Problem Solving
At Danielle’s clothing boutique, if an item does not sell for eight weeks, she marks it down by 15%. If it remains unsold after that, she marks it down an additional 5% each week until she can no longer make a profit. Then she donates it to charity.

Rafael wants to buy a coat originally priced $150, but he can’t afford more than $110. If Danielle paid $100 for the coat, during which week(s) could Rafael buy the coat within his budget? Justify your answer.
Type below:
_____________

Answer:
The expression for the markdown on the 8th week is p – 0.15p = 0.85p since it will get marked down 15% on the 8th week.
The expression for the additional markdowns is p – 0.05p = 0.95p since it will get marked down an additional 5% every week after the 8th week.
On the 8th week, it will be marked down to 0.85(150) = 127.50. This is more than Rafael can afford.
On the 9th week, it will be marked down to 0.95(127.50) = 121.13. This is still more than Rafael can afford.
On the 10th week, it will be marked down to 0.95(121.13) = 115.07. This is still more than Rafael can afford.
On the 11th week, it will be marked down to 0.95(115.07) = 109.32. Rafael can afford this price so he must wait until the 11th week.

Applications of Percent – Guided Practice – Page No. 156

Question 1.
5% of $30 =
$ _______

Answer: $1.5

Explanation:
We have to find:
5% of $30
0.50 × 30 = $1.5

Question 2.
15% of $70 =
$ _______

Answer: $10.5

Explanation:
We have to find:
15% of $70
0.15 × 70 = 10.5

Question 3.
0.4% of $100 =
$ _______

Answer: $0.40

Explanation:
We have to find:
0.4% of $100
0.004 × 100 = 0.40

Question 4.
150% of $22 =
$ _______

Answer: $33

Explanation:
We have to find:
150% of $22
1.5 × 22 = 33

Question 5.
1% of $80 =
$ _______

Answer: $0.8

Explanation:
We have to find:
1% of $80
0.01 × 80 = 0.8

Question 6.
200% of $5 =
$ _______

Answer: $10

Explanation:
We have to find:
200% of $5
2 × 5 = 10

Question 7.
Brandon buys a radio for $43.99 in a state where the sales tax is 7%.
a. How much does he pay in taxes?
$ _______

Answer: 3.08

Explanation:
We have to find the amount he pays in taxes by multiplying the cost by the sales tax percentage in decimal form remember to round to 2 decimal places.
43.99(0.07) = 3.08

Question 7.
b. What is the total Brandon pays for the radio?
$ _______

Answer: 47.07

Explanation:
To find the total Brandon pays for the radio we have to add the sales tax amount to the cost to find the total amount he pays.
43.99 + 3.08 = 47.07
Thus the total Brandon pays for the radio is $47.07.

Question 8.
Luisa’s restaurant bill comes to $75.50, and she leaves a 15% tip. What is Luisa’s total restaurant bill?
$ _______

Answer: $86.25

Explanation:
Given that,
Luisa’s restaurant bill comes to $75.50, and she leaves a 15% tip.
Use the formula for the total restaurant bill:
T = P + x. P
Where T represents the total bill, P represents Luisa’s bill and x represents percents for tip, then the total restaurant bill is:
T = 75 + 0.15 (75)
T = 75 + 11.25
T = $86.25
Therefore Lusia’s total restaurant bill is $86.25

Question 9.
Joe borrowed $2,000 from the bank at a rate of 7% simple interest per year. How much interest did he pay in 5 years?
$ _______

Answer: 700

Explanation:
Joe borrowed $2,000 from the bank at a rate of 7% simple interest per year.
We have to find the amount of interest per year
2000(0.07) = 140
Find the amount of interest for 5 years
140(5) = 700
Thus Joe pays $700 in 5 years.

Question 10.
You have $550 in a savings account that earns 3% simple interest each year. How much will be in your account in 10 years?
$ _______

Answer: $715

Explanation:
Given,
You have $550 in a savings account that earns 3% simple interest each year.
Use the formula for simple interest:
Bt = B0(1 + tr)
Where t is time interval, Bt is money after t years, B0 is deposit and r is interest for one year, then the formula becomes:
B10 = B0(1 + 10.r)
B10 = 550(1 + 10 (0.03))
B10 = $715
In your account after 10 years will be $715.

Question 11.
Martin finds a shirt on sale for 10% off at a department store. The original price was $20. Martin must also pay 8.5% sales tax.
a. How much is the shirt before taxes are applied?
$ _______

Answer: 18

Explanation:
We have to find the sales price of the shirt
20 – 0.1(20) = 20 – 2 = 18
The price of the shirt before taxes are applied is $18.

Question 11.
b. How much is the shirt after taxes are applied?
$ _______

Answer: 19.53

Explanation:
We have to find the price after sales tax
18 + 0.085(18) = 18 + 1.53 = 19.53
The price of the shirt after taxes are applied is $19.53

Question 12.
Teresa’s restaurant bill comes to $29.99 before tax. If the sales tax is 6.25% and she tips the waiter 20%, what is the total cost of the meal?
$ _______

Answer: 37.86

Explanation:
Given,
Teresa’s restaurant bill comes to $29.99 before tax. If the sales tax is 6.25% and she tips the waiter 20%.
Find the amount of sales tax
29.99(0.0625) = 1.87
Find the amount of the tip
29.99(0.20) = 6.00
The total cost by adding the bill account, sales tax, and tip amount.
29.99 + 1.87 + 6.00 = 37.86
Thus the total cost of the meal is $37.86

Essential Question Check-In

Question 13.
How can you determine the total cost of an item including tax if you know the price of the item and the tax rate?
Type below:
_____________

Answer: You can find the total cost of an item including tax by first multiplying the price of the item by the tax rate in decimal form to get the amount of sales tax. Then add the amount of sales tax to the price to get the total cost.

Applications of Percent – Independent Practice – Page No. 157

Question 14.
Emily’s meal costs $32.75 and Darren’s meal costs $39.88. Emily treats Darren by paying for both meals, and leaves a 14% tip. Find the total cost.
$ _______

Answer: 82.80

Explanation:
Emily’s meal costs $32.75 and Darren’s meal costs $39.88.
So, the total cost of the meals before tip is $32.75 + $39.88 = $72.63
Emily treats Darren by paying for both meals and leaves a 14% tip.
$72.63 = 0.14(72.63) ≈ $10.17
Round to two decimal places since dollar amounts must be rounded to the nearest cent.
The total cost that Dareen pays is then cost before tip + amount of tip = $72.63 + $10.17 = $82.80

Question 15.
The Jayden family eats at a restaurant that is having a 15% discount promotion. Their meal costs $78.65, and they leave a 20% tip. If the tip applies to the cost of the meal before the discount, what is the total cost of the meal?
$ _______

Answer: 82.58

Explanation:
The Jayden family eats at a restaurant that is having a 15% discount promotion.
The total cost of the meal = cost of meal + tip amount – discount amount
Their meal costs $78.65, and they leave a 20% tip.
We need to find the tip amount and the discount amount using the given cost of the meal, tip percent, and discount percent.
20% of 78.65 = 0.20 × 78.65 = $15.73
Since the cost of the meal before the discount is $78.65 and the discount percent is 15%, then the amount of the discount is
15% of 78365 = 0.15 × $78.65 ≈ $11.80
The total cost is then
78.65 + 15.73 – 11.80 = $82.58

Question 16.
A jeweler buys a ring from a jewelry maker for $125. He marks up the price by 135% for sale in his store. What is the selling price of the ring with 7.5% sales tax?
$ _______

Answer: 315.78

Explanation:
A jeweler buys a ring from a jewelry maker for $125. He marks up the price by 135% for sale in his store.
125 × 1.35 = 168.75
We can find the retail price by adding the markup to the purchase price
125 + 168.75 = 293.75
The amount of sales tax is 293.75 × 0.075 = 22.03
We can find the selling price by adding the tax amount to the retail price.
293.75 + 22.03 = 315.78
Therefore the selling price of the ring with 7.5% sales tax is $315.78

Question 17.
Luis wants to buy a skateboard that usually sells for $79.99. All merchandise is discounted by 12%. What is the total cost of the skateboard if Luis has to pay a state sales tax of 6.75%?
$ _______

Answer: 75.14

Explanation:
Given,
Luis wants to buy a skateboard that usually sells for $79.99. All merchandise is discounted by 12%.
79.99 × 0.12 = 9.60
79.99 – 9.60 = 70.39
First, we need to find the amount paid in taxes and then add that to the discount price to get the total cost.
70.39 × 0.0675 = 4.75
70.39 + 4.75 = 75.14
The total cost of the skateboard if Luis has to pay a state sales tax of 6.75% is $75.14

Question 18.
Kedar earns a monthly salary of $2,200 plus a 3.75% commission on the amount of his sales at a men’s clothing store. What would he earn this month if he sold $4,500 in clothing? Round to the nearest cent.
$ _______

Answer: 2368.75

Explanation:
Given,
Kedar earns a monthly salary of $2,200 plus a 3.75% commission on the amount of his sales at a men’s clothing store.
4500 × 0.0375 = 168.75
The total earnings can be known by adding his monthly salary and his commission.
2200 + 168.75 = 2368.75

Question 19.
Danielle earns a 7.25% commission on everything she sells at the electronics store where she works. She also earns a base salary of $750 per week. How much did she earn last week if she sold $4,500 in electronics merchandise? Round to the nearest cent.
$ _______

Answer: 1076.25

Explanation:
Danielle earns a 7.25% commission on everything she sells at the electronics store where she works.
She also earns a base salary of $750 per week.
The amount she made in the commission is 4500 × 0.0725 = 326.25
We can find the total earnings by adding her weekly pay and commission.
750 + 326.25 = 1076.25
Thus she earns $1076.25 last week if she sold $4,500 in electronics merchandise.

Question 20.
Francois earns a weekly salary of $475 plus a 5.5% commission on sales at a gift shop. How much would he earn in a week if he sold $700 in goods? Round to the nearest cent.
$ _______

Answer: 513.50

Explanation:
Given that, Francois earns a weekly salary of $475 plus a 5.5% commission on sales at a gift shop.
The amount he made in commission
700 × 0.055 = 38.50
We can find the total amount he earned by adding his weekly pay and commission
475 + 38.50 = $513.50

Question 21.
Sandra is 4 feet tall. Pablo is 10% taller than Sandra, and Michaela is 8% taller than Pablo
a. Explain how to find Michaela’s height with the given information.
Type below:
_____________

Answer:
First we have to find 10% of Sandra’s height: 0.10 × 4 = 0.4
This means that Pablo is then 4 + 0.4 = 4.4 feet tall.
Next find 8% of Pablo’s height: 4.4 × 0.08 = 0.352
This means that Michaela is 4.4 + 0.353 = 4.752 feet tall.

Question 21.
b. What is Michaela’s approximate height in feet and inches?
_______ feet _______ inches

Answer:
Convert from feet to inches.
1 feet = 12 inches
4.752 = 4 + 0.752
0.752 = 12 × 0.752 = 9 inches
4 feet = 12 × 4 = 48 inches
Thus the approximate height of Michaela is 4 feet 9 inches.

Question 22.
Eugene wants to buy jeans at a store that is giving $10 off everything. The tag on the jeans is marked 50% off. The original price is $49.98.
a. Find the total cost if the 50% discount is applied before the $10 discount.
$ _______

Answer: $14.99

Explanation:
Given that,
Eugene wants to buy jeans at a store that is giving $10 off everything.
The tag on the jeans is marked 50% off. The original price is $49.98.
0.5 × 49.98 = 24.99
Now subtract $10 discount.
24.99 – 10 = 14.99
The total cost if the 50% discount is applied before the $10 discount is $14.99

Question 22.
b. Find the total cost if the $10 discount is applied before the 50% discount.
$ _______

Answer: $19.99

Explanation:
We have to find the price after the $10 discount then find 50% of that price to find the discounted price.
49.98 – 10 = 39.98
0.5 × 39.98 = 19.99
Thus the total cost if the $10 discount is applied before the 50% discount is $19.99

Applications of Percent – Page No. 158

Question 23.
Multistep
Eric downloads the coupon shown and goes shopping at Gadgets Galore, where he buys a digital camera for $95 and an extra battery for $15.99.
a. What is the total cost if the coupon is applied to the digital camera?

$ _______

Answer: 101.49

Explanation:
Use the formula for the discount price:
DP = P – x.P
Price for the digital camera:
DP = 95 – 0.1(95)
DP = 95 – 9.5
DP = $85.5
Total cost = 85.5 + 15.99 = $101.49

Question 23.
b. What is the total cost if the coupon is applied to the extra battery?
$ _______

Answer: 109.391

Explanation:
Use the formula for the discount price:
DP = P – x.P
Price for the digital camera:
DP = 15.99 – 0.1(15.99)
DP = 15.99 – 1.599
DP = $14.399
Total cost = 95 + 14.399 = $109.391

Question 23.
c. To which item should Eric apply the discount? Explain.
____________

Answer: He should apply the discount to the digital camera because then the total cost is the lower.

Question 23.
d. Eric has to pay 8% sales tax after the coupon is applied. How much is his total bill?
$ _______

Answer:
Use formula for Discount price
If he uses coupon for the digital camera then his total cost will be
T = DP + 0.08 × DP
T = 101.49 + 8.1192
T = $109.6029
If he uses coupon for the extra battery his total cost will be
T = DP + 0.08 × DP
T = 109.391 + 0.08(109.391)
T = $118.14228

Question 24.
Two stores are having sales on the same shirts. The sale at Store 1 is “2 shirts for $22” and the sale at Store 2 is “Each $12.99 shirt is 10% off”.
a. Explain how much will you save by buying at Store 1.
$ _______

Answer:
For store 1, the shirts are 2 for $22. Ecah shirt then costs $22 ÷ 2 = $11
At store 2, each shirt is 10% off of $12.99 so each shirt costs:
$12.99 – 0.1(12.99) = $12.99 – $1.30 = $11.69
You will then save $11.69 – $11.00 = 0.69 per shirt if you buy them from Store 1.

Question 24.
b. If Store 3 has shirts originally priced at $20.98 on sale for 55% off, does it have a better deal than the other stores? Justify your answer.
_______

Answer:
If Store 3 sells shirts at 55% off of $20.98, then each shirt costs:
$20.98 – 0.55($20.98) = $20.98 – $11.54 = $9.44
This is lower than the costs per shirt of Store 1 and Store 2 so it has a better deal.

H.O.T.

Focus on Higher Order Thinking

Question 25.
Analyze Relationships
Marcus can choose between a monthly salary of $1,500 plus 5.5% of sales or $2,400 plus 3% of sales. He expects sales between $5,000 and $10,000 a month. Which salary option should he choose? Explain.
_______

Answer: Second Salary option is better

Explanation:
E = 1500 + 0.055(5000)
E = 1500 + 275
E = $1775
In the second case he will earn
E = 2400 + 0.03(5000)
E = 2400 + 150
E = $2550

Question 26.
Multistep
In chemistry class, Bob recorded the volume of a liquid as 13.2 mL. The actual volume was 13.7 mL. Use the formula to find percent error of Bob’s measurement to the nearest tenth of a percent.
_______ %

Answer: 3.6%

Explanation:

|13.2 – 13.7|/13.7 = |-0.5|/13.7
0.5/13.7 ≈ 0.036 = 3.6%

MODULE QUIZ – 5.1 Percent Increase and Decrease – Page No. 159

Find the percent change from the first value to the second.

Question 1.
36; 63
_______ %

Answer: 75%

Explanation:
Use the formula percent change = amount of change/first value
amount of change = 27
First value = 36
(63 – 36)/36 = 27/36 = 0.75 = 75%

Question 2.
50; 35
_______ %

Answer: 30%

Explanation:
Use the formula percent change = amount of change/first value
amount of change = 15
First value = 50
(50 – 35)/35 = 15/50 = 0.3 = 30%

Question 3.
40; 72
_______ %

Answer: 80%

Explanation:
Use the formula percent change = amount of change/first value
amount of change = 32
First value = 40
(72 – 40)/40 = 32/40 = 0.8 = 80%

5.2 Markup and Markdown

Use the original price and the markdown or markup to find the retail price.

Question 5.
Original price: $60; Markup: 15%
$ _______

Answer: $69

Explanation:
Use the formula retail price = original price + markup
60 + 60 × 0.15 = 60 + 9= 69

Question 6.
Original price: $32; Markup: 12.5%
$ _______

Answer: 36

Explanation:

Use the formula retail price = original price + markup

32 + 32 × 0.125 = 32 + 4 = $36

Question 7.
Original price: $50; Markdown: 22%
$ _______

Answer: 39

Explanation:

Use the formula retail price = original price + markup

50 – 50 × 0.22 = 50 – 11 = 39

Question 8.
Original price: $125; Markdown: 30%
$ _______

Answer: 87.50

Explanation:

Use the formula retail price = original price + markup

125 – 125 × 0.3 = 125 – 37.50 = 87.50

5.3 Applications of Percent

Question 9.
Mae Ling earns a weekly salary of $325 plus a 6.5% commission on sales at a gift shop. How much would she make in a work week if she sold $4,800 worth of merchandise?
$ _______

Answer: 637

Explanation:

Mae Ling weekly earnings is equal to her weekly salary plus her commission.

Since she earns 6.5 % commission on sales, if she sold $4800 worth of merchandise, her commission earnings  would be 6.5 % of 4800 = 0.065 × 4800 = $312.

Since her weekly salary is 325, then her total weekly earnings is $325 + $312 = $637

Question 10.
Ramon earns $1,735 each month and pays $53.10 for electricity. To the nearest tenth of a percent, what percent of Ramon’s earnings are spent on electricity each month?
_______ %

Answer: 3.1%

Explanation:

Divide the electric payment by his monthly pay

53.10/1735 = 0.031 = 3.1%

Question 11.
James, Priya, and Siobhan work in a grocery store. James makes $7.00 per hour. Priya makes 20% more than James, and Siobhan makes 5% less than Priya. How much does Siobhan make per hour?
$ _______

Answer: 7.98 per hour

Explanation:

Since James makes $7 per hour and priya makes 20% more than this, find 20% of 7 and then add that to 7 to find the pay per hour for Priya.

7 + 0.2(7) = 7 + 1.40 = 8.40

Since Priya makes $8.40 per hour and Siobhan makes 5% less than this, find 5% of 8.40 and subtract that from 8.40 to find the pay per hour of Siobhan.

8.40 – 0.05(8.40) = 8.40 – 0.42 = 7.98

Question 12.

The Hu family goes out for lunch, and the price of the meal is $45. The sales tax on the meal is 6%, and the family also leaves a 20% tip on the pre-tax amount. What is the total cost of the meal?
$ _______

Answer: 56.70

Explanation:

Find the amount of tax

45 × 0.06 = 2.70

Find the amount of tip

45 × 0.20 = 9

Find the total cost by adding the cost of the meal, the tax, and the tip.

45 + 2.70 + 9 = $56.70

Essential Question

Question 13.
Give three examples of how percents are used in the real-world. Tell whether each situation represents a percent increase or a percent decrease.
Type below:
____________

Answer:

One example could be giving a tip when you eat at a restaurant. Since the cost increases, it represents a percent increase.

Second example is tax on purchase. Since the price increases it is a percent increase.

Third example is using a coupon when buying an item. Since the price decreases, it is a percent decrease.

Selected Response – Page No. 160

Question 1.
Zalmon walks \(\frac{3}{4}\) of a mile in \(\frac{3}{10}\) of an hour. What is his speed in miles per hour?
Options:
a. 0.225 miles per hour
b. 2.3 miles per hour
c. 2.5 miles per hour
d. 2.6 miles per hour

Answer: 2.5 miles per hour

Explanation:
Given that,
Zalmon walks \(\frac{3}{4}\) of a mile in \(\frac{3}{10}\) of an hour.
Divide the number of miles by the number of hours to get his speed in miles per hour.
\(\frac{3}{4}\) ÷ \(\frac{3}{10}\)
\(\frac{3}{4}\) ÷ \(\frac{10}{3}\) = \(\frac{5}{2}\)
Convert the fraction into the decimal form.
\(\frac{5}{2}\) = 2.5 miles per hour
Thus the correct answer is option C.

Question 2.
Find the percent change from 70 to 56.
Options:
a. 20% decrease
b. 20% increase
c. 25% decrease
d. 25% increase

Answer: 20% increase

Explanation:
Use the percent change = amount of change/original amount.
Since the number decreased from 70 to 56, it is a percent decrease.
= (70 – 56)/70 = \(\frac{14}{70}\) = 0.2 = 20%
Thus the correct answer is option A.

Question 3.
The rainfall total two years ago was 10.2 inches. Last year’s total was 20% greater. What was last year’s rainfall total?
Options:
a. 8.16 inches
b. 11.22 inches
c. 12.24 inches
d. 20.4 inches

Answer: 12.24 inches

Explanation:
Given,
The rainfall total two years ago was 10.2 inches. Last year’s total was 20% greater.
Find 20% of 10.2
10.2 × 0.20 = 2.04
Add the value to the original amount of 10.2
10.2 + 2.04 = 12.24
Therefore the correct answer is option C.

Question 4.
A pair of basketball shoes was originally priced at $80, but was marked up 37.5%. What was the retail price of the shoes?
Options:
a. $50
b. $83
c. $110
d. $130

Answer: $110

Explanation:
A pair of basketball shoes was originally priced at $80, but was marked up 37.5%.
Use the formula retail price = original price + markup
80 + 80 × 0.375 = 80 + 30 = 110
Thus the correct answer is option C.

Question 5.
The sales tax rate in Jan’s town is 7.5%. If she buys 3 lamps for $23.59 each and a sofa for $769.99, how much sales tax does she owe?
Options:
a. $58.85
b. $63.06
c. $67.26
d. $71.46

Answer: $63.06

Explanation:
The sales tax rate in Jan’s town is 7.5%.
If she buys 3 lamps for $23.59 each and a sofa for $769.99
Total cost before tax is 3 × 23.59 + 769.99
= 70.77 + 769.99 = 840.76
Find the amount of tax by multiplying the tax rate and total cost from the above solution and then round to 2 decimal place.
840.76 × 0.075 = 63.06
Thus the correct answer is option B.

Question 6.
The day after a national holiday, decorations were marked down 40%. Before the holiday, a patriotic banner cost $5.75. How much did the banner cost after the holiday?
Options:
a. $1.15
b. $2.30
c. $3.45
d. $8.05

Answer: $3.45

Explanation:
The day after a national holiday, decorations were marked down 40%. Before the holiday, a patriotic banner cost $5.75.
use the formula retail price = original price – markdown
5.75 – 5.75 × 0.4 = 5.75 – 2.30 = 3.45
Thus the correct answer is option C.

Question 7.
Dustin makes $2,330 each month and pays $840 for rent. To the nearest tenth of a percent, what percent of Dustin’s earnings are spent on rent?
Options:
a. 84%
b. 63.9%
c. 56.4%
d. 36.1%

Answer: 36.1%

Explanation:
Dustin makes $2,330 each month and pays $840 for rent.
Divide his rent by his monthly income. round to three decimal places and then convert to percent form.
840/2330 = 0.361 = 36.1%
Thus the correct answer is option D.

Question 8.
A scuba diver is positioned at -30 feet. How many feet will she have to rise to change her position to -12 feet?
Options:
a. -42 ft
b. -18 ft
c. 18 ft
d. 42 ft

Answer: 18 ft

Explanation:
Given,
A scuba diver is positioned at -30 feet.
-12 – (-30) = 12 + 30 = 18 feet
Thus the correct answer is option C.

Question 9.
A bank offers an annual simple interest rate of 8% on home improvement loans. Tobias borrowed $17,000 over a period of 2 years. How much did he repay altogether?
Options:
a. $1360
b. $2720
c. $18360
d. $19720

Answer: $19720

Explanation:
Given that,
A bank offers an annual simple interest rate of 8% on home improvement loans.
Tobias borrowed $17,000 over a period of 2 years
Find the amount of interest he paid using the formula
I = prt
where p is the amount borrowed
r is the interest rate
t is the number of years
17000 × 0.08 × 2 = 2720
Add the amount borrowed and amount of interest
17000 + 2720 = 19720.
Thus the correct answer is option D.

Mini-Task

Question 10.
The granola Summer buys used to cost $6.00 per pound, but it has been marked up 15%.
a. How much did it cost Summer to buy 2.6 pounds of granola at the old price?
$ ___________

Answer: $15.60

Explanation:
Multiply 2.6 by the old price of $6
2.6 × 6 = 15.60
It costs $15.60 to buy 2.6 pounds of granola at the old price.

Question 10.
b. How much does it cost her to buy 2.6 pounds of granola at the new price?
$ _______

Answer: $17.94

Explanation:
Find the new price using the formula retail price = original price + markup
Then find the total cost by buying 2.6 pounds at the new price.
6 + 6 × 0.15 = 6 + 0.9 = 6.90
2.6 × 6.90 = 17.94
The new price is $17.94

Question 10.
c. Suppose Summer buys 3.5 pounds of granola. How much more does it cost at the new price than at the old price?
$ _______

Answer: $3.15

Explanation:
3.5 × 6 = 21
3.5 × 6.90 = 24.15
24.15 – 21 = 3.15

Module 5 – Page No. 162

EXERCISES

Question 1.
Michelle purchased 25 audio files in January. In February she purchased 40 audio files. Find the percent increase.
_______ %

Answer: 60%

Explanation:
Given,
Michelle purchased 25 audio files in January. In February she purchased 40 audio files.
Use the percent change = amount of change/original amount.
(40 -25)/25 = 15/25 = 0.6 = 60%
Thus the percent increase is 60%

Question 2.
Sam’s dog weighs 72 pounds. The vet suggests that for the dog’s health, its weight should decrease by 12.5 percent. According to the vet, what is a healthy weight for the dog?
_______ pounds

Answer: 63 pounds

Explanation:
Given,
Sam’s dog weighs 72 pounds. The vet suggests that for the dog’s health, its weight should decrease by 12.5 percent.
72 × 0.125 = 9
Find a healthy weight by subtracting the change in weight from the original weight
72 – 9 = 63
The healthy weight of the dog is 63 pounds.

