UNIT 10 PRACTICE PROBLEMS

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1 UNIT 10 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 Fraction Ratio of Running Sneakers to Total Sneakers Ratio of Tennis Sneakers to Total Sneakers Colon a to b language Are the ratios in the table a Part-Whole comparison or a Part-Part comparison? Explain 1

2 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 2

3 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: 3

4 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: 4

5 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 blue marbles for 42 green 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 5

6 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 $ A 100 ounce box costs $ 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 Unit rate in dollars per ounce Large Box Unit rate in dollars 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. 6

7 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 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 corresponding proportion. 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 corresponding proportion. 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. 7

8 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 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 corresponding proportion. d) Using the unit rate of gallons per hour, how much water will leak in 13.5 hours? Also write the corresponding proportion. 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. 8

9 13. Last week your worked 16 hours and earned $192. a) Use this information to complete the table below. Hours 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 corresponding proportion. 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. 9

10 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 by the scale factor of. 10

11 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 by the scale factor of. 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 by the scale factor of. 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. 11

12 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 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 12

13 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? 13

UNIT 7 MULTIPLICATIVE AND PROPORTIONAL REASONING

UNIT 7 MULTIPLICATIVE AND PROPORTIONAL REASONING INTRODUCTION In this Unit, we will learn about the concepts of multiplicative and proportional reasoning. Some of the ideas will seem familiar such as ratio,