crystal - ms. wilson's math classes · a. crystal ran 10 kilometers in 64 minutes. crystal ran...

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1. In Brazil, about 20 acres of rainforest are destroyed each minute. At this rate, how much rainforest is destroyed per day? SOLUTION: At the rate of 20 acres per minute, there are 28,800 acres of rainforest in Brazil destroyed per day. 2. Lexi can paint 5 yards of fencing in one hour. At this rate, how many inches does she paint per minute? SOLUTION: At the rate of 5 yards per hour, Lexi can paint 3 inches per minute. Complete each conversion. Round to the nearest hundredth, if necessary. 3. 8 in. ≈ _ cm SOLUTION: Use 1 in. ≈ 2.54 cm. 4. 5 L ≈ _ gal SOLUTION: Use 1 L ≈ 0.264 gal. 5. 15 oz ≈ _ g SOLUTION: Use 1 oz ≈ 28.35 g. 6. 24 cm ≈ _ in. eSolutions Manual - Powered by Cognero Page 1 5-4 Converting Rates

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Page 1: Crystal - Ms. Wilson's Math Classes · a. Crystal ran 10 kilometers in 64 minutes. Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming

1. In Brazil, about 20 acres of rainforest are destroyed each minute. At this rate, how much rainforest is destroyed per day?

SOLUTION:  

At the rate of 20 acres per minute, there are 28,800 acres of rainforest in Brazil destroyed per day.

2. Lexi can paint 5 yards of fencing in one hour. At this rate, how many inches does she paint per minute?

SOLUTION:  

At the rate of 5 yards per hour, Lexi can paint 3 inches per minute.

Complete each conversion. Round to the nearest hundredth, if necessary.3. 8 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

4. 5 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

5. 15 oz ≈ _ g

SOLUTION:  Use 1 oz ≈ 28.35 g.

6. 24 cm ≈ _ in.

SOLUTION:  Use 1 cm ≈ 0.394 in.

7. 9 pt ≈ _ L

SOLUTION:  Use 1 pt ≈ 0.473 L.

8. 3 m ≈ _ ft

SOLUTION:  Use 1 m ≈ 3.279 ft.

9. An elephant can eat up to 440 pounds of vegetation every day. How many grams per minute is this? Round to the nearest hundredth.

SOLUTION:  

An elephant can eat about 138.72 grams of vegetation per minute.

10. A candy company can produce 4800 sour lemon candies per minute. How many candies can they produce each hour?

SOLUTION:  

The company can produce 288,000 candies each hour.

11. In a recent year, 51.9 billion aluminum cans were recycled. About how many cans per week is this?

SOLUTION:  

About 1 billion aluminum cans were recycled per week.

12. The average American student spends almost 1500 hours per year watching television. To the nearest hundredth, how many minutes per day is this?

SOLUTION:  

The average American student spends 246.58 minutes per day watching television.

13. A thrill ride at an amusement park travels 55 miles per hour. To the nearest hundredth, how many feet per second is this?

SOLUTION:  

The thrill ride travels about 80.67 feet per second.

Complete each conversion. Round to the nearest hundredth, if necessary.14. 4 L ≈ _ qt

SOLUTION:  Use 1 L ≈ 1.057 qt.

15. 16 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

16. 13 m ≈ _ ft

SOLUTION:  Use 1 ft ≈ 0.305 m.

17. 8 yd ≈ _ m

SOLUTION:  Use 1 yd ≈ 0.914 m.

18. 18 lb ≈ _ kg

SOLUTION:  Use 1 lb ≈ 0.454 kg.

19. 7 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

20. 1500 g ≈ _ oz

SOLUTION:  Use 1 oz ≈ 28.35 g.

21. 15 ft ≈ _ m

SOLUTION:  Use 1 ft ≈ 0.305 m.

22. 28 fl oz ≈ _ mL

SOLUTION:  Use 1 fl oz ≈ 29.574 mL.

23. The velocity of sound through wood at 0° Celsius is 1454 meters per second. How many miles is this per hour? Round to the nearest hundredth.

SOLUTION:  

The velocity of sound through wood is approximately 3250.68 miles per hour.

24. A certain car in Canada can travel 15 kilometers per 1 liter of gasoline. How many miles per gallon is this? Round to the nearest hundredth.

SOLUTION:  

The car can travel approximately 35.28 miles per gallon.

Complete each conversion. Round to the nearest hundredth, if necessary.25. 8 in. ≈ _ mm

SOLUTION:  Use 1 in. ≈ 2.54 cm and 1 cm = 10 mm.

26. 16 L ≈ _ c

SOLUTION:  Use 1 L ≈ 2.114 pt and 1 pt = 2 cups.

27. 2 km ≈ _ yd

SOLUTION:  Use 1 km = 1000 m and 1 m ≈ 1.094 yd.

28. 250 fl oz ≈ _ L

SOLUTION:  Use 1 fl oz ≈ 29.574 mL and 1000 mL = 1 L.

29. 2750 g ≈ _ lb

SOLUTION:  Use 1 g ≈ 0.035 oz and 16 oz = 1 lb.

30. 5 gal ≈ _ mL

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 L = 1000 mL.

31. Crystal’s times for each portion of a triathlon are shown in the table. Round to the nearest hundredth.

a. How many meters per second did she run? b. What was her speed in miles per hour for the aquabike portion (swimming and biking)?

SOLUTION:  a. Crystal ran 10 kilometers in 64 minutes.

Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming and biking was 1.5 + 40 or 41.5 kilometers. Her time for theseportions was 40 + 86 or 126 minutes.

Crystal’s speed for the aquabike portion was about 12.27 miles per hour.

Order each group of rates from least to greatest.32. 100 oz/min, 2500 g/min, 10 lb/min

SOLUTION:  

5.51 lb/min < 6.25 lb/min < 10 lb/min Ordered from least to greatest, the rates are 2500 g/min, 100 oz/min, and 10 lb/min.

100 oz/min

2500 g/min

10 lb/min

33. 500 m/h, 7 yd/min, 6 in./s

SOLUTION:  

4.20 in./s < 5.47 in./s < 6 in./s Ordered from least to greatest, the rates are 7 yd/min, 500 m/h, and 6 in./s.

500 m/h

7 yd/min

6 in./s

34. 32 mi/gal, 15 m/mL, 6600 yd/qt

SOLUTION:  

6600 yd/qt < 14,080 yd/qt < 15,524 yd/qt Ordered from least to greatest, the rates are 6600 yd/qt, 32 mi/gal, and 15 m/mL.

32 mi/gal

15 m/mL

6600 yd/qt

35. 500 kg/h, 5 oz/s, 18 lb/min

SOLUTION:  

4.8 oz/s < 4.90 oz/s < 5 oz/s Ordered from least to greatest, the rates are 18 lb/min, 500 kg/h, and 5 oz/s.

500 kg/h

5 oz/s

18 lb/min

36. The sprinkler system in the Willis Tower pumps up to 1500 gallons of water per minute. How many liters of water

can the system pump in  minute? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L.

Divide the rate by 4 to find the amount of water pumped in  minute.

The water system in the Sears Tower can pump 1419.38 liters of water in  minute.

37. The average American consumes 20 gallons of ice cream in one year. At this rate, how many liters of ice cream will50 Americans consume in one week? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 yr = 52 wk.

Multiply the rate by 50 to find how many liters 50 Americans consume.

So, 50 Americans consume about 72.79 liters of ice cream per week.

Replace each _ with <, >, or = to make a true sentence.38. 10 m _ 390 in.

SOLUTION:  Use 1 m ≈ 3.279 ft and 1 ft = 12 in.

39. 520 oz _ 15 kg

SOLUTION:  Use 1 oz ≈ 28.35 g and 1000 g = 1 kg.

40. 14 pt _ 6622 mL

SOLUTION:  Use 1 pt ≈ 0.473 L and 1 L = 1000 mL.

Financial Literacy Use dimensional analysis and the table below to make each conversion. Round to the nearest hundredth, if necessary.

41. 150 dollars to euros

SOLUTION:  

So, 150 dollars is equal to 118.5 euros.

42. 275 dollars to pounds

SOLUTION:  

So, 275 dollars is equal to 175.18 pounds.

43. 570 yuan to dollars

SOLUTION:  

So, 570 yuan is equal to 89.41 dollars.

44. 500 pesos to dollars

SOLUTION:  

So, 500 pesos is approximately equal to 37.19 dollars.

45. Model with Mathematics Write and solve a real-world problem in which dimensional analysis is used to convert square feet to square yards. Hint: 1 square yard = 9 square feet

SOLUTION:  Sample answer: Macha needs 120 square feet of carpeting for her bedroom. How many square yards does she need?

Maria needs square yards.

46. Be Precise Give two examples of different measurements that are equivalent to 10 centimeters per second.

SOLUTION:  Sample answers:

Two measurements equivalent to 10 centimeters per second are 600 centimeters per minute and 360 meters per hour.

47. WHICH ONE DOESN’T BELONG? Select the rate that does not have the same value as the other three. Explain your reasoning.

SOLUTION:  Convert each rate to miles per hour and compare the values.

The rate that does not belong is 500 ft/min. All of the other rates are equal to 60 mi/h.

60 mi/h

88 ft/sec

500 ft/min

1440 mi/day

48. Persevere with Problems A recipe for fruit punch uses the ingredients shown. About how many cups of each ingredient are needed? Round to the nearest tenth.

SOLUTION:  Use 1000 mL = 1L, 1 L ≈ 2.114 pt, and 1 pt = 2 cups.  Cranberry juice:

  Apple juice:

  Pineapple juice:

  Lemon juice:

  Club soda:

49. Identify Structure What property of multiplication allows you to multiply a rate by a conversion factor without changing its value? Explain.

SOLUTION:  

The Identity Property of Multiplication allows you to multiply a rate by a conversion factor without changing its value

because the conversion factor is equal to 1. For example, multiplying by  is the same as multiplying by 1 

because 12 inches equals 1 foot.

50. Building on the Essential Question Explain how you would convert 10 miles per hour to meters per second.

SOLUTION:  Sample answer: Use dimensional analysis.

So, 10 miles per hour is approximately equal to 4.47 meters per second.

51. A speed of 55 miles per hour is the same rate as which of the following?

 

A  34 kilometers per hourB  50 kilometers per hourC  88 kilometers per hourD  98 kilometers per hour

SOLUTION:  Use 1 mi ≈ 1.609 kilometers.

55 miles per hour is approximately equal to 88 kilometers per hour. Choice C is correct.

52. A piece of notebook paper measures  inches by 11 inches. Which of the following metric approximations is the 

same?

 

F  2 m by 2.8 mG  3 cm by 4 cmH  22 cm by 28 cmJ  30 m by 40 m

SOLUTION:  Use 1 in. ≈ 2.54 centimeters.

The approximate metric dimensions of a piece of notebook paper are 22 cm by 28 cm. Choice H is correct.

53. A car’s mileage is registered at 29,345.5 miles. The driver sees a sign that warns of road work in 1000 feet. What will be the car’s mileage when the road work begins?

 

A  29,345.7B  29,345.9C  29,356.2D  29,356.5

SOLUTION:  To find the car’s mileage when the road work begins, find the sum of the current mileage and the distance to the

road work, in miles.

29,345.5 + 0.2 = 29,345.7 When the road work begins, the mileage will be 29,345.7. Choice A is correct.

54. SHORT RESPONSE Convert 565 miles per hour to feet per second. Show the procedure you used.

SOLUTION:  Use dimensional analysis and the following conversion facts to convert 565 miles per hour to feet per second.1 mile = 5280 feet 1 hour = 60 min = 3600 seconds

 or 828.67 feet per second

Express each rate as a unit rate. Round to the nearest tenth or to the nearest cent, if necessary.55. $183 for 4 concert tickets

SOLUTION:  

The unit rate is $45.75 per ticket.