Question 3.
The original price of a barbecue grill is $79.50. The grill is marked down 15%. What is the sale price of the grill?
$ _______

Answer: 67.57

Explanation:
Given,
The original price of a barbecue grill is $79.50. The grill is marked down 15%.
Use the formula sale price = original price – markdown
= 79.50 – 79.50 × 0.15 = 79.50 – 11.93 = $67.57
Thus the sale price of the grill is $67.57

Question 4.
A sporting goods store marks up the cost s of soccer balls by 250%. Write an expression that represents the retail cost of the soccer balls. The store buys soccer balls for $5.00 each. What is the retail price of the soccer balls?
$ _______

Answer: $17.5

Explanation:
Use the formula retail price = original price + markup to find the expression for an original price of s and a markup percentage of 250%
s + 2.5s = 3.5s
substitute s = 5 into the expression to find the retail price
3.5 × 5 = 17.50
Thus the retail price of the soccer balls is $17.50

Unit 2 Performance Tasks – Page No. 163

Question 1.
Viktor is a bike tour operator and needs to replace two of his touring bikes. He orders two bikes from the sporting goods store for a total of $2,000 and pays using his credit card. When the bill arrives, he reads the following information:
Balance: $2000
Annual interest rate: 14.9%
Minimum payment due: $40
Late fee: $10 if payment not received by 3/1/2013
a. To keep his good credit, Viktor promptly sends in a minimum payment of $40. When the next bill arrives, it looks a lot like the previous bill.
Balance: $1,984.34
Annual interest rate: 14.9%
Minimum payment due: $40
Late fee: $10 if payment not received by 4/1/2013
Explain how the credit card company calculated the new balance. Notice that the given interest rate is annual, but the payment is monthly.
Type below:
_____________

Answer:
We have to find the balance after the first bill by subtracting the $40 payment from the original balance of $2000.
Balance after first bill: 2000 – 40 = 1960
Then find the amount of interest charged on the second bill by multiplying the balance of $1960 by the interest rate.
Remember since the interest rate is annually you have to divide it by 12 to get the monthly interest rate.
Interest on the second bill: 1960 × 0.149/12 = 24.34
And then add this interest amount to the balance of $1960 to get the balance on the second bill.
New balance: 1960 + 24.34 = 1984.34

Question 1.
b. Viktor was upset about the new bill, so he decided to send in $150 for his April payment. The minimum payment on his bill is calculated as 2% of the balance (rounded to the nearest dollar) or $20, whichever is greater. Fill out the details for Viktor’s new bill.
Type below:
_____________

Answer:
Find the balance after the $150 payment. The interest rate hasn’t changed so the annual interest rate on this new bill is the same as the previous bills.
balance after payment: 1984.34 – 150 = 1834.34
annual interest rate: 14/9%
Find the interest charged on the third bill. find the balance on the third bill by adding the interest charged to the balance of $1834.34.
interest on the third bill: 1834.34 × 0.149/12 = 22.78
balance: 1834.34 + 22.78 = 1857.12
To find what the minimum payment will be, first find 2% of the balance.
2% of balance: 0.02 × 1857.12 = 37.14
Minimum payment due: $37.00
Since this is greater than $20, the minimum payment is 2% of the balance rounded to the nearest dollar giving $37 as the payment.
The later fee date is one month after the late fee date of 04/01/2013 on the previous bill which gives 05/01/2013.

Question 1.
c. Viktor’s bank offers a credit card with an introductory annual interest rate of 9.9%. He can transfer his current balance for a fee of $40. After one year, the rate will return to the bank’s normal rate, which is 13.9%. The bank charges a late fee of $15. Give two reasons why Viktor should transfer the balance and two reasons why he should not
Type below:
_____________

Answer: Two reasons he should transfer is that the lower introductory rate would mean less interest charged in the first year and a lower normal rate would mean less interest charged after that first year as well. Two reasons he shouldn’t transfer the balance is that he would have to pay a transfer fee of $40 and that the late fee is $15 instead of $10 if he transfers the balance.

Unit 2 Performance Tasks (con’td) – Page No. 164

Question 2.
The table below shows how far several animals can travel at their maximum speeds in a given time.
a. Write each animal’s speed as a unit rate in feet per second.

Elk: _________ feet per second
Giraffe: _________ feet per second
Zebra: _________ feet per second

Answer:
By seeing the above table we can find the unit rates by dividing the distance traveled by the time in second.
elk: 33 ÷ 1/2 = 33 ×  2 = 66 feet per second
Giraffe: 115 ÷ 2 1/2 = 115 ÷ 5/2 = 115 2/5 = 46 feet per second
Zebra: 117 ÷ 2 = 58.5 feet per second

Question 2.
b. Which animal has the fastest speed?
_____________

Answer: The elk had the greatest unit rate so it has the fastest speed.

Question 2.
c. How many miles could the fastest animal travel in 2 hours if it maintained the speed you calculated in part a? Use the formula d = rt and round your answer to the nearest tenth of a mile. Show your work.
Elk: _________ miles
Giraffe: _________ miles
Zebra: _________ miles

Answer:
Elk: 90 miles
Giraffe: 62 miles
Zebra: 72 miles

Explanation:

There are 60 seconds in a minute and 60 minutes in an hour so there are 2 × 60 × 60 = 7200 seconds in 2 hours.
Multiply the unit rate of the elk by 7200 seconds to get the distance traveled in feet.
There are 5280 feet in 1 mile so divide the distance in feet by 5280 to get the distances in miles.
Elk:
66 × 7200 =  475200 feet
Now convert from feet to miles
475200 feet = 90 miles
Giraffe: 46 feet per second
62 × 7200 = 331200 feet
Now convert from feet to miles.
331200 = 62 miles
Zebra: 58.5 feet per second
58.5 × 7200 = 421200 feet
Now convert from feet to miles.
421200 feet = 72 miles

Question 3.
d. The data in the table represents how fast each animal can travel at its maximum speed. Is it reasonable to expect the animal from part b to travel that distance in 2 hours? Explain why or why not.
______

Answer: It is not reasonable. An animal can only travel at its maximum speed for a short amount of time which is usually only for a couple of minutes.

Selected Response – Page No. 165

Question 1.
If the relationship between distance y in feet and time x in seconds is proportional, which rate is represented by \(\frac{y}{x}\) = 0.6?
Options:
a. 3 feet in 5 s
b. 3 feet in 9 s
c. 10 feet in 6 s
d. 18 feet in 3 s

Answer: 3 feet in 5 s

Explanation:
\(\frac{y}{x}\) = 0.6
0.6 = \(\frac{6}{10}\)
Since \(\frac{6}{10}\) = \(\frac{3}{5}\), it represents a rate of 3 feet in 5 seconds,
Therefore the correct answer is option A.

Question 2.
The Baghrams make regular monthly deposits in a savings account. The graph shows the relationship between the number x of months and the amount y in dollars in the account.
What is the equation for the deposit?

Options:
a. \(\frac{y}{x}\) = $25/month
b. \(\frac{y}{x}\) = $40/month
c. \(\frac{y}{x}\) = $50/month
d. \(\frac{y}{x}\) = $75/month

Answer: \(\frac{y}{x}\) = $50/month

Explanation:
By seeing the above graph we can say that the point is (2, 100). This means that \(\frac{y}{x}\) = \(\frac{100}{2}\) = 50.
Thus the correct answer is option C.

Question 3.
What is the decimal form of −4 \(\frac{7}{8}\)?
Options:
a. -4.9375
b. -4.875
c. -4.75
d. -4.625

Answer: -4.875

Explanation:
Given the fraction
−4 \(\frac{7}{8}\)
First divide \(\frac{7}{8}\) = 0.875
4 + 0.875 = 4.875
So, −4 \(\frac{7}{8}\) = -4.875
Therefore the answer is option B.

Question 4.
Find the percent change from 72 to 90.
Options:
a. 20% decrease
b. 20% increase
c. 25% decrease
d. 25% increase

Answer: 25% increase

Explanation:
Use the formula percent change = amount of change/original amount.
the value increased from 72 to 90 so it is a percent increase.
(90-72)/72 = 18/72 = 0.25 = 25%
Thus the correct answer is option D.

Question 5.
A store had a sale on art supplies. The price p of each item was marked down 60%. Which expression represents the new price?
Options:
a. 0.4p
b. 0.6p
c. 1.4p
d. 1.6p

Answer: 0.4p

Explanation:
Given that,
A store had a sale on art supplies.
The price p of each item was marked down 60%
Use the formula sale price = original price – markdown
p is the original price and the markdown percent is 40% then combine the like terms.
p – 0.6p = 0.4p
Therefore the correct answer is option A.

Question 6.
Clarke borrows $16,000 to buy a car. He pays simple interest at an annual rate of 6% over a period of 3.5 years. How much does he pay altogether?
Options:
a. $18800
b. $19360
c. $19920
d. $20480

Answer: $19360

Explanation:
Given,
Clarke borrows $16,000 to buy a car.
He pays simple interest at an annual rate of 6% over a period of 3.5 years.
Find the total amount of interest using the formula
I = prt
where p is the amount borrowed
r is the rate of interest
t is the number of years
16000 × 0.06 × 3.5 = 3360
Now add the amount of interest to the amount borrowed to find the total amount
16000 + 3360 = 19,360
Thus the correct answer is option B.

Question 7.
To which set or sets does the number 37 belong?
Options:
a. integers only
b. rational numbers only
c. integers and rational numbers only
d. whole numbers, integers, and rational numbers

Answer: whole numbers, integers, and rational numbers

Explanation:
37 can be written as 37/1 so it is a rational number. 37 doesn’t have a decimal or fraction so it is an integer. Since it is a positive integer, it is also a whole number.
Thus a suitable answer is option D.

Page No. 166

Question 8.
In which equation is the constant of proportionality 5?
Options:
a. x = 5y
b. y = 5x
c. y = x + 5
d. y = 5 – x

Answer: y = 5x

Explanation:
Directly proportional equations are of the form y = kx
where k is the constant of proportionality.
If k = 5, then the equation is y = 5x.
Thus the correct answer is option B.

Question 9.
Suri earns extra money by dog walking. She charges $6.25 to walk a dog once a day 5 days a week and $8.75 to walk a dog once a day 7 days a week. Which equation represents this relationship?
Options:
a. y = 7x
b. y = 5x
c. y = 2.50x
d. y = 1.25x

Answer: y = 1.25x

Explanation:
Given that,
Suri earns extra money by dog walking. She charges $6.25 to walk a dog once a day 5 days a week and $8.75 to walk a dog once a day 7 days a week.
Since 6.25/5 = 1.25
So, the equation is y = 1.25x
where x is the number of days and y is the total charge.
So, the correct answer is option D.

Question 10.
Randy walks \(\frac{1}{2}\) mile in each \(\frac{1}{5}\) hour. How far will Randy walk in one hour?
Options:
a. \(\frac{1}{2}\) miles
b. 2 miles
c. 2 \(\frac{1}{2}\) miles
d. 5 miles

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

Explanation:
Given,
Randy walks \(\frac{1}{2}\) mile in each \(\frac{1}{5}\) hour.
\(\frac{1}{2}\) ÷ \(\frac{1}{5}\)
\(\frac{1}{2}\) × \(\frac{5}{1}\) = \(\frac{5}{2}\)
Convert the fraction to the improper fractions.
\(\frac{5}{2}\) = 2 \(\frac{1}{2}\) miles
Therefore the correct answer is option C.

Question 11.
On a trip to Spain, Sheila bought a piece of jewelry that cost $56.75. She paid for it with her credit card, which charges a foreign transaction fee of 3%. How much was the foreign transaction fee?
Options:
a. $0.17
b. $1.07
c. $1.70
d. $17.00

Answer: $1.70

Explanation:
On a trip to Spain, Sheila bought a piece of jewelry that cost $56.75.
She paid for it with her credit card, which charges a foreign transaction fee of 3%
Find the foreign transaction fee amount by multiplying the cost by the foreign transaction fee percentage.
56.75 × 0.03 = 1.70
Thus the correct answer is option C.

Question 12.
A baker is looking for a recipe that has the lowest unit rate for flour per batch of muffins. Which recipe should she use?
Options:
a. \(\frac{1}{2}\) cup flour for \(\frac{2}{3}\) batch
b. \(\frac{2}{3}\) cup flour for \(\frac{1}{2}\) batch
c. \(\frac{3}{4}\) cup flour for \(\frac{2}{3}\) batch
d. \(\frac{1}{3}\) cup flour for \(\frac{1}{4}\) batch

Answer: \(\frac{1}{2}\) cup flour for \(\frac{2}{3}\) batch

Explanation:
a. \(\frac{1}{2}\) ÷ \(\frac{2}{3}\) = \(\frac{1}{2}\) × \(\frac{3}{2}\) = \(\frac{3}{4}\)
b. \(\frac{2}{3}\) ÷ \(\frac{1}{2}\) = \(\frac{2}{3}\) × \(\frac{2}{1}\) = \(\frac{4}{3}\) = 1 \(\frac{1}{3}\)
c. \(\frac{3}{4}\) ÷ \(\frac{2}{3}\) = \(\frac{3}{4}\) × \(\frac{3}{2}\) = \(\frac{9}{8}\) = 1 \(\frac{1}{8}\)
d. \(\frac{1}{3}\) ÷ \(\frac{1}{4}\) = \(\frac{1}{3}\) ÷ \(\frac{4}{1}\) = 1 \(\frac{1}{3}\)
Thus the correct answer is option A.

Mini-Task

Question 13.
Kevin was able to type 2 pages in 5 minutes, 3 pages in 7.5 minutes, and 5 pages in 12.5 minutes.
a. Make a table of the data.
Type below:
___________

Answer:

Question 13.
b. Graph the relationship between the number of pages typed and the number of minutes.

Type below:
___________

Answer:

Question 13.
c. Explain how to use the graph to find the unit rate.
Type below:
___________

Answer: The unit rate is 2.5 pages per minute

Explanation:
By using the graph we need to find the slope of the line.
We can do this by using the formula of a slope:
m = (y2-y1)/(x2-x1) = (7.5-5)/(3-2) = 2.5
Thus the unit rate is 2.5 pages per minute.

Conclusion:

Hope the answers provided in Go Math Answer Key Grade 7 Chapter 5 Percent Increase and Decrease are quite satisfactory for all the students. Refer to our Go Math 7th Grade Chapter 5 Percent Increase and Decrease to get the solutions with best explanations. After your preparation test your math skills by solving the questions in the performance tasks.

Go Math Grade 3 Answer Key Chapter 8 Understand Fractions includes all the topics covered in Chapter 8. Major Motto behind providing the Go Math Answer Key for Grade 3 Chapter 8 is to make the students familiar with the concepts. Download Go Math Grade 3 Answer Key Understand Fractions free of cost and prepare whenever you want. If you are preparing for 3rd standard exams you can always look up to HMH Go Math Solution Key Grade 3 Chapter 8 Understand Fractions.

Grade 3 Go Math Answer Key Chapter 8 Understand Fractions

Have an overview of Grade 3 HMH Go Math Solutions Key for Chapter 8 Understand Fractions and the lessons in Chapter 8. utilize the Answer Keys of Go Math 3rd Std Chapter 8 Understand Fractions and be prepared for the exams. Practice using the Practice Questions at the end of the chapter and test your preparation level and bridge the knowledge gap accordingly.

Lesson 1: Equal Parts of a Whole

• Equal Parts of a Whole Page No 447
• Equal Parts of a Whole Lesson Check – Page No 448

Lesson 2: Equal Shares

• Equal Shares Page No 453
• Equal Shares Lesson Check Page No 454

Lesson 3: Unit Fractions of a Whole

• Unit Fractions of a Whole Page No 459
• Unit Fractions of a Whole Lesson Check Page No 460

Lesson 4: Fractions of a Whole

• Fractions of a Whole Page No 465
• Fractions of a Whole Lesson Check Page No 466

Lesson 5: Fractions on a Number Line

• Fractions on a Number Line Page No 471
• Fractions on a Number Line Lesson Check Page No 472

Chapter 8 Mid-Chapter Checkpoint

• Page No 473
• Page No 474

Lesson 6: Relate Fractions and Whole Numbers

• Relate Fractions and Whole Numbers Page No 478
• Relate Fractions and Whole Numbers Page No 479
• Relate Fractions and Whole Numbers Lesson Check Page No 480

Lesson 7: Fractions of a Group

• Fractions of a Group Page No 485
• Fractions of a Group Lesson Check Page No 486

Lesson 8: Find Part of a Group Using Unit Fractions

• Find Part of a Group Using Unit Fractions Page No 491
• Find Part of a Group Using Unit Fractions Lesson Check Page No 492

Lesson 9: Problem Solving

• Find the Whole Group Using Unit Fractions Page No 497
• Find the Whole Group Using Unit Fractions Lesson Check Page No 498

Chapter 8 Understand Fractions Review/Test

• Page No – 499
• Page No – 500
• Page No – 501
• Page No – 502
• Page No – 503
• Page No – 504

Equal Parts for a Whole – Page No 447

Write the number of equal parts. Then write the name for the parts.

Question 1:

Equal Parts: ___________
Name: _______________

Answer:

i) 4
ii) Fourths

Explanation:
From the above figure, we can see that the circle is divided into 4 equal parts and the parts are named as fourths.

Question 2:

Equal Parts: ___________
Name: _______________

Answer:
i) 3
ii) Thirds

Explanation:
The rectangle is divided into 3 equal parts. The name for those parts is thirds.

Question 3:

Equal Parts: ____________
Name: ________________

Answer:
i) 2
ii) Halves

Explanation:
The square is diagonally cut into 2 triangles. As it is a square the triangles will be of the same size. Therefore the triangles are equal and the name for the parts is halves.

Question 4:

Equal Parts: _____________
Name: _________________

Answer:
i) 6
ii) Sixths

Explanation:
Here we can see a rectangle that is separated into 6 equal parts. As it is divided into 6 parts it is named as sixths.

Write whether the shape is divided into equal parts or unequal parts

Question 5:

____________ Parts

Answer:
Unequal

Explanation:
The triangle is cut into 2 but the size and shape are not the same. So, by seeing the figure we can say that the parts are unequal.

Question 6:

____________ Parts

Answer:
Equal

Explanation:
In the above figure, we can observe that the trapezium is divided into 3 triangles of equal parts.

Problem Solving

Question 7:
Diego cuts a round pizza into eight equal slices. What is the name for the parts?
____________

Answer:
Eighths

Explanation:
Diego cuts a round pizza into 8 equal slices. So the name for the parts is eighths.

Question 8:
Madison is making a placemat. She divides it into 6 equal parts to color. What is the name for the parts?____________

Answer:
Sixths

Explanation:
If the placemat is cut into 6 equal parts then the parts are named as sixths.

Equal Parts of a Whole – Lesson Check – Page No 448

Question 1:
How many equal parts are in this shape?

Options:
i. 3
ii. 4
iii. 5
iv. 6

Answer:
ii (4)

Explanation:
In the figure, the rectangle is divided into 4 equal parts.

Question 2:
What is the name for the equal parts of the whole?

Options:
i. Fourths
ii. Sixths
iii. Eighths
iv. Thirds

Answer:
iii (Eighths)

Explanation:
From the above fig, we can see 8 triangles. Therefore the name for the parts is eighths.

Spiral Review

Question 3:
Use a related multiplication fact to find the quotient.
49 ÷ 7 = ___

Options:
i. 6
ii. 7
iii. 8
iv. 9

Answer:
ii (7)

Explanation:
Given,
49 ÷ 7 = ___
49/7 = 7
49 is divisible by 7 by 7 times. Therefore the remainder is 0 and the quotient is 7.

Question 4:
Find the unknown factor and quotient.
9 × __ = 45
Options:
i. 4
ii. 5
iii. 6
iv. 7

Answer:
ii (5)

Explanation:
Given,
9 × __ = 45
45/9 = 5
Therefore the unknown factor of 9 × __ = 45 is 5.

Question 5:
There are 5 pairs of socks in one package. Matt buys 3 packages of socks. How many pairs of socks in all does Matt buy?
Options:
i. 30
ii. 15
iii. 10
iv. 8

Answer:
ii (15)

Explanation:
Given that, there are 5 pairs of socks in 1 package.
If Matt buys 3 packages of socks then multiply 5 with 3. We get 15.
Therefore, Matt buys 15 pairs of socks.

Question 6:
Mrs. McCarr buys 9 packages of markers for an art project. Each package has 10 markers. How many markers in all does Mrs. McCarr buy?
Options:
i. 10
ii. 19
iii. 81
iv. 90

Answer:
iv (90)

Explanation:
Given,
Mrs. McCarr buys 9 packages of marks for an art project
There are 10 markers in each package.

To find:
How many markers did Mrs. McCarr buy
In order to know the markers she bought we need to multiply the number of packages with total number of markers in each package.
i.e, 9 × 10 = 90
Therefore, the total number of markers in 9 packages is 90.

Equal Shares – Page No 453

Question 1:
6 friends share 3 sandwiches equally.

Answer:
3 Sixths of a Sandwich

Explanation:
There are 3 sandwiches and 6 friends need to share it equally
So, divide the total number of sandwiches by number of friends i.e., 3/6 = 1/2
So, the equal share of 6 sandwiches is 3 sixths or 1 half of a sandwich.

Question 2:
8 classmates share 4 pizzas equally.

Answer:
4 Eighths, or 1 half of a pizza.

Explanation:
Given,
Number of pizzas = 4
Number of classmates = 8
In order to share the pizzas equally, we need to divide 4 by 8
4/8 = 1/2
So, the 8 classmates can share 4 eighths or 1 half of a pizza.

Question 3:
4 teammates share 5 granola bars equally. Draw to show how much each person gets. Shade the amount that one person gets. Write the answer.

Answer:
5 fourths of a granola bar.

Explanation:
Given that, the number of teammates = 4
and number of granola bars = 5
Number of granola bars/Number of teammates= 5/4
So, the answer is 5 fourths of a granola bars.

Problem Solving

Question 4:
Three brothers share 2 sandwiches equally. How much of a sandwich does each brother get?

Answer:
2 thirds of a sandwich

Explanation:
To know how much sandwich does each brother get,
we have to divide no. of sandwiches by no. of brothers
i.e, 2/3
So, each brother gets 2 thirds of a sandwich.

Question 5:
Six neighbors share 4 pies equally. How much of a pie does each neighbor get?

Answer:
4 sixths or 1 sixth or 2 thirds of a pie

Explanation:
Given that, 6 neighbors share 4 pies equally
To know how much of a pie does each neighbor get
we need to divide number of pies by number of neighbors
4/6 = 2/3

(or)

1/6 of each pie

Equal Shares Lesson Check Page No 454

Question 1:
Two friends share 3 fruit bars equally. How much does each friend get?

Options:
i. 1 Half
ii. 2 Thirds
iii. 2 Halves
iv. 3 Halves

Answer:
iv (3 Halves)

Explanation:
Total number of fruit bars/ Number of friends = 3/2
So, each friend gets 3 halves of the fruit bar

Question 2:
Four brothers share 3 pizzas equally. How much of a pizza does each brother get?

Options:
i. 3 halves
ii. 4 third
iii. 3 fourths
iv. 2 fourths

Answer:
iii. (3 fourths)

Explanation:
Given,
No. of pizzas = 3
No. of brothers = 4
In order to share the pizzas,
we need to divide No. of pizzas/No. of brothers = 3/4
So, the answer is 3 fourths.

Spiral Review

Question 3:
Find the quotient.
3)27
Options:
i. 6
ii. 7
iii. 7
iv. 9

Answer:
iv (9)

Explanation:
To find quotient:
Divide 27/3 = 9
Therefore the quotient of 3)27 is 9

Question 4:
Tyrice put 4 cookies in each of 7 bags. How many cookies in all did he put in the bags?
Options:
i. 11
ii. 28
iii. 32
iv. 40

Answer:
ii (28)

Explanation:
Given that, Tyrice put 4 cookies in each of 7 bags
Total no. of cookies = 4
Total no. of bags = 7
To find:
How many cookies in all did he put in the bags,
We need to multiply No. of bags with No. of cookies
we get 7 × 4 = 28
Therefore, the Total Number of cookies in all the bags is 28.

Question 5:
Ryan earns $5 per hour raking leaves. He earned $35. How many hours did he rake leaves?
Options:
i. 5 hours
ii. 6 hours
iii. 7 hours
iv. 35 hours

Answer:
iii (7 hours)

Explanation:
Given,
Ryan earns $5 per hour
To find how many hours did he rake leaves to earn $35
Divide 35 by 5, we get
35/5 = 7
So, Ryan raked leaves for 7 hours to earn $35

Question 6:
Hannah has 229 horse stickers and 164 kitten stickers. How many more horse stickers than kitten stickers does Hannah have?
Options:
i. 45
ii. 65
iii. 145
iv. 293

Answer:
ii (65)

Explanation:
Total no. of horse stickers Hannah has is 229
No. of kitten stickers Hannah has is 164
To know how many more horse stickers than kitten stickers does Hannah have,
we need to subtract no. of horse stickers and no. of kitten stickers
i.e., 229 – 164 = 65
So, the answer is 65

Unit Fractions of a Whole Page No 459

Write the number of equal parts in the whole. Then write the fraction that names the shaded part.

Question 1:

__________ equal parts __________

Answer:
i) 6
ii) 1/6

Explanation:
The rectangle is divided into 6 equal parts. From the figure, we observe that one block is shaded. So, the fraction name of the shaded part is 1/6.

Question 2:

__________ equal parts

__________

Answer:

i) 2
ii) 1/2

Explanation:
There are 2 right-angled triangles in which one part is shaded. Therefore, the fractional name for the shaded part is 1/2

Question 3:

__________ equal parts

__________

Answer:

i) 4
ii) 1/4

Explanation:
The circle is divided into 4 equal parts and one part is shaded among them. The fraction that names the shaded part is 1/4

Question 4:

__________ equal parts

__________

Answer:

i) 3
ii) 1/3

Explanation:
In the above fig, we see that the trapezium is divided into 3 equal triangles and the fraction name of the shaded part is 1/3.

Question 5:
1/3 is 

Answer:

Question 6:
1/8 is 

Answer:

Question 7:
Tyler made a pan of cornbread. He cut it into 8 equal pieces and ate 1 piece. What fraction of the cornbread did Tyler eat?
________

Answer:
1/8

Explanation:
There are 8 pieces of cornbread. Tyler ate 1 piece out of 8 cornbread.
The fraction of cornbread that Tyler ate is 1/8

Question 8:
Anna cut an apple into 4 equal pieces. She gave 1 piece to her sister. What fraction of the apple did Anna give to her sister?
________

Answer:
1/4

Explanation:
Anna cut an apple into 4 pieces. She gave 1 piece of apple to her sister.
One piece of apple/ Total Number of pieces = 1/4

Unit Fractions of a Whole Lesson Check Page No 460

Question 1:
What fraction names the shaded part?

Options:
i. 1/3
ii. 1/4
iii. 1/6
iv. 1/8

Answer:
ii (1/4)

Explanation:
There are 4 blocks in the rectangle and one part is shaded among them. So the answer is 1/4

Question 2:
Tasha cut a fruit bar into 3 equal parts. She ate 1 part. What fraction of the fruit bar did Tasha eat?
Options:
i. 1/2
ii. 1/3
iii. 1/4
iv. 1/6

Answer:
ii (1/3)

Explanation:
The fruit bar is cut into 3 equal parts and Tasha ate one part. So, the fraction name of the fruit bar that Tasha ate is 1/3

Spiral Review
Question 3:
Alex has 5 lizards. He divides them equally among 5 cages. How many lizards do Alex put in each cage?
i. 0
ii. 1
iii. 5
iv. 10

Answer:
ii (1)

Explanation:
Alex has 5 lizards and put them equally in 5 cages. That means Alex has put one lizard in one cage.

