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Unit 7 – Practice Problems

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UNIT 7 – PRACTICE PROBLEMS

1 – 3: Represent the following scenarios as ratios in the indicated ways. Then determine if the comparison is

part to part or part to whole.

1. In Kate’s yoga class, there were 15 women for every 4 men. Write the following ratios for this situation

using the given numbers and then write a simplified ratio. Include units in each of your answers.

Form Ratio of Women to Men Ratio of Men to Women

Fraction

Colon

“a to b” language

Are the ratios in the table a Part-Whole comparison or a Part-Part comparison? Explain.

2. Theo has 18 pairs of sneakers. Twelve pairs are for running and 6 pairs are for tennis. Write the

following ratios for this situation using the given numbers and then write a simplified ratio. Include

units in each of your answers.

Form Ratio of Running Sneakers to

Total Sneakers

Ratio of Tennis Sneakers to Total

Sneakers

Fraction

Colon

“a to b” language

Are the ratios in the table a Part-Whole comparison or a Part-Part comparison? Explain


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3. Fran’s drama club has 16 adult members and 12 high school members. Write the following ratios for

this situation using the given numbers and then write a simplified ratio. Include units in each of your

answers.

Form Ratio of Adult

Members to High

School Members

Ratio of High

School Members to

Adult Members

Ratio of Adult

Members to Total

Members

Ratio of High School

Members to Total

Members

Fraction

Colon

“a to b”

language

Are the ratios in the table a Part-Whole comparison or a Part-Part comparison? Explain

4 – 6: Represent the following scenarios as ratios in the indicated ways. Then use this information to answer

the corresponding questions.

4. Lucas sells vacuums. There are two types of vacuums for sale; deluxe and economy. He sells 2 deluxe

versions for every 6 economy versions.

Write the following ratios in fraction form. Include units in your answers.

Ratio of deluxe vacuums to economy vacuums

Ratio of economy vacuums to deluxe vacuums

Ratio of deluxe vacuums to both types of vacuums

Ratio of economy vacuums to both types of vacuums


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5. Lucas sold 120 vacuums this month. Use this information and the double number lines below to

represent this scenario. Then approximate how many deluxe vacuums he sold and how many economy

vacuums he sold.

a) Diagram for Deluxe Vacuums:

b) Symbolic Representation:

c) Approximate number of deluxe vacuums sold:

d) Corresponding Proportional Statement:

e) Diagram for Economy Vacuums:

f) Symbolic Representation:

g) Approximate number of economy vacuums sold:

h) Corresponding Proportional Statement:


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6. Fred and Barney like to collect marbles. Fred’s favorite color marble is blue. Barney’s favorite color

marble is green. They decide to make a trade. Fred will give Barney 2 green marbles for every 3 blue

marbles Barney gives Fred.

Write the following ratios in fraction form. Include units in your fractions.

a) The ratio of the trade of green marbles to blue marbles:

b) The ratio of the trade of blue marbles to green marbles:

c) Suppose Fred has 12 green marbles. How many blue marbles would Barney have to give Fred in

trade? Use this information and the double number lines below to represent this scenario and find the

result.

d) Symbolic Representation:

e) Number of blue marbles for 12 green marbles:

f) Corresponding Proportional Statement:


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g) Suppose Barney has 27 blue marbles. How many green marbles would Fred have to give Barney in

trade? Use this information and the double number lines below to represent this scenario and find the

result.

h) Symbolic Representation:

i) Number of green marbles for 27 blue marbles:

j) Corresponding Proportional Statement:

7 – 10: Represent the following scenarios as rates and unit rates in the indicated ways.

7. Meri ate 5 cookies for a total of 175 calories.

Rate in calories

per cookies

Unit rate in calories

per cookie

Rate in cookies

per calories

Unit rate in cookies

per calorie


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8. James went on a road trip. He traveled at a constant speed and drove 315 miles in 5 hours.

Rate in miles

per hours

Unit rate in miles

per hour

Rate in hours

per miles

Unit rate in hours

per mile

9. May bought a bottle of aspirin at the store. She bought 250 pills for $4.25.

Rate in pills

per dollars

Unit rate in pills

per dollar

Rate in dollars

per pills

Unit rate in dollars

per pill

10. Callie is buying detergent at the grocery store. A 150 ounce box costs $18.87. A 100 ounce box costs

$12.73.

a) Determine the following unit rates for the small 100 ounce box and large 150 ounce box. Write your

unit rates as decimals rounded to four decimal places.

Small Box

Unit rate in ounces

per dollar

Large Box

Unit rate in ounces

per dollar

Small Box


per ounce

Large Box


per ounce

Based on the information in the table above, complete the following statements.

b) The __________ box is a better buy because it costs ________ dollars per ounce.

c) The __________ box is a better buy because you get ________ ounces per dollar.


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11 – 13: Represent the following scenarios as unit rates in the indicated ways. Then use this information to

answer the corresponding questions.

11. Daniel can jog 8 miles in 2 hours.

a) Use this information to fill in the chart below. Use decimals when needed.