56. 100 feet in 14.5 seconds

SOLUTION:  

The unit rate is about 6.9 feet per second.

57. 254.1 miles on 10.5 gallons

SOLUTION:  

The unit rate is 24.2 miles per gallon.

58. 9 inches of snow in 12 hours

SOLUTION:  

Rounded to the nearest tenth, the unit rate is 0.8 inches per hour.

59. Financial Literacy Mrs. Gallagher wants to buy the package of soda that is less expensive per can. Which pack of sodas shown should she buy? Explain your reasoning.

SOLUTION:  

The 6-pack of soda costs about $0.37 per can. The 12-pack of soda costs about $0.35 per can. So, the 12-pack is less expensive.

Express each ratio as a fraction in simplest form.60. 12 cars out of 30 vehicles

SOLUTION:  

61. 5 cups to 5 quarts

SOLUTION:  Convert 5 quarts to cups. There are 4 cups in 1 quart.

62. 15 soccer balls out of 35 balls

SOLUTION:  

63. 8 pencils to 20 crayons

SOLUTION:  

Simplify each expression.64. (x – 3) + 2

SOLUTION:  

65. (8 • y) • (–4)

SOLUTION:  

66. 25 + (d –8)

SOLUTION:  

67. 9(5m)

SOLUTION:  

68. (x + 1) – 9

SOLUTION:  

69. 5(3 • r)

SOLUTION:  

70. Clive is making hamburgers for a cookout. How many -pound hamburgers can he make from  pounds of 

ground beef?

SOLUTION:  Words: The amount of ground beef needed for each hamburger multiplied by the number of hamburgers equals the total amount of ground beef. Variable: Let h = the number of hamburgers

Equation:

Clive can make 11 hamburgers.

Find each product or quotient.71. –12 • (–10)

SOLUTION:  The product of two integers with the same sign is positive. So, –12 • (–10) = 120.

72. –18 ÷ 3

SOLUTION:  The quotient of two integers with different signs is negative. So, –18 ÷ 3 = –6.

73. 9 • (–14)

SOLUTION:  The product of two integers with different signs is negative. So, 9 • (–14) = –126.

74. 54 ÷ (–6)

SOLUTION:  The quotient of two integers with different signs is negative. So, 54 ÷ (–6) = –9.

75. –14 • 2

SOLUTION:  The product of two integers with different signs is negative. So, –14 • 2 = –28.

76. –72 ÷ (–4)

SOLUTION:  The quotient of two integers with the same sign is positive. So, –72 ÷ (–4) = 18.

eSolutions Manual - Powered by Cognero Page 1

5-4 Converting Rates

Page 2: Crystal - Ms. Wilson's Math Classes · a. Crystal ran 10 kilometers in 64 minutes. Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming

1. In Brazil, about 20 acres of rainforest are destroyed each minute. At this rate, how much rainforest is destroyed per day?

SOLUTION:  

At the rate of 20 acres per minute, there are 28,800 acres of rainforest in Brazil destroyed per day.

2. Lexi can paint 5 yards of fencing in one hour. At this rate, how many inches does she paint per minute?

SOLUTION:  

At the rate of 5 yards per hour, Lexi can paint 3 inches per minute.

Complete each conversion. Round to the nearest hundredth, if necessary.3. 8 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

4. 5 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

5. 15 oz ≈ _ g

SOLUTION:  Use 1 oz ≈ 28.35 g.

6. 24 cm ≈ _ in.

SOLUTION:  Use 1 cm ≈ 0.394 in.

7. 9 pt ≈ _ L

SOLUTION:  Use 1 pt ≈ 0.473 L.

8. 3 m ≈ _ ft

SOLUTION:  Use 1 m ≈ 3.279 ft.

9. An elephant can eat up to 440 pounds of vegetation every day. How many grams per minute is this? Round to the nearest hundredth.

SOLUTION:  

An elephant can eat about 138.72 grams of vegetation per minute.

10. A candy company can produce 4800 sour lemon candies per minute. How many candies can they produce each hour?

SOLUTION:  

The company can produce 288,000 candies each hour.

11. In a recent year, 51.9 billion aluminum cans were recycled. About how many cans per week is this?

SOLUTION:  

About 1 billion aluminum cans were recycled per week.

12. The average American student spends almost 1500 hours per year watching television. To the nearest hundredth, how many minutes per day is this?

SOLUTION:  

The average American student spends 246.58 minutes per day watching television.

13. A thrill ride at an amusement park travels 55 miles per hour. To the nearest hundredth, how many feet per second is this?

SOLUTION:  

The thrill ride travels about 80.67 feet per second.

Complete each conversion. Round to the nearest hundredth, if necessary.14. 4 L ≈ _ qt

SOLUTION:  Use 1 L ≈ 1.057 qt.

15. 16 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

16. 13 m ≈ _ ft

SOLUTION:  Use 1 ft ≈ 0.305 m.

17. 8 yd ≈ _ m

SOLUTION:  Use 1 yd ≈ 0.914 m.

18. 18 lb ≈ _ kg

SOLUTION:  Use 1 lb ≈ 0.454 kg.

19. 7 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

20. 1500 g ≈ _ oz

SOLUTION:  Use 1 oz ≈ 28.35 g.

21. 15 ft ≈ _ m

SOLUTION:  Use 1 ft ≈ 0.305 m.

22. 28 fl oz ≈ _ mL

SOLUTION:  Use 1 fl oz ≈ 29.574 mL.

23. The velocity of sound through wood at 0° Celsius is 1454 meters per second. How many miles is this per hour? Round to the nearest hundredth.

SOLUTION:  

The velocity of sound through wood is approximately 3250.68 miles per hour.

24. A certain car in Canada can travel 15 kilometers per 1 liter of gasoline. How many miles per gallon is this? Round to the nearest hundredth.

SOLUTION:  

The car can travel approximately 35.28 miles per gallon.

Complete each conversion. Round to the nearest hundredth, if necessary.25. 8 in. ≈ _ mm

SOLUTION:  Use 1 in. ≈ 2.54 cm and 1 cm = 10 mm.

26. 16 L ≈ _ c

SOLUTION:  Use 1 L ≈ 2.114 pt and 1 pt = 2 cups.

27. 2 km ≈ _ yd

SOLUTION:  Use 1 km = 1000 m and 1 m ≈ 1.094 yd.

28. 250 fl oz ≈ _ L

SOLUTION:  Use 1 fl oz ≈ 29.574 mL and 1000 mL = 1 L.

29. 2750 g ≈ _ lb

SOLUTION:  Use 1 g ≈ 0.035 oz and 16 oz = 1 lb.

30. 5 gal ≈ _ mL

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 L = 1000 mL.

31. Crystal’s times for each portion of a triathlon are shown in the table. Round to the nearest hundredth.

a. How many meters per second did she run? b. What was her speed in miles per hour for the aquabike portion (swimming and biking)?

SOLUTION:  a. Crystal ran 10 kilometers in 64 minutes.

Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming and biking was 1.5 + 40 or 41.5 kilometers. Her time for theseportions was 40 + 86 or 126 minutes.

Crystal’s speed for the aquabike portion was about 12.27 miles per hour.

Order each group of rates from least to greatest.32. 100 oz/min, 2500 g/min, 10 lb/min

SOLUTION:  

5.51 lb/min < 6.25 lb/min < 10 lb/min Ordered from least to greatest, the rates are 2500 g/min, 100 oz/min, and 10 lb/min.

100 oz/min

2500 g/min

10 lb/min

33. 500 m/h, 7 yd/min, 6 in./s

SOLUTION:  

4.20 in./s < 5.47 in./s < 6 in./s Ordered from least to greatest, the rates are 7 yd/min, 500 m/h, and 6 in./s.

500 m/h

7 yd/min

6 in./s

34. 32 mi/gal, 15 m/mL, 6600 yd/qt

SOLUTION:  

6600 yd/qt < 14,080 yd/qt < 15,524 yd/qt Ordered from least to greatest, the rates are 6600 yd/qt, 32 mi/gal, and 15 m/mL.

32 mi/gal

15 m/mL

6600 yd/qt

35. 500 kg/h, 5 oz/s, 18 lb/min

SOLUTION:  

4.8 oz/s < 4.90 oz/s < 5 oz/s Ordered from least to greatest, the rates are 18 lb/min, 500 kg/h, and 5 oz/s.

500 kg/h

5 oz/s

18 lb/min

36. The sprinkler system in the Willis Tower pumps up to 1500 gallons of water per minute. How many liters of water

can the system pump in  minute? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L.

Divide the rate by 4 to find the amount of water pumped in  minute.

The water system in the Sears Tower can pump 1419.38 liters of water in  minute.

37. The average American consumes 20 gallons of ice cream in one year. At this rate, how many liters of ice cream will50 Americans consume in one week? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 yr = 52 wk.

Multiply the rate by 50 to find how many liters 50 Americans consume.

So, 50 Americans consume about 72.79 liters of ice cream per week.

Replace each _ with <, >, or = to make a true sentence.38. 10 m _ 390 in.

SOLUTION:  Use 1 m ≈ 3.279 ft and 1 ft = 12 in.

39. 520 oz _ 15 kg

SOLUTION:  Use 1 oz ≈ 28.35 g and 1000 g = 1 kg.

40. 14 pt _ 6622 mL

SOLUTION:  Use 1 pt ≈ 0.473 L and 1 L = 1000 mL.

Financial Literacy Use dimensional analysis and the table below to make each conversion. Round to the nearest hundredth, if necessary.

41. 150 dollars to euros

SOLUTION:  

So, 150 dollars is equal to 118.5 euros.

42. 275 dollars to pounds

SOLUTION:  

So, 275 dollars is equal to 175.18 pounds.

43. 570 yuan to dollars

SOLUTION:  

So, 570 yuan is equal to 89.41 dollars.

44. 500 pesos to dollars

SOLUTION:  

So, 500 pesos is approximately equal to 37.19 dollars.

45. Model with Mathematics Write and solve a real-world problem in which dimensional analysis is used to convert square feet to square yards. Hint: 1 square yard = 9 square feet

SOLUTION:  Sample answer: Macha needs 120 square feet of carpeting for her bedroom. How many square yards does she need?

Maria needs square yards.

46. Be Precise Give two examples of different measurements that are equivalent to 10 centimeters per second.

SOLUTION:  Sample answers:

Two measurements equivalent to 10 centimeters per second are 600 centimeters per minute and 360 meters per hour.

47. WHICH ONE DOESN’T BELONG? Select the rate that does not have the same value as the other three. Explain your reasoning.

SOLUTION:  Convert each rate to miles per hour and compare the values.

The rate that does not belong is 500 ft/min. All of the other rates are equal to 60 mi/h.

60 mi/h

88 ft/sec

500 ft/min

1440 mi/day

48. Persevere with Problems A recipe for fruit punch uses the ingredients shown. About how many cups of each ingredient are needed? Round to the nearest tenth.

SOLUTION:  Use 1000 mL = 1L, 1 L ≈ 2.114 pt, and 1 pt = 2 cups.  Cranberry juice:

  Apple juice:

  Pineapple juice:

  Lemon juice:

  Club soda:

49. Identify Structure What property of multiplication allows you to multiply a rate by a conversion factor without changing its value? Explain.

SOLUTION:  

The Identity Property of Multiplication allows you to multiply a rate by a conversion factor without changing its value

because the conversion factor is equal to 1. For example, multiplying by  is the same as multiplying by 1 

because 12 inches equals 1 foot.

50. Building on the Essential Question Explain how you would convert 10 miles per hour to meters per second.

SOLUTION:  Sample answer: Use dimensional analysis.

So, 10 miles per hour is approximately equal to 4.47 meters per second.