Question 4:
Find the product.
8 × 1 = _
i. 0
ii. 1
iii. 8
iv. 9

Answer:
iii (8)

Explanation:
We know that any number multiplied with 1 is itself. Therefore the multiplication of 8 and 1 is 8.

Question 5:
Leo bought 6 chew toys for his new puppy. Each chew toy cost $4. How much did Leo spend in all for the chew toys?
i. $10
ii. $12
iii. $18
iv. $24

Answer:
iv ($24)

Explanation:
Given,
Leo bought 6 chew toys for his new puppy
Each toy costs $4.
1 — $4
6 —?
Cross multiplication is applied here,
we get 6 × 4 = 24
Therefore the cost of 6 chew toys is $24.

Question 6:
Lilly is making a picture graph. Each picture of a star is equal to two books she has read. The row for the month of December has 3 stars. How many books did Lilly read during the month of December?
i. 3
ii. 5
iii. 6
iv. 9

Answer:
iii (6)
Explanation:
Given that each picture of star equals 2 books
The row for the month of December has 3 stars.
Let’s apply the cross multiplication method here,
1 star — 2 books
3 stars —?
3 × 2 = 6
So, the answer to the above question is 6

Fractions of a Whole Page No 465

Write the fraction that names each part. Write a fraction in words and in numbers to name the shaded part.
Question 1:

Each Part is _______ . _______ sixths
____________

Answer:
i) 1/6
ii) Three
iii) 3/6

Explanation:
The above figure is Hexagon which consists of 6 sides. So each part of a hexagon is 1/6 and we can see that three parts are shaded. The fraction form of the shaded part is three sixths i.e., 3/6

Question 2:

Each Part is ________. ______ eighths
_____________

Answer:
i) 1/8
ii) Five
iii) 5/8

Explanation:
There are 8 blocks in the rectangle out of which 5 parts are shaded. Each part of the rectangle is 1/8 and the name for the shaded part is Five Eights. The fraction of the shaded part is 5/8.

Question 3:

Each Part is ________. ______ thirds
_____________

Answer:
i) 1/3
ii) Two
iii) 2/3

Explanation:
Here we can see 3d form a triangle, each part is 1/3. Two sides are shaded in it so, the name for the shaded part is two thirds. The shaded part will be in the numerator and the total parts will be in the denominator. Hence the fraction form for the above fig is 2/3.

Question 4:

Each Part is ________. ______ fourths
_____________

Answer:
i) 1/4
ii) Three
iii) 3/4

Explanation:
The square is divided into 4 equal triangles. Each part of the square is 1/4 and there are 3 shaded triangles in the square box. The name for the shaded parts is three fourths i.e., 3/4

Question 5:
Four out of six

Each Part is ______________

Answer:
4/6

Explanation:
The circle is divided into 6 parts of which four parts are shaded. So, the numerator will be the shaded part and the denominator will be the total number of parts. So the answer is 4/6.

Question 6:
Eight out of eight

Each Part is ______________

Answer:
8/8

Explanation:
The fig above shows that the circle is equally divided into 8 parts out of which all the parts are shaded. So, the fraction form of the shaded part is 8/8.

Question 7:
Emma makes a poster for the school’s spring concert. She divides the poster into 8 equal parts. She uses two of the parts for the title. What fraction of the poster does Emma use for the title?
_________________

Answer:
2/8

Explanation:
Given,
Emma divides the poster into 8 equal parts
She uses 2 parts for the title
So, the total number of parts will be in the denominator and the used parts will be in the numerator
Therefore the answer is 2/8.

Question 8:
Lucas makes a flag. It has 6 equal parts. Five of the parts are red. What fraction of the flag is red?
_________________

Answer:
5/6

Explanation:
Luca makes a flag which has 6 equal parts, in which 5 of the parts are red.
The fraction of the flag is which is in red is?
5 parts of red will be in the numerator and the 6 will be in the denominator
So, the fraction of the flag red is 5/6.

Fractions of a Whole Lesson Check Page No 466

Question 1:
What fraction names the shaded part?

Options:
i. 4/6
ii. 2/4
iii. 4/8
iv. 2/6

Answer:
i (4/6)

Explanation:
The rectangle is divided into 6 equal parts. Among them, 4 parts of the rectangle are shaded. So the fraction name of the shaded part is 4/6.

Question 2:
What fraction names the shaded part?

Options:
i. One fourth
ii. One third
iii. Three fourths
iv. Four thirds

Answer:
iii (Three fourths)

Explanation:
The above figure shows that the triangle is divided into 4 parts equally in which 3 parts are shaded. Therefore, the shaded part will be in the numerator and the total parts will be in the denominator. So, the fraction name of the shaded part is three fourths.

Question 3:
Sarah biked for 115 minutes last week. Jennie biked for 89 minutes last week. How many minutes in all did the girls bike?
Options:
i. 26 minutes
ii. 194 minutes
iii. 204 minutes
iv. 294 minutes

Answer:
iii (204 minutes)

Explanation:
Given that,
Sarah biked for 115 minutes and,
Jennie biked for 89 minutes
To find:
How many minutes in all did the girls bike
To find the total minutes we need to add the bike ride time of both Sarah and Jennie
i.e., 115 + 89 = 204 minutes

Question 4:
Harrison made a building using 124 blocks. Greyson made a building using 78 blocks. How many more blocks did Harrison use than Greyson did?
Options:
i. 46
ii. 56
iii. 154
iv. 202

Answer:
i (46)

Explanation:
i) Harrison made a building using 124 blocks
ii) Greyson made a building using 78 blocks
In order to know how many more blocks did Harrison use than Greyson did we need to subtract the blocks made by Harrison with Blocks made by Greyson
124 – 78 = 46
Therefore the answer is 46.

Question 5:
Von bought a bag of 24 dog treats. He gives his puppy 3 treats a day. How many days will the bag of dog treats last?
Options:
i. 3 days
ii. 6 days
iii. 8 days
iv. 21 days

Answer:
iii (8 days)

Explanation:
Given,
Von bought a bag of 24 dog treats
He gives his puppy 3 treats a day
To find:
How many days will the bag of dog treats last
Here we have to divide no. of bag treats by puppy treats a day
24/3 = 8

Question 6:
How many students chose swimming?

Options:
i. 5
ii. 10
iii. 20
iv. 25

Answer:
iv (25)

Explanation:
From the figure, we can observe that there are 5 students who choose swimming. But each student is equal to 5 votes.
So, 5 × 5 = 25
Therefore the students who swimming are 25

Fractions on a Number Line Page No 471

Use fraction strips to help you complete the number line. Then locate and draw a point for the fraction.
Question 1:
1/3

Answer:

Question 2:
3/4

Answer:

Write the fraction that names the point.

Question 3:
Point A ________

Answer: 2/8

Explanation:
The Number lies between 0 and 1 and each point is divided into 1/8. So, it starts from 0/8 to 8/8. Now we have to locate point A i.e., 2/8 because the number that lies after 1/8 is 2/8.

Question 4:
Point B ________

Answer: 5/8

Explanation:
As we have discussed before point B lies between 4/8 and 6/8. So, the location of point B is 5/8.

Question 5:
Point C ________

Answer: 7/8

Explanation:
The location of Point C lies between 6/8 and 8/8. Therefore the number between 6/8 and 8/8 is 7/8.

Problem Solving

Question 6:
Jade ran 6 times around her neighborhood to complete a total of 1 mile. How many times will she need to run to complete 5/6 of a mile?
_____

Answer: 5 times

Explanation:
Given,
6 laps around the neighborhood = 1 mile
That means each lap = 1/6th of a mile
In order to complete 5/6 of a mile she has to run 5 times

Question 7:
A missing fraction on a number line is located exactly halfway between 3/6 and 5/6. What is the missing fraction?
_____

Answer: 4/6

Explanation:
Given that the missing fraction on a number line is located between 3/6 and 5/6. The number that lies between 3 and 5 is 4. So, the missing fraction is 4/6.

Fractions on a Number Line Lesson Check Page No 472

Question 1:
Which fraction names point G on the number line?

Options:
i. 1/4
ii. 2/4
iii. 4/4
iv. 4/1

Answer:
i. (1/4)

Explanation:
The fraction on the number line lies between 0/4 and 4/4 i.e., 0 to 1. The location of point G lies between 0/4 and 2/4. The number between 0 and 2 is 1. Therefore the fraction of Point G is 1/4.

Question 2:
Which fraction names point R on the number line?

Options:
i. 1/3
ii. 2/3
iii. 3/3
iv. 3/2

Answer:
ii (2/3)

Explanation:
The number line starts from 0/3 and ends at 3/3. Point R is between 1/3 and 3/3. So, the fraction name of Point R on Number line is 2/3

Spiral Review

Question 3:
Each table in the cafeteria can seat 10 students. How many tables are needed to seat 40 students?
Options:
i. 10
ii. 8
iii. 5
iv. 4

Answer:
iv (4)

Explanation:
Given,
1 table in the cafeteria can seat 10 students
The tables are needed to seat 40 students =?
1 —- 10 students
?—- 40 students
40/10 = 4
Therefore tables are needed to seat 40 students = 4

Question 4:
Which is an example of the Commutative Property of Multiplication?

Options:
i. 6 × 1 = 6 × 1
ii. 4 + 9 = 4 × 9
iii. 4 × 9 = 9 × 4
iv. 6 × 3 = 2 × 9

Answer:
iii (4 × 9 = 9 × 4)

Explanation:
The multiplication rule for the commutative property is ab = ba. Therefore the answer is 4 × 9 = 9 × 4.

Question 5:
Pedro shaded part of a circle. Which fraction names the shaded part?

Options:
i. 1/8
ii. 1/7
iii. 7/8
iv. 8/7

Answer:
iii (7/8)

Explanation:
The circle is divided into 8 equal parts. In that 7 parts are shaded. So, the fraction name for the shaded part is 7/8.

Question 6:
Which is true?
Options:
i. 8 ÷ 1 = 8
ii. 8 ÷ 8 = 8
iii. 8 × 0 = 8
iv. 1 =  8 × 1

Answer:
i (8 ÷ 1 = 8)

Explanation:
Any number divided by  1 is itself.
8/1 = 8
So the answer is 8 ÷ 1 = 8

Mid-Chapter Checkpoint Page No 473

Vocabulary

Choose the best term from the box to complete the sentence.

Question 1:
A ____________ is a number that names part of a whole or part of a group.

Answer: Fraction

Explanation:
The fraction is the one that divides the whole into equal parts or each part of the group.

Question 2:
The ___________ tells how many equal parts are in the whole or in the group.

Answer: Denominator

Explanation:
The part of a fraction that lies below the line and which shows the total number of equal parts in the whole.

Concept And Skills

Write the number of equal parts. Then write the name for the parts.

Question 3:

Equal Parts: ________
Name: ____________

Answer:
i. 2
ii. Halves

Explanation:
The trapezium is divided into two equal parts and the name for the parts is halves.

Question 4:

Equal Parts: ________
Name: ____________

Answer:
i. 8
ii. Eighths

Explanation:
From the above fig, we can observe that there are 8 equal parts that are in the shape of a square. The name for the parts of the figure is Eighths.

Question 5:

Equal Parts: ________
Name: ____________

Answer:
i. 4
ii. Fourths

Explanation:
The figure is the shape of a rectangle and it is divided into 4 right triangles. So, the equal parts of the rectangle are 4 and the name for the parts is fourths.

Write the number of equal parts in the whole. Then write the fraction that names the shaded part.

Question 6:

Equal Parts ________
Shaded Parts _______

Answer:
i. 3
ii. 1/3

Explanation:
A circle is divided equally into 3 parts and one part is shaded among them. So, the fraction that names the shaded part is 1/3

Question 7:

Equal Parts ________
Shaded Parts _______

Answer:
i. 6
ii. 1/6

Explanation:
The above figure is divided into 6 equal parts in the shape of the triangle. Only one part of the triangle is shaded among them. Therefore the fraction name for it is 1/6.

Question 8:

Equal Parts ________
Shaded Parts _______

Answer:
i. 4
ii. 1/4

Explanation:
Observe the above figure, there are 4 equal parts of the triangle in which one part is shaded. So, the fraction name for the shaded part is 1/4.

Mid-Chapter Checkpoint Page No 474

Write the fraction that names the point.

Question 9:
Point A ______

Answer: 1/6

Explanation:
The Number line lies from 0/6 and 6/6 in the fraction form. Point A lies between 0/6 and 3/6. So, the location of point A is 1/6

Question 10:
Point B ______

Explanation:
Point B lies between point A and 3/6. We know that Point A is 1/6. The number between 1/6 and 3/6 is 2/6. So, point B is 2/6.

Answer: 2/6

Question 11:
Point C ______

Explanation:
Point C is located between 4/6 and 6/6. The number between 4 and 6 is 5. Therefore the fraction that names Point C is 5/6.

Answer: 5/6

Question 12:
Jessica ordered a pizza. What fraction of the pizza has mushrooms? What fraction of the pizza does not have mushrooms?

Answer:
i. 2/8
ii. 6/8

Explanation:
Given,
Jessica ordered a pizza in which 2 parts of pizza has mushrooms
We need to write the fraction of the pizza that has mushrooms
Total Number of slices = 8
Pizza that has mushrooms = 2
Pizza that does not have mushrooms = 6
The fraction of the pizza that has mushrooms = 2/8
The fraction of the pizza that does not have mushrooms = 6/8

Question 13:
Which fraction names the shaded part?

Answer:
i. 8 Equal Parts
ii. 5/8

Explanation:
The figure shows that the rectangle is divided into 8 equal parts. Five parts are shaded in that rectangle. So, the fraction name for the parts that are shaded is 5/8.

Question 14:
Six friends share 3 oatmeal squares equally. How much of an oatmeal square does each friend get?

Answer: 3/6

Explanation:
Total no. of friends = 6
Number of oatmeal squares = 3
Total no. of friends will be in the denominator and the oatmeal in the numerator.
So the answer is 3/6 or 1/2.

Relate Fractions and Whole Numbers Page No 478

Make Connections Draw a model of the fraction or fraction greater than 1. Then write it as a whole number.

Question 12:
8/4 = _____

Answer:

Question 13:
6/6 = _____

Answer:

Question 14:
5/1 = _____

Answer:

Question 15:
Jeff rode his bike around a bike trail that was 1/3 of a mile long. He rode around the trail 9 times. Write a fraction greater than 1 for the distance. How many miles did Jeff ride?

Answer: 3 miles

Explanation:
Given,
Jeff rode his bike around a bike trail that was 1/3 of a mile long
He rode around the trail 9 times
In order to know how many miles did Jeff Ride
We need to multiply 1/3 with 9
= 9 × 1/3
= 3 miles

Question 16:
What’s the Error? Andrea drew the number line below. She said that 9/8 and 1 are equal. Explain her error

Answer:
The error of Andrea is that she has located the point 1 on 9/8, but it must lie on 8/8.

Explanation:
Not Equal. Because 9/8 and 1 are not the same. Point 1 must be located on 8/8.

Question 17:
Each shape is 1 whole. Which numbers name the parts that are shaded? Mark all that apply.

Options:
i. 4
ii. 6
iii. 26/6
iv. 24/6
v. 6/4

Answer:
iv (24/6)

Explanation:
There are four circles and each circle is divided into six parts. All parts are shaded in each group. So, the total number of shaded parts is 24. The numerator consists of a number of shaded parts and the denominator contains a number of parts in each circle.
= 24/6

Relate Fractions and Whole Numbers Page No 479

Use the number line to find whether the two numbers are equal. Write equal or not equal.

Question 1:
0/6 and 1
____

Answer:
Not equal

Explanation:
The points 0/6 and 1 does not lie on the same point. So, the numbers 0/6 and 1 are not equal

Question 2:
1 and 6/6
____

Answer:
Equal

Explanation:
6/6 = 1
So 6/6 and 1 are equal

Question 3:
1/6 and 6/6
____

Answer:
Not Equal

Explanation:
The points 1/6 and 6/6 does not lie on the same point. So, 1/6 and 6/6 are not equal.

Question 4:

2 = ____

Answer: 4/2

Explanation:
There are 2 circles and each circle is divided into two parts.
Total number of equal parts = 4
Number of circles =
So, 4/2 = 2

Question 5:

4 = ____

Answer: 12/3

Explanation:
From the above figure, we can see 4 circles which are divided 3 parts individually.
Number of Equal parts = 12
So, 12/3 = 4

Question 6:

3 = ____

Answer: 12/4

Explanation:
Total Number of equal parts = 12
Equal parts in each circle = 4
Therefore, 12/4 = 3

Question 7:

1 = _____

Answer: 8/8

Explanation:
A circle is divided into 8 equal parts and all are shaded. So, the fraction name for the shaded parts is 8/8.

Problem Solving

Question 8:
Rachel jogged along a trail that was 1/4 of a mile long. She jogged along the trail 8 times. How many miles did Rachel jog in all?
______ miles

Answer: 8/4 or 2 miles

Explanation:
Given,
Rachel jogged along a trail that was 1/4 of a mile long
And, She jogged along the trail 8 times
8 × 1/4 = 8/4 = 2
Therefore the answer is 2 miles.

Question 9:
Jon ran around a track that was 1/8 of a mile long. He ran around the track 24 times. How many miles did Jon run in all?
______ miles

Answer: 24/8 or 3 miles

Explanation:
Given that, Jon ran around a track that was 1/8 of a mile long
He ran around the track 24 times
24 × 1/8 = 24/8 = 3
So, the miles did Jon run in all is 3 miles

Relate Fractions and Whole Numbers Lesson Check Page No 480

Question 1:
Each shape is 1 whole. Which fraction greater than 1 names the parts that are shaded?

Options:
i. 6/18
ii. 3/6
iii. 6/3
iv. 18/6

Answer:
iv (18/6)

Explanation:
There are 3 circles which are divided into 6 parts = 18 parts
Each circle has 6 shaded parts
= 18/6

Question 2:
Each shape is 1 whole. Which fraction greater than 1 names the parts that are shaded?

Options:
i. 8/2
ii. 16/8
iii. 8/16
iv. 2/8

Answer:
ii (16/8)

Explanation:
There are two are which are divided into 8 parts = 8 × 2 = 16
Number of shaded parts in 1 circle = 8
So the answer is 16/8

Spiral Review

Question 3:
Tara has 598 pennies and 231 nickels. How many pennies and nickels does she have in all?
598 + 231

Options:
i. 719
ii. 729
iii. 819
iv. 829

Answer:
iv (829)

Explanation:
598 + 231 = 829

Question 4:
Dylan read 6 books. Kylie read double the number of books that Dylan read. How many books did Kylie read?
Options:
i. 4
ii. 8
iii. 12
iv. 14

Answer:
iii (12)

Explanation:
Given,
Dylan read 6 books
Kylie read double the number of books that Dylan read
That means Kylie reads 2 times greater than Dylan
6 × 2 = 12
Therefore Kylie reads 12 books

Question 5:
Alyssa divides a granola bar into halves. How many equal parts are there?
Options:
i. 2
ii. 3
iii. 4
iv. 6

Answer:
i (2)

Explanation:
Given that, Alyssa divides a granola bar into halves
Halves mean 2. So there are 2 equal parts

Question 6:
There are 4 students in each small reading group. If there are 24 students in all, how many reading groups are there?
Options:
i. 5
ii. 6
iii. 7
iv. 8

Answer:
ii (6)

Explanation:
Given that there are 4 students in each small reading group
To find:
how many reading groups are there for 24 students
So, Total number of students/ No. of students in each small reading group
i.e., 24/4 = 6

Fractions of a Group Page No 485

Write a fraction to name the shaded part of each group.
Question 1:

______

Answer: 6/8

Explanation:
There are 8 triangles in 4 blocks and 6 triangles are shaded among them. So, the fraction to name the shaded part is 6/8.

Question 2:

______

Answer: 3/6

Explanation:
In the above figure, we can observe that there are 6 stars in 2 groups and three stars are shaded. Shaded stars will be in the numerator and the total number of stars in the denominator. So, the answer is 3/6

Write a whole number and a fraction greater than 1 to name the part filled. Think: 1 container = 1

Question 3:

______

Answer:
i. 2
ii. 8/4

Explanation:
The figure shows that there are two containers and four circles are shaded. One container is the mirror image of another container. So, we can see 8 shaded circles. So, the fraction greater than 1 to name the part filled is 8/4.

Question 4:

______

Answer:
i. 3
ii. 18/6

Explanation:
Here we can see three egg trays and all six parts are filled. By seeing the above figure we can understand that egg tray is the mirror image of other trays. So, we can see 18 parts filled. So, the fraction to the part filled is 18/6

Draw a quick picture. Then, write a fraction to name the shaded part of the group.

Question 5:
Draw 4 circles. Shade 2 circles.
_____

Question 6:
Draw 6 circles. Make 3 groups. Shade 1 group.
_____

Problem Solving

Question 7:
Brian has 3 basketball cards and 5 baseball cards. What fraction of Brian’s cards are baseball cards?
______

Answer: 5/8

Explanation:
Given,
Brian has 3 basketball cards and 5 baseball cards
Total Number of cards = 5 + 3 = 8
The fraction of Brian’s cards are baseball cards =?
5/5+3 = 5/8

Question 8:
Sophia has 3 pink tulips and 3 white tulips. What fraction of Sophia’s tulips are pink?
______

Answer: 3/6 or 1/2

Explanation:
Number of pink tulips Sophia has = 3
and No. of white tulips Sophia has = 3
Total Number of tulips = 3 + 3 = 6
To find the fraction of Sophia’s tulips are pink
= No. of pink tulips/Total No. of tulips
= 3/6

Fractions of a Group Lesson Check Page No 486

Question 1:
What fraction of the group is shaded?

Options:
i. 5/3
ii. 5/8
iii. 3/5
iv. 3/8

Answer:
ii (5/8)

Explanation:
There are a group of 8 circles and five are shaded in it. So, the fraction of the shaded group is 5/8

Question 2:
What fraction of the group is shaded?

Options:
i. 1/4
ii. 1/2
iii. 2/4
iv. 4/1

Answer
i. (1/4)

Explanation:
It is a group of four squares in which one block is shaded. So, the fraction of the shaded part is 1/4

Spiral Review

Question 3:
Which number sentence does the array represent?

Options:
i. 4 × 7 = 28
ii. 3 × 8 = 24
iii. 3 × 7 = 21
iv. 3 × 6 = 18

Answer:
iii (3 × 7 = 21)

Explanation:
Total Number of Rows = 3
Total Number of Columns = 7
Rows × Columns = 3 × 7 = 21

Question 4:
Juan has 436 baseball cards and 189 football cards. How many more baseball cards than football cards does Juan have?
Options:
i. 625
ii. 353
iii. 347
iv. 247

Answer:
iv (247)

Explanation:
No. of baseball cards that Juan has = 436
No. of football cards that Juan has = 189
To know how many more baseball cards than football cards does Juan have,
we need to subtract No. of baseball cards and No. of football cards
= 436 – 189
= 247

Question 5:
Sydney bought 3 bottles of glitter. Each bottle of glitter costs $6. How much did Sydney spend in all on the bottles of glitter?
Options:
i. $24
ii. $18
iii. $12
iv. $9

Answer:
ii ($18)

Explanation:
Given,
Sydney bought 3 bottles of glitter
Each bottle of glitter costs = $6
Cross multiplication method is applied here,
1 bottle — $6
3 bottles –?
3 × 6 = 18
Therefore, the cost of 3 bottles of glitter = $18

Question 6:
Add
262 + 119
Options:
i. 143
ii. 371
iii. 381
iv. 481

Answer:

iii (381)

Explanation:
Addition of 262 and 119
262 + 119 = 381

Find Part of a Group Using Unit Fractions Page No 491

Circle equal groups to solve. Count the number of items in 1 group.
Question 1:

1/4 of 12 = ___

Answer: 3

Explanation:
To solve the problem we can multiply the numerator with the whole number and divide by the denominator
= (1 × 12)/4
= 12/4
= 3

Question 2:

1/8 of 16 = ___

Answer: 2

Explanation:
In order to solve the problem we have to do product of 16 and 1/8
= 16 × 1/8
= 16/8
=2

Question 3:

1/3 of 12 = ___

Answer: 4

Explanation:
The product of 1/3 and 12 is
(1 × 12)/3 = 12/3
We can cancel 12 in 3 table by 4 times
Therefore, 12/3 = 4

Question 4:

1/3 of 9 = ___

Answer:3

Explanation:
We can label 1/3 and 9 as number and denominator of a whole number
= 9 × 1/3
= 3

Question 5:

1/6 of 18 = ___

Answer:3

Explanation:
The product of 1/6 and 18 is
(1 × 18)/3
= 6

Question 6:

1/2 of 4 = ___

Answer:2

Explanation:
It is a product of a fraction and whole numbers
The numerator is 1 and 4 and denominator is 2
1 × 4/2
=2

Problem Solving

Question 7:
Marco drew 24 pictures. He drew 1/6 of them in art class. How many pictures did Marco draw in art class?
______ Pictures

Answer: 4

Explanation:
Given that Marco drew 24 picture
He drew 1/6 of them in art class
In order to know the pictures did Marco draw in art class
We have to multiply 1/6 with 24
we get,
24 ×1/6
= 24/6
= 4

Question 8:
Caroline has 16 marbles. One-eighth of them are blue. How many of Caroline’s marbles are blue?
______ Marbles

Answer: 2

Explanation:
Number of marbles that Caroline has = 16
In that 1/8 are blue

To find:
Number of Caroline’s marbles are blue
So we have to do product of 16 and 1/8
1/8 × 16
16/8 = 2

Therefore Number of Caroline’s marbles are blue is 2

Find Part of a Group Using Unit Fractions Lesson Check Page No 492

Question 1:
Ms. Davis made 12 blankets for her grandchildren. One third of the blankets are blue. How many blue blankets did she make?

Options:
i. 3
ii. 4
iii. 9
iv. 12

Answer:
ii (4)

Explanation:
Number of blankets made for her grandchildren = 12
1/3rd of the blankets are blue
In order to know the count of blue blankets
Multiply 12 with 1/3
= (12 ×1)/3
= 4

Question 2:
Jackson mowed 16 lawns. One fourth of the lawns are on Main Street. How many lawns on Main Street did Jackson mow?