Hours 1 2 3 4 5 6

Miles

b) What is Daniel’s unit rate of speed in miles per hour? How can you determine this from the table?

c) Using the unit rate of miles per hour, how far will Daniel jog in 8 hours? Also write the

corresponding proportion.

d) Using the unit rate of miles per hour, how far will Daniel jog in 3.75 hours? Also write the


e) What is Daniel’s unit rate of hours per mile?

f) Using the unit rate of hours per mile, how long will it take Daniel to jog in 20 miles? Also write the


g) Using the unit rate of hours per mile, how long will it take Daniel to jog in 26.2 miles? Also write

the corresponding proportion.


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12. Samantha’s bathtub has a leaking faucet. She puts a bucket under the leak to catch the water so she can

measure the leak. Three hours later, Samantha checks the bucket and it has 4.5 gallons of water in it.

a) Use this information to complete the table below.

Hours 1 3 6 12 24

Gallons

b) What is leak’s unit rate of in gallons per hour? How can you determine this from the table?

c) Using the unit rate of gallons per hour, how much water will leak in 9 hours? Also write the


d) Using the unit rate of gallons per hour, how much water will leak in 13.5 hours? Also write the


e) What is leak’s unit rate in hours per gallon?

f) Using the unit rate of hours per gallon, how long will it take for the bucket to contain 3 gallons of

water? Also write the corresponding proportion.


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13. Last week your worked 16 hours and earned $192.

a) Use this information to complete the table below.

Hours 1 2 4 8 16 32

Dollars

b) What is your unit pay rate in dollars per hour? How can you determine this from the table?

c) Using your unit pay rate in dollars per hour, how much would you earn in 12 hours? Also write the


d) Using your unit pay rate in dollars per hour, how much would you earn in 33.5 hours? Also write

the corresponding proportion.

e) What is you unit pay rate in hours per dollar?

f) Using your unit pay rate in hours per dollar, how many hours will you need to work to earn $522?

Also write the corresponding proportion.

g) You need $165 to pay your electric bill. How many hours do you need to work to cover your

electric bill? Round up to the nearest hour.


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14. Verify that the following figures are similar by finding the indicated scale factor between each

corresponding pair of sides.

a) Complete the table by finding the indicated ratios to determine the scale factors between the figures.

Ratio of the shortest side of Figure B to the shortest side of Figure A

Ratio of the longest side of Figure B to the longest side of Figure A

Ratio of the medium side of Figure B to the medium side of Figure A

b) Figure B is _______ times as large as Figure A.

c) To scale Figure A to the size of Figure B, multiply the length of each side of Figure A

by the scale factor of ______.

d) Complete the table by finding the indicated ratios to determine the scale factors between the figures.

Ratio of the shortest side of Figure A to the shortest side of Figure B

Ratio of the longest side of Figure A to the longest side of Figure B

Ratio of the medium side of Figure A to the medium side of Figure B

e) Figure A is _______ times as large as Figure B.

f) To scale Figure B to the size of Figure A, multiply the length of each side of Figure B



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15. Use the following figures to answer the questions.

a) Find the scale factor from Figure A to Figure B and complete the sentence below.

To scale Figure A to the size of Figure B, multiply the length of each side of Figure A


b) Find the scale factor from Figure B to Figure A and complete the sentence below.

c) To scale Figure B to the size of Figure A, multiply the length of each side of Figure B


d) Use a scale factor to find the length of side a. Show your work.

e) Use a scale factor to find the length of side b. Show your work.


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16. Write each ratio as a fraction in simplest form.

a. 3 to 9 b. 4:12

c. 12 inches

24 inches d. 14 to 42

e. 16

42

17. Write each rate as a fractions in simplest form. Include units in your answer.

a. 30 miles in 4 hours b. 24 inches to 4 feet

c. 12 boys to 18 girls d. 18 cars to 32 bicycles

18. . Write the unit rate for each of the following. Round to two decimals.

a. 150 miles in 3 hours b. 24 minutes to 2 feet

c. $18.25 for 4 gallons d. $1.45 for 6 ounces

e. 74 pounds per 12 square inches


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19. If the scale on a map is 1 inch to 20 miles, what is the actual distance between two towns that are 3

inches apart on the map?

20. In November 2012 President Obama visited Phnom Penh, Cambodia as part of a summit of Asian

leaders. Traffic in the city came to almost a complete standstill with cars moving at a rate of 2 miles in 4

hours. At this rate, how long would it take to travel a distance of 3.5 miles?

21. Ryan works a part-time job mowing lawns and can easily mow 3 lawns in 5 hours. If he got very busy

one day and mowed 7 lawns, how long did it take him?

22. The director of a day care center can feed 7 children lunch for a week with 4 pounds of macaroni and

cheese. If she has 16 pounds of macaroni and cheese, how many children can she feed lunch for a week?

unit 7 practice problems - wordpress.com...2017/08/02 · unit 7 – practice problems 8 12....

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