51. A speed of 55 miles per hour is the same rate as which of the following?

 

A  34 kilometers per hourB  50 kilometers per hourC  88 kilometers per hourD  98 kilometers per hour

SOLUTION:  Use 1 mi ≈ 1.609 kilometers.

55 miles per hour is approximately equal to 88 kilometers per hour. Choice C is correct.

52. A piece of notebook paper measures  inches by 11 inches. Which of the following metric approximations is the 

same?

 

F  2 m by 2.8 mG  3 cm by 4 cmH  22 cm by 28 cmJ  30 m by 40 m

SOLUTION:  Use 1 in. ≈ 2.54 centimeters.

The approximate metric dimensions of a piece of notebook paper are 22 cm by 28 cm. Choice H is correct.

53. A car’s mileage is registered at 29,345.5 miles. The driver sees a sign that warns of road work in 1000 feet. What will be the car’s mileage when the road work begins?

 

A  29,345.7B  29,345.9C  29,356.2D  29,356.5

SOLUTION:  To find the car’s mileage when the road work begins, find the sum of the current mileage and the distance to the

road work, in miles.

29,345.5 + 0.2 = 29,345.7 When the road work begins, the mileage will be 29,345.7. Choice A is correct.

54. SHORT RESPONSE Convert 565 miles per hour to feet per second. Show the procedure you used.

SOLUTION:  Use dimensional analysis and the following conversion facts to convert 565 miles per hour to feet per second.1 mile = 5280 feet 1 hour = 60 min = 3600 seconds

 or 828.67 feet per second

Express each rate as a unit rate. Round to the nearest tenth or to the nearest cent, if necessary.55. $183 for 4 concert tickets

SOLUTION:  

The unit rate is $45.75 per ticket.

56. 100 feet in 14.5 seconds

SOLUTION:  

The unit rate is about 6.9 feet per second.

57. 254.1 miles on 10.5 gallons

SOLUTION:  

The unit rate is 24.2 miles per gallon.

58. 9 inches of snow in 12 hours

SOLUTION:  

Rounded to the nearest tenth, the unit rate is 0.8 inches per hour.

59. Financial Literacy Mrs. Gallagher wants to buy the package of soda that is less expensive per can. Which pack of sodas shown should she buy? Explain your reasoning.

SOLUTION:  

The 6-pack of soda costs about $0.37 per can. The 12-pack of soda costs about $0.35 per can. So, the 12-pack is less expensive.

Express each ratio as a fraction in simplest form.60. 12 cars out of 30 vehicles

SOLUTION:  

61. 5 cups to 5 quarts

SOLUTION:  Convert 5 quarts to cups. There are 4 cups in 1 quart.

62. 15 soccer balls out of 35 balls

SOLUTION:  

63. 8 pencils to 20 crayons

SOLUTION:  

Simplify each expression.64. (x – 3) + 2

SOLUTION:  

65. (8 • y) • (–4)

SOLUTION:  

66. 25 + (d –8)

SOLUTION:  

67. 9(5m)

SOLUTION:  

68. (x + 1) – 9

SOLUTION:  

69. 5(3 • r)

SOLUTION:  

70. Clive is making hamburgers for a cookout. How many -pound hamburgers can he make from  pounds of 

ground beef?

SOLUTION:  Words: The amount of ground beef needed for each hamburger multiplied by the number of hamburgers equals the total amount of ground beef. Variable: Let h = the number of hamburgers

Equation:

Clive can make 11 hamburgers.

Find each product or quotient.71. –12 • (–10)

SOLUTION:  The product of two integers with the same sign is positive. So, –12 • (–10) = 120.

72. –18 ÷ 3

SOLUTION:  The quotient of two integers with different signs is negative. So, –18 ÷ 3 = –6.

73. 9 • (–14)

SOLUTION:  The product of two integers with different signs is negative. So, 9 • (–14) = –126.

74. 54 ÷ (–6)

SOLUTION:  The quotient of two integers with different signs is negative. So, 54 ÷ (–6) = –9.

75. –14 • 2

SOLUTION:  The product of two integers with different signs is negative. So, –14 • 2 = –28.

76. –72 ÷ (–4)

SOLUTION:  The quotient of two integers with the same sign is positive. So, –72 ÷ (–4) = 18.

eSolutions Manual - Powered by Cognero Page 2

5-4 Converting Rates

Page 3: Crystal - Ms. Wilson's Math Classes · a. Crystal ran 10 kilometers in 64 minutes. Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming

1. In Brazil, about 20 acres of rainforest are destroyed each minute. At this rate, how much rainforest is destroyed per day?

SOLUTION:  

At the rate of 20 acres per minute, there are 28,800 acres of rainforest in Brazil destroyed per day.

2. Lexi can paint 5 yards of fencing in one hour. At this rate, how many inches does she paint per minute?

SOLUTION:  

At the rate of 5 yards per hour, Lexi can paint 3 inches per minute.

Complete each conversion. Round to the nearest hundredth, if necessary.3. 8 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

4. 5 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

5. 15 oz ≈ _ g

SOLUTION:  Use 1 oz ≈ 28.35 g.

6. 24 cm ≈ _ in.

SOLUTION:  Use 1 cm ≈ 0.394 in.

7. 9 pt ≈ _ L

SOLUTION:  Use 1 pt ≈ 0.473 L.

8. 3 m ≈ _ ft

SOLUTION:  Use 1 m ≈ 3.279 ft.

9. An elephant can eat up to 440 pounds of vegetation every day. How many grams per minute is this? Round to the nearest hundredth.

SOLUTION:  

An elephant can eat about 138.72 grams of vegetation per minute.

10. A candy company can produce 4800 sour lemon candies per minute. How many candies can they produce each hour?

SOLUTION:  

The company can produce 288,000 candies each hour.

11. In a recent year, 51.9 billion aluminum cans were recycled. About how many cans per week is this?

SOLUTION:  

About 1 billion aluminum cans were recycled per week.

12. The average American student spends almost 1500 hours per year watching television. To the nearest hundredth, how many minutes per day is this?

SOLUTION:  

The average American student spends 246.58 minutes per day watching television.

13. A thrill ride at an amusement park travels 55 miles per hour. To the nearest hundredth, how many feet per second is this?

SOLUTION:  

The thrill ride travels about 80.67 feet per second.

Complete each conversion. Round to the nearest hundredth, if necessary.14. 4 L ≈ _ qt

SOLUTION:  Use 1 L ≈ 1.057 qt.

15. 16 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

16. 13 m ≈ _ ft

SOLUTION:  Use 1 ft ≈ 0.305 m.

17. 8 yd ≈ _ m

SOLUTION:  Use 1 yd ≈ 0.914 m.

18. 18 lb ≈ _ kg

SOLUTION:  Use 1 lb ≈ 0.454 kg.

19. 7 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

20. 1500 g ≈ _ oz

SOLUTION:  Use 1 oz ≈ 28.35 g.

21. 15 ft ≈ _ m

SOLUTION:  Use 1 ft ≈ 0.305 m.

22. 28 fl oz ≈ _ mL

SOLUTION:  Use 1 fl oz ≈ 29.574 mL.

23. The velocity of sound through wood at 0° Celsius is 1454 meters per second. How many miles is this per hour? Round to the nearest hundredth.

SOLUTION:  

The velocity of sound through wood is approximately 3250.68 miles per hour.

24. A certain car in Canada can travel 15 kilometers per 1 liter of gasoline. How many miles per gallon is this? Round to the nearest hundredth.

SOLUTION:  

The car can travel approximately 35.28 miles per gallon.

Complete each conversion. Round to the nearest hundredth, if necessary.25. 8 in. ≈ _ mm

SOLUTION:  Use 1 in. ≈ 2.54 cm and 1 cm = 10 mm.

26. 16 L ≈ _ c

SOLUTION:  Use 1 L ≈ 2.114 pt and 1 pt = 2 cups.

27. 2 km ≈ _ yd

SOLUTION:  Use 1 km = 1000 m and 1 m ≈ 1.094 yd.

28. 250 fl oz ≈ _ L

SOLUTION:  Use 1 fl oz ≈ 29.574 mL and 1000 mL = 1 L.

29. 2750 g ≈ _ lb

SOLUTION:  Use 1 g ≈ 0.035 oz and 16 oz = 1 lb.

30. 5 gal ≈ _ mL

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 L = 1000 mL.

31. Crystal’s times for each portion of a triathlon are shown in the table. Round to the nearest hundredth.

a. How many meters per second did she run? b. What was her speed in miles per hour for the aquabike portion (swimming and biking)?

SOLUTION:  a. Crystal ran 10 kilometers in 64 minutes.

Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming and biking was 1.5 + 40 or 41.5 kilometers. Her time for theseportions was 40 + 86 or 126 minutes.

Crystal’s speed for the aquabike portion was about 12.27 miles per hour.

Order each group of rates from least to greatest.32. 100 oz/min, 2500 g/min, 10 lb/min

SOLUTION:  

5.51 lb/min < 6.25 lb/min < 10 lb/min Ordered from least to greatest, the rates are 2500 g/min, 100 oz/min, and 10 lb/min.

100 oz/min

2500 g/min

10 lb/min

33. 500 m/h, 7 yd/min, 6 in./s

SOLUTION:  

4.20 in./s < 5.47 in./s < 6 in./s Ordered from least to greatest, the rates are 7 yd/min, 500 m/h, and 6 in./s.

500 m/h

7 yd/min

6 in./s

34. 32 mi/gal, 15 m/mL, 6600 yd/qt

SOLUTION:  

6600 yd/qt < 14,080 yd/qt < 15,524 yd/qt Ordered from least to greatest, the rates are 6600 yd/qt, 32 mi/gal, and 15 m/mL.

32 mi/gal

15 m/mL

6600 yd/qt

35. 500 kg/h, 5 oz/s, 18 lb/min

SOLUTION:  

4.8 oz/s < 4.90 oz/s < 5 oz/s Ordered from least to greatest, the rates are 18 lb/min, 500 kg/h, and 5 oz/s.

500 kg/h

5 oz/s

18 lb/min

36. The sprinkler system in the Willis Tower pumps up to 1500 gallons of water per minute. How many liters of water

can the system pump in  minute? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L.

Divide the rate by 4 to find the amount of water pumped in  minute.

The water system in the Sears Tower can pump 1419.38 liters of water in  minute.

37. The average American consumes 20 gallons of ice cream in one year. At this rate, how many liters of ice cream will50 Americans consume in one week? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 yr = 52 wk.

Multiply the rate by 50 to find how many liters 50 Americans consume.

So, 50 Americans consume about 72.79 liters of ice cream per week.

Replace each _ with <, >, or = to make a true sentence.38. 10 m _ 390 in.

SOLUTION:  Use 1 m ≈ 3.279 ft and 1 ft = 12 in.

39. 520 oz _ 15 kg

SOLUTION:  Use 1 oz ≈ 28.35 g and 1000 g = 1 kg.

40. 14 pt _ 6622 mL

SOLUTION:  Use 1 pt ≈ 0.473 L and 1 L = 1000 mL.

Financial Literacy Use dimensional analysis and the table below to make each conversion. Round to the nearest hundredth, if necessary.

41. 150 dollars to euros

SOLUTION:  

So, 150 dollars is equal to 118.5 euros.

42. 275 dollars to pounds

SOLUTION:  

So, 275 dollars is equal to 175.18 pounds.

43. 570 yuan to dollars

SOLUTION:  

So, 570 yuan is equal to 89.41 dollars.

44. 500 pesos to dollars

SOLUTION:  

So, 500 pesos is approximately equal to 37.19 dollars.

45. Model with Mathematics Write and solve a real-world problem in which dimensional analysis is used to convert square feet to square yards. Hint: 1 square yard = 9 square feet

SOLUTION:  Sample answer: Macha needs 120 square feet of carpeting for her bedroom. How many square yards does she need?