Options:
i. 4
ii. 6
iii. 8
iv. 12

Answer:
i (4)

Explanation:
Given that Jackson mowed 16 lawns
One-fourth of the lawns are on Main Street

To find:
How many lawns on Main Street did Jackson mow?
Product of 16 and 1/4
= 16 × 1/4
= 4

Question 3:
Find the difference.
509 – 175
Options:
i. 334
ii. 374
iii. 434
iv. 474

Answer:
i.  (334)

Explanation:
The difference between the 1st number and 2nd number is
509 – 175 = 334

Question 4:
Find the quotient.
6)54
Options:
i. 6
ii. 7
iii. 8
iv. 9

Answer:
iv. (9)

Explanation:
Divide 54 by 6
54/6 = 9
So, the remainder is 0 and quotient is 9

Question 5:
There are 226 pets entered in the pet show. What is 226 rounded to the nearest hundred?
Options:
i. 200
ii. 220
iii. 300
iv. 400

Answer:
i. (200)

Explanation:
The word form of 226 is two hundred and twenty-six.
The number which is near to 226 is 200. Because the number is less than 250.
So, the nearest hundred to 226 is 200.

Question 6:
Ladonne made 36 muffins. She put the same number of muffins on each of 4 plates. How many muffins did she put on each plate?
Options:
i. 3
ii. 6
iii. 9
iv. 12

Answer:
iii (9)

Explanation:
Given,
Ladonne made 36 muffins
She put the same no. of muffins on each of 4 plates
No. of muffins on 4 plates/ Total No. of muffins
= 36/4
= 9

Problem Solving – Find the Whole Group Using Unit Fractions Page No 497

Draw a quick picture to solve.

Question 1:
Katrina has 2 blue ribbons for her hair. One fourth of all her ribbons are blue. How many ribbons does Katrina have in all?

____ ribbons

Answer:
8 ribbons

Explanation:
Given,
Katrina has 2 blue ribbons for her hair
1/4th of all ribbons are blue
To know how many ribbons that Katrina has,
we have to divide the number of blue ribbons by 1/4th of all ribbons are blue
we get, 2 ÷ 1/4 = (2 × 4)/1
= 2 × 4 = 8
Therefore, the answer to the above question is 8 ribbons.

Question 2:
One-eighth of Tony’s books are mystery books. He has 3 mystery books. How many books does Tony have in all?
______ Books

Answer:
24 Books

Explanation:
Given that, Tony has 3 mystery books
Out of which 1/8th of tony’s books are mystery books
So, to find how many books does Tony have in all
Divide 3 by 1/8, we get
3 ÷ 1/8
(3 ×8)/1 = 24

Question 3:
Brianna has 4 pink bracelets. One-third of all her bracelets are pink. How many bracelets does Brianna have?
______ Bracelets

Answer:
12 Bracelets

Explanation:
No. of pink bracelets that Brianna has = 4
1/3rd of all her bracelets are pink
Divide No. of pink bracelets by 1/3rd of all her pink bracelets
we get,
4 ÷ 1/3
4 × 3 = 12
So, the answer is 12 bracelets

Question 4:
Ramal filled 3 pages in a stamp album. This is one sixth of the pages in the album. How many pages are there in Ramal’s stamp album?
______ pages

Answer:
18 pages

Explanation:
Given,
Ramal filled 3 pages in a stamp album
one-sixth of the pages in the album
3 ÷ 1/6 = 3 × 6 = 18 pages

Question 5:
Jeff helped repair one half of the bicycles in a bike shop last week. If Jeff worked on 5 bicycles, how many bicycles did the shop repair in all last week?
______ bicycles

Answer:
10 bicycles

Explanation:
Jeff helped repair 1/2 of the bicycles in a bike shop last week
Jeff worked on 5 bicycles
5 divided by 1/2
5 × 2/1 = 10 bicycles

Question 6:
Layla collects postcards. She has 7 postcards from Europe. Her postcards from Europe are one third of her total collection. How many postcards in all does Layla have?
______ postcards

Answer:
21 postcards

Explanation:
Layla collects postcards in which 7 postcards are from Europe
Postcards from Europe of her total collection = 1/3
7 divided by 1/3
we get, 7 × 3 = 21
Therefore, the postcards in all do Layla has 21 postcards

Find the Whole Group Using Unit Fractions Lesson Check Page No 498

Question 1:
A zoo has 2 male lions. One-sixth of the lions are male lions. How many lions are there at the zoo?
Options:
i. 2
ii. 6
iii. 8
iv. 12

Answer:
iv (12)

Explanation:
Male lions in the Zoo = 2
1/6th of the lions are male in the zoo
2 ÷ 1/6
= 2 × 6
= 12

Question 2:
Max has 5 red model cars. One-third of his model cars are red. How many model cars does Max have?
Options:
i. 15
ii. 12
iii. 10
iv. 8

Answer:
i.  (15)

Explanation:
Given,
Max has 5 red model cars
1/3rd of the cars are red
So we need to divide 5 by 1/3,
we get 3 × 5 = 15
Therefore the answer is 15

Spiral Review

Question 3:
There are 382 trees in the local park. What is the number of trees rounded to the nearest hundred?
Options:
i. 300
ii. 380
iii. 400
iv. 500

Answer:
iii. (400)

Explanation:
Given that there are 382 trees in the local park.
This is nearer to the number 400. So the round figure of 382 is 400

Question 4:
The Jones family is driving 458 miles on their vacation. So far, they have driven 267 miles. How many miles do they have left to drive?
458 – 267
Options:
i. 191
ii. 201
iii. 211
iv. 291

Answer:
i.  (191)

Explanation:
Jones family is driving 458 miles on their vacation
They have driven 267 miles
In this, we have to subtract 458 with 267,
we get, 191

Question 5:
Ken has 6 different colors of marbles. He has 9 marbles of each color. How many marbles does Ken have in all?
Options:
i. 15
ii. 45
iii. 54
iv. 63

Answer:
iii (54)

Explanation:
Given,
Ken has 6 different colors of marbles
Ken has 9 marbles of each color
To know the total number of marbles multiply different colors of marbles with each marble color
= 6 × 9 = 54

Question 6:
Eight friends share two pizzas equally. How much of a pizza does each friend get?

Options:
i. 8 halves
ii. 4 eighths
iii. 2 sixths
iv. 2 eighths

Answer:
iv (2 eighths)

Explanation:
There are 2 pizzas and eight friends need to share those pizzas
so, we have 2 by 8
Each friend gets 2/8 and the fraction name is 2 eighths

Chapter 8 Understanding Fractions Review Test – Page No 499

Review/Test

Question 1:
Each shape is divided into equal parts. Select the shapes that show thirds. Mark all that apply.

Options:
i.
ii.
iii.
iv.

Answer: ii & iv

Explanation: From the given figures we can observe that there are thirds in Fig ii & iv.

Question 2:
What fraction names the shaded part of the shape?

Options:
i. 8 sixths
ii. 8 eighths
iii. 6 eighths
iv. 2 sixths

Answer:
iii (6 eighths)

Explanation:
A rectangle is divided into a group of eight parts and 6 parts are shaded. The fraction name of the shaded parts is 6 eighths.

Question 3:
Omar shaded a model to show the part of the lawn that he finished mowing. What fraction names the shaded part? Explain how you know how to write the fraction.

Answer: 1/8

Explanation:
From the figure, we can see that there are eight triangles and only one part is shaded. So, the fraction of the shaded part is 1/8.

No. of Shaded parts must be given in the numerator and the number of parts or whole group will be in the denominator.

Chapter 8 Understanding Fractions Review Test – Page No 500

Question 4:
What fraction names point A on the number line?

Point A ___

Answer: 1/6

Explanation:
A number line is shown in the figure above,
Each point is equal to 1/6
The point is located after 0/6. So, Point A is 1/6.

Question 5:
Jamal folded this piece of paper into equal parts. Circle the word that makes the sentence true.

The Paper is folded into

Options:
i. Sixths
ii. Eighths
iii. Fourths

Answer: Eighths

Explanation:
From the figure, we can see that the paper is divided into 8 equal parts. So, the paper is folded into eighths.

Question 6:
Caleb took 18 photos at the zoo. One sixth of his photos are of giraffes. How many of Caleb’s photos are of giraffes?
_______ photos

Answer: 3 photos

Explanation:
Given that,
Caleb took 18 photos at the zoo
1/6th of the photos are giraffes
To know the no. of Caleb’s photos are of giraffes
Simplify 18 and 1/6
18/6 = 3

Question 7:
Three teachers share 2 packs of paper equally.

How much paper does each teacher get? Mark all that apply.
Options:
i. 3 halves of a pack
ii. 2 thirds of a pack
iii. 3 sixths of a pack
iv. 1 half of a pack
v. 1 third of a pack

Answer:
ii (2 thirds of a pack)

Explanation:
No. of teachers = 3
No. of Packs of paper = 2
3 teachers should share 2 packs of paper
i.e., No. of Paper Packs/ No. of teachers = 2/3
The fraction name is 2 thirds of a pack

Chapter 8 Understanding Fractions Review Test – Page No 501

Question 8:
Lilly shaded this design.

Select one number from each column to show the part of the design that Lilly shaded.

Answer:
i. Numerator 1
ii. Denominator 4
iii. Numerator 5

Explanation:
The task is to observe the figure and identify the number from each column i.e., Numerator and Denominator Column. Lilly has Shaded the 1st column 1st block i.e, 1, Next 2nd Column 2nd block is shaded so 4, and at last 1st column 3rd block is shaded so numerator 5.

Question 9:
Marcus baked a loaf of banana bread for a party. He cut the loaf into equal size pieces. At the end of the party, there were 6 pieces left. Explain how you can find the number of pieces in the whole loaf if Marcus told you that 1/3 of the loaf was left. Use a drawing to show your work.
____ pieces

Answer: 18 pieces

Explanation:
Given,
Marcus baked a loaf of banana bread for a party. He cut the loaf into equal size pieces
At the end of the party, there were 6 pieces left.
Marcus told you that 1/3 of the loaf was left
To find:
Number of pieces in the whole loaf = x
1/3 × x = 6
x = 6 × 3
x = 18
So, the total number of pieces in the whole loaf is 18

Chapter 8 Understanding Fractions Review Test – Page No 502

Question 10:
The model shows one whole. What fraction of the model is NOT shaded?

____

Answer: 2/4

Explanation:
The square is divided to 4 equal triangles. In that two parts are shaded and two parts are not shaded.
Thus the fraction for the non shaded part is 2/4

Question 11:
Together, Amy and Thea make up 1/4 of the midfielders on the soccer team. How many midfielders are on the team? Show your work.
_____ midfielders

Answer: 8

Explanation:
1/4 of the midfielders on the soccer team represents 2 midfielders
If we divide no. of midfielders into 4 equal groups, then each group will have 2 midfielders
1/4 × x = 2
x = 4 × 2
x = 8
Thus 8 midfielders are on the team

Question 12:
Six friends share 4 apples equally. How much apple does each friend get?

Answer: 1 apple

Question 13:
Each shape is 1 whole.

For numbers, 13a–13e, choose Yes or No to show whether the number names the parts that are shaded.

a. 4
i. Yes
ii. No

Answer:
i. Yes

b. 8
i. Yes
ii. No

Answer:
i. Yes

c. 8/2
i. Yes
ii. No

Answer:
ii. No

d. 8/4
i. Yes
ii. No

Answer:
i. Yes

e. 2/8
i. Yes
ii. No

Answer:
ii. No

Chapter 8 Understanding Fractions Review Test – Page No 503

Question 14:
Alex has 3 baseballs. He brings 2 baseballs to school. What fraction of his baseballs does Alex bring to school?
____

Answer: 2/3

Explanation:
Total Number of baseballs that Alex have = 3
He brings 2 baseballs to school
The fraction of baseballs that brings to school = No. of baseballs brings to school/total no. of baseballs
= 2/3

Question 15:
Janeen and Nicole each made fruit salad for a school event.
Part A
Janeen used 16 pieces of fruit to make her salad. If 1/4 of the fruits were peaches, how many peaches did she use? Make a drawing to show your work.
____ peaches

Answer:4
No. of pieces Janeen used to make her fruit salad = 16
In that 1/4 of the fruits were peaches
how many peaches did she use is?
Multiply No. of fruit pieces with 1/4 of the fruits were peaches
we get,
16 × 1/4
= 16/4
= 4

Part B
Nicole used 24 pieces of fruit. If 1/6 of them were peaches, how many peaches in all did Janeen and Nicole use to make their fruit salads? Explain how you found your answer.
____ peaches

Answer: 8

Explanation:
No. of peaches Janeen used in her fruit salad = 4
Total number of fruit pieces Nicole used = 24
If 1/6 of them were peaches
24 × 1/6 = 4
To know total no. of peaches that Janeen and Nicole used
We have to add the number of peaches in the fruit salad of Janeen and Nicole
= 4 + 4
= 8

Question 16:
There are 8 rows of chairs in the auditorium. Three of the rows are empty. What fraction of the rows are empty?
_____ rows

Answer: 3/8

Explanation:
Given: Total Number of rows of chairs in the auditorium = 8
In that three rows are empty
The fraction of the rows that are empty is 3/8

Chapter 8 Understanding Fractions Review Test – Page No 504

Question 17:
Tara ran 3 laps around her neighborhood for a total of 1 mile yesterday. Today she wants to run 2/3 of a mile. How many laps will she need to run around her neighborhood?

____ laps

Answer: 2 laps

Explanation:
Given that,
Tara ran 3 laps around her neighborhood for a total of 1 mile
she wants to run 2/3 of a mile
1 mile —- 3 laps
2/3 mile — x
1 × x = (3 ×2)/3
x = 6/3
x = 2
Thus it takes 2 laps to run around her neighborhood

Question 18:
Gary painted some shapes.

Select one number from each column to show a fraction greater than 1 that names the parts Gary painted.

_____

Answer:

Question 19:
Angelo rode his bike around a bike trail that was 1/4 of a mile long. He rode his bike around the trail 8 times. Angelo says he rode a total of 8/4 miles. Teresa says he is wrong and that he actually rode 2 miles. Who is correct? Use words and drawings to explain how you know.
_____

Answer: 2 miles
Both Angelo and Teresa are correct
8/4 and 2 are same

Grade 3 HMH Go Math Answer Key PDF Chapter 8 covers questions from exercises, practice tests, assessment tests, etc. Improve your math knowledge and learn the concepts underlying effectively using our HMH Go Math 3rd Grade Chapter 8 Understand Fractions Anwer Key. To practice, more such questions check out Go Math Grade 3 Answer Key Chapter 8 Understand Fractions Extra Practice.

We wish the knowledge shared on Go Math Grade 3 Chapter 8 Understand Fractions has helped you in your preparation. If you need any help you can always look up to the Step by Step Solutions provided in our 3rd Grade Go Math Chapter 8 Understand Fractions.

Go Math Grade 4 Answer Key Homework FL Chapter 13 Algebra: Perimeter and Area Review/Test support students to improve their subject knowledge on the perimeter and area of the different shapes & gain maths skills. The answers provided in this chapter are designed by the math experts. Go ahead and download the Go Math Grade 4 Answer key pdf, to find out the Perimeter and Area of the rectangle, square, and etc. concepts easily.

Go Math Grade 4 Answer Key Homework FL Chapter 13 Algebra: Perimeter and Area Review/Test

Go Math Solution Key of grade 4 chapter 13 will provide perfect solutions in a step-by-step manner with a clear explanation of every question. Go Math taught explicitly about Perimeter and Area of different Shapes with the help of images, indicating images with arrows, and numbers. So, make use of this pdf formatted lesson-wise Go Math Grade 4 Answer Key Homework FL Chapter 13 Algebra: Perimeter and Area Review/Test & check your solutions within no time.

Chapter: 13 – Review/Test 

• Review/Test – Page No. 519
• Review/Test – Page No. 520
• Review/Test – Page No. 521
• Review/Test – Page No. 522

Review/Test – Page No. 519

Choose the best term from the box.

Question 1.
The number of square units needed to cover a flat surface is the ______________.
_________

Answer: Area
The number of square units needed to cover a flat surface is the area.

Question 2.
The distance around a shape is the ____________.
_________

Answer: Perimeter
The distance around a shape is the Perimeter.

Find the area of the rectangle or combined rectangles.

Question 3.

A = _____ square feet

Answer: 112 square feet

Explanation:
Given,
length = 14 ft
Width = 8 ft
Area of the rectangle = l × w
A = 14 ft × 8 ft
A = 112 square feet
Thus the area of the rectangle for the above figure is 112 square feet.

Question 4.

A = _____ square centimeters

Answer: 65 square cm.

Explanation:
Figure 1:
S = 3 cm
Area of the square = s × s
A = 3 cm × 3 cm
A = 9 square cm
Figure 2:
b = 11 cm
h = 4 cm
Area of the rectangle = b × h
A = 11 cm × 4 cm
A = 44 square cm
Figure 3:
b = 2 cm
h = 6 cm
Area of the rectangle = b × h
A = 2 cm × 6 cm
A = 12 square cm
Area of the composite figure is 9 sq. cm + 44 sq. cm + 12 sq. cm = 65 square cm.

Find the unknown measure of the rectangle.

Question 5.

A = _____ square yards

Answer: 136 square yard

Explanation:
Figure 1:
b = 12 yd
h = 8 yd
Area of the rectangle = b × h
A = 12 yd × 8 yd
A = 96 square yard.
Figure 2:
b = 16 yd
h = 1 yd
Area of the rectangle = b × h
A = 16 yd × 1 yd
A = 16 square yard.
Figure 3:
b = 4 yd
h = 6 yd
Area of the rectangle = b × h
A = 4 yd × 6 yd
A = 24 square yard.
The area of the composite figure is 96 square yard + 16 square yard + 24 square yard = 136 square yard.

Question 6.

Perimeter = 60 meters
width = _____ m

Answer: 12 m

Explanation:
Given,
Perimeter = 60 meters
length = 18 m
width = _____ m
The perimeter of the rectangle = l + w + l + w
P = 2l + 2w
60 m = 2 × 18 m + 2w
60 m – 36 m = 2w
2w = 24
w = 24/2
w = 12 meters
Thus the width of the above rectangle is 12 meters.

Question 7.

Area = 91 square feet
height = _____ feet

Answer: 13 ft

Explanation:
Given,
Area = 91 square feet
base = 7 ft
height = _____ feet
Area of the rectangle = b × h
91 sq ft = 7 ft × h
h = 91/7
h = 13 ft
Thus the height of the above rectangle is 13 ft.

Question 8.

Area = 60 square inches
base = _____ in.

Answer: 10 inches

Explanation:
Given,
Area = 60 square inches
height = 6 in
base = _____ in.
Area of the rectangle = b × h
60 square inches = b × 6 in
b = 60/6
b = 10 inches
Thus the base of the above rectangle is 10 inches.

Question 9.
What is the perimeter of a rectangle with a length of 13 feet and a width of 9 feet?
P = _____ ft

Answer: 44 ft

Explanation:
Given,
l = 13 ft
w = 9 ft
The perimeter of the rectangle = l + w + l + w
P = 13 ft + 9 ft + 13 ft + 9 ft
P = 44 ft
Thus the perimeter of the rectangle is 44 ft.

Review/Test – Page No. 520

Fill in the bubble completely to show your answer.

Question 10.
Which pair of shapes has the same area?
Options:
a.
b.
c.
d.

Answer:

Explanation:
a.
4 × 2 = 8
3 × 3 = 9
8 ≠ 9
b.
4 × 4 = 16
3 × 5 = 15
16 ≠ 15
c.
3 × 4 = 12
2 × 6 = 12
12 = 12
Thus the correct answer is option c.

Question 11.
Jamie’s mom wants to enlarge her rectangular garden by adding a new rectangular section. The garden is now 96 square yards. What will the total area of the garden be after she adds the new section?
Options:
a. 84 square yards
b. 96 square yards
c. 180 square yards
d. 192 square yards

Answer: 192 square yards

Explanation:
Given that,
Jamie’s mom wants to enlarge her rectangular garden by adding a new rectangular section. The garden is now 96 square yards.
Add 96 square yards to the rectangular garden.
96 square yards + 96 square yards = 192 square yards
Thus the correct answer is option d.

Question 12.
A rectangular yoga studio has an area of 153 square feet. The width of the studio is 9 feet. What is the length of the studio?
lenght = _____ ft

Answer: 17 ft

Explanation:
Given,
A rectangular yoga studio has an area of 153 square feet.
The width of the studio is 9 feet.
Area of the rectangle = l × w
153 square feet = l × 9 ft
l = 153/9
l = 17 ft
Therefore the length of the studio is 17 feet.

Review/Test – Page No. 521

Fill in the bubble completely to show your answer.

Question 13.
Mr. Patterson had a rectangular deck with an area of 112 square feet built in his backyard. Which could be a diagram of Mr. Patterson’s deck?
Options:
a.
b.
c.
d.

Answer: c.

Explanation:
Given,
Mr. Patterson had a rectangular deck with an area of 112 square feet built in his backyard.
Area of the rectangle = l × w
A = 28 ft × 4 ft
A = 112 square feet
Thus the correct answer is option c.

Question 14.
The town indoor pool is in a rectangular building. Marco is laying tile around the rectangular pool. How many square meters of tile will Marco need?

Options:
a. 96 square meters
b. 252 square meters
c. 572 square meters
d. 892 square meters

Answer: 252 square meters

Explanation:
The outer rectangle is
l = 26 m
w = 22 m
Area of the rectangle = l × w
A = 26 m × 22 m
A = 572 square meters
The inner rectangle is
l = 20 m
w = 16 m
Area of the rectangle = l × w
A = 20 m × 16 m
A = 320 square meters
Thus the square meters of tile will Marco need is 572 – 320 = 252 square meters.

Review/Test – Page No. 522

Question 15.
A drawing of a high school pool is shown below.

What is the area of the pool? Explain how you know.
_______ square yards

Answer:

Explanation:
Figure 1:
l = 10 yd
w = 15 yd
Area of the rectangle = l × w
A = 10 yd × 15 yd
A = 150 square yard
Figure 2:
l = 15 yd
w = 10 yd
Area of the rectangle = l × w
A = 15 yd × 10 yd
A = 150 square yard
Figure 3:
l = 10 yd
w = 5 yd
Area of the rectangle = l × w
A = 10 yd × 5 yd
A = 50 square yard
Area of the pool = 150 square yard + 150 square yard + 50 square yard = 350 square yard

Question 16.
Mr. Brown has 24 meters of fencing. He wants to build a rectangular pen for his rabbits.

A. Draw two different rectangles that Mr. Brown could build. Use only whole numbers for the lengths of the sides of each rectangle. Label the length of each side.
Type below:
_________

Answer:

Question 16.
B. Find the area in square meters of each rabbit pen you made in Part A. Show your work.
Type below:
_________

Answer: 20 square meters

Explanation:
l = 10m
w = 2m
Area of the rectangle = l × w
A = 10 m × 2 m
A = 20 square meters
Therefore the area in square meters of each rabbit pen is 20 square meters.

Question 16.
C. If you were Mr. Brown, which of the two pens above would you construct for your rabbits? Explain why.
Type below:
_________

Answer: I would construct the second figure for the two rabbit pens.

Conclusion:

Once you go through the Go Math Grade 4 Review Test Solutions of ch 13, then students can immediately discover the perimeter and area of shapes. Stay Connected with us to get the Go Math Grade 4 Answer Key Chapter 13 Algebra: Perimeter and Area along with Go Math Grade 4 Answer Key Homework Practice FL Chapter 13 Algebra: Perimeter and Area pdf.

Download Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables pdf for free of cost. It is very important for the students to learn the fundamentals at the secondary level. In order to help you guys, we are providing the answers to all the questions in HMH Go Math Grade 6 Chapter 9 Solution Key Independent and Dependent Variables.

Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables

The Independent and Dependent Variables chapter consists of the topics like equations and tables, analyze relationships, graphs etc. It is essential for students to know the relationship between the graphs and tables in this chapter. You can know different methods of solving the problems by using Go Math Grade 6 Solution Key Chapter 9 Independent and Dependent Variables. All you have to do is to tap the below-given links.

Lesson 1: Independent and Dependent Variables

• Share and Show – Page No. 493
• Unlock the Problem – Page No. 494
• Independent and Dependent Variables – Page No. 495
• Lesson Check – Page No. 496

Lesson 2: Equations and Tables

• Share and Show – Page No. 499
• Cause and Effect – Page No. 500
• Equations and Tables – Page No. 501
• Lesson Check – Page No. 502

Lesson 3: Problem Solving • Analyze Relationships

• Share and Show – Page No. 505
• On Your Own – Page No. 506
• Problem Solving Analyze Relationships – Page No. 507
• Lesson Check – Page No. 508

Mid-Chapter Checkpoint

• Mid-Chapter Checkpoint – Vocabulary – Page No. 509
• Mid-Chapter Checkpoint – Page No. 510

Lesson 4: Graph Relationships

• Share and Show – Page No. 513
• Problem Solving + Applications – Page No. 514
• Graph Relationships – Page No. 515
• Lesson Check – Page No. 516

Lesson 5: Equations and Graphs

• Share and Show – Page No. 519
• Problem Solving + Applications – Page No. 520
• Equations and Graphs – Page No. 521
• Lesson Check – Page No. 522

Chapter 9 Review/Test

• Chapter 9 Review/Test – Page No. 523
• Chapter 9 Review/Test – Page No. 524
• Chapter 9 Review/Test – Page No. 525
• Chapter 9 Review/Test – Page No. 526
• Chapter 9 Review/Test – Page No. 527
• Chapter 9 Review/Test – Page No. 528

Share and Show – Page No. 493

Identify the independent and dependent variables. Then write an equation to represent the relationship between them.

Question 1.
An online store lets customers have their name printed on any item they buy. The total cost c in dollars is the price of the item p in dollars plus $3.99 for the name.
Type below:
________________

Answer: c = p + $3.99

Explanation:
The independent variable is c, the price of the item because it is not going to depend on anything else.
The dependent variable is p because the total cost depends on how many items there are, whether your name is marked on it, etc.
The equation would be:
c = p + $3.99

Question 2.
A raft travels downriver at a rate of 6 miles per hour. The total distance d in miles that the raft travels is equal to the rate times the number of hours h.
Type below:
________________

Answer: d = 6 × h

Explanation:
Speed of the raft= 6 miles per hour
Total distance (d) of the raft = rate × number of hours h
The dependent variable is the number of hours h
The independent variable is distance d.
The equation would be:
d = 6 × h

Question 3.
Apples are on sale for $1.99 a pound. Sheila buys p pounds of apples for a total cost of c dollars.
Type below:
________________

Answer: c = p × $1.99

Explanation:
Apples are on sale for $1.99 a pound
p = pounds of apples
c = total cost of dollars
The equation would be:
c = p × $1.99
c is the independent variable.
p is the dependent variable.

On Your Own

Identify the independent and dependent variables. Then write an equation to represent the relationship between them.