Maria needs square yards.

46. Be Precise Give two examples of different measurements that are equivalent to 10 centimeters per second.

SOLUTION:  Sample answers:

Two measurements equivalent to 10 centimeters per second are 600 centimeters per minute and 360 meters per hour.

47. WHICH ONE DOESN’T BELONG? Select the rate that does not have the same value as the other three. Explain your reasoning.

SOLUTION:  Convert each rate to miles per hour and compare the values.

The rate that does not belong is 500 ft/min. All of the other rates are equal to 60 mi/h.

60 mi/h

88 ft/sec

500 ft/min

1440 mi/day

48. Persevere with Problems A recipe for fruit punch uses the ingredients shown. About how many cups of each ingredient are needed? Round to the nearest tenth.

SOLUTION:  Use 1000 mL = 1L, 1 L ≈ 2.114 pt, and 1 pt = 2 cups.  Cranberry juice:

  Apple juice:

  Pineapple juice:

  Lemon juice:

  Club soda:

49. Identify Structure What property of multiplication allows you to multiply a rate by a conversion factor without changing its value? Explain.

SOLUTION:  

The Identity Property of Multiplication allows you to multiply a rate by a conversion factor without changing its value

because the conversion factor is equal to 1. For example, multiplying by  is the same as multiplying by 1 

because 12 inches equals 1 foot.

50. Building on the Essential Question Explain how you would convert 10 miles per hour to meters per second.

SOLUTION:  Sample answer: Use dimensional analysis.

So, 10 miles per hour is approximately equal to 4.47 meters per second.

51. A speed of 55 miles per hour is the same rate as which of the following?

 

A  34 kilometers per hourB  50 kilometers per hourC  88 kilometers per hourD  98 kilometers per hour

SOLUTION:  Use 1 mi ≈ 1.609 kilometers.

55 miles per hour is approximately equal to 88 kilometers per hour. Choice C is correct.

52. A piece of notebook paper measures  inches by 11 inches. Which of the following metric approximations is the 

same?

 

F  2 m by 2.8 mG  3 cm by 4 cmH  22 cm by 28 cmJ  30 m by 40 m

SOLUTION:  Use 1 in. ≈ 2.54 centimeters.

The approximate metric dimensions of a piece of notebook paper are 22 cm by 28 cm. Choice H is correct.

53. A car’s mileage is registered at 29,345.5 miles. The driver sees a sign that warns of road work in 1000 feet. What will be the car’s mileage when the road work begins?

 

A  29,345.7B  29,345.9C  29,356.2D  29,356.5

SOLUTION:  To find the car’s mileage when the road work begins, find the sum of the current mileage and the distance to the

road work, in miles.

29,345.5 + 0.2 = 29,345.7 When the road work begins, the mileage will be 29,345.7. Choice A is correct.

54. SHORT RESPONSE Convert 565 miles per hour to feet per second. Show the procedure you used.

SOLUTION:  Use dimensional analysis and the following conversion facts to convert 565 miles per hour to feet per second.1 mile = 5280 feet 1 hour = 60 min = 3600 seconds

 or 828.67 feet per second

Express each rate as a unit rate. Round to the nearest tenth or to the nearest cent, if necessary.55. $183 for 4 concert tickets

SOLUTION:  

The unit rate is $45.75 per ticket.

56. 100 feet in 14.5 seconds

SOLUTION:  

The unit rate is about 6.9 feet per second.

57. 254.1 miles on 10.5 gallons

SOLUTION:  

The unit rate is 24.2 miles per gallon.

58. 9 inches of snow in 12 hours

SOLUTION:  

Rounded to the nearest tenth, the unit rate is 0.8 inches per hour.

59. Financial Literacy Mrs. Gallagher wants to buy the package of soda that is less expensive per can. Which pack of sodas shown should she buy? Explain your reasoning.

SOLUTION:  

The 6-pack of soda costs about $0.37 per can. The 12-pack of soda costs about $0.35 per can. So, the 12-pack is less expensive.

Express each ratio as a fraction in simplest form.60. 12 cars out of 30 vehicles

SOLUTION:  

61. 5 cups to 5 quarts

SOLUTION:  Convert 5 quarts to cups. There are 4 cups in 1 quart.

62. 15 soccer balls out of 35 balls

SOLUTION:  

63. 8 pencils to 20 crayons

SOLUTION:  

Simplify each expression.64. (x – 3) + 2

SOLUTION:  

65. (8 • y) • (–4)

SOLUTION:  

66. 25 + (d –8)

SOLUTION:  

67. 9(5m)

SOLUTION:  

68. (x + 1) – 9

SOLUTION:  

69. 5(3 • r)

SOLUTION:  

70. Clive is making hamburgers for a cookout. How many -pound hamburgers can he make from  pounds of 

ground beef?

SOLUTION:  Words: The amount of ground beef needed for each hamburger multiplied by the number of hamburgers equals the total amount of ground beef. Variable: Let h = the number of hamburgers

Equation:

Clive can make 11 hamburgers.

Find each product or quotient.71. –12 • (–10)

SOLUTION:  The product of two integers with the same sign is positive. So, –12 • (–10) = 120.

72. –18 ÷ 3

SOLUTION:  The quotient of two integers with different signs is negative. So, –18 ÷ 3 = –6.

73. 9 • (–14)

SOLUTION:  The product of two integers with different signs is negative. So, 9 • (–14) = –126.

74. 54 ÷ (–6)

SOLUTION:  The quotient of two integers with different signs is negative. So, 54 ÷ (–6) = –9.

75. –14 • 2

SOLUTION:  The product of two integers with different signs is negative. So, –14 • 2 = –28.

76. –72 ÷ (–4)

SOLUTION:  The quotient of two integers with the same sign is positive. So, –72 ÷ (–4) = 18.

eSolutions Manual - Powered by Cognero Page 3

5-4 Converting Rates

Page 4: Crystal - Ms. Wilson's Math Classes · a. Crystal ran 10 kilometers in 64 minutes. Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming

1. In Brazil, about 20 acres of rainforest are destroyed each minute. At this rate, how much rainforest is destroyed per day?

SOLUTION:  

At the rate of 20 acres per minute, there are 28,800 acres of rainforest in Brazil destroyed per day.

2. Lexi can paint 5 yards of fencing in one hour. At this rate, how many inches does she paint per minute?

SOLUTION:  

At the rate of 5 yards per hour, Lexi can paint 3 inches per minute.

Complete each conversion. Round to the nearest hundredth, if necessary.3. 8 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

4. 5 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

5. 15 oz ≈ _ g

SOLUTION:  Use 1 oz ≈ 28.35 g.

6. 24 cm ≈ _ in.

SOLUTION:  Use 1 cm ≈ 0.394 in.

7. 9 pt ≈ _ L

SOLUTION:  Use 1 pt ≈ 0.473 L.

8. 3 m ≈ _ ft

SOLUTION:  Use 1 m ≈ 3.279 ft.

9. An elephant can eat up to 440 pounds of vegetation every day. How many grams per minute is this? Round to the nearest hundredth.

SOLUTION:  

An elephant can eat about 138.72 grams of vegetation per minute.

10. A candy company can produce 4800 sour lemon candies per minute. How many candies can they produce each hour?

SOLUTION:  

The company can produce 288,000 candies each hour.

11. In a recent year, 51.9 billion aluminum cans were recycled. About how many cans per week is this?

SOLUTION:  

About 1 billion aluminum cans were recycled per week.

12. The average American student spends almost 1500 hours per year watching television. To the nearest hundredth, how many minutes per day is this?

SOLUTION:  

The average American student spends 246.58 minutes per day watching television.

13. A thrill ride at an amusement park travels 55 miles per hour. To the nearest hundredth, how many feet per second is this?

SOLUTION:  

The thrill ride travels about 80.67 feet per second.

Complete each conversion. Round to the nearest hundredth, if necessary.14. 4 L ≈ _ qt

SOLUTION:  Use 1 L ≈ 1.057 qt.

15. 16 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

16. 13 m ≈ _ ft

SOLUTION:  Use 1 ft ≈ 0.305 m.

17. 8 yd ≈ _ m

SOLUTION:  Use 1 yd ≈ 0.914 m.

18. 18 lb ≈ _ kg

SOLUTION:  Use 1 lb ≈ 0.454 kg.

19. 7 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

20. 1500 g ≈ _ oz

SOLUTION:  Use 1 oz ≈ 28.35 g.

21. 15 ft ≈ _ m

SOLUTION:  Use 1 ft ≈ 0.305 m.

22. 28 fl oz ≈ _ mL

SOLUTION:  Use 1 fl oz ≈ 29.574 mL.

23. The velocity of sound through wood at 0° Celsius is 1454 meters per second. How many miles is this per hour? Round to the nearest hundredth.

SOLUTION:  

The velocity of sound through wood is approximately 3250.68 miles per hour.

24. A certain car in Canada can travel 15 kilometers per 1 liter of gasoline. How many miles per gallon is this? Round to the nearest hundredth.

SOLUTION:  

The car can travel approximately 35.28 miles per gallon.

Complete each conversion. Round to the nearest hundredth, if necessary.25. 8 in. ≈ _ mm

SOLUTION:  Use 1 in. ≈ 2.54 cm and 1 cm = 10 mm.

26. 16 L ≈ _ c

SOLUTION:  Use 1 L ≈ 2.114 pt and 1 pt = 2 cups.

27. 2 km ≈ _ yd

SOLUTION:  Use 1 km = 1000 m and 1 m ≈ 1.094 yd.

28. 250 fl oz ≈ _ L

SOLUTION:  Use 1 fl oz ≈ 29.574 mL and 1000 mL = 1 L.

29. 2750 g ≈ _ lb

SOLUTION:  Use 1 g ≈ 0.035 oz and 16 oz = 1 lb.

30. 5 gal ≈ _ mL

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 L = 1000 mL.

31. Crystal’s times for each portion of a triathlon are shown in the table. Round to the nearest hundredth.

a. How many meters per second did she run? b. What was her speed in miles per hour for the aquabike portion (swimming and biking)?

SOLUTION:  a. Crystal ran 10 kilometers in 64 minutes.

Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming and biking was 1.5 + 40 or 41.5 kilometers. Her time for theseportions was 40 + 86 or 126 minutes.

Crystal’s speed for the aquabike portion was about 12.27 miles per hour.

Order each group of rates from least to greatest.32. 100 oz/min, 2500 g/min, 10 lb/min

SOLUTION:  

5.51 lb/min < 6.25 lb/min < 10 lb/min Ordered from least to greatest, the rates are 2500 g/min, 100 oz/min, and 10 lb/min.

100 oz/min

2500 g/min

10 lb/min

33. 500 m/h, 7 yd/min, 6 in./s

SOLUTION:  

4.20 in./s < 5.47 in./s < 6 in./s Ordered from least to greatest, the rates are 7 yd/min, 500 m/h, and 6 in./s.

500 m/h

7 yd/min

6 in./s

34. 32 mi/gal, 15 m/mL, 6600 yd/qt

SOLUTION:  

6600 yd/qt < 14,080 yd/qt < 15,524 yd/qt Ordered from least to greatest, the rates are 6600 yd/qt, 32 mi/gal, and 15 m/mL.

32 mi/gal

15 m/mL

6600 yd/qt

35. 500 kg/h, 5 oz/s, 18 lb/min

SOLUTION:  

4.8 oz/s < 4.90 oz/s < 5 oz/s Ordered from least to greatest, the rates are 18 lb/min, 500 kg/h, and 5 oz/s.

500 kg/h

5 oz/s

18 lb/min

36. The sprinkler system in the Willis Tower pumps up to 1500 gallons of water per minute. How many liters of water

can the system pump in  minute? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L.

Divide the rate by 4 to find the amount of water pumped in  minute.

The water system in the Sears Tower can pump 1419.38 liters of water in  minute.

37. The average American consumes 20 gallons of ice cream in one year. At this rate, how many liters of ice cream will50 Americans consume in one week? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 yr = 52 wk.

Multiply the rate by 50 to find how many liters 50 Americans consume.

So, 50 Americans consume about 72.79 liters of ice cream per week.

Replace each _ with <, >, or = to make a true sentence.38. 10 m _ 390 in.

SOLUTION:  Use 1 m ≈ 3.279 ft and 1 ft = 12 in.

39. 520 oz _ 15 kg

SOLUTION:  Use 1 oz ≈ 28.35 g and 1000 g = 1 kg.

40. 14 pt _ 6622 mL

SOLUTION:  Use 1 pt ≈ 0.473 L and 1 L = 1000 mL.

Financial Literacy Use dimensional analysis and the table below to make each conversion. Round to the nearest hundredth, if necessary.

41. 150 dollars to euros

SOLUTION:  

So, 150 dollars is equal to 118.5 euros.

42. 275 dollars to pounds

SOLUTION:  

So, 275 dollars is equal to 175.18 pounds.

43. 570 yuan to dollars

SOLUTION:  

So, 570 yuan is equal to 89.41 dollars.

44. 500 pesos to dollars

SOLUTION:  

So, 500 pesos is approximately equal to 37.19 dollars.

45. Model with Mathematics Write and solve a real-world problem in which dimensional analysis is used to convert square feet to square yards. Hint: 1 square yard = 9 square feet

SOLUTION:  Sample answer: Macha needs 120 square feet of carpeting for her bedroom. How many square yards does she need?

Maria needs square yards.

46. Be Precise Give two examples of different measurements that are equivalent to 10 centimeters per second.

SOLUTION:  Sample answers:

Two measurements equivalent to 10 centimeters per second are 600 centimeters per minute and 360 meters per hour.

47. WHICH ONE DOESN’T BELONG? Select the rate that does not have the same value as the other three. Explain your reasoning.

SOLUTION:  Convert each rate to miles per hour and compare the values.

The rate that does not belong is 500 ft/min. All of the other rates are equal to 60 mi/h.

60 mi/h

88 ft/sec

500 ft/min

1440 mi/day

48. Persevere with Problems A recipe for fruit punch uses the ingredients shown. About how many cups of each ingredient are needed? Round to the nearest tenth.

SOLUTION:  Use 1000 mL = 1L, 1 L ≈ 2.114 pt, and 1 pt = 2 cups.  Cranberry juice:

  Apple juice:

  Pineapple juice:

  Lemon juice:

  Club soda:

49. Identify Structure What property of multiplication allows you to multiply a rate by a conversion factor without changing its value? Explain.

SOLUTION:  

The Identity Property of Multiplication allows you to multiply a rate by a conversion factor without changing its value

because the conversion factor is equal to 1. For example, multiplying by  is the same as multiplying by 1 

because 12 inches equals 1 foot.

50. Building on the Essential Question Explain how you would convert 10 miles per hour to meters per second.

SOLUTION:  Sample answer: Use dimensional analysis.

So, 10 miles per hour is approximately equal to 4.47 meters per second.

51. A speed of 55 miles per hour is the same rate as which of the following?

 

A  34 kilometers per hourB  50 kilometers per hourC  88 kilometers per hourD  98 kilometers per hour

SOLUTION:  Use 1 mi ≈ 1.609 kilometers.

55 miles per hour is approximately equal to 88 kilometers per hour. Choice C is correct.

52. A piece of notebook paper measures  inches by 11 inches. Which of the following metric approximations is the 

same?

 

F  2 m by 2.8 mG  3 cm by 4 cmH  22 cm by 28 cmJ  30 m by 40 m

SOLUTION:  Use 1 in. ≈ 2.54 centimeters.

The approximate metric dimensions of a piece of notebook paper are 22 cm by 28 cm. Choice H is correct.

53. A car’s mileage is registered at 29,345.5 miles. The driver sees a sign that warns of road work in 1000 feet. What will be the car’s mileage when the road work begins?

 

A  29,345.7B  29,345.9C  29,356.2D  29,356.5

SOLUTION:  To find the car’s mileage when the road work begins, find the sum of the current mileage and the distance to the

road work, in miles.

29,345.5 + 0.2 = 29,345.7 When the road work begins, the mileage will be 29,345.7. Choice A is correct.

54. SHORT RESPONSE Convert 565 miles per hour to feet per second. Show the procedure you used.

SOLUTION:  Use dimensional analysis and the following conversion facts to convert 565 miles per hour to feet per second.1 mile = 5280 feet 1 hour = 60 min = 3600 seconds

 or 828.67 feet per second

Express each rate as a unit rate. Round to the nearest tenth or to the nearest cent, if necessary.55. $183 for 4 concert tickets

SOLUTION:  

The unit rate is $45.75 per ticket.

56. 100 feet in 14.5 seconds

SOLUTION:  

The unit rate is about 6.9 feet per second.

57. 254.1 miles on 10.5 gallons

SOLUTION:  

The unit rate is 24.2 miles per gallon.

58. 9 inches of snow in 12 hours

SOLUTION:  

Rounded to the nearest tenth, the unit rate is 0.8 inches per hour.

59. Financial Literacy Mrs. Gallagher wants to buy the package of soda that is less expensive per can. Which pack of sodas shown should she buy? Explain your reasoning.

SOLUTION:  

The 6-pack of soda costs about $0.37 per can. The 12-pack of soda costs about $0.35 per can. So, the 12-pack is less expensive.

Express each ratio as a fraction in simplest form.60. 12 cars out of 30 vehicles

SOLUTION:  

61. 5 cups to 5 quarts

SOLUTION:  Convert 5 quarts to cups. There are 4 cups in 1 quart.

62. 15 soccer balls out of 35 balls

SOLUTION:  

63. 8 pencils to 20 crayons

SOLUTION:  

Simplify each expression.64. (x – 3) + 2

SOLUTION:  

65. (8 • y) • (–4)

SOLUTION:  

66. 25 + (d –8)

SOLUTION:  

67. 9(5m)

SOLUTION:  

68. (x + 1) – 9

SOLUTION:  

69. 5(3 • r)

SOLUTION:  

70. Clive is making hamburgers for a cookout. How many -pound hamburgers can he make from  pounds of 

ground beef?

SOLUTION:  Words: The amount of ground beef needed for each hamburger multiplied by the number of hamburgers equals the total amount of ground beef. Variable: Let h = the number of hamburgers

Equation:

Clive can make 11 hamburgers.

Find each product or quotient.71. –12 • (–10)

SOLUTION:  The product of two integers with the same sign is positive. So, –12 • (–10) = 120.

72. –18 ÷ 3

SOLUTION:  The quotient of two integers with different signs is negative. So, –18 ÷ 3 = –6.

73. 9 • (–14)

SOLUTION:  The product of two integers with different signs is negative. So, 9 • (–14) = –126.

74. 54 ÷ (–6)

SOLUTION:  The quotient of two integers with different signs is negative. So, 54 ÷ (–6) = –9.

75. –14 • 2

SOLUTION:  The product of two integers with different signs is negative. So, –14 • 2 = –28.

76. –72 ÷ (–4)

SOLUTION:  The quotient of two integers with the same sign is positive. So, –72 ÷ (–4) = 18.

eSolutions Manual - Powered by Cognero Page 4

5-4 Converting Rates

Page 5: Crystal - Ms. Wilson's Math Classes · a. Crystal ran 10 kilometers in 64 minutes. Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming

1. In Brazil, about 20 acres of rainforest are destroyed each minute. At this rate, how much rainforest is destroyed per day?

SOLUTION:  

At the rate of 20 acres per minute, there are 28,800 acres of rainforest in Brazil destroyed per day.

2. Lexi can paint 5 yards of fencing in one hour. At this rate, how many inches does she paint per minute?

SOLUTION:  

At the rate of 5 yards per hour, Lexi can paint 3 inches per minute.

Complete each conversion. Round to the nearest hundredth, if necessary.3. 8 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

4. 5 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

5. 15 oz ≈ _ g

SOLUTION:  Use 1 oz ≈ 28.35 g.

6. 24 cm ≈ _ in.

SOLUTION:  Use 1 cm ≈ 0.394 in.

7. 9 pt ≈ _ L

SOLUTION:  Use 1 pt ≈ 0.473 L.

8. 3 m ≈ _ ft

SOLUTION:  Use 1 m ≈ 3.279 ft.

9. An elephant can eat up to 440 pounds of vegetation every day. How many grams per minute is this? Round to the nearest hundredth.

SOLUTION:  

An elephant can eat about 138.72 grams of vegetation per minute.

10. A candy company can produce 4800 sour lemon candies per minute. How many candies can they produce each hour?

SOLUTION:  

The company can produce 288,000 candies each hour.

11. In a recent year, 51.9 billion aluminum cans were recycled. About how many cans per week is this?

SOLUTION:  

About 1 billion aluminum cans were recycled per week.

12. The average American student spends almost 1500 hours per year watching television. To the nearest hundredth, how many minutes per day is this?

SOLUTION:  

The average American student spends 246.58 minutes per day watching television.

13. A thrill ride at an amusement park travels 55 miles per hour. To the nearest hundredth, how many feet per second is this?

SOLUTION:  

The thrill ride travels about 80.67 feet per second.

Complete each conversion. Round to the nearest hundredth, if necessary.14. 4 L ≈ _ qt

SOLUTION:  Use 1 L ≈ 1.057 qt.

15. 16 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

16. 13 m ≈ _ ft

SOLUTION:  Use 1 ft ≈ 0.305 m.

17. 8 yd ≈ _ m

SOLUTION:  Use 1 yd ≈ 0.914 m.

18. 18 lb ≈ _ kg

SOLUTION:  Use 1 lb ≈ 0.454 kg.

19. 7 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

20. 1500 g ≈ _ oz

SOLUTION:  Use 1 oz ≈ 28.35 g.

21. 15 ft ≈ _ m

SOLUTION:  Use 1 ft ≈ 0.305 m.

22. 28 fl oz ≈ _ mL

SOLUTION:  Use 1 fl oz ≈ 29.574 mL.

23. The velocity of sound through wood at 0° Celsius is 1454 meters per second. How many miles is this per hour? Round to the nearest hundredth.

SOLUTION:  

The velocity of sound through wood is approximately 3250.68 miles per hour.

24. A certain car in Canada can travel 15 kilometers per 1 liter of gasoline. How many miles per gallon is this? Round to the nearest hundredth.

SOLUTION:  

The car can travel approximately 35.28 miles per gallon.

Complete each conversion. Round to the nearest hundredth, if necessary.25. 8 in. ≈ _ mm

SOLUTION:  Use 1 in. ≈ 2.54 cm and 1 cm = 10 mm.

26. 16 L ≈ _ c

SOLUTION:  Use 1 L ≈ 2.114 pt and 1 pt = 2 cups.

27. 2 km ≈ _ yd

SOLUTION:  Use 1 km = 1000 m and 1 m ≈ 1.094 yd.

28. 250 fl oz ≈ _ L

SOLUTION:  Use 1 fl oz ≈ 29.574 mL and 1000 mL = 1 L.

29. 2750 g ≈ _ lb

SOLUTION:  Use 1 g ≈ 0.035 oz and 16 oz = 1 lb.

30. 5 gal ≈ _ mL

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 L = 1000 mL.

31. Crystal’s times for each portion of a triathlon are shown in the table. Round to the nearest hundredth.

a. How many meters per second did she run? b. What was her speed in miles per hour for the aquabike portion (swimming and biking)?