Question 4.
Sean can make 8 paper birds in an hour. The total number of birds b is equal to the number of birds he makes per hour times the number of hours h.
Type below:
________________

Answer: b = 8h

Explanation:
Given that,
Sean can make 8 paper birds in an hour.
The total number of birds b is equal to the number of birds he makes per hour times the number of hours h.
b = number of birds
h = number of hours
The equation would be:
b = 8 × h
b is the independent variable.
h is the dependent variable.

Question 5.
Billy has $25. His father is going to give him more money. The total amount t Billy will have is equal to the amount m his father gives him plus the $25 Billy already has.
Type below:
________________

Answer: t = m + $25

Explanation:
Billy has $25. His father is going to give him more money.
The total amount t Billy will have is equal to the amount m his father gives him plus the $25 Billy already has.
The equation would be:
t = m + $25
t is the independent variable
m is the dependent variable.

Question 6.
Connect Symbols and Words Describe a situation that can be represented by the equation c = 12b.
Type below:
________________

Answer:
Melinda is making necklaces. She uses 12 beads for each necklace. The total number of beads b depends on the cost of the necklace c.
The equation is c = 12n

Question 7.
Belinda pays $4.25 for each glass she buys. The total cost c is equal to the price per glass times the number of glasses n plus $9.95 for shipping and handling. Write an equation and use it to find how much it will cost Belinda to buy 12 glasses.
Type below:
________________

Answer:
Belinda pays $4.25 for each glass she buys. The total cost c is equal to the price per glass times the number of glasses n plus $9.95 for shipping and handling.
The equation is: c = 4.25n + 9.95
Now we have to find the cost of 12 glasses.
c = 4.25(12) + 9.95
c = 60.95
It takes $60.95 to buy 12 glasses.

Unlock the Problem – Page No. 494

Question 8.
Benji decides to save $15 per week to buy a computer program. Write an equation that models the total amount t in dollars Benji will have saved in w weeks.
a. What does the variable t represent?
Type below:
________________

Answer: t represents the total amount in dollars Banji saved.

Question 8.
b. Which is the dependent variable? Which is the independent variable? How do you know?
Type below:
________________

Answer:
w is the dependent variable.
t is the independent variable.
w is dependent because it represents the number of weeks. So, we have to multiply 15 with w.
t is an independent variable because t determines the value of dependent variable.

Question 8.
c. How can you find the total amount saved in w weeks?
Type below:
________________

Answer: We can find the total amount saved in w weeks by multiplying 15 with w.

Question 8.
d. Write an equation for the total amount that Benji will have saved.
Type below:
________________

Answer: t = 15w

Question 9.
Coach Diaz is buying hats for the baseball team. The total cost c is equal to the number of hats n that he buys times the sum of the price per hat h and a $2 charge per hat to have the team name printed on it. Write an equation that can be used to find the cost of the hats.
Type below:
________________

Answer: c = n + 2h

Explanation:
Coach Diaz is buying hats for the baseball team.
The total cost c is equal to the number of hats n that he buys times the sum of the price per hat h and a $2 charge per hat to have the team name printed on it.
c represents the total cost.
n is the number of hats
h is the price per hat.
The equation is c is equal to the number of hats plus price per hat and $2.
c = n + 2h

Question 10.
A steel cable that is \(\frac{1}{2}\) inch in diameter weighs 0.42 pound per foot. The total weight in pounds w is equal to 0.42 times of the number of feet f of steel cable. Choose the letter or equation that makes each sentence true.
The independent variable is ______________ .
The dependent variable is ______________ .
The equation that represents the relationship between the variables is ______________ .

Answer:
A steel cable that is \(\frac{1}{2}\) inch in diameter weighs 0.42 pound per foot.
The total weight in pounds w is equal to 0.42 times of the number of feet f of steel cable.
The equation would be:
w = 0.2f
f is the dependent variable
w is the dependent variable.

Independent and Dependent Variables – Page No. 495

Identify the independent and dependent variables. Then write an equation to represent the relationship between them.

Question 1.
Sandra has a coupon to save $3 off her next purchase at a restaurant. The cost of her meal c will be the price of the food p that she orders, minus $3.
Type below:
________________

Answer: c = p – 3

Explanation:
Given,
Sandra has a coupon to save $3 off her next purchase at a restaurant.
The cost of her meal c will be the price of the food p that she orders, minus $3.
c is the independent variable
p is the dependent variable
The equation would be:
c = p – 3

Question 2.
An online clothing store charges $6 for shipping, no matter the price of the items. The total cost c in dollars is the price of the items ordered p plus $6 for shipping.
Type below:
________________

Answer: c = p + 6

Explanation:
Given,
An online clothing store charges $6 for shipping, no matter the price of the items.
The total cost c in dollars is the price of the items ordered p plus $6 for shipping.
The equation would be:
c = p + $6
where c = cost in dollars
p is the price of items
The independent variable is c.
The dependent variable is p

Question 3.
Melinda is making necklaces. She uses 12 beads for each necklace. The total number of beads b depends on the number of necklaces n.
Type below:
________________

Answer: b = 12n

Explanation:
Melinda is making necklaces. She uses 12 beads for each necklace.
The total number of beads b depends on the number of necklaces n.
b = total number of beads
n = number of necklaces
The equation would be:
b = 12n
b is the independent variable
n is the dependent variable.

Problem Solving

Question 4.
Maria earns $45 for every lawn that she mows. Her earnings e in dollars depend on the number of lawns n that she mows. Write an equation that represents this situation.
Type below:
________________

Answer: e = 45n

Explanation:
Maria earns $45 for every lawn that she mows.
Her earnings e in dollars depend on the number of lawns n that she mows.
e = earnings in dollars
n = number of lawns
The equation would be:
e = 45n
e is the independent variable.
n is the dependent variable.

Question 5.
Martin sells cars. He earns $100 per day, plus any commission on his sales. His daily salary s in dollars depends on the amount of commission c. Write an equation to represent his daily salary.
Type below:
________________

Answer: s = 100 + c

Explanation:
Martin sells cars. He earns $100 per day, plus any commission on his sales. His daily salary s in dollars depends on the amount of commission c.
c = amount of commission
s = salary in dollars
The equation would be:
s = 100 + c
s is the independent variable.
c is the dependent variable.

Question 6.
Write a situation in which one unknown is dependent on another unknown. Write an equation for your situation and identify the dependent and independent variables.
Type below:
________________

Answer:
Byron is playing a game. He earns 10 points for each question he answers correctly. His total score s equals the number of correct answers a time a.
Answer:
Dependent variable: s
Independent variable: a
Equation: s = 10a

Lesson Check – Page No. 496

Question 1.
There are 12 boys in a math class. The total number of students s depends on the number of girls in the class g. Write an equation that represents this situation.
Type below:
________________

Answer: s = 12 + g

Explanation:
There are 12 boys in a math class.
The total number of students s depends on the number of girls in class g.
The equation would be:
s = 12 + g
s is the independent variable.
g is the dependent variable.

Question 2.
A store received a shipment of soup cans. The clerk put an equal number of cans on each of 4 shelves. Write an equation to represent the relationship between the total number of cans t and the number of cans on each shelf n.
Type below:
________________

Answer: n = t ÷ 4

Explanation:
A store received a shipment of soup cans. The clerk put an equal number of cans on each of 4 shelves.
t = number of cans.
n = number of cans on each shelf.
The equation would be:
n = t ÷ 4
n is the independent variable.
t is the dependent variable.

Spiral Review

Question 3.
The formula F = \(\frac{9}{5}\)C + 32 gives the Fahrenheit temperature for a Celsius temperature of C degrees. Gwen measured a Celsius temperature of 35 degrees. What is this temperature in degrees Fahrenheit?
______ °F

Answer: 95 degrees

Explanation:
The formula F = \(\frac{9}{5}\)C + 32 gives the Fahrenheit temperature for a Celsius temperature of C degrees.
C = 35
F = 9C ÷ 5 + 32
F = 9(35) ÷ 5 + 32
F = 315 ÷ 5 + 32
F = 63 + 32
F = 95 degrees

Question 4.
Write an equation to represent this sentence. The difference of a number n and 1.8 is 2.
Type below:
________________

Answer: n – 1.8 = 2

Explanation:
The difference of a number n and 1.8 is 2.
The phrase difference is nothing but subtraction.
The equation would be:
n – 1.8 = 2

Question 5.
Drew drank 4 cups of orange juice. This is \(\frac{2}{5}\) of the total amount of juice that was in the container. Solve \(\frac{2}{5}\)x = 4 to find the number of cups x of juice in the container. How much juice was in the container?
______ cups

Answer: 10 cups

Explanation:
Drew drank 4 cups of orange juice. This is \(\frac{2}{5}\) of the total amount of juice that was in the container.
\(\frac{2}{5}\)x = 4
2 × x = 4 × 5
2x = 20
x = 20/2
x = 10
Thus there are 10 cups of juice in the container.

Question 6.
Graph x ≤ ^–4.5 on a number line.
Type below:
________________

Answer:

Share and Show – Page No. 499

Use the equation to complete the table.

Question 1.
y = x + 3

Type below:
________________

Answer:
Substitute the value of x in the above equation.
The equation is x + 3.

Question 2.
y = 2x + 1

Type below:
________________

Answer:
Substitute the value of x in the above equation.
The equation is y = 2x + 1

On Your Own

Write an equation for the relationship shown in the table. Then find the unknown value in the table.

Question 3.

Type below:
________________

Answer:
The equation is y = 2x
The output is multiple of 2 and x
For x = 10
The output is y = 2x
y = 2 × 10 = 20

Question 4.

Type below:
________________

Answer:
y = x ÷ 2
The output is the quotient of x and 2.
The output for x = 40 is
y = 40 ÷ 2
y = 20

Question 5.
The table shows the current cost of buying apps for a cell phone. Next month, the price of each app will double. Write an equation you can use to find the total cost y of buying x apps next month.

Type below:
________________

Answer: y = 3x

Explanation:
The equation is multiple of 3 and x.
The equation is y = 3x

Question 6.
A beach resort charges $1.50 per hour plus $4.50 to rent a bicycle. The equation c = 1.50x + 4.50 gives the total cost c of renting a bicycle for x hours. Use numbers and words to explain how to find the cost c of renting a bicycle for 6 hours.

Type below:
________________

Answer:
A beach resort charges $1.50 per hour plus $4.50 to rent a bicycle.
The equation c = 1.50x + 4.50 gives the total cost c of renting a bicycle for x hours.
For x = 1
c = 1.50(1) + 4.50
c = 1.50 + 4.50
c = $6.00
For x = 2
c = 1.50(2) + 4.50
c = 3.00 + 4.50
c = $7.50
For x = 3
c = 1.50(3) + 4.50
c = 4.50 + 4.50
c = $9.00
For x = 4
c = 1.50(4) + 4.50
c = 6.00 + 4.50
c = $10.50

</aCause and Effect – Page No. 500

The reading skill cause and effect can help you understand how a change in one variable may cause a change in another variable.

In karate, a person’s skill level is often shown by the color of his or her belt. At Sara’s karate school, students must pass a test to move from one belt level to the next. Each test costs $23. Sara hopes to move up 3 belt levels this year. How will this affect her karate expenses?

Question 7.
Write an equation to show the relationship between cause and effect. Then use the equation to solve the problem.
Type below:
________________

Answer: y = 23x

Explanation:
Let x represent the number of belt levels Sara moves up and let y represent the increase in dollars in her karate expenses.
Write the equation:
y = 23x
Sara plans to move up 3 levels, so replace x with 3
y = 23 × 3
y = 69
So, if Sara moves up 3 belt levels this year, her karate expenses will increase by $69.

Write an equation to show the relationship between cause and effect. Then use the equation to solve the problem.

Question 8.
Classes at Tony’s karate school cost $29.50 per month. This year he plans to take 2 more months of classes than he did last year. How will this affect Tony’s karate expenses?
Type below:
________________

Answer:
The equation is y = 29.50x
where x is the number of additional classes
y is the increase in dollars in expenses.
Tony plans to take 2 more months of classes so his expenses will increase by y = 29.5 × 2 = $59

Question 9.
Write an Equation A sporting goods store regularly sells karate uniforms for $35.90 each. The store is putting karate uniforms on sale for 10% off. How will this affect the price of a karate uniform?
Type below:
________________

Answer:
The equation is y = 35.90x
where x is the percent of the discount and y is the decrease in dollars in the sales price.
For a 10% discount the price will decrease by y = 35.90 × 0.01 = $3.59

Equations and Tables – Page No. 501

Use the equation to complete the table.

Question 1.
y = 6x

Type below:
________________

Answer:
The equation is y = 6x
Substitute the value of x in the above equation.

Question 2.
y = x − 7

Type below:
________________

Answer:
The equation is y = x – 7
Substitute the value of x in the equation.
Use the equation to get the output y.

Question 3.
y = 3x + 4

Type below:
________________

Answer:
The equation is y = 3x + 4
Substitute the value of x in the above equation.
Use the equation to get the output y.

Write an equation for the relationship shown in the table. Then find the unknown value in the table.

Question 4.

Type below:
________________

Answer: y = 8x

Explanation:
The equation is the multiple of 8.
The equation is y = 8x
Substitute x = 3 in the equation.
y = 8(3) = 24
Thus the unknown value is 24.

Question 5.

Type below:
________________

Answer: y = x ÷ 2

Explanation:
The equation is divisible by 2.
The equation is y = x ÷ 2
Substitute x = 22 in the equation.
y = x ÷ 2
y = 22 ÷ 2
y = 11
Therefore the unknown value is 11.

Problem Solving

Question 6.
Tickets to a play cost $11 each. There is also a service charge of $4 per order. Write an equation for the relationship that gives the total cost y in dollars for an order of x tickets.
Type below:
________________

Answer: 11x + 4

Explanation:
Given,
Tickets to a play cost $11 each.
There is also a service charge of $4 per order.
y represents the total cost in dollars.
x represents the order of tickets.
The equation is y = 11x + 4

Question 7.
Write an equation for the relationship shown in the table. Then use the equation to find the estimated number of shrimp in a 5-pound bag.

Type below:
________________

Answer: y = 24x

Explanation:
The equation is the multiple of 24.
The equation is y = 24x

Question 8.
Write a word problem that can be represented by a table and equation. Solve your problem and include the table and equation.
Type below:
________________

Answer:
Susie ran a race. She ran 5 miles an hour and the race took her x hours to complete.
y = 5x
Use the equation to get the output y.

Lesson Check – Page No. 502

Question 1.
Write an equation that represents the relationship shown in the table.

Type below:
________________

Answer: y = x – 4

Explanation:
The relationship between x and y is y = x – 4.
We get the output when we subtract 4 from x.

Question 2.
There is a one-time fee of $27 to join a gym. The monthly cost of using the gym is $18. Write an equation for the relationship that gives the total cost y in dollars of joining the gym and using it for x months.
Type below:
________________

Answer: y = 18x + 27

Explanation:
Given,
There is a one-time fee of $27 to join a gym. The monthly cost of using the gym is $18.
Here y represents the total coast in dollars of joining the gym.
x represents months.
So, the equation would be: y = 18x + 27

Spiral Review

Question 3.
Mindy wants to buy several books that each cost $10. She has a coupon for $6 off her total cost. Write an expression to represent her total cost in dollars for b books.
Type below:
________________

Answer: 10b – 6

Explanation:
Given,
Mindy wants to buy several books that each cost $10.
She has a coupon for $6 off her total cost.
b represents the total cost in dollars for b books.
So, the equation to represent the total cost is 10b – 6.

Question 4.
When a coupon of $1.25 off is used, the cost of a taco meal is $4.85. The equation p – 1.25 = 4.85 can be used to find the regular price p in dollars of a taco meal. How much does a regular taco meal cost?
$ _______

Answer: 6.10

Explanation:
Given,
When a coupon of $1.25 off is used, the cost of a taco meal is $4.85.
The equation is p – 1.25 = 4.85
p = 4.85 + 1.25
p = 6.10
Therefore the taco meal cost $6.10.

Question 5.
Which of the following are solutions to the inequality n > ^–7?
n = ^–7 n = ^–6.9 n = ^–7.2 n = ^–6\(\frac{1}{2}\)
Type below:
________________

Answer: n = -7

Explanation:
Substitute the value of n in the inequality.
n > ^–7
n = -7
-7 > -7
Thus -7 is the solution.
n = ^–6.9
-6.9 > -7
-6.9 is not the solution.
n = ^–7.2
-7.2 > -7
-7.2 is less than – 7
Thus -7.2 is not the solution.
n = ^–6\(\frac{1}{2}\)
^–6\(\frac{1}{2}\) > -7
^–6\(\frac{1}{2}\) is not the solution.

Question 6.
Marcus sold brownies at a bake sale. He sold d dollars worth of brownies. He spent $5.50 on materials, so his total profit p in dollars can be found by subtracting $5.50 from his earnings. Write an equation that represents this situation.
Type below:
________________

Answer: p = d – 5.50

Explanation:
Marcus sold brownies at a bake sale. He sold d dollars worth of brownies.
He spent $5.50 on materials, so his total profit p in dollars can be found by subtracting $5.50 from his earnings.
p represents the total profit in dollars.
d is the dollars worth of brownies.
The equation is p = d – 5.50

Share and Show – Page No. 505

Question 1.
A soccer coach is ordering shirts for the players. The table shows the total cost based on the number of shirts ordered. How much will it cost the coach to order 18 shirts?

$ _______

Answer: 270

Explanation:
First, find a pattern and write an equation.
The cost is $15 multiplied by the number of shirts.
c = $15 × n
Next, use the equation to find the cost of 18 shirts.
c = $15 × n
c = $15 × 18
c = $270
So, the cost of 18 shirts is $270.

Question 2.
What if the coach spent $375 to purchase a number of shirts? Could you use the same equation to find how many shirts the coach bought? Explain.
Type below:
________________

Answer:
Yes, I could use the same equation.
I could substitute 375 for the variable c and solve for n.

Question 3.
The table shows the number of miles the Carter family drove over time. If the pattern continues, will the Carter family have driven more than 400 miles in 8 hours? Explain.

Type below:
________________

Answer: 376 miles

Explanation:
First, find a pattern and write an equation.
The distance is 47 miles multiplied by the number of hours.
y = 47 × x
Next, use the equations to find the distance for 8 hours.
y = 47x
y = 47 × 8
y = 376
So, the family will have driven 376 miles in 8 hours, which is less than 400 miles.

Question 4.
Look for a Pattern The Carter family drove a total of 564 miles. Describe how to use the pattern in the table to find the number of hours they spent driving.
Type below:
________________

Answer: 12 hours

Explanation:
The equation is y = 47x
Next, use the equation to find the number of hours for 564 miles.
564 = 47 × x
x = 564/47
x = 12
So, the Carter family spent 12 hours driving for 564 miles.

On Your Own – Page No. 506

Question 5.
A group of dancers practiced for 4 hours in March, 8 hours in April, 12 hours in May, and 16 hours in June. If the pattern continues, how many hours will they practice in November?
_______ hours

Answer: 36 hours

Explanation:
Given that, a group of dancers practiced for 4 hours in March, 8 hours in April, 12 hours in May, and 16 hours in June.
The equation would be h = 4m
m = 9
h = 4 × 9 = 36
Thus the group practiced 36 hours in the month of November.

Question 6.
The table shows the number of hours Jacob worked and the amount he earned each day.

At the end of the week, he used his earnings to buy a new pair of skis. He had $218 left over. How much did the skis cost?
$ _______

Answer: 142

Explanation:
First, add the total amount he earned.
60 + 84 + 72 + 96 + 48 = 360
Jacob earned $360 for the week.
If he has $218 leftover, this means that the cost of the skis is 360 – 218 = 14
Therefore the cost of the skis is $142.

Question 7.
Pose a Problem Look back at Problem 6. Use the data in the table to write a new problem in which you could use the strategy to find a pattern. Then solve the problem.
Type below:
________________

Answer:
How much money would Jacob earn if he worked for 10 hours?
From the table, we can see that the pattern is that Jacob earns $12 per hour.
The equation is s = 12h
Where s is the total pay and h is the number of hours worked.
s = 12h
s = 12 × 10
s = 120
Thus Jacob earned $120 for 10 hours.

Question 8.
Draw Conclusions Marlon rode his bicycle 9 miles the first week, 18 miles the second week, and 27 miles the third week. If the pattern continues, will Marlon ride exactly 100 miles in a week at some point? Explain how you determined your answer.
Type below:
________________

Answer: No, Marlon will not ride exactly 100 miles in a week at some point.
Each number in the pattern is a multiple of 9 and 100 is not a multiple of 9.

Question 9.
A diving instructor ordered snorkels. The table shows the cost based on the number of snorkels ordered.

If the diving instructor spent $1,024, how many snorkels did he order? Use numbers and words to explain your answer.
_______ snorkels

Answer: 32

Explanation:
Use the table to find the equation.
c represents the cost based on the number of snorkels.
s represents the number of snorkels
The equation would be:
c = 32s
The diving instructor spent $1,024
c = 1024
1024 = 32s
s = 1024/32
s = 32
Thus the diving instructor gets 32 snorkels for $1024.

Problem Solving Analyze Relationships – Page No. 507

The table shows the number of cups of yogurt needed to make different amounts of a fruit smoothie. Use the table for 1–3.

Question 1.
Write an equation to represent the relationship.
Type below:
________________

Answer: c = 3b

Explanation:
c represents number of cups of yogurt
b represents the batches
From the table, we can observe that b is multiplied with 3 to get cups of yogurt.
So, the equation to find the number of cups of yogurt is c = 3b

Question 2.
How much yogurt is needed for 9 batches of smoothie?
_______ cups

Answer: 27

Explanation:
Given that there are 9 batches of smoothie.
By using the above equation we can find the number of cups.
c = 3b
c = 3 × 9 = 27 cups
Thus 27 cups of yogurt is need to make 9 batches of smoothie.

Question 3.
Jerry used 33 cups of yogurt to make smoothies. How many batches did he make?
_______ batches

Answer: 11 batches

Explanation:
Jerry used 33 cups of yogurt to make smoothies.
Use the equation to find the batches.
c = 3b
33 = 3b
b = 33/3
b = 11
Therefore jerry made 11 batches of smoothie.

The table shows the relationship between Winn’s age and his sister’s age. Use the table for 4–5.

Question 4.
Write an equation to represent the relationship.
Type below:
________________

Answer: s = w + 4

Explanation:
By using the table we can find the relationship between wine’s age and wine’s sister’s age.
Winn’s sister’s age will be the sum of Winn’s age and 4.
So, the equation is s = w + 4

Question 5.
When Winn is 14 years old, how old will his sister be?
_______ years old

Answer: 18

Explanation:
Use the equation s = w + 4
W = 14 years
s = 14 + 4
s = 18 years
Thus winn’s sister’s age is 18 years.

Question 6.
Write a problem for the table. Use a pattern and an equation to solve your problem.

Type below:
________________

Answer: m = 16h

Explanation:
Jerry runs 16 miles per hour. How many miles he can run in 5 hours?
The equation is m = 16h
m = 16 × 5 = 80 miles
Therefore jerry runs 80 miles in 5 hours.

Lesson Check – Page No. 508

Question 1.
The table shows the total cost c in dollars of n gift baskets. What will be the cost of 9 gift baskets?

Answer: $108

Explanation:
By seeing the above we can say that the equation is
c = 12n
n = 9
Use the equation to find the cost of 9 gift baskets.
c = 12 × 9
c = $108
Thus the cost of 9 gift baskets is $108.

Question 2.
The table shows the number of minutes m that Tara has practiced after d days. If Tara has practiced for 70 minutes, how many days has she practiced?

_______ days

Answer: 2 days

Explanation:
The table shows the number of minutes m that Tara has practiced after d days.
The equation would be
m = 35d
If Tara has practiced for 70 minutes
m = 70
Use the equation to find the number of days she practiced.
70 = 35d
d = 70/35
d = 2 days
Thus Tara has practiced 2 days.

Spiral Review

Question 3.
Soccer shirts cost $15 each, and soccer shorts cost $18 each. The expression 15n + 18n represents the total cost in dollars of n uniforms. Simplify the expression by combining like terms.
Type below:
________________

Answer: 33n

Explanation:
Soccer shirts cost $15 each, and soccer shorts cost $18 each.
The expression 15n + 18n represents the total cost in dollars of n uniforms.
Now combine the like terms.
15n + 18n = 33n

Question 4.
What is an equation that represents the relationship in the table?

Type below:
________________

Answer: y = x ÷ 2

Explanation:
By seeing the above table we can find the relationship between x and y.
y is the quotient of x and 2.
We get the value of y when you divide x by 2.
The equation is y = x ÷ 2

Question 5.
The lowest price of an MP3 of a song in an online store is $0.99. Write an inequality that represents the price p in dollars of any MP3 in the store.
Type below:
________________

Answer:
The lowest price of an MP3 of a song in an online store is $0.99.
p represents the price in dollars.
The inequality is p ≥ 0.99.

Question 6.
Marisol plans to make 9 mini-sandwiches for every 2 people attending her party. Write a ratio that is equivalent to Marisol’s ratio.
Type below:
________________

Answer: 9:2

Explanation:
Given that, Marisol plans to make 9 mini-sandwiches for every 2 people attending her party.
The ratio will be 9:2
Now we need to write the equivalent ratio for the 9 sandwiches for every 2 people i.e, 9:2
We know that the equivalent ratio can be written as
9/2 × 3/3 = 27/6
9/2 × 5/5 = 45/6
Thus the equivalent fractions are 27/6 and 45/6.

Mid-Chapter Checkpoint – Vocabulary – Page No. 509

Choose the best term from the box to complete the sentence.

Question 1.
A(n) _____ has a value that determines the value of another quantity.
Type below:
________________

Answer: Independent variable
An Independent variable has a value that determines the value of another quantity.

Question 2.
A variable whose value is determined by the value of another quantity is called a(n) _____.
Type below:
________________

Answer: Dependent variable
A variable whose value is determined by the value of another quantity is called a Dependent variable.

Concepts and Skills

Identify the independent and dependent variables.

Question 3.
Marco spends a total of d dollars on postage to mail party invitations to each of g guests.
Type below:
________________

Answer:
dependent variable: d
independent variable: g

Question 4.
Sophie has a doll collection with 36 dolls. She decides to sell s dolls to a museum and has r dolls remaining.
Type below:
________________

Answer:
dependent variable: r
independent variable: s

Write an equation for the relationship shown in the table. Then find the unknown value in the table.

Question 5.

Type below:
________________

Answer: 49

Explanation:
The equation is y = 7x
x = 7
y = 7 × 7 = 49
Thus the unknown value y is 49.

Question 6.

Type below:
________________

Answer: 12

Explanation:
The equation for the above table is
y = x ÷ 5
Use the equation to find the value of y where x = 60
y = 60 ÷ 5
y = 12
Thus the unknown value is 12.

Write an equation that describes the pattern shown in the table.

Question 7.
The table shows how the number of pepperoni slices used depends on the number of pizzas made.