SOLUTION:  a. Crystal ran 10 kilometers in 64 minutes.

Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming and biking was 1.5 + 40 or 41.5 kilometers. Her time for theseportions was 40 + 86 or 126 minutes.

Crystal’s speed for the aquabike portion was about 12.27 miles per hour.

Order each group of rates from least to greatest.32. 100 oz/min, 2500 g/min, 10 lb/min

SOLUTION:  

5.51 lb/min < 6.25 lb/min < 10 lb/min Ordered from least to greatest, the rates are 2500 g/min, 100 oz/min, and 10 lb/min.

100 oz/min

2500 g/min

10 lb/min

33. 500 m/h, 7 yd/min, 6 in./s

SOLUTION:  

4.20 in./s < 5.47 in./s < 6 in./s Ordered from least to greatest, the rates are 7 yd/min, 500 m/h, and 6 in./s.

500 m/h

7 yd/min

6 in./s

34. 32 mi/gal, 15 m/mL, 6600 yd/qt

SOLUTION:  

6600 yd/qt < 14,080 yd/qt < 15,524 yd/qt Ordered from least to greatest, the rates are 6600 yd/qt, 32 mi/gal, and 15 m/mL.

32 mi/gal

15 m/mL

6600 yd/qt

35. 500 kg/h, 5 oz/s, 18 lb/min

SOLUTION:  

4.8 oz/s < 4.90 oz/s < 5 oz/s Ordered from least to greatest, the rates are 18 lb/min, 500 kg/h, and 5 oz/s.

500 kg/h

5 oz/s

18 lb/min

36. The sprinkler system in the Willis Tower pumps up to 1500 gallons of water per minute. How many liters of water

can the system pump in  minute? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L.

Divide the rate by 4 to find the amount of water pumped in  minute.

The water system in the Sears Tower can pump 1419.38 liters of water in  minute.

37. The average American consumes 20 gallons of ice cream in one year. At this rate, how many liters of ice cream will50 Americans consume in one week? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 yr = 52 wk.

Multiply the rate by 50 to find how many liters 50 Americans consume.

So, 50 Americans consume about 72.79 liters of ice cream per week.

Replace each _ with <, >, or = to make a true sentence.38. 10 m _ 390 in.

SOLUTION:  Use 1 m ≈ 3.279 ft and 1 ft = 12 in.

39. 520 oz _ 15 kg

SOLUTION:  Use 1 oz ≈ 28.35 g and 1000 g = 1 kg.

40. 14 pt _ 6622 mL

SOLUTION:  Use 1 pt ≈ 0.473 L and 1 L = 1000 mL.

Financial Literacy Use dimensional analysis and the table below to make each conversion. Round to the nearest hundredth, if necessary.

41. 150 dollars to euros

SOLUTION:  

So, 150 dollars is equal to 118.5 euros.

42. 275 dollars to pounds

SOLUTION:  

So, 275 dollars is equal to 175.18 pounds.

43. 570 yuan to dollars

SOLUTION:  

So, 570 yuan is equal to 89.41 dollars.

44. 500 pesos to dollars

SOLUTION:  

So, 500 pesos is approximately equal to 37.19 dollars.

45. Model with Mathematics Write and solve a real-world problem in which dimensional analysis is used to convert square feet to square yards. Hint: 1 square yard = 9 square feet

SOLUTION:  Sample answer: Macha needs 120 square feet of carpeting for her bedroom. How many square yards does she need?

Maria needs square yards.

46. Be Precise Give two examples of different measurements that are equivalent to 10 centimeters per second.

SOLUTION:  Sample answers:

Two measurements equivalent to 10 centimeters per second are 600 centimeters per minute and 360 meters per hour.

47. WHICH ONE DOESN’T BELONG? Select the rate that does not have the same value as the other three. Explain your reasoning.

SOLUTION:  Convert each rate to miles per hour and compare the values.

The rate that does not belong is 500 ft/min. All of the other rates are equal to 60 mi/h.

60 mi/h

88 ft/sec

500 ft/min

1440 mi/day

48. Persevere with Problems A recipe for fruit punch uses the ingredients shown. About how many cups of each ingredient are needed? Round to the nearest tenth.

SOLUTION:  Use 1000 mL = 1L, 1 L ≈ 2.114 pt, and 1 pt = 2 cups.  Cranberry juice:

  Apple juice:

  Pineapple juice:

  Lemon juice:

  Club soda:

49. Identify Structure What property of multiplication allows you to multiply a rate by a conversion factor without changing its value? Explain.

SOLUTION:  

The Identity Property of Multiplication allows you to multiply a rate by a conversion factor without changing its value

because the conversion factor is equal to 1. For example, multiplying by  is the same as multiplying by 1 

because 12 inches equals 1 foot.

50. Building on the Essential Question Explain how you would convert 10 miles per hour to meters per second.

SOLUTION:  Sample answer: Use dimensional analysis.

So, 10 miles per hour is approximately equal to 4.47 meters per second.

51. A speed of 55 miles per hour is the same rate as which of the following?

 

A  34 kilometers per hourB  50 kilometers per hourC  88 kilometers per hourD  98 kilometers per hour

SOLUTION:  Use 1 mi ≈ 1.609 kilometers.

55 miles per hour is approximately equal to 88 kilometers per hour. Choice C is correct.

52. A piece of notebook paper measures  inches by 11 inches. Which of the following metric approximations is the 

same?

 

F  2 m by 2.8 mG  3 cm by 4 cmH  22 cm by 28 cmJ  30 m by 40 m

SOLUTION:  Use 1 in. ≈ 2.54 centimeters.

The approximate metric dimensions of a piece of notebook paper are 22 cm by 28 cm. Choice H is correct.

53. A car’s mileage is registered at 29,345.5 miles. The driver sees a sign that warns of road work in 1000 feet. What will be the car’s mileage when the road work begins?

 

A  29,345.7B  29,345.9C  29,356.2D  29,356.5

SOLUTION:  To find the car’s mileage when the road work begins, find the sum of the current mileage and the distance to the

road work, in miles.

29,345.5 + 0.2 = 29,345.7 When the road work begins, the mileage will be 29,345.7. Choice A is correct.

54. SHORT RESPONSE Convert 565 miles per hour to feet per second. Show the procedure you used.

SOLUTION:  Use dimensional analysis and the following conversion facts to convert 565 miles per hour to feet per second.1 mile = 5280 feet 1 hour = 60 min = 3600 seconds

 or 828.67 feet per second

Express each rate as a unit rate. Round to the nearest tenth or to the nearest cent, if necessary.55. $183 for 4 concert tickets

SOLUTION:  

The unit rate is $45.75 per ticket.

56. 100 feet in 14.5 seconds

SOLUTION:  

The unit rate is about 6.9 feet per second.

57. 254.1 miles on 10.5 gallons

SOLUTION:  

The unit rate is 24.2 miles per gallon.

58. 9 inches of snow in 12 hours

SOLUTION:  

Rounded to the nearest tenth, the unit rate is 0.8 inches per hour.

59. Financial Literacy Mrs. Gallagher wants to buy the package of soda that is less expensive per can. Which pack of sodas shown should she buy? Explain your reasoning.

SOLUTION:  

The 6-pack of soda costs about $0.37 per can. The 12-pack of soda costs about $0.35 per can. So, the 12-pack is less expensive.

Express each ratio as a fraction in simplest form.60. 12 cars out of 30 vehicles

SOLUTION:  

61. 5 cups to 5 quarts

SOLUTION:  Convert 5 quarts to cups. There are 4 cups in 1 quart.

62. 15 soccer balls out of 35 balls

SOLUTION:  

63. 8 pencils to 20 crayons

SOLUTION:  

Simplify each expression.64. (x – 3) + 2

SOLUTION:  

65. (8 • y) • (–4)

SOLUTION:  

66. 25 + (d –8)

SOLUTION:  

67. 9(5m)

SOLUTION:  

68. (x + 1) – 9

SOLUTION:  

69. 5(3 • r)

SOLUTION:  

70. Clive is making hamburgers for a cookout. How many -pound hamburgers can he make from  pounds of 

ground beef?

SOLUTION:  Words: The amount of ground beef needed for each hamburger multiplied by the number of hamburgers equals the total amount of ground beef. Variable: Let h = the number of hamburgers

Equation:

Clive can make 11 hamburgers.

Find each product or quotient.71. –12 • (–10)

SOLUTION:  The product of two integers with the same sign is positive. So, –12 • (–10) = 120.

72. –18 ÷ 3

SOLUTION:  The quotient of two integers with different signs is negative. So, –18 ÷ 3 = –6.

73. 9 • (–14)

SOLUTION:  The product of two integers with different signs is negative. So, 9 • (–14) = –126.

74. 54 ÷ (–6)

SOLUTION:  The quotient of two integers with different signs is negative. So, 54 ÷ (–6) = –9.

75. –14 • 2

SOLUTION:  The product of two integers with different signs is negative. So, –14 • 2 = –28.

76. –72 ÷ (–4)

SOLUTION:  The quotient of two integers with the same sign is positive. So, –72 ÷ (–4) = 18.

eSolutions Manual - Powered by Cognero Page 5

5-4 Converting Rates

Page 6: Crystal - Ms. Wilson's Math Classes · a. Crystal ran 10 kilometers in 64 minutes. Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming

1. In Brazil, about 20 acres of rainforest are destroyed each minute. At this rate, how much rainforest is destroyed per day?

SOLUTION:  

At the rate of 20 acres per minute, there are 28,800 acres of rainforest in Brazil destroyed per day.

2. Lexi can paint 5 yards of fencing in one hour. At this rate, how many inches does she paint per minute?

SOLUTION:  

At the rate of 5 yards per hour, Lexi can paint 3 inches per minute.

Complete each conversion. Round to the nearest hundredth, if necessary.3. 8 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

4. 5 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

5. 15 oz ≈ _ g

SOLUTION:  Use 1 oz ≈ 28.35 g.

6. 24 cm ≈ _ in.

SOLUTION:  Use 1 cm ≈ 0.394 in.

7. 9 pt ≈ _ L

SOLUTION:  Use 1 pt ≈ 0.473 L.

8. 3 m ≈ _ ft

SOLUTION:  Use 1 m ≈ 3.279 ft.

9. An elephant can eat up to 440 pounds of vegetation every day. How many grams per minute is this? Round to the nearest hundredth.

SOLUTION:  

An elephant can eat about 138.72 grams of vegetation per minute.

10. A candy company can produce 4800 sour lemon candies per minute. How many candies can they produce each hour?

SOLUTION:  

The company can produce 288,000 candies each hour.

11. In a recent year, 51.9 billion aluminum cans were recycled. About how many cans per week is this?

SOLUTION:  

About 1 billion aluminum cans were recycled per week.

12. The average American student spends almost 1500 hours per year watching television. To the nearest hundredth, how many minutes per day is this?

SOLUTION:  

The average American student spends 246.58 minutes per day watching television.

13. A thrill ride at an amusement park travels 55 miles per hour. To the nearest hundredth, how many feet per second is this?

SOLUTION:  

The thrill ride travels about 80.67 feet per second.

Complete each conversion. Round to the nearest hundredth, if necessary.14. 4 L ≈ _ qt

SOLUTION:  Use 1 L ≈ 1.057 qt.

15. 16 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

16. 13 m ≈ _ ft

SOLUTION:  Use 1 ft ≈ 0.305 m.

17. 8 yd ≈ _ m

SOLUTION:  Use 1 yd ≈ 0.914 m.

18. 18 lb ≈ _ kg

SOLUTION:  Use 1 lb ≈ 0.454 kg.

19. 7 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

20. 1500 g ≈ _ oz

SOLUTION:  Use 1 oz ≈ 28.35 g.

21. 15 ft ≈ _ m

SOLUTION:  Use 1 ft ≈ 0.305 m.