Type below:
_______________

Answer: y = 17x

Explanation:
The table shows how the number of pepperoni slices used depends on the number of pizzas made.
y is 17 times of x.
The equation for the above table is y = 17x

Question 8.
Brayden is training for a marathon. The table shows how the number of miles he runs depends on which week of training he is in.

Type below:
________________

Answer: m = w + 5

Explanation:
Brayden is training for a marathon. The table shows how the number of miles he runs depends on which week of training he is in.
m is equal to the sum of w and 5.
Thus the equation is m = w + 5.

Page No. 510

Question 9.
The band has a total of 152 members. Some of the members are in the marching band, and the rest are in the concert band. Write an equation that models how many marching band members m there are if there are c concert band members.
Type below:
________________

Answer: m = 152 – c

Explanation:
Given,
The band has a total of 152 members. Some of the members are in the marching band, and the rest are in the concert band.
m is equal to the difference of 152 and c.
The equation is m = 152 – c

Question 10.
A coach is ordering baseball jerseys from a website. The jerseys cost $15 each, and shipping is $8 per order. Write an equation that can be used to determine the total cost y, in dollars, for x jerseys.
Type below:
________________

Answer: y = 15x + 8

Explanation:
A coach is ordering baseball jerseys from a website.
The jerseys cost $15 each, and shipping is $8 per order.
y is equal to 15 times x plus 8
The equation is y = 15x + 8.

Question 11.
Amy volunteers at an animal shelter. She worked 10 hours in March, 12 hours in April, 14 hours in May, and 16 hours in June. If the pattern continues, how many hours will she work in December?
_______ hours

Answer: 28 hours

Explanation:
Amy volunteers at an animal shelter.
She worked 10 hours in March, 12 hours in April, 14 hours in May, and 16 hours in June.
As she started working from the march. December will be the 10th month.
Keep on adding 2 hours for each month you get 28 hours for December.
Thus she worked 28 hours in December.

Question 12.
Aaron wants to buy a new snowboard. The table shows the amount that he has saved. If the pattern in the table continues, how much will he have saved after 1 year?

$ _______

Answer: $540

Explanation:
Aaron wants to buy a new snowboard. The table shows the amount that he has saved.
The equation will be s = 45m
s is the money saved
m is the number of months
1 year = 12 months
s = 45 × 12
s = 540
Thus he saved $540 after 1 year.

Share and Show – Page No. 513

Graph the relationship represented by the table.

Question 1.

Type below:
________________

Answer: y = 50x

Question 2.

Type below:
________________

Answer: y = 5x

Graph the relationship represented by the table to find the unknown value of y.

Question 3.

Type below:
________________

Answer: 3

Question 4.

Type below:
________________

Answer: 6

On Your Own

Practice: Copy and Solve Graph the relationship represented by the table to find the unknown value of y.

Question 5.

Type below:
________________

Answer: 5

Question 6.

Type below:
________________

Answer: 7

Problem Solving + Applications – Page No. 514

The table at the right shows the typical price of a popular brand of corn cereal over time. Use the table for 7–8.

Question 7.
Use Graphs Complete the table below to show the cost of buying 1 to 5 boxes of corn cereal in 1988. Then graph the relationship on the coordinate plane at right.

Type below:
________________

Answer:

Question 8.
Suppose you graphed the cost of buying 1 to 5 boxes of corn cereal using the 1968 price and the 2008 price. Explain how those graphs would compare to the graph you made using the 1988 price.
Type below:
________________

Answer:
The points on both graphs would lie on a line, but the line for the 1968 costs would rise less steeply than the line for 1988 costs and the line for the 2008 costs would rise more steeply than the line for 1988 costs.

Question 9.
A bookstore charges $4 for shipping, no matter how many books you buy. Irena makes a graph showing the shipping cost for 1 to 5 books. She claims that the points she graphed lie on a line. Does her statement make sense? Explain.
Type below:
________________

Answer: Yes her statement makes sense.
The points on the graph are (1,4), (2,4), (3,4), (4,4). These points lie on the horizontal line.

Question 10.
Graph the relationship represented by the table to find the unknown value of y.

Type below:
________________

Answer: 3

Graph Relationships – Page No. 515

Graph the relationship represented by the table.

Question 1.

Type below:
________________

Answer: y = 25x

Question 2.

Type below:
________________

Answer:

Graph the relationship represented by the table to find the unknown value of y.

Question 3.

Type below:
________________

Answer: 6

Question 4.

Type below:
________________

Answer: 2

Problem Solving

Question 5.
Graph the relationship represented by the table.

Type below:
________________

Answer: y = 15x

Question 6.
Use the graph to find the cost of purchasing 5 DVDs.
$ ______

Answer:
The above graph shows that the cost of 5 DVDs is $75.

Question 7.
Both tables and graphs can be used to represent relationships between two variables. Explain how tables and graphs are similar and how they are different.
Type below:
________________

Answer:
Tables and graphs can be useful tools for helping people make decisions. However, they only provide part of a story. Inferences often have to be made from the data shown. As well as being able to identify clearly what the graph or table is telling us, it is important to identify what parts of the story are missing.

Lesson Check – Page No. 516

Question 1.
Mei wants to graph the relationship represented by the table. Write an ordered pair that is a point on the graph of the relationship.

Type below:
________________

Answer: y = 8x

Question 2.
An online bookstore charges $2 to ship any book. Cole graphs the relationship that gives the total cost y in dollars to buy and ship a book that costs x dollars. Name an ordered pair that is a point on the graph of the relationship.
Type below:
________________

Answer:
An online bookstore charges $2 to ship any book.
Cole graphs the relationship that gives the total cost y in dollars to buy and ship a book that costs x dollars.
y = x + 2
x = 4
y = 4 + 2
y = 6
The ordered pair is (4,6)

Spiral Review

Question 3.
Write an expression that is equivalent to 6(g + 4).
Type below:
________________

Answer:
6(g + 4)
6 × g + 6 × 4
6g + 24

Question 4.
There are 6 girls in a music class. This represents \(\frac{3}{7}\) of the entire class. Solve \(\frac{3}{7}\)s = 6 to find the number of students, s, in the class.
_____ students

Answer: 14

Explanation:
There are 6 girls in a music class. This represents \(\frac{3}{7}\) of the entire class.
\(\frac{3}{7}\)s = 6
3 × s = 6 × 7
3s = 42
s = 42/3
s = 14
There are 14 students in the class.

Question 5.
Graph n > ^–2 on a number line.
Type below:
________________

Answer:

Question 6.
Sam is ordering lunch for the people in his office. The table shows the cost of lunch based on the number of people. How much will lunch cost for 35 people?

$ _____

Answer: 280

Explanation:
Sam is ordering lunch for the people in his office.
The table shows the cost of lunch based on the number of people.
The equation is c = 8n
c = 8 × 35
c = 280
Thus the lunch cost for 35 people is $280.

Share and Show – Page No. 519

Graph the linear equation.

Question 1.
y = x + 2
Type below:
________________

Answer:

Question 2.
y = 3x
Type below:
________________

Answer:

Write the linear equation for the relationship shown by the graph.

Question 3.

Type below:
________________

Answer: y = x – 1

Question 4.
Type below:
________________

On Your Own

Graph the linear equation.

Question 5.
y = x + 1
Type below:
________________

Answer:

Question 6.
y = 2x − 1
Type below:
________________

Answer:

Question 7.
Identify Relationships The graph shows the number of loaves of bread y that Kareem bakes in x hours. Write the linear equation for the relationship shown by the graph.

Type below:
________________

Answer:
The ordered pairs are (1,1), (2,2), (4,4), (5,5)
Look for a pattern among the pairs: each y value is the same as the corresponding x-value.
The equation is y = x
y = x

Problem Solving + Applications – Page No. 520

The graph shows the growth of a bamboo plant. Use the graph for 8–9.

Question 8.
Write a linear equation for the relationship shown by the graph. Use your equation to predict the height of the bamboo plant after 7 days.
Type below:
________________

Answer:
Write the ordered pairs from the graph: (1,50), (2,100), (3,150), (4,200), (5,250).
Look for a pattern among the pairs: each y value is 50 times the corresponding x value.
The equation is y = 50x
For x = 7, the solution is y = 50 × 7 = 350.
So, the height of the bamboo plant after 7 days will be 350 centimeters.

Question 9.
The height y in centimeters of a second bamboo plant is given by the equation y = 30x, where x is the time in days. Describe how the graph showing the growth of this plant would compare to the graph showing the growth of the first plant.
Type below:
________________

Answer: The line of the graph for the second plant would be less steep than the line of the graph for the first plant.

Question 10.
Maria graphed the linear equation y = x + 3. Then she used her ruler to draw a vertical line through the point (4, 0). At what point do the two lines intersect?
Type below:
________________

Answer:
y = x + 3
y = 4 + 0 = 4
y = 4 + 3 = 7
The coordinate is (4, 7)

Question 11.
Antonio claims the linear equation for the relationship shown by the graph is y = \(\frac{1}{2}\)x + 2. Use numbers and words to support Antonio’s claim.

Type below:
________________

Answer:
The ordered pairs (2,3) and (6,5) on the line make the equation.
y = \(\frac{1}{2}\)x + 2
y = 1/2 × 2 + 2
y = 1 + 2 = 3
y = 1/2 × 6 + 2
y = 3 + 2 = 5

Equations and Graphs – Page No. 521

Graph the linear equation.

Question 1.
y = x − 3
Type below:
________________

Answer:

Question 2.
y = x ÷ 3
Type below:
________________

Answer:

Write a linear equation for the relationship shown by the graph.

Question 3.

Type below:
________________

Answer:
By seeing the above graph we can say that the equation is
y = x + 1

Question 4.

Type below:
________________

Answer:
The ordered pairs are (1,4), (1.5,6), (2,8)
By seeing the above pairs we can say that the equation is y = 4x

Problem Solving

Question 5.
Dee is driving at an average speed of 50 miles per hour. Write a linear equation for the relationship that gives the distance y in miles that Dee drives in x hours.
Type below:
________________

Answer: y = 50x

Explanation:
Dee is driving at an average speed of 50 miles per hour.
y represents the distance in miles
x is the number of hours.
y is equal to the product of 50 and x.
y = 50x

Question 6.
Graph the relationship from Exercise 5.
Type below:
________________

Answer:

Question 7.
Explain how to write a linear equation for a line on a graph.
Type below:
________________

Answer:
To write an equation in slope-intercept form, given a graph of that equation, pick two points on the line and use them to find the slope.

Lesson Check – Page No. 522

Question 1.
A balloon rises at a rate of 10 feet per second. What is the linear equation for the relationship that gives the height y in feet of the balloon after x seconds?
Type below:
________________

Answer: The linear equation for the relationship is y = 10x

Question 2.
Write the linear equation that is shown by the graph.

Type below:
________________

Answer:
Write the ordered pairs from the graph: (3,3), (5,5), (8,8)
Look for a pattern among the pairs: each y value is the same as the corresponding x-value.
The equation is y = x

Spiral Review

Question 3.
Of the three expressions shown, which two are equivalent?
3 + 2(9 + 2n)     7(3 + 4n)         21 + 4n
Type below:
________________

Answer:
3 + 2(9 + 2n) = 3 + 18 + 4n = 21 + 4n
7(3 + 4n) = 21 + 28n
Thus  21 + 4n and 3 + 2(9 + 2n) are equivalent.

Question 4.
Which of the following are solutions of j ≥ 0.6?
j = 1      j = ^–0.6       j = \(\frac{3}{5}\)       j = 0.12        j = 0.08
Type below:
________________

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

Explanation:
Substitute the values of j in the inequality.
j = 1
1 ≥ 0.6
1 is greater than 0.6 but not equal.
Thus 1 is not the solution of j ≥ 0.6.
j = ^–0.6
-0.6 ≥ 0.6
-0.6 is less than 0.6
Thus -0.6 is not the solution of j ≥ 0.6.
j = \(\frac{3}{5}\)
\(\frac{3}{5}\) ≥ 0.6
\(\frac{3}{5}\) = 0.6
0.6 ≥ 0.6
Thus \(\frac{3}{5}\) is the solution.
j = 0.12
0.12 ≥ 0.6
0.12 is less than 0.6.
Thus 0.12 is not the solution of j ≥ 0.6.
j = 0.08
0.08 ≥ 0.6
0.08 is less than 0.6.
Thus 0.08 is not the solution of j ≥ 0.6.

Question 5.
Red grapes cost $2.49 per pound. Write an equation that shows the relationship between the cost c in dollars and the number of pounds of grapes p.
Type below:
________________

Answer: c = 2.49p

Explanation:
Given,
Red grapes cost $2.49 per pound.
c is the cost in dollars.
p is the number of pounds of grapes.
The equation c is equal to the product of the number of pounds of grapes and $2.49
c = 2.49p

Question 6.
It costs $8 per hour to rent a bike. Niko graphs this relationship using x for number of hours and y for total cost in dollars. Write an ordered pair that is a point on the graph of the relationship.
Type below:
________________

Answer: (5,40)

Explanation:
Given,
It costs $8 per hour to rent a bike.
Niko graphs this relationship using x for the number of hours and y for the total cost in dollars.
y = 8x

Chapter 9 Review/Test – Page No. 523

Question 1.
A box of peanut butter crackers contains 12 individual snacks. The total number of individual snacks s is equal to 12 times the number of boxes of crackers b.
The independent variable is _____.
The dependent variable is _____.
The equation that represents the relationship between the variables is _____.

Answer:
The independent variable is b.
The dependent variable is s.
The equation that represents the relationship between the variables is s = 12b.

Question 2.
A stationery store charges $8 to print logos on paper purchases. The total cost c is the price of the paper p plus $8 for printing the logo.
For numbers 2a–2d, select True or False for each statement.
2a. The total cost c depends on the price of the paper.
2b. c is the dependent variable.
2c. p is the independent variable.
2d. The equation that represents the relationship between the variables is c = 8p.
2a. ____________
2b. ____________
2c. ____________
2d. ____________

Answer:
2a. True
2b. True
2c. True
2d. False

Explanation:
2a. c represents the relationship between the two quantities.
So, the statement “The total cost c depends on the price of the paper” is true.
2b. c is the total cost so the statement “c is the dependent variable” is true.
2c. p represents the price to print logos
So, the statement “p is the independent variable” is true.
2d. The total cost c is the price of the paper p plus $8 for printing the logo.
The equation would be:
c = 8 + p
Thus the statement “The equation that represents the relationship between the variables is c = 8p” is false.

Question 3.
An electrician charges $75 an hour for labor and an initial fee of $65. The total cost c equals 75 times the number of hours x plus 65. Write an equation for the relationship and use the equation to complete the table.

Type below:
________________

Answer: c = 75x + 65
Substitute the value of x in the equation.

Page No. 524

Question 4.
The community center offers classes in arts and crafts. There is a registration fee of $125 and each class costs $79. The total cost c in dollars equals 79 times the number of classes n plus 125.

For numbers 4a–4d, select True or False for each statement.
4a. The registration fee is $120.
4b. n is the independent variable.
4c. c is the dependent variable.
4d. The cost for 7 classes is $678.
4a. ____________
4b. ____________
4c. ____________
4d. ____________

Answer:
4a. False
4b. True
4c. True
4d. True

Explanation:
4a. The registration fee is $120.
The registration fee is $125, not $120.
So, the statement is false.
4b. n is the independent variable.
n represents the number of classes.
The statement is true.
4c. c is the dependent variable.
c depends on the registration fee.
Thus the statement is true.
4d. The cost for 7 classes is $678
79 × 7 + 125 = $678
Thus the statement is true.

Question 5.
Ms. Walsh is buying calculators for her class. The table shows the total cost based on the number of calculators purchased.

If Ms. Walsh spent a total of $525, how many calculators did she buy? Use numbers and words to explain your answer.
Type below:
________________

Answer:
She bought 35 calculators. I found a pattern and wrote the equation c = 15n.
Since I know that Mrs.Walsh spent a total of $525, I can substitute 525 for c and solve for n
525 = 15n
n = 35

Chapter 9 Review/Test – Page No. 525

Question 6.
The table shows the number of cups of lemonade that can be made from cups of lemon juice.

Mary Beth says the number of cups of lemon juice j depends on the number of cups of lemonade l. She says the equation j = 7l represents the relationship between the cups of lemon juice j and the cups of lemonade l. Is Mary Beth correct? Use words and numbers to explain why or why not.
Type below:
________________

Answer:
Mary Beth is not correct. The number of cups of lemonade l depends on the number of cups of lemon juice j.
So l is the dependent variable and j is the independent variable.
The equation showing the relationship is l = 7j

Question 7.
For numbers 7a–7d, choose Yes or No to indicate whether the points, when graphed, would lie on the same line.
7a. (1, 6), (2, 4), (3, 2), (4, 0)
7b. (1, 1), (2, 4), (3, 9), (4, 16)
7c. (1, 3), (2, 5), (3, 7), (4, 9)
7d. (1, 8), (2, 10), (3, 12), (4, 14)
7a. ____________
7b. ____________
7c. ____________
7d. ____________

Answer:
7a. Yes

7b. No

7c. Yes

7d. Yes

Question 8.
Graph the relationship represented by the table to find the unknown value.

Type below:
________________

Answer: 10

Chapter 9 Review/Test – Page No. 526

Question 9.
Graph the relationship represented by the table.

Type below:
________________

Answer:

Question 10.
Miranda’s wages are $15 per hour. Write a linear equation that gives the wages w in dollars that Miranda earns in h hours.
Type below:
________________

Answer: w = 15h

Question 11.
The table shows the number of miles m that Lucinda could walk in h hours.

Graph the relationship between hours h and miles m. Then write the equation that shows the relationship.
Type below:
________________

Answer: m = 4h

Chapter 9 Review/Test – Page No. 527

Question 12.
Delonna walks 4 miles per day for exercise. The total number of miles m she walks equals 4 times the number of days d she walks.
What is the dependent variable?
What is the independent variable?
Write the equation that represents the relationship between the m and d.
Type below:
________________

Answer:
The equation is m = 4d
m is the dependent variable
d is the independent variable.

Question 13.
Lacy is staying at a hotel that costs $85 per night. The total cost c in dollars of Lacy’s stay is 85 times the number of nights n she stays.
For numbers 13a–13d, select True or False for each statement.
13a. The number of nights n is dependent on the cost c.
13b. n is the independent variable.
13c. c is the dependent variable.
13d. The equation that represents the total cost is c = 85n.
13a. ____________
13b. ____________
13c. ____________
13d. ____________

Answer:
13a. False
13b. True
13c. True
13d. True

Explanation:
13a. The number of nights n is dependent on the cost c.
n is independent on the cost c.
So, the statement is false.
13b. n is the independent variable.
The statement is true.
13c. c is the dependent variable.
c is dependent because it depends on the cost c.
So, the statement is true.
13d. The equation that represents the total cost is c = 85n.
The equation is true.

Question 14.
A taxi cab company charges an initial fee of $5 and then $4 per mile for a ride. Use the equation c = 4x + 5 to complete the table.

Type below:
________________

Answer:
Substitute the value of x in the equation.
We get,

Chapter 9 Review/Test – Page No. 528

Question 15.
A grocery display of cans is arranged in the form of a pyramid with 1 can in the top row, 3 in the second row from the top, 5 in the third row, and 7 in the fourth row. The total number of cans c equals 2 times the row r minus 1. Use the equation c = 2r − 1 to complete the table.

Type below:
________________

Answer:
A grocery display of cans is arranged in the form of a pyramid with 1 can in the top row, 3 in the second row from the top, 5 in the third row, and 7 in the fourth row.
c = 2r − 1
Substitute r in the equation.

Question 16.
The graph shows the number of words Mason read in a given amount of minutes. If Mason continues to read at the same rate, how many words will he have read in 5 minutes?

______ words

Answer: 1000 words
By seeing the above graph we can say that Mason can read 1000 words in 5 minutes.

Question 17.
Casey claims the linear equation for the relationship shown by the graph is c = 25j. Use numbers and words to support Casey’s claim.

Type below:
________________

Answer: The ordered pairs (1,25), (3,75), (5,125) and (7,175) each make the equation c = 25j

Conclusion:

I wish the details prevailed in the Go Math Grade 6 Answer Key Chapter 9 is helpful for you. Share this pdf link with your friends and help them to overcome the difficulties. If you have any doubts regarding the solutions you can leave a comment in the comment section.

Students to master mathematical concepts must require the best resources to understand the logic and learn the concept easily. The only resource that helps all grade 4 students are Go Math Grade 4 Answer Key Homework Practice FL Chapter 8 Multiply Fractions by Whole Numbers. With the help of Grade 4 Go Math Solutions Homework Practice FL Ch 8 Multiply Fractions by Whole Numbers, students can learn the fundamentals and become a master in maths. So, students are recommended to utilize the detailed solutions covered in Go Math Grade 4 Answer Key Chapter 8.

Go Math Grade 4 Answer Key Homework Practice FL Chapter 8 Multiply Fractions by Whole Numbers

Refer to the concepts of Homework Practice FL Chapter 8 Multiply Fractions by Whole Numbers before you ace up your preparation. Click on the links provided here and get a free pdf of chapterwise Go Math 4th Grade Answer Key Homework Practice FL Chapter 8 Multiply Fractions by Whole Numbers and practice the problems regularly on your own for experiencing the best learnings.

Lesson: 1 – Multiples of Unit Fractions

• Common Core – Multiply Fractions by Whole Numbers – Page No. 157
• Common Core – Multiply Fractions by Whole Numbers – Page No. 158

Lesson: 2 – Multiples of Fractions

• Common Core – Multiply Fractions by Whole Numbers – Page No. 159
• Common Core – Multiply Fractions by Whole Numbers – Page No. 160

Lesson: 3 – Multiply a Fraction by a Whole Number Using Models

• Common Core – Multiply Fractions by Whole Numbers – Page No. 161
• Common Core – Multiply Fractions by Whole Numbers – Page No. 162

Lesson: 4 – Multiply a Fraction or Mixed Number by a Whole Number.

• Common Core – Multiply Fractions by Whole Numbers – Page No. 163
• Common Core – Multiply Fractions by Whole Numbers – Page No. 164

Lesson: 5 – Problem Solving Comparison

• Common Core – Multiply Fractions by Whole Numbers – Page No. 165
• Common Core – Multiply Fractions by Whole Numbers – Page No. 166

Lesson: 6

• Common Core – Multiply Fractions by Whole Numbers – Page No. 167
• Common Core – Multiply Fractions by Whole Numbers – Page No. 168

Common Core – Multiply Fractions by Whole Numbers – Page No. 157

Multiples of Unit Fractions

Write the fraction as a product of a whole number and a unit fraction.

Question 1.

Explanation:
Given that 5/6 or 5 sixth-size parts.
Each sixth-size part of the given fraction can be shown by the unit fraction 1/6.
You can use unit fractions to show 5/6
5/6 = 5 x 1/6.

Question 2.
\(\frac{7}{8}\)
Type below:
_________

Answer:
7 x 1/8

Explanation:
Given that 7/8 or 7 eighth-size parts.
Each eighth-size part of the given fraction can be shown by the unit fraction 1/8.
You can use unit fractions to show 7/8
7/8 = 7 x 1/8.

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

Answer:
5 x 1/3

Explanation:
Given that 5/3 or 5 third-size parts.
Each third-size part of the given fraction can be shown by the unit fraction 1/3.
You can use unit fractions to show 5/6
5/3 = 5 x 1/3.

Question 4.
\(\frac{9}{10}\)
Type below:
_________

Answer:
9 x 1/10

Explanation:
Given that 9/10 or 9 tenth-size parts.
Each tenth-size part of the given fraction can be shown by the unit fraction 1/10.
You can use unit fractions to show 9/10
9/10 = 9 x 1/10.

Question 5.
\(\frac{3}{4}\)
Type below:
_________

Answer:
3 x 1/4

Explanation:
Given that 3/4 or 3 fourth-size parts.
Each fourth-size part of the given fraction can be shown by the unit fraction 1/4.
You can use unit fractions to show 5/6
3/4 = 3 x 1/4.

Question 6.
\(\frac{11}{12}\)
Type below:
_________

Answer:
11 x 1/12

Explanation:
Given that 11/12 or 11 twelve-size parts.
Each twelve-size part of the given fraction can be shown by the unit fraction 1/12.
You can use unit fractions to show 5/6
11/12 = 11 x 1/12.

Question 7.
\(\frac{4}{6}\)
Type below:
_________

Answer:
4 x 1/6

Explanation:
Given that 4/6 or 4 sixth-size parts.
Each sixth-size part of the given fraction can be shown by the unit fraction 1/6.
You can use unit fractions to show 4/6
4/6 = 4 x 1/6.

Question 8.
\(\frac{8}{20}\)
Type below:
_________

Answer:
8 x 1/20

Explanation:
Given that 8/20 or 8 twenty-size parts.
Each twenty-size part of the given fraction can be shown by the unit fraction 1/20.
You can use unit fractions to show 8/20
8/20 = 8 x 1/20.

Question 9.
\(\frac{13}{100}\)
Type below:
_________

Answer:
13 x 1/100

Explanation:
Given that 13/100 or 13 hundred-size parts.
Each hundred-size part of the given fraction can be shown by the unit fraction 1/100.
You can use unit fractions to show 13/100
13/100 = 13 x 1/100.

List the next four multiples of the unit fraction.

Question 10.
\(\frac{1}{5}\),
Type below:
_________

Answer:
2/5, 3/5, 4/5, 5/5

Explanation:

2/5, 3/5, 4/5, 5/5

Question 11.
\(\frac{1}{8}\),
Type below:
_________

Answer:
2/8, 3/8, 4/8, 5/8

Explanation:

2/8, 3/8, 4/8, 5/8

Problem Solving

Question 12.
So far, Monica has read \(\frac{5}{6}\) of a book. She has read the same number of pages each day for 5 days. What fraction of the book does Monica read each day?
\(\frac{□}{□}\) of the book

Answer: 1/6 of the book

Explanation:
Monica has read 5/6 of a book. She has read the same number of pages each day for 5 days.
For 1 day, she read one page. In total, she read 5 pages in 5 days. So, Monica read 1/6 of a book each day.

Question 13.
So far, Monica has read \(\frac{3}{8}\) of a book. She has read the same number of pages each day for 5 days. What fraction of the book does Monica read each day?
\(\frac{□}{□}\) pound of cheese

Answer: 1/8 pound of cheese

Explanation:
Nicholas buys 3/8 pound of cheese. He bought 3 sandwiches. Then, he applied 3/8 pound of cheese on 3 sandwiches. So, 3 x 1/8 cheese he put on 3 sandwiches. So, for one sandwich he put 1/8 pound of cheese.