22. 28 fl oz ≈ _ mL

SOLUTION:  Use 1 fl oz ≈ 29.574 mL.

23. The velocity of sound through wood at 0° Celsius is 1454 meters per second. How many miles is this per hour? Round to the nearest hundredth.

SOLUTION:  

The velocity of sound through wood is approximately 3250.68 miles per hour.

24. A certain car in Canada can travel 15 kilometers per 1 liter of gasoline. How many miles per gallon is this? Round to the nearest hundredth.

SOLUTION:  

The car can travel approximately 35.28 miles per gallon.

Complete each conversion. Round to the nearest hundredth, if necessary.25. 8 in. ≈ _ mm

SOLUTION:  Use 1 in. ≈ 2.54 cm and 1 cm = 10 mm.

26. 16 L ≈ _ c

SOLUTION:  Use 1 L ≈ 2.114 pt and 1 pt = 2 cups.

27. 2 km ≈ _ yd

SOLUTION:  Use 1 km = 1000 m and 1 m ≈ 1.094 yd.

28. 250 fl oz ≈ _ L

SOLUTION:  Use 1 fl oz ≈ 29.574 mL and 1000 mL = 1 L.

29. 2750 g ≈ _ lb

SOLUTION:  Use 1 g ≈ 0.035 oz and 16 oz = 1 lb.

30. 5 gal ≈ _ mL

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 L = 1000 mL.

31. Crystal’s times for each portion of a triathlon are shown in the table. Round to the nearest hundredth.

a. How many meters per second did she run? b. What was her speed in miles per hour for the aquabike portion (swimming and biking)?

SOLUTION:  a. Crystal ran 10 kilometers in 64 minutes.

Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming and biking was 1.5 + 40 or 41.5 kilometers. Her time for theseportions was 40 + 86 or 126 minutes.

Crystal’s speed for the aquabike portion was about 12.27 miles per hour.

Order each group of rates from least to greatest.32. 100 oz/min, 2500 g/min, 10 lb/min

SOLUTION:  

5.51 lb/min < 6.25 lb/min < 10 lb/min Ordered from least to greatest, the rates are 2500 g/min, 100 oz/min, and 10 lb/min.

100 oz/min

2500 g/min

10 lb/min

33. 500 m/h, 7 yd/min, 6 in./s

SOLUTION:  

4.20 in./s < 5.47 in./s < 6 in./s Ordered from least to greatest, the rates are 7 yd/min, 500 m/h, and 6 in./s.

500 m/h

7 yd/min

6 in./s

34. 32 mi/gal, 15 m/mL, 6600 yd/qt

SOLUTION:  

6600 yd/qt < 14,080 yd/qt < 15,524 yd/qt Ordered from least to greatest, the rates are 6600 yd/qt, 32 mi/gal, and 15 m/mL.

32 mi/gal

15 m/mL

6600 yd/qt

35. 500 kg/h, 5 oz/s, 18 lb/min

SOLUTION:  

4.8 oz/s < 4.90 oz/s < 5 oz/s Ordered from least to greatest, the rates are 18 lb/min, 500 kg/h, and 5 oz/s.

500 kg/h

5 oz/s

18 lb/min

36. The sprinkler system in the Willis Tower pumps up to 1500 gallons of water per minute. How many liters of water

can the system pump in  minute? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L.

Divide the rate by 4 to find the amount of water pumped in  minute.

The water system in the Sears Tower can pump 1419.38 liters of water in  minute.

37. The average American consumes 20 gallons of ice cream in one year. At this rate, how many liters of ice cream will50 Americans consume in one week? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 yr = 52 wk.

Multiply the rate by 50 to find how many liters 50 Americans consume.

So, 50 Americans consume about 72.79 liters of ice cream per week.

Replace each _ with <, >, or = to make a true sentence.38. 10 m _ 390 in.

SOLUTION:  Use 1 m ≈ 3.279 ft and 1 ft = 12 in.

39. 520 oz _ 15 kg

SOLUTION:  Use 1 oz ≈ 28.35 g and 1000 g = 1 kg.

40. 14 pt _ 6622 mL

SOLUTION:  Use 1 pt ≈ 0.473 L and 1 L = 1000 mL.

Financial Literacy Use dimensional analysis and the table below to make each conversion. Round to the nearest hundredth, if necessary.

41. 150 dollars to euros

SOLUTION:  

So, 150 dollars is equal to 118.5 euros.

42. 275 dollars to pounds

SOLUTION:  

So, 275 dollars is equal to 175.18 pounds.

43. 570 yuan to dollars

SOLUTION:  

So, 570 yuan is equal to 89.41 dollars.

44. 500 pesos to dollars

SOLUTION:  

So, 500 pesos is approximately equal to 37.19 dollars.

45. Model with Mathematics Write and solve a real-world problem in which dimensional analysis is used to convert square feet to square yards. Hint: 1 square yard = 9 square feet

SOLUTION:  Sample answer: Macha needs 120 square feet of carpeting for her bedroom. How many square yards does she need?

Maria needs square yards.

46. Be Precise Give two examples of different measurements that are equivalent to 10 centimeters per second.

SOLUTION:  Sample answers:

Two measurements equivalent to 10 centimeters per second are 600 centimeters per minute and 360 meters per hour.

47. WHICH ONE DOESN’T BELONG? Select the rate that does not have the same value as the other three. Explain your reasoning.

SOLUTION:  Convert each rate to miles per hour and compare the values.

The rate that does not belong is 500 ft/min. All of the other rates are equal to 60 mi/h.

60 mi/h

88 ft/sec

500 ft/min

1440 mi/day

48. Persevere with Problems A recipe for fruit punch uses the ingredients shown. About how many cups of each ingredient are needed? Round to the nearest tenth.

SOLUTION:  Use 1000 mL = 1L, 1 L ≈ 2.114 pt, and 1 pt = 2 cups.  Cranberry juice:

  Apple juice:

  Pineapple juice:

  Lemon juice:

  Club soda:

49. Identify Structure What property of multiplication allows you to multiply a rate by a conversion factor without changing its value? Explain.

SOLUTION:  

The Identity Property of Multiplication allows you to multiply a rate by a conversion factor without changing its value

because the conversion factor is equal to 1. For example, multiplying by  is the same as multiplying by 1 

because 12 inches equals 1 foot.

50. Building on the Essential Question Explain how you would convert 10 miles per hour to meters per second.

SOLUTION:  Sample answer: Use dimensional analysis.

So, 10 miles per hour is approximately equal to 4.47 meters per second.

51. A speed of 55 miles per hour is the same rate as which of the following?

 

A  34 kilometers per hourB  50 kilometers per hourC  88 kilometers per hourD  98 kilometers per hour

SOLUTION:  Use 1 mi ≈ 1.609 kilometers.

55 miles per hour is approximately equal to 88 kilometers per hour. Choice C is correct.

52. A piece of notebook paper measures  inches by 11 inches. Which of the following metric approximations is the 

same?

 

F  2 m by 2.8 mG  3 cm by 4 cmH  22 cm by 28 cmJ  30 m by 40 m

SOLUTION:  Use 1 in. ≈ 2.54 centimeters.

The approximate metric dimensions of a piece of notebook paper are 22 cm by 28 cm. Choice H is correct.

53. A car’s mileage is registered at 29,345.5 miles. The driver sees a sign that warns of road work in 1000 feet. What will be the car’s mileage when the road work begins?

 

A  29,345.7B  29,345.9C  29,356.2D  29,356.5

SOLUTION:  To find the car’s mileage when the road work begins, find the sum of the current mileage and the distance to the

road work, in miles.

29,345.5 + 0.2 = 29,345.7 When the road work begins, the mileage will be 29,345.7. Choice A is correct.

54. SHORT RESPONSE Convert 565 miles per hour to feet per second. Show the procedure you used.

SOLUTION:  Use dimensional analysis and the following conversion facts to convert 565 miles per hour to feet per second.1 mile = 5280 feet 1 hour = 60 min = 3600 seconds

 or 828.67 feet per second

Express each rate as a unit rate. Round to the nearest tenth or to the nearest cent, if necessary.55. $183 for 4 concert tickets

SOLUTION:  

The unit rate is $45.75 per ticket.

56. 100 feet in 14.5 seconds

SOLUTION:  

The unit rate is about 6.9 feet per second.

57. 254.1 miles on 10.5 gallons

SOLUTION:  

The unit rate is 24.2 miles per gallon.

58. 9 inches of snow in 12 hours

SOLUTION:  

Rounded to the nearest tenth, the unit rate is 0.8 inches per hour.

59. Financial Literacy Mrs. Gallagher wants to buy the package of soda that is less expensive per can. Which pack of sodas shown should she buy? Explain your reasoning.

SOLUTION:  

The 6-pack of soda costs about $0.37 per can. The 12-pack of soda costs about $0.35 per can. So, the 12-pack is less expensive.

Express each ratio as a fraction in simplest form.60. 12 cars out of 30 vehicles

SOLUTION:  

61. 5 cups to 5 quarts

SOLUTION:  Convert 5 quarts to cups. There are 4 cups in 1 quart.

62. 15 soccer balls out of 35 balls

SOLUTION:  

63. 8 pencils to 20 crayons

SOLUTION:  

Simplify each expression.64. (x – 3) + 2

SOLUTION:  

65. (8 • y) • (–4)

SOLUTION:  

66. 25 + (d –8)

SOLUTION:  

67. 9(5m)

SOLUTION:  

68. (x + 1) – 9

SOLUTION:  

69. 5(3 • r)

SOLUTION:  

70. Clive is making hamburgers for a cookout. How many -pound hamburgers can he make from  pounds of 

ground beef?

SOLUTION:  Words: The amount of ground beef needed for each hamburger multiplied by the number of hamburgers equals the total amount of ground beef. Variable: Let h = the number of hamburgers

Equation:

Clive can make 11 hamburgers.

Find each product or quotient.71. –12 • (–10)

SOLUTION:  The product of two integers with the same sign is positive. So, –12 • (–10) = 120.

72. –18 ÷ 3

SOLUTION:  The quotient of two integers with different signs is negative. So, –18 ÷ 3 = –6.

73. 9 • (–14)

SOLUTION:  The product of two integers with different signs is negative. So, 9 • (–14) = –126.

74. 54 ÷ (–6)

SOLUTION:  The quotient of two integers with different signs is negative. So, 54 ÷ (–6) = –9.

75. –14 • 2

SOLUTION:  The product of two integers with different signs is negative. So, –14 • 2 = –28.

76. –72 ÷ (–4)

SOLUTION:  The quotient of two integers with the same sign is positive. So, –72 ÷ (–4) = 18.

eSolutions Manual - Powered by Cognero Page 6

5-4 Converting Rates

Page 7: Crystal - Ms. Wilson's Math Classes · a. Crystal ran 10 kilometers in 64 minutes. Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming

1. In Brazil, about 20 acres of rainforest are destroyed each minute. At this rate, how much rainforest is destroyed per day?

SOLUTION:  

At the rate of 20 acres per minute, there are 28,800 acres of rainforest in Brazil destroyed per day.

2. Lexi can paint 5 yards of fencing in one hour. At this rate, how many inches does she paint per minute?

SOLUTION:  

At the rate of 5 yards per hour, Lexi can paint 3 inches per minute.

Complete each conversion. Round to the nearest hundredth, if necessary.3. 8 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

4. 5 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

5. 15 oz ≈ _ g

SOLUTION:  Use 1 oz ≈ 28.35 g.

6. 24 cm ≈ _ in.

SOLUTION:  Use 1 cm ≈ 0.394 in.

7. 9 pt ≈ _ L

SOLUTION:  Use 1 pt ≈ 0.473 L.

8. 3 m ≈ _ ft

SOLUTION:  Use 1 m ≈ 3.279 ft.