Common Core – Multiply Fractions by Whole Numbers – Page No. 158

Lesson Check

Question 1.
Selena walks from home to school each morning and back home each afternoon. Altogether, she walks \(\frac{2}{3}\) mile each day. How far does Selena live from school?
Options:
a. \(\frac{1}{3}\) mile
b. \(\frac{2}{3}\) mile
c. 1 \(\frac{1}{3}\) miles
d. 2 miles

Answer: a. 1/3 mile

Explanation:
Selena walks from home to school each morning and back home each afternoon.
Altogether, she walks 2/3 miles each day.
The distance between home and school will remain the same.
So, 2/3 x 1/2 = 1/3 mile far Selena live from the school.
Thus the correct answer is option a.

Question 2.
Will uses \(\frac{3}{4}\) cup of olive oil to make 3 batches of salad dressing. How much oil does Will use for one batch of salad dressing?
Options:
a. \(\frac{1}{4}\) cup
b. \(\frac{1}{3}\) cup
c. 2 \(\frac{1}{3}\) cups
d. 3 cups

Answer: \(\frac{1}{4}\) cup

Explanation:
Will uses 3/4 cups of olive oil to make 3 batches of salad dressing.
To know the one batch of salad dressing, we need to take one part of salad dressing = 1/3.
So, 3/4 x 1/3 = 1/4 cup of olive oil will use for one batch of salad dressing.
Thus the correct answer is option a.

Spiral Review

Question 3.
Liza bought \(\frac{5}{8}\) pound of trail mix. She gives \(\frac{2}{8}\) pound of trail mix to Michael. How much trail mix does Liza have left?
Options:
a. \(\frac{1}{8}\) pound
b. \(\frac{2}{8}\) pound
c. \(\frac{3}{8}\) pound
d. \(\frac{4}{8}\) pound

Answer: c. 3/8 pound

Explanation:
Liza bought 58 pound of trail mix. She gives 28 pounds of trail mix to Michael.
So, Liza has left 5/8 – 2/8 = 3/8 trail mix.
Thus the correct answer is option c.

Question 4.
Leigh has a piece of rope that is 6 \(\frac{2}{3}\) feet long. How do you write 6 \(\frac{2}{3}\) as a fraction greater than 1?
Options:
a. \(\frac{11}{3}\) pound
b. \(\frac{15}{3}\) pound
c. \(\frac{20}{3}\) pound
d. \(\frac{62}{3}\) pound

Answer: c. 20/3

Explanation:
Multiply the denominator with the whole number. i.e Multiply 3 with 6 in the given example, 6 (2/3).
3 x 6 =18.
Add 18 + 2 =20.
Keep the Denominator the same i.e. 3.
The obtained fraction is 20/3.
Thus the correct answer is option c.

Question 5.
Randy’s house number is a composite number. Which of the following could be Randy’s house number?
Options:
a. 29
b. 39
c. 59
d. 79

Answer: b. 39

Explanation:
The composite numbers can be defined as the whole numbers that have more than two factors. Whole numbers that are not prime are composite numbers because they are divisible by more than two numbers. 39 is the composite number. 39 is divide by 13 and 3.
Thus the correct answer is option b.

Question 6.
Mindy buys 12 cupcakes. Nine of the cupcakes have chocolate frosting and the rest have vanilla frosting. What fraction of the cupcakes have vanilla frosting?
Options:
a. \(\frac{1}{4}\)
b. \(\frac{1}{3}\)
c. \(\frac{2}{3}\)
d. \(\frac{3}{4}\)

Answer: a. 1/4

Explanation:
Mindy buys 12 cupcakes.
Nine of the cupcakes have chocolate frosting = 9/12.
The rest have vanilla frosting. So, there are 3 cups remained = 3/12 = 1/4.
1/4 cupcakes have vanilla frosting.
Thus the correct answer is option a.

Common Core – Multiply Fractions by Whole Numbers – Page No. 159

Multiples of Fractions

List the next four multiples of the fraction.

Question 1.
\(\frac{3}{5}\),
Type below:
_________

Answer:
6/5, 9/5, 12/5, 20/5

Explanation:
1 x 3/5 = 3/5.
2 x 3/5 = 6/5.
3 x 3/5 = 9/5.
4 x 3/5 = 12/5.
5 x 4/5 = 20/5.
The next four multiples of 3/5 are 6/5, 9/5, 12/5, 20/5.

Question 2.
\(\frac{2}{6}\),
Type below:
_________

Answer:
4/6, 6/6, 8/6, 10/6

Explanation:
1 x 2/6 = 2/6.
2 x 2/6 = 4/6.
3 x 2/6 = 6/6.
4 x 2/6 = 8/6.
5 x 2/6 = 10/6.
The next four multiples of 2/6 are 4/6, 6/6, 8/6, 10/6.

Question 3.
\(\frac{4}{8}\),
Type below:
_________

Answer:
8/8, 12/8, 16/8, 20/8

Explanation:
1 x 4/8 = 4/8.
2 x 4/8 = 8/8.
3 x 4/8 = 12/8.
4 x 4/8 = 16/8.
5 x 4/8 = 20/8.
The next four multiples of 4/8 are 8/8, 12/8, 16/8, 20/8.

Question 4.
\(\frac{5}{10}\),
Type below:
_________

Answer:
10/10, 15/10, 20/10, 25/10

Explanation:
1 x 5/10 = 5/10.
2 x 5/10 = 10/10.
3 x 5/10 = 15/10.
4 x 5/10 = 20/10.
5 x 5/10 = 25/10.
The next four multiples of 5/10 are 10/10, 15/10, 20/10, 25/10.

Write the product as the product of a whole number and a unit fraction.

Question 5.

2 × \(\frac{4}{5}\) =
Type Below:
_________

Answer: 8/5 = 8 x 1/5

Explanation:
1 group of 4/5 = 4/5
2 groups of 4/5 = 8/5
2 x 4/5 = 8/5 = 8 x 1/5.

Question 6.

5 × \(\frac{2}{3}\) =
Type below:
_________

Answer:
10/3 = 10 x 1/3

Explanation:
1 group of 2/3 = 2/3
2 group of 2/3 = 4/3
3 group of 2/3 = 6/3
4 group of 2/3 = 8/3
5 group of 2/3 = 10/3
5 x 2/3 = 10/3 = 10 x 1/3.

Problem Solving

Question 7.
Jessica is making 2 loaves of banana bread. She needs \(\frac{3}{4}\) cup of sugar for each loaf. Her measuring cup can only hold \(\frac{1}{4}\) cup of sugar. How many times will Jessica need to fill the measuring cup in order to get enough sugar for both loaves of bread?
_____ times

Answer: 6 times

Explanation:
Jessica is making 2 loaves of banana bread. She needs a 3/4 cup of sugar for each loaf.
For 2 loaves, she needs 2 x 3/4 = 6/4 cups of sugar.
Her measuring cup can only hold 1/4 cup of sugar. So, to get the 3/4 cup of sugar, she needs to fill the cup 3 times. 1/4 + 1/4 + 1/4 = 3/4.
So, to fill 2 loaves, she needs to fill cup 3 x 2 = 6 times.

Question 8.
A group of four students is performing an experiment with salt. Each student must add \(\frac{3}{8}\) teaspoon of salt to a solution. The group only has a \(\frac{1}{8}\) teaspoon measuring spoon. How many times will the group need to fill the measuring spoon in order to perform the experiment?
_____ times

Answer: 12 times

Explanation:
A group of four students is performing an experiment with salt. Each student must add a 3/8 teaspoon of salt to a solution. 4 x 3/8 = 12/8 teaspoon of salt required to finish the experiment.
If they have 1/8 teaspoon measuring spoon, 12 x 1/8.
So, the group needs to fill the measuring spoon 12 times in order to perform the experiment.

Common Core – Multiply Fractions by Whole Numbers – Page No. 160

Lesson Check

Question 1.
Eloise made a list of some multiples of \(\frac{5}{8}\). Which of the following lists could be Eloise’s list?
Options:
a. \(\frac{5}{8}, \frac{10}{16}, \frac{15}{24}, \frac{20}{32}, \frac{25}{40}\)
b. \(\frac{5}{8}, \frac{10}{8}, \frac{15}{8}, \frac{20}{8}, \frac{25}{8}\)
c. \(\frac{5}{8}, \frac{6}{8}, \frac{7}{8}, \frac{8}{8}, \frac{9}{8}\)
d. \(\frac{1}{8}, \frac{2}{8}, \frac{3}{8}, \frac{4}{8}, \frac{5}{8}\)

Answer: b. 5/8, 10/8, 15/8, 20/8, 25/8
Explanation:
1 x 5/8 = 5/8.
2 x 5/8 = 10/8.
3 x 5/8 = 15/8.
4 x 5/8 = 20/8.
5 x 5/8 = 25/8.
The next four multiples of 5/8 are \(\frac{5}{8}, \frac{10}{8}, \frac{15}{8}, \frac{20}{8}, \frac{25}{8}\)
Thus the correct answer is option b.

Question 2.
David is filling five \(\frac{3}{4}\) quart bottles with a sports drink. His measuring cup only holds \(\frac{1}{4}\) quart. How many times will David need to fill the measuring cup in order to fill the 5 bottles?
Options:
a. 5
b. 10
c. 15
d. 20

Answer: c. 15

Explanation:
David is filling five 3/4 quart bottles with a sports drink = 5 x 3/4 = 15/4.
His measuring cup only holds 1/4 quart.
So, 15 x 1/4. David needs to fill the measuring cup 15 times in order to fill the 5 bottles.
Thus the correct answer is option c.

Spiral Review

Question 3.
Ira has 128 stamps in his stamp album. He has the same number of stamps on each of the 8 pages. How many stamps are on each page?
Options:
a. 12
b. 14
c. 16
d. 18

Answer: c. 16

Explanation:
Ira has 128 stamps in his stamp album. He has the same number of stamps on each of the 8 pages.
128/8 = 16 stamps on each page.
So, there are 16 stamps on each page.
Thus the correct answer is option b.

Question 4.
Ryan is saving up for a bike that costs $198. So far, he has saved $15 per week for the last 12 weeks. How much more money does Ryan need in order to be able to buy the bike?
Options:
a. $ 8
b. $ 18
c. $ 48
d. $ 180

Answer: b. $ 18

Explanation:
Ryan is saving up for a bike that costs $198.
So far, he has saved $15 per week for the last 12 weeks = $15 x 12 = $180.
$198 – $180 = $18 need in order to buy the bike.
Thus the correct answer is option b.

Question 5.
Tina buys 3 \(\frac{7}{8}\) yards of material at the fabric store. She uses it to make a skirt. Afterward, she has 1 \(\frac{3}{8}\) yards of the fabric leftover. How many yards of material did Tina use?
Options:
a. 1 \(\frac{4}{8}\)
b. 2 \(\frac{1}{8}\)
c. 2 \(\frac{4}{8}\)
d. 5 \(\frac{2}{8}\)

Answer: c. 2  4/8

Explanation:
Tina buys 3 7/8 yards of material at the fabric store. She uses it to make a skirt. Afterward, she has 1 3/8 yards of the fabric leftover.
3 -1 = 2; 7/8 – 3/8 = 4/8.
So, the answer is 2 \(\frac{4}{8}\).
Thus the correct answer is option c.

Question 6.
Which list shows the fractions in order from least to greatest?
Options:
a. \(\frac{2}{3}, \frac{3}{4}, \frac{7}{12}\)
b. \(\frac{7}{12}, \frac{3}{4}, \frac{2}{3}\)
c. \(\frac{3}{4}, \frac{2}{3}, \frac{7}{12}\)
d. \(\frac{7}{12}, \frac{2}{3}, \frac{3}{4}\)

Answer: d. \(\frac{7}{12}, \frac{2}{3}, \frac{3}{4}\)

Explanation:
2/3 = 0.666
3/4 = 0.75
7/12 = 0.5833
\(\frac{7}{12}, \frac{2}{3}, \frac{3}{4}\)
Thus the correct answer is option d.

Common Core – Multiply Fractions by Whole Numbers – Page No. 161

Multiply a Fraction by a Whole Number Using Models

Multiply.

Question 1.

Question 2.
3 × \(\frac{2}{5}\) = \(\frac{□}{□}\)

Answer:

3 x 2/5 = 6/5

Question 3.
7 × \(\frac{3}{10}\) = \(\frac{□}{□}\)

Answer:

7 x 3/10 = 21/10

Question 4.
3 × \(\frac{5}{12}\) = \(\frac{□}{□}\)

Answer:

3 x 5/12 = 15/12

Question 5.
6 × \(\frac{3}{4}\) = \(\frac{□}{□}\)

Answer:

6 x 3/4 = 18/4

Question 6.
4 × \(\frac{2}{8}\) = \(\frac{□}{□}\)

Answer:

4 x 2/8 = 8/8

Question 7.
5 × \(\frac{2}{3}\) = \(\frac{□}{□}\)

Answer:

5 x 2/3 = 10/3

Question 8.
2 × \(\frac{7}{8}\) = \(\frac{□}{□}\)

Answer:

2 x 7/8 = 14/8

Question 9.
6 × \(\frac{4}{5}\) = \(\frac{□}{□}\)

Answer:

6 x 4/5 = 28/5

Problem Solving

Question 10.
Matthew walks \(\frac{5}{8}\) mile to the bus stop each morning. How far will he walk in 5 days?
\(\frac{□}{□}\)

Answer: 25/8 miles

Explanation:
Matthew walks 5/8 mile to the bus stop each morning.
In 5 days, 5 x 5/8 = 25/8 miles.

Question 11.
Emily uses \(\frac{2}{3}\) cup of milk to make one batch of muffins. How many cups of milk will Emily use if she makes 3 batches of muffins?
\(\frac{□}{□}\)

Answer: 6/3 cups of milk

Explanation:
Emily uses a 2/3 cup of milk to make one batch of muffins.
Emily use 3 x 2/3 = 6/3 cups of milk to make 3 batches of muffins

Common Core – Multiply Fractions by Whole Numbers – Page No. 162

Lesson Check

Question 1.
Aleta’s puppy gained \(\frac{3}{8}\) pound each week for 4 weeks. Altogether, how much weight did the puppy gain during the 4 weeks?
Options:
a. \(\frac{8}{12}\) pound
b. 1 \(\frac{2}{8}\) pounds
c. \(\frac{12}{8}\) pounds
d. 4 \(\frac{3}{8}\) pounds

Answer: \(\frac{12}{8}\) pounds

Explanation:
Aleta’s puppy gained 3/8 pound each week.
It gained 4 x 3/8 = 12/8 pounds in 4 weeks.
Thus the correct answer is option c.

Question 2.
Pedro mixes \(\frac{3}{4}\) teaspoon of plant food into each gallon of water. How many teaspoons of plant food should Pedro mix into 5 gallons of water?
Options:
a. \(\frac{3}{20}\) teaspoon
b. \(\frac{4}{15}\) teaspoon
c. \(\frac{8}{4}\) teaspoons
d. \(\frac{15}{4}\) teaspoons

Answer: d. \(\frac{15}{4}\) teaspoons

Explanation:
If Pedro mixes 3/4 teaspoon of plant food into each gallon of water, then 5 x 3/4 = 15/4 teaspoon of plant food mix into 5 gallons of water.
Thus the correct answer is option d.

Spiral Review

Question 3.
Ivana has \(\frac{3}{4}\)pound of hamburger meat. She makes 3 hamburger patties. Each patty weighs the same amount. How much does each hamburger patty weigh?
Options:
a. \(\frac{1}{4}\) pound
b. \(\frac{1}{3}\) pound
c. 2 \(\frac{1}{4}\) pounds
d. 3 pounds

Answer: a. \(\frac{1}{4}\) pound

Explanation:
Ivana has 3/4 pound of hamburger meat. She makes 3 hamburger patties.
Each patty weighs the same amount. So, each hamburger patty weighs 1/4 pound.
Thus the correct answer is option a.

Question 4.
Which of the following expressions is NOT equal to \(\frac{7}{10}\)?
Options:
a. \(\frac{5}{10}+\frac{1}{10}+\frac{1}{10}\)
b. \(\frac{2}{10}+\frac{2}{10}+\frac{3}{10}\)
c. \(\frac{3}{10}+\frac{3}{10}+\frac{2}{10}\)
d. \(\frac{4}{10}+\frac{2}{10}+\frac{1}{10}\)

Answer: c. 3/10+3/10+2/10

Explanation:
a. 5/10+1/10+1/10 = 7/10
b. 2/10+2/10+3/10 = 7/10
c. 3/10+3/10+2/10 = 8/10
d. 4/10+2/10+1/10 = 7/10
The expression not equal to \(\frac{7}{10}\) is \(\frac{8}{10}\)
Thus the correct answer is option c.

Question 5.
Lance wants to find the total length of 3 boards. He uses the expression \(3 \frac{1}{2}+\left(2+4 \frac{1}{2}\right)\). How can Lance rewrite the expression using both the Associative and Commutative Properties of Addition?
Options:
a. \(5+4 \frac{1}{2}\)
b. \(\left(3 \frac{1}{2}+2\right)+4 \frac{1}{2}\)
c. \(2+\left(3 \frac{1}{2}+4 \frac{1}{2}\right)\)
d. \(3 \frac{1}{2}+\left(4 \frac{1}{2}+2\right)\)

Answer: She can write as (3 1/2 + 2) + 4 1/2

Question 6.
Which of the following statements is true?
Options:
a. \(\frac{5}{8}>\frac{9}{10}\)
b. \(\frac{5}{12}>\frac{1}{3}\)
c. \(\frac{3}{6}>\frac{4}{5}\)
d. \(\frac{1}{2}>\frac{3}{4}\)

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

Explanation:
0.625 > 0.9
0.416 > 0.333
0.5 > 0.8
0.5 > 0.75
Thus the correct answer is option d.

Common Core – Multiply Fractions by Whole Numbers – Page No. 163

Multiply a Fraction or Mixed Number by a Whole Number.

Multiply. Write the product as a mixed number.

Question 1.

Answer:
1  5/10

Explanation:
5 × 3/10 = 15/10 = 1 and remainder is 5. So, the mixed fraction is 1  5/10

Question 2.
3 × \(\frac{3}{5}\) =
_____ \(\frac{□}{□}\)

Answer:
1 × 4/5

Explanation:
3 × 3/5 = 9/5 = 1 and remainder is 4. So, the mixed fraction is 1  4/5

Question 3.
5 × \(\frac{3}{4}\) =
_____ \(\frac{□}{□}\)

Answer:
3  3/4
Explanation:
15/4 = 3 and the remainder is 3. So, the mixed fraction is 3  3/4

Question 4.
4 × 1 \(\frac{1}{5}\) =
_____ \(\frac{□}{□}\)

Answer:
4  4/5
Explanation:
1 ×15 = 6/5.
4 x 6/5 = 24/5 = 4 and the remainder is 4. So, the mixed fraction is 4× 4/5

Question 5.
2 × 2 \(\frac{1}{3}\) =
_____ \(\frac{□}{□}\)

Answer:
4  2/3
Explanation:
2 13 = 7/3.
2 x 7/3 = 14/3.
14/3 = 4 and the remainder is 2. So, the mixed fraction is 4 2/3

Question 6.
5 × 1 \(\frac{1}{6}\) =
_____ \(\frac{□}{□}\)

Answer: 5 5/6

Explanation:
1 1/6 = 7/6
5 x 7/6 = 35/6.
35/6 = 5 and the remainder is 5.
So, the mixed fraction is 5 5/6

Question 7.
2 × 2 \(\frac{7}{8}\) =
_____ \(\frac{□}{□}\)

Answer: 6 1/1

Explanation:
2 7/8 = 23/8
2 x 23/8 = 46/8 = 6 1/1

Question 8.
7 × 1 \(\frac{3}{4}\) =
_____ \(\frac{□}{□}\)

Answer: 9 3/4

Explanation:
1 3/4 = 7/4
7 x 7/4 = 39/4
39/4 = 9 and the remainder is 3.
So, the mixed fraction is 9 3/4

Question 9.
8 × 1 \(\frac{3}{5}\) =
_____ \(\frac{□}{□}\)

Answer: 12 4/5

Explanation:
1 3/5 = 8/5
8 x 8/5 = 64/5
64/5 = 12 and the remainder is 4.
So, the mixed fraction is 12 4/5

Problem Solving

Question 10.
Brielle exercises for \(\frac{3}{4}\) hour each day for 6 days in a row. Altogether, how many hours does she exercise during the 6 days?
_____ \(\frac{□}{□}\)

Answer: 4 2/4

Explanation:
6 x 3/4 = 18/4 = 4 and the remainder is 2.
So, the mixed fraction is 4 2/4.

Question 11.
A recipe for quinoa calls for 2 \(\frac{2}{3}\) cups of milk. Conner wants to make 4 batches of quinoa. How much milk does he need?
_____ \(\frac{□}{□}\)

Answer: 10 2/3

Explanation:
quinoa calls for 8/3 cups of milk. Conner wants to make 4 batches of quinoa.
So, 4 x 8/3 = 32/3 = 10 and the remainder is 2.
So, the mixed fraction is 10 2/3

Common Core – Multiply Fractions by Whole Numbers – Page No. 164

Lesson Check

Question 1.
A mother is 1 \(\frac{3}{4}\) times as tall as her son. Her son is 3 feet tall. How tall is the mother?
Options:
a. 4 \(\frac{3}{4}\) feet
b. 5 \(\frac{1}{4}\) feet
c. 5 \(\frac{1}{2}\) feet
d. 5 \(\frac{3}{4}\) feet

Answer: b. 5 1/4 feet

Explanation:
A mother is 1 3/4 times as tall as her son. Her son is 3 feet tall.
So, 3 x 7/4 = 21/4 = 5 and the remainder is 1.
The mixed fraction is 5 1/4 feet.
Thus the correct answer is option b.

Question 2.
The cheerleaders are making a banner that is 8 feet wide. The length of the banner is 1 \(\frac{1}{3}\) times the width of the banner. How long is the banner?
Options:
a. 8 \(\frac{1}{3}\) feet
b. 8 \(\frac{3}{8}\) feet
c. 10 \(\frac{1}{3}\) feet
d. 10 \(\frac{2}{3}\) feet

Answer: d. 10 2/3 feet

Explanation:
The cheerleaders are making a banner that is 8 feet wide. The length of the banner is 1 1/3 times the width of the banner.
So, 8 x 4/3 = 32/3 =10 and the remainder is 2.
The mixed fraction is 10 2/3 feet.
Thus the correct answer is option d.

Spiral Review

Question 3.
Karleigh walks \(\frac{5}{8}\) mile to school every day. How far does she walk to school in 5 days?
Options:
a. \(\frac{5}{40}\) mile
b. \(\frac{25}{40}\) mile
c. \(\frac{10}{8}\) miles
d. \(\frac{25}{8}\) miles

Answer: d. 25/8 miles

Explanation:
5 x 5/8 = 25/8.
Thus the correct answer is option d.

Question 4.
Which number is a multiple of \(\frac{4}{5}\)?
Options:
a. \(\frac{8}{10}\)
b. \(\frac{12}{15}\)
c. \(\frac{16}{20}\)
d. \(\frac{12}{5}\)

Answer: d. 12/5

Explanation:
The multiple of 45 has the denominator 5.
So, 12/5 is the correct answer.
Thus the correct answer is option d.

Question 5.
Jo cut a key lime pie into 8 equal-size slices. The next day, \(\frac{7}{8}\) of the pie is left. Jo puts each slice on its own plate. How many plates does she need?
Options:
a. 5
b. 6
c. 7
d. 8

Answer: c. 7

Explanation:
Jo cut a key lime pie into 8 equal-size slices.
The next day, 78 of the pie is left. Jo puts each slice on its own plate.
She needs 7 plates.
Thus the correct answer is option c.

Question 6.
Over the weekend, Ed spent 1 \(\frac{1}{4}\) hours doing his math homework and 1 \(\frac{3}{4}\) hours doing his science project. Altogether, how much time did Ed spend doing homework over the weekend?
Options:
a. 3 hours
b. 2 \(\frac{3}{4}\) hours
c. 2 \(\frac{1}{2}\) hours
d. 2 hours

Answer: a. 3 hours

Explanation:
Given,
Over the weekend, Ed spent 1 \(\frac{1}{4}\) hours doing his math homework and 1 \(\frac{3}{4}\) hours doing his science project.
5/4 + 7/4 = 12/4 = 3 hours
Thus the correct answer is option a.

Common Core – Multiply Fractions by Whole Numbers – Page No. 165

Problem Solving Comparison

Problems with Fractions

Read each problem and solve.

Question 1.
A shrub is 1 \(\frac{2}{3}\) feet tall. A small tree is 3 times as tall as the shrub. How tall is the tree?

Answer: 5 feet

Explanation:

Question 2.
You run 1 \(\frac{3}{4}\) miles each day. Your friend runs 4 times as far as you do. How far does your friend run each day?
_________ miles

Answer: 7 miles

Explanation:
Given,
You run 1 \(\frac{3}{4}\) miles each day.
Your friend runs 4 times as far as you do.
4 x 7/4 = 7 miles each day

Question 3.
At the grocery store, Ayla buys 1 \(\frac{1}{3}\) pounds of ground turkey. Tasha buys 2 times as much ground turkey as Ayla. How much ground turkey does Tasha buy?
_____ \(\frac{□}{□}\) pounds

Answer: 2 2/3 pounds

Explanation:
Given,
At the grocery store, Ayla buys 1 \(\frac{1}{3}\) pounds of ground turkey.
Tasha buys 2 times as much ground turkey as Ayla.
2 x 4/3 = 8/3 = 2 and the remainder is 2.
The mixed fraction is 2 2/3 pounds.

Question 4.
When Nathan’s mother drives him to school, it takes \(\frac{1}{5}\) hour. When Nathan walks to school, it takes him 4 times as long to get to school. How long does it take Nathan to walk to school?
\(\frac{□}{□}\) hours

Answer: 4/5 hours

Explanation:
Given,
When Nathan’s mother drives him to school, it takes \(\frac{1}{5}\) hour.
When Nathan walks to school, it takes him 4 times as long to get to school.
4 x 1/5 = 4/5 hour
It takes 4/5 hour Nathan to walk to school.

Common Core – Multiply Fractions by Whole Numbers – Page No. 166

Lesson Check

Question 1.
A Wilson’s Storm Petrel is a small bird with a wingspan of 1 \(\frac{1}{3}\) feet. A California Condor is a larger bird with a wingspan almost 7 times as wide as the wingspan of the petrel. About how wide is the wingspan of the California Condor?
Options:
a. \(\frac{4}{21}\) foot
b. 2 \(\frac{1}{3}\) feet
c. 7 \(\frac{1}{3}\) feet
d. 9 \(\frac{1}{3}\) feet

Answer: d. 9 1/3 feet

Explanation:
Given,
A Wilson’s Storm Petrel is a small bird with a wingspan of 1 \(\frac{1}{3}\) feet.
A California Condor is a larger bird with a wingspan almost 7 times as wide as the wingspan of the petrel.
Convert from mixed fraction to the improper fraction.
1 1/3 = 4/3.
7 x 4/3 = 28/3 feet = 9 and the remainder is 1.
The mixed fraction is 9 1/3
Thus the correct answer is option d.

Question 2.
The walking distance from the Empire State Building in New York City to Times Square is about \(\frac{9}{10}\) mile. The walking distance from the Empire State Building to Sue’s hotel is about 8 times as far. About how far is Sue’s hotel from the Empire State Building?
Options:
a. \(\frac{9}{80}\) mile
b. \(\frac{72}{80}\) mile
c. 1 \(\frac{7}{10}\) miles
d. 7 \(\frac{2}{10}\) miles

Answer: d. 7 2/10 miles

Explanation:
Given,
The walking distance from the Empire State Building in New York City to Times Square is about \(\frac{9}{10}\) mile.
The walking distance from the Empire State Building to Sue’s hotel is about 8 times as far.
8 x 9/10 mile = 72/10 mile = 7 and the remainder is 2.
The mixed fraction is 7 2/10 miles.
Thus the correct answer is option d.

Spiral Review

Question 3.
Which of the following expressions is NOT equal to 3 × 2 \(\frac{1}{4}\)?
Options:
a. \(3 \times \frac{9}{4}\)
b. (3 × 2) + (3 × \(\frac{1}{4}\))
c. 6 \(\frac{3}{4}\)
d. 3 × 2 + \(\frac{1}{4}\)

Answer: d. 3 × 2 + 14

Explanation:
3 × 2 14 = 3 x 9/4 = 27/4
a. 3 × 94 = 27/4
b. (3 × 2) + (3 × 14) = 6 + 3/4 = 27/4
c. 6 3/4 = 27/4
d. 3 × 2 + 14 = 6 + 1/4 = 25/4
Thus the correct answer is option d.

Question 4.
At a bake sale, Ron sells \(\frac{7}{8}\) of an apple pie and \(\frac{5}{8}\) of a cherry pie. Altogether, how much pie does he sell at the bake sale?
Options:
a. \(\frac{2}{8}\)
b. \(\frac{12}{16}\)
c. \(\frac{12}{8}\)
d. \(\frac{35}{8}\)

Answer: c. 12/8

Explanation:
Given,
At a bake sale, Ron sells \(\frac{7}{8}\) of an apple pie and \(\frac{5}{8}\) of a cherry pie.
7/8 + 5/8 = 12/8
The bake sale 12/8 pie.
Thus the correct answer is option c.

Question 5.
On a ruler, which measurement is between \(\frac{3}{16}\) inch and \(\frac{7}{8}\) inch?
Options:
a. \(\frac{1}{16}\) inch
b. \(\frac{1}{8}\) inch
c. \(\frac{11}{16}\) inch
d. \(\frac{15}{16}\) inch

Answer: c. 11/16 inch

Explanation:
Subtract \(\frac{3}{16}\) inch and \(\frac{7}{8}\)
Make denominators as common.
\(\frac{7}{8}\) × \(\frac{2}{2}\) = \(\frac{14}{16}\)
\(\frac{14}{16}\) – \(\frac{3}{16}\) = \(\frac{11}{16}\) inch.
Thus the correct answer is option c.

Question 6.
Which of the following numbers is composite?
Options:
a. 4
b. 3
c. 2
d. 1

Answer:
a. 4

Explanation:
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself.
The factors of 4 are 1, 2, 4.
4 has more than 2 factors.
Thus the correct answer is option a.

Common Core – Multiply Fractions by Whole Numbers – Page No. 167

Lesson 8.1

Write the fraction as a product of a whole number and a unit fraction.

Question 1.
\(\frac{5}{6}\) =
Type below:
________

Answer: 5 x 1/6

Explanation:
Given that 5/6 or 5 sixth-size parts.
Each sixth-size part of the given fraction can be shown by the unit fraction 1/6.
You can use unit fractions to show 5/6
\(\frac{5}{6}\) = 5 x 1/6.

Question 2.
\(\frac{7}{8}\) =
Type below:
________

Answer: 7 x 1/8

Explanation:
Given that 7/8 or 7 eighth-size parts.
Each eighth-size part of the given fraction can be shown by the unit fraction 1/8.
You can use unit fractions to show 7/8
\(\frac{7}{8}\) = 7 x 1/8.

Question 3.
\(\frac{3}{5}\) =
Type below:
________

Answer: 5 x 1/3

Explanation:
Given that 5/3 or 5 third-size parts.
Each third-size part of the given fraction can be shown by the unit fraction 1/3.
You can use unit fractions to show 5/6
5/3 = 5 x 1/3.

List the next four multiples of the unit fraction

Question 4.
\(\frac{1}{2}\),
Type below:
________

Answer: 2/2, 3/2, 4/2, 5/2

Explanation:
1 x 1/2 = 1/2.
2 x 1/2 = 2/2.
3 x 1/2 = 3/2.
4 x 1/2 = 4/2.
5 x 1/2 = 5/2.
The next four multiples of 1/2 are 2/2, 3/2, 4/2, 5/2.

Question 5.
\(\frac{1}{6}\),
Type below:
________

Answer: 2/6, 3/6, 4/6, 5/6,6/6.

Explanation:
1 x 1/6 = 1/6.
2 x 1/6 = 2/6.
3 x 1/6 = 3/6.
4 x 1/6 = 4/6.
5 x 1/6 = 5/6.
6 x 1/6 = 6/6.
The next four multiples of 1/6 are 2/6, 3/6, 4/6, 5/6,6/6.

Lesson 8.2

List the next four multiples of the fraction.

Question 6.
\(\frac{3}{10}\),
Type below:
________

Answer: 6/10, 9/10, 12/10, 15/10

Explanation:
1 × 3/10 = 3/10
2 × 3/10 = 6/10
3 × 3/10 = 9/10
4 × 3/10 = 12/10
5 × 3/10 = 15/10

Question 7.
\(\frac{7}{12}\),
Type below:
________

Answer: 7/12, 14/12, 21/12, 28/12, 35/12

Explanation:
1 × 7/12 = 7/12
2 × 7/12 = 14/12
3 × 7/12 = 21/12
4 × 7/12 = 28/12
5 × 7/12 = 35/12

Write the product as the product of a whole number and a unit fraction.

Question 8.

2 × \(\frac{3}{6}\) =
Type below:
________

Answer:
1 group of \(\frac{3}{6}\) is \(\frac{3}{6}\)
2 groups of \(\frac{3}{6}\) is \(\frac{6}{6}\)
2 × \(\frac{3}{6}\) = \(\frac{6}{6}\)

Question 9.

3 × \(\frac{2}{8}\) =
Type below:
________

Explanation:
1 group of \(\frac{2}{8}\) is \(\frac{2}{8}\)
2 group of \(\frac{2}{8}\) is \(\frac{4}{8}\)
3 group of \(\frac{2}{8}\) is \(\frac{6}{8}\)
3 × \(\frac{2}{8}\) = \(\frac{6}{8}\)

Common Core – Multiply Fractions by Whole Numbers – Page No. 168

Lesson 8.3

Multiply.

Question 1.
3 × \(\frac{7}{10}\) =
\(\frac{□}{□}\)

Answer: \(\frac{21}{10}\)

Explanation:
Multiply 7 and 3
3 × 7 = 21
3 × \(\frac{7}{10}\) = \(\frac{21}{10}\)

Question 2.
5 × \(\frac{4}{8}\) =
\(\frac{□}{□}\)

Answer: 20/8

Explanation:
Multiply 5 and 4
5 × 4 = 20
5 × \(\frac{4}{8}\) = \(\frac{20}{8}\)

Question 3.
4 × \(\frac{6}{12}\) =
\(\frac{□}{□}\)

Answer: 24/12

Explanation:
Multiply 4 and 6
4 × 6 = 24
4 × \(\frac{6}{12}\) = \(\frac{24}{12}\)

Question 4.
2 × \(\frac{3}{4}\) =
\(\frac{□}{□}\)

Answer: 6/4

Explanation:
Multiply 2 and 3
2 × 3 = 6
2 × \(\frac{3}{4}\) = \(\frac{6}{4}\)

Question 5.
6 × \(\frac{3}{5}\) =
\(\frac{□}{□}\)

Answer: 18/5

Explanation:
Multiply 6 and 3
6 × 3 =18
6 × \(\frac{3}{5}\) = \(\frac{18}{5}\)

Question 6.
7 × \(\frac{2}{10}\) =
\(\frac{□}{□}\)

Answer: 14/10

Explanation:
Multiply 7 and 2.
7 × 2 =14
7 × \(\frac{2}{10}\) = \(\frac{14}{10}\)

Lesson 8.4

Multiply. Write the product as a mixed number.

Question 7.
4 × \(\frac{8}{10}\) =
_____ \(\frac{□}{□}\)

Answer: 3 2/10

Explanation:
Given,
4 × \(\frac{8}{10}\)
First multiply 4 and 8
4 × 8 = 32
4 × \(\frac{8}{10}\) = 32/10
Now convert from improper fraction to the mixed fraction.
32/10 = 3 \(\frac{2}{10}\)

Question 8.
3 × \(\frac{5}{6}\) =
_____ \(\frac{□}{□}\)

Answer: 2 3/6

Explanation:
Given,
3 × \(\frac{5}{6}\)
First multiply 3 and 5.
3 × 5 =15
3 × \(\frac{5}{6}\) = 15/6
Now convert from improper fraction to the mixed fraction.
15/6 = 2 3/6

Question 9.
2 × 3 \(\frac{1}{3}\) =
_____ \(\frac{□}{□}\)

Answer: 6 2/3

Explanation:
Given,
2 × 3 \(\frac{1}{3}\)
3 \(\frac{1}{3}\) = 10/3
2 × 10/3 = 20/3
Now convert from improper fraction to the mixed fraction.
20/3 = 6 2/3

Question 10.
4 × 2 \(\frac{2}{5}\) =
_____ \(\frac{□}{□}\)

Answer: 9 3/5

Explanation:
Given,
4 × 2 \(\frac{2}{5}\)
2 \(\frac{2}{5}\) = 4/5
4 × 12/5 = 48/5
Now convert from improper fraction to the mixed fraction.
48/5 = 9 3/5

Question 11.
5 × 1 \(\frac{7}{8}\) =
_____ \(\frac{□}{□}\)

Answer: 9 3/8

Explanation:
Given,
5 × 1 \(\frac{7}{8}\)
5 × 15/5 = 75/5
Now convert from improper fraction to the mixed fraction.
75/5 = 9 3/8

Question 12.
3 × 3 \(\frac{3}{4}\) =
_____ \(\frac{□}{□}\)

Answer: 11 1/4

Explanation:
Given,
3 × 3 \(\frac{3}{4}\)
3 × 15/4 = 45/4
Now convert from improper fraction to the mixed fraction.
45/4 = 11 1/4

Lesson 8.5

Question 13.
A shrub in Pam’s back yard is about 1 \(\frac{3}{8}\) feet tall. A small tree in her back yard is 7 times as tall as the shrub. About how tall is the tree?
_____ \(\frac{□}{□}\) feet

Answer: 9 5/2 feet.
Explanation:
Given,
A shrub in Pam’s back yard is about 1 \(\frac{3}{8}\) feet tall.
A small tree in her back yard is 7 times as tall as the shrub.
9.625 ft because 1 3/8 × 7 is equal to 9 5/2 feet
Therefore the tree is 9 5/2 feet.

Question 14.
A puppy weighs \(\frac{9}{10}\) pound. Its mother weighs 8 times as much. How much does the mother weigh?
_____ \(\frac{□}{□}\) pounds

Answer: 7 \(\frac{2}{10}\) pounds

Explanation:
Given,
A puppy weighs \(\frac{9}{10}\) pound. Its mother weighs 8 times as much.
\(\frac{9}{10}\) × 8 = 72/10
Convert from improper fraction to the mixed fraction.
72/10 = 7 \(\frac{2}{10}\) pounds
Thus the mother weigh 7 \(\frac{2}{10}\) pounds.

Conclusion:

Here the provided HMH Go Math Solution Key for Grade 4 Homework Practice FL Chapter 8 Multiply Fractions by Whole Numbers will increase your subject knowledge & get good scores in the exams. By understanding the difficulty of fractions, it can be easy to grasp the logic and tricks to solve the covered number of questions from Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers.

Are you looking everywhere to learn about Go Math Grade 3 Answer Key Chapter 6 Understand Division? This Answer Key includes topics like related multiplication and division facts, repeated subtraction, number of equal groups, and so on. Those who are preparing for the Grade 3 Ch 6 will find the HMH Go Math Grade 3 Answer Key Chapter 6 Understand Division extremely helpful. You can identify your knowledge gap by solving the Questions from 3rd Grade Go Math Answer Key Chapter 6 Understand Division.

Go Math Grade 3 Answer Key Chapter 6 Understand Division

Before you begin your preparation learn the topics included in Grade 3 Go Math Answer Key Chapter Understand Division. You can always look up to Go Math Grade 3 Chapter 6 Key as a reference to clear all your queries. Practice the problems in 3rd Grade Go Math Answer Key Ch 6 Understand Division and understand the concepts easily.

Lesson 1: Problem Solving • Model Division

• Model Division Page No 305
• Model Division Page No 306

Lesson 2: Size of Equal Groups

• Size of Equal Groups Page No 311
• Size of Equal Groups Page No 312

Lesson 3: Number of Equal Groups

• Number of Equal Groups Page No 317
• Number of Equal Groups Page No 318

Lesson 4: Model with Bar Models

• Model with Bar Models Page No 323
• Model with Bar Models Page No 324

Lesson 5: Algebra • Relate Subtraction and Division

• Relate Subtraction and Division Page No 329
• Relate Subtraction and Division Page No 330

Mid-Chapter Checkpoint

• Mid-Chapter Checkpoint Page No 331
• Mid-Chapter Checkpoint Page No 332

Lesson 6: Investigate • Model with Arrays

• Model with Arrays Page No 337
• Model with Arrays Page No 338

Lesson 7: Algebra • Relate Multiplication and Division

• Relate Multiplication and Division Page No 343
• Relate Multiplication and Division Page No 344

Lesson 8: Algebra • Write Related Facts

• Write Related Facts Page No 349
• Write Related Facts Page No 350

Lesson 9: Algebra • Division Rules for 1 and 0

• Division Rules for 1 and 0 Page No 355
• Division Rules for 1 and 0 Page No 356

Chapter 6 Review/Test

• Review/Test Page No 361
• Review/Test Page No 362

Model Division Page No 305

Question 1.
Six customers at a toy store bought 18 jump ropes. Each customer bought the same number of jump ropes. How many jump ropes did each customer buy?
__________

Answer: 3 jump ropes

Explanation:

Given that there are Six customers at a toy store bought 18 jump ropes
Each customer bought the same number of jump ropes
To know the number of jump roses that each customer bought
You must place each jump ropes until all the jump ropes are used.
That means 18 jump ropes to all 6 customers
= 18 ÷ 6 = 3
Therefore each customer bought 3 jump ropes

Question 2.
Hiro has 36 pictures of his summer trip. He wants to put them in an album. Each page of the album holds 4 pictures. How many pages will Hiro need for his pictures?
__________

Answer: 9 pages

Explanation:

Hiro has 36 pictures of his summer trip. He wants to put them in an album
Each page of the album holds 4 pictures
Make it into the equal groups and put 4 pictures in each page
= 36 ÷ 4 = 9
Thus Hiro need 9 pages for his pictures

Question 3.
Katia has 42 crayons in a box. She buys a storage bin that has 6 sections. She puts the same number of crayons in each section. How many crayons does Katia put in each section of the storage bin?
__________

Answer: 7 crayons

Explanation:

Katia has 42 crayons in a box
She buys a storage bin that has 6 sections
Make 42 crayons as a group and place 1 crayon in each section. Then you get 7 crayons in each section
42 ÷ 6 = 42/6 = 7
Therefore 7 crayons do Katia put in each section of the storage bin

Question 4.
Ms. Taylor’s students give cards to each of the 3 class parent helpers. There are 24 cards. How many cards will each helper get if the students give an equal number of cards to each helper?
__________

Answer: 8 cards

Explanation:

Ms. Taylor’s students give cards to each of the 3 class parent helpers
Total number of cards = 24
Make 3 equal groups and place each card for 3 class parent helpers
You get 8 cards for each helper
24 ÷ 3 = 8

Question 5.
Jamie divides 20 baseball stickers equally among 5 of his friends. How many stickers does each friend get?
__________

Answer: 4 stickers

Explanation:

Jamie divides 20 baseball stickers equally among 5 of his friends
Give each baseball sticker to each friend and repeat the process until you finish all the stickers
So, each friend gets 4 baseball stickers.
20 ÷ 5 = 4 stickers

Model Division Page No 306

Question 1.
Maria buys 15 apples at the store and places them into bags. She puts 5 apples into each bag. How many bags does Maria use for all the apples?
Options:
a. 2
b. 3
c. 4
d. 10

Answer: 3

Explanation:

Maria buys 15 apples at the store and places them into bags
She puts 5 apples into each bag
That means each bag contains 5 apples
Now, Divide the apples into equal groups and place them in each bag
15 ÷ 5 = 3
Therefore Maria uses 3 bags to put 15 apples.

Question 2.
Tom’s neighbor is fixing a section of his walkway. He has 32 bricks that he is placing in 8 equal rows. How many bricks will Tom’s neighbor place in each row?
Options:
a. 3
b. 4
c. 5
d. 6

Answer: 4

Explanation:

Given: Tom’s neighbor is fixing a section of his walkway
He has 32 bricks that he is placing in 8 equal rows
Now place each brick in all 8 rows  equally and repeat until the bricks are over
32 ÷ 8 = 4
So, you get 4 bricks in each row
Thus the correct answer is option B

Question 3.
Find the unknown factor.
7 × _ = 56
Options:
a. 6
b. 7
c. 8
d. 9

Answer: 8

Explanation:

Let the unknown factor be x
7 × x = 56

So, the correct answer is option C

Question 4.
How many students practiced the piano more than 3 hours a week?

Options:
a. 2
b. 6
c. 8
d. 10

Answer: 6

Explanation:

3 students practiced the piano for 4 hours
2 students practiced the piano for 5 hours and
1 student practiced the piano for 6 hours
= 3 + 2 + 1 = 6
The above line plot shows that there are 6 students who practiced the piano for more than 3 hours

Question 5.
Count equal groups to find how many there are.

Options:
a. 3
b. 4
c. 12
d. 16

Answer: 12

Explanation:

The above figure shows that there are 4 circles and each circle is divided into 3 equal groups
So, multiply number of circles with equal groups
= 4 × 3 = 12
Thus the correct answer is option C

Question 6.
Which is another way to group the factors?
(3 × 2) × 5
Options:
a. (3 + 2) + 5
b. (3 × 2) + 5
c. 3 × (2 + 5)
d. 3 × (2 × 5)

Answer: 3 × (2 × 5)

Explanation:

The another way to group (3 × 2) × 5 is 3 × (2 × 5)
Because there is no change in the symbol and number
So, the correct answer is option D

Size of Equal Groups Page No 311

Use counters or draw a quick picture. Make equal groups. Complete the table.

Question 1.

Answer:

Explanation:

1. No. of counters = 15
Number of equal groups = 3
Place 1 counter to each group, you get 5 in each group

2. No. of counters = 21
Number of equal groups = 7
Place 1 counter to each group, you get 3 in each group

3. No. of counters = 28
Number of equal groups = 7
Place 1 counter to each group, you get 4 in each group

4. No. of counters = 32
Number of equal groups = 4
Place 1 counter to each group, you get 8 in each group

5. No. of counters = 9
Number of equal groups = 3
Place 1 counter to each group, you get 3 in each group

6. No. of counters = 18
Number of equal groups = 3
Place 1 counter to each group, you get 6 in each group

7. No. of counters = 20
Number of equal groups = 5
Place 1 counter to each group, you get 4 in each group

8. No. of counters = 16
Number of equal groups = 8
Place 1 counter to each group, you get 2 in each group

9. No. of counters = 35
Number of equal groups = 5
Place 1 counter to each group, you get 7 in each group

10. No. of counters = 24
Number of equal groups = 3
Place 1 counter to each group, you get 8 in each group

Question 11.
Alicia has 12 eggs that she will use to make 4 different cookie recipes. If each recipe calls for the same number of eggs, how many eggs will she use in each recipe?
__________

Answer: 3 eggs

Explanation:

Total number of eggs Alicia has = 12
she will use to make 4 different cookie recipes
Make 4 groups and place 12 eggs in each group
You get 3 eggs in each group
12/4 = 3 eggs

Question 12.
Brett picked 27 flowers from the garden. He plans to give an equal number of flowers to each of 3 people. How many flowers will each person get?
__________

Answer: 9 flowers

Explanation:

Given,
Brett picked 27 flowers from the garden
He plans to give an equal number of flowers to each of 3 people
Give each flower to 3 people until 27 flowers complete
So, Each person get 9 flowers
27 ÷ 3 = 9 flowers

Size of Equal Groups Page No 312

Question 1.
Ryan has 21 pencils. He wants to put the same number of pencils in each of 3 pencil holders. How many pencils will he put in each pencil holder?
Options:
a. 6
b. 7
c. 8
d. 9

Answer: 7

Explanation:

Ryan has 21 pencils
He wants to put the same number of pencils in each of 3 pencil holders
Split it into 3 groups and share each pencil to each group
You get 7 pencils for each of 3 groups
21/3 = 7
Thus the correct answer is option B

Question 2.
Corrine is setting out 24 plates on 6 tables for a dinner. She sets the same number of plates on each table. How many plates does Corrine set on each table?
Options:
a. 3
b. 4
c. 5
d. 6

Answer: 4

Explanation:

Given,
Corrine is setting out 24 plates on 6 tables for a dinner
She sets the same number of plates on each table
Make a group of 6 tables and place 1 plate for each group
You get 4 plates for each table
24/6 = 4 plates
So, the correct answer is Option B

Question 3.
Each table has 4 legs. How many legs do 4 tables have?
Options:
a. 1
b. 8
c. 16
d. 20

Answer: 16

Explanation:

Given that Each table has 4 legs
4 tables have x number of legs
x = 4 × 4 = 16
Therefore 4 tables have 16 legs

Question 4.
Tina has 3 stacks of 5 CDs on each of 3 shelves. How many CDs does she have in all?
Options:
a. 14
b. 30
c. 35
d. 45

Answer: 45

Given,
Tina has 3 stacks of 5 CDs on each of 3 shelves
How many CDs does she have in all = x
To know the number of CDs in all we have to multiply no. of stacks, no. of CDs on each of 3 shelves
x = 3 × 5 × 3 = 15 × 3 = 45
So, the answer is option D

Question 5.
What is the unknown factor?
7 × _= 35
Options:
a. 4
b. 5
c. 6
d. 7

Answer: 5

Explanation:

Let the unknown factor be x
7 × x = 35
x = 35/7 = 5
Therefore the correct answer is option B

Question 6.
Which of the following describes a pattern in the table?

Options:
a. Add 2.
b. Multiply by 2.
c. Multiply by 3.
d. Add 12.

Answer: Multiply by 3.

Explanation:

Add 3 yo-yos for each pack and multiply no. of pans by 3

Number of Equal Groups Page No 317

Draw counters on your MathBoard. Then circle equal groups. Complete the table.

Question 1.

Answer:

Explanation:

1. No. of counters = 24
Number in each group = 8
24/8 = 3
So, the number of equal groups = 3

2. No. of counters = 35
Number in each group = 7
35/7 = 5
So, the number of equal groups = 5

3. No. of counters = 30
Number in each group = 5
30/5 = 6
So, the number of equal groups = 6

4. No. of counters = 16
Number in each group = 4
16/4 = 4
So, the number of equal groups = 4

5. No. of counters = 12
Number in each group = 6
12/6 = 2
So, the number of equal groups = 2

6. No. of counters = 36
Number in each group = 9
36/9 = 4
So, the number of equal groups = 4

7. No. of counters = 18
Number in each group = 3
18/3 = 6
So, the number of equal groups = 6

8. No. of counters = 15
Number in each group = 5
15/5 = 3
So, the number of equal groups = 3

9. No. of counters = 28
Number in each group = 4
28/4 = 7
So, the number of equal groups = 7

10. No. of counters = 27
Number in each group = 3
27/3 = 9
So, the number of equal groups = 9

Question 11.
In his bookstore, Toby places 21 books on shelves, with 7 books on each shelf. How many shelves does Toby need?
__________

Answer: 3 shelves

Explanation:

Toby places 21 books on shelves, with 7 books on each shelf
No. of shelves does Toby need = x
x = 21/7 = 3
Thus Toby need 3 shelves

Question 12.
Mr. Holden has 32 quarters in stacks of 4 on his desk. How many stacks of quarters are on his desk?
__________

Answer: 8 stacks

Explanation:

Mr. Holden has 32 quarters in stacks of 4 on his desk
No. of stacks of quarters on his desk = y
y × 4 = 32
y = 32/4 = 8 stacks
No. of stacks of quarters on his desk = 8 stacks

Number of Equal Groups Page No 318

Question 1.
Ramon works at a clothing store. He puts 24 pairs of jeans into stacks of 8. How many stacks does Ramon make?
Options:
a. 5
b. 4
c. 3
d. 2

Answer: 3

Explanation:

Ramon puts 24 pairs of jeans into stacks of 8
Split the pair of jeans to 8 groups of the stack
You get 3 pair of jeans for each stack
24/8 = 3
Therefore the correct answer is option C

Question 2.
There are 36 people waiting in line for a hayride. Only 6 people can ride on each wagon. If each wagon is full, how many wagons are needed for all 36 people?
Options:
a. 5
b. 6
c. 7
d. 8

Answer: 6

Explanation:

There are 36 people waiting in line for a hayride.
Only 6 people can ride on each wagon
Split 36 people into 6 groups
That means 36/6 = 6 Wagons
So, the correct answer is option B

Question 3.
Which multiplication sentence does the array show?

Options:
a. 4 × 5 = 20
b. 4 × 6 = 24
c. 4 × 7 = 28
d. 4 × 8 = 32

Answer: 4 × 7 = 28

Explanation:

There are 4 rows and 7 columns
rows × columns = 4 × 7 = 28
Thus the answer is option C

Question 4.
Austin buys 4 boxes of nails for his project. There are 30 nails in each box. How many nails does Austin buy in all?
Options:
a. 12
b. 34
c. 70
d. 120

Answer: 120

Explanation:

Given,
Austin buys 4 boxes of nails for his project
There are 30 nails in each box
No. of nails does Austin buy in all = 30 + 30 + 30 + 30
4 × 30 = 120
So, the correct answer is option D

Question 5.
Which describes the number sentence?
8 + 0 + 8
Options:
a. odd + odd = odd
b. Identity Property of Addition
c. even + even = even
d. Commutative Property of Addition