9. An elephant can eat up to 440 pounds of vegetation every day. How many grams per minute is this? Round to the nearest hundredth.

SOLUTION:  

An elephant can eat about 138.72 grams of vegetation per minute.

10. A candy company can produce 4800 sour lemon candies per minute. How many candies can they produce each hour?

SOLUTION:  

The company can produce 288,000 candies each hour.

11. In a recent year, 51.9 billion aluminum cans were recycled. About how many cans per week is this?

SOLUTION:  

About 1 billion aluminum cans were recycled per week.

12. The average American student spends almost 1500 hours per year watching television. To the nearest hundredth, how many minutes per day is this?

SOLUTION:  

The average American student spends 246.58 minutes per day watching television.

13. A thrill ride at an amusement park travels 55 miles per hour. To the nearest hundredth, how many feet per second is this?

SOLUTION:  

The thrill ride travels about 80.67 feet per second.

Complete each conversion. Round to the nearest hundredth, if necessary.14. 4 L ≈ _ qt

SOLUTION:  Use 1 L ≈ 1.057 qt.

15. 16 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

16. 13 m ≈ _ ft

SOLUTION:  Use 1 ft ≈ 0.305 m.

17. 8 yd ≈ _ m

SOLUTION:  Use 1 yd ≈ 0.914 m.

18. 18 lb ≈ _ kg

SOLUTION:  Use 1 lb ≈ 0.454 kg.

19. 7 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

20. 1500 g ≈ _ oz

SOLUTION:  Use 1 oz ≈ 28.35 g.

21. 15 ft ≈ _ m

SOLUTION:  Use 1 ft ≈ 0.305 m.

22. 28 fl oz ≈ _ mL

SOLUTION:  Use 1 fl oz ≈ 29.574 mL.

23. The velocity of sound through wood at 0° Celsius is 1454 meters per second. How many miles is this per hour? Round to the nearest hundredth.

SOLUTION:  

The velocity of sound through wood is approximately 3250.68 miles per hour.

24. A certain car in Canada can travel 15 kilometers per 1 liter of gasoline. How many miles per gallon is this? Round to the nearest hundredth.

SOLUTION:  

The car can travel approximately 35.28 miles per gallon.

Complete each conversion. Round to the nearest hundredth, if necessary.25. 8 in. ≈ _ mm

SOLUTION:  Use 1 in. ≈ 2.54 cm and 1 cm = 10 mm.

26. 16 L ≈ _ c

SOLUTION:  Use 1 L ≈ 2.114 pt and 1 pt = 2 cups.

27. 2 km ≈ _ yd

SOLUTION:  Use 1 km = 1000 m and 1 m ≈ 1.094 yd.

28. 250 fl oz ≈ _ L

SOLUTION:  Use 1 fl oz ≈ 29.574 mL and 1000 mL = 1 L.

29. 2750 g ≈ _ lb

SOLUTION:  Use 1 g ≈ 0.035 oz and 16 oz = 1 lb.

30. 5 gal ≈ _ mL

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 L = 1000 mL.

31. Crystal’s times for each portion of a triathlon are shown in the table. Round to the nearest hundredth.

a. How many meters per second did she run? b. What was her speed in miles per hour for the aquabike portion (swimming and biking)?

SOLUTION:  a. Crystal ran 10 kilometers in 64 minutes.

Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming and biking was 1.5 + 40 or 41.5 kilometers. Her time for theseportions was 40 + 86 or 126 minutes.

Crystal’s speed for the aquabike portion was about 12.27 miles per hour.

Order each group of rates from least to greatest.32. 100 oz/min, 2500 g/min, 10 lb/min

SOLUTION:  

5.51 lb/min < 6.25 lb/min < 10 lb/min Ordered from least to greatest, the rates are 2500 g/min, 100 oz/min, and 10 lb/min.

100 oz/min

2500 g/min

10 lb/min

33. 500 m/h, 7 yd/min, 6 in./s

SOLUTION:  

4.20 in./s < 5.47 in./s < 6 in./s Ordered from least to greatest, the rates are 7 yd/min, 500 m/h, and 6 in./s.

500 m/h

7 yd/min

6 in./s

34. 32 mi/gal, 15 m/mL, 6600 yd/qt

SOLUTION:  

6600 yd/qt < 14,080 yd/qt < 15,524 yd/qt Ordered from least to greatest, the rates are 6600 yd/qt, 32 mi/gal, and 15 m/mL.

32 mi/gal

15 m/mL

6600 yd/qt

35. 500 kg/h, 5 oz/s, 18 lb/min

SOLUTION:  

4.8 oz/s < 4.90 oz/s < 5 oz/s Ordered from least to greatest, the rates are 18 lb/min, 500 kg/h, and 5 oz/s.

500 kg/h

5 oz/s

18 lb/min

36. The sprinkler system in the Willis Tower pumps up to 1500 gallons of water per minute. How many liters of water

can the system pump in  minute? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L.

Divide the rate by 4 to find the amount of water pumped in  minute.

The water system in the Sears Tower can pump 1419.38 liters of water in  minute.

37. The average American consumes 20 gallons of ice cream in one year. At this rate, how many liters of ice cream will50 Americans consume in one week? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 yr = 52 wk.

Multiply the rate by 50 to find how many liters 50 Americans consume.

So, 50 Americans consume about 72.79 liters of ice cream per week.

Replace each _ with <, >, or = to make a true sentence.38. 10 m _ 390 in.

SOLUTION:  Use 1 m ≈ 3.279 ft and 1 ft = 12 in.

39. 520 oz _ 15 kg

SOLUTION:  Use 1 oz ≈ 28.35 g and 1000 g = 1 kg.

40. 14 pt _ 6622 mL

SOLUTION:  Use 1 pt ≈ 0.473 L and 1 L = 1000 mL.

Financial Literacy Use dimensional analysis and the table below to make each conversion. Round to the nearest hundredth, if necessary.

41. 150 dollars to euros

SOLUTION:  

So, 150 dollars is equal to 118.5 euros.

42. 275 dollars to pounds

SOLUTION:  

So, 275 dollars is equal to 175.18 pounds.

43. 570 yuan to dollars

SOLUTION:  

So, 570 yuan is equal to 89.41 dollars.

44. 500 pesos to dollars

SOLUTION:  

So, 500 pesos is approximately equal to 37.19 dollars.

45. Model with Mathematics Write and solve a real-world problem in which dimensional analysis is used to convert square feet to square yards. Hint: 1 square yard = 9 square feet

SOLUTION:  Sample answer: Macha needs 120 square feet of carpeting for her bedroom. How many square yards does she need?

Maria needs square yards.

46. Be Precise Give two examples of different measurements that are equivalent to 10 centimeters per second.

SOLUTION:  Sample answers:

Two measurements equivalent to 10 centimeters per second are 600 centimeters per minute and 360 meters per hour.

47. WHICH ONE DOESN’T BELONG? Select the rate that does not have the same value as the other three. Explain your reasoning.

SOLUTION:  Convert each rate to miles per hour and compare the values.

The rate that does not belong is 500 ft/min. All of the other rates are equal to 60 mi/h.

60 mi/h

88 ft/sec

500 ft/min

1440 mi/day

48. Persevere with Problems A recipe for fruit punch uses the ingredients shown. About how many cups of each ingredient are needed? Round to the nearest tenth.

SOLUTION:  Use 1000 mL = 1L, 1 L ≈ 2.114 pt, and 1 pt = 2 cups.  Cranberry juice:

  Apple juice:

  Pineapple juice:

  Lemon juice:

  Club soda:

49. Identify Structure What property of multiplication allows you to multiply a rate by a conversion factor without changing its value? Explain.

SOLUTION:  

The Identity Property of Multiplication allows you to multiply a rate by a conversion factor without changing its value

because the conversion factor is equal to 1. For example, multiplying by  is the same as multiplying by 1 

because 12 inches equals 1 foot.

50. Building on the Essential Question Explain how you would convert 10 miles per hour to meters per second.

SOLUTION:  Sample answer: Use dimensional analysis.

So, 10 miles per hour is approximately equal to 4.47 meters per second.

51. A speed of 55 miles per hour is the same rate as which of the following?

 

A  34 kilometers per hourB  50 kilometers per hourC  88 kilometers per hourD  98 kilometers per hour

SOLUTION:  Use 1 mi ≈ 1.609 kilometers.

55 miles per hour is approximately equal to 88 kilometers per hour. Choice C is correct.

52. A piece of notebook paper measures  inches by 11 inches. Which of the following metric approximations is the 

same?

 

F  2 m by 2.8 mG  3 cm by 4 cmH  22 cm by 28 cmJ  30 m by 40 m

SOLUTION:  Use 1 in. ≈ 2.54 centimeters.

The approximate metric dimensions of a piece of notebook paper are 22 cm by 28 cm. Choice H is correct.

53. A car’s mileage is registered at 29,345.5 miles. The driver sees a sign that warns of road work in 1000 feet. What will be the car’s mileage when the road work begins?

 

A  29,345.7B  29,345.9C  29,356.2D  29,356.5

SOLUTION:  To find the car’s mileage when the road work begins, find the sum of the current mileage and the distance to the

road work, in miles.

29,345.5 + 0.2 = 29,345.7 When the road work begins, the mileage will be 29,345.7. Choice A is correct.

54. SHORT RESPONSE Convert 565 miles per hour to feet per second. Show the procedure you used.

SOLUTION:  Use dimensional analysis and the following conversion facts to convert 565 miles per hour to feet per second.1 mile = 5280 feet 1 hour = 60 min = 3600 seconds

 or 828.67 feet per second

Express each rate as a unit rate. Round to the nearest tenth or to the nearest cent, if necessary.55. $183 for 4 concert tickets

SOLUTION:  

The unit rate is $45.75 per ticket.

56. 100 feet in 14.5 seconds

SOLUTION:  

The unit rate is about 6.9 feet per second.

57. 254.1 miles on 10.5 gallons

SOLUTION:  

The unit rate is 24.2 miles per gallon.

58. 9 inches of snow in 12 hours

SOLUTION:  

Rounded to the nearest tenth, the unit rate is 0.8 inches per hour.

59. Financial Literacy Mrs. Gallagher wants to buy the package of soda that is less expensive per can. Which pack of sodas shown should she buy? Explain your reasoning.

SOLUTION:  

The 6-pack of soda costs about $0.37 per can. The 12-pack of soda costs about $0.35 per can. So, the 12-pack is less expensive.

Express each ratio as a fraction in simplest form.60. 12 cars out of 30 vehicles

SOLUTION:  

61. 5 cups to 5 quarts

SOLUTION:  Convert 5 quarts to cups. There are 4 cups in 1 quart.

62. 15 soccer balls out of 35 balls

SOLUTION:  

63. 8 pencils to 20 crayons

SOLUTION:  

Simplify each expression.64. (x – 3) + 2

SOLUTION:  

65. (8 • y) • (–4)

SOLUTION:  

66. 25 + (d –8)

SOLUTION:  

67. 9(5m)

SOLUTION:  

68. (x + 1) – 9

SOLUTION:  

69. 5(3 • r)

SOLUTION:  

70. Clive is making hamburgers for a cookout. How many -pound hamburgers can he make from  pounds of 

ground beef?

SOLUTION:  Words: The amount of ground beef needed for each hamburger multiplied by the number of hamburgers equals the total amount of ground beef. Variable: Let h = the number of hamburgers

Equation:

Clive can make 11 hamburgers.

Find each product or quotient.71. –12 • (–10)

SOLUTION:  The product of two integers with the same sign is positive. So, –12 • (–10) = 120.

72. –18 ÷ 3

SOLUTION:  The quotient of two integers with different signs is negative. So, –18 ÷ 3 = –6.

73. 9 • (–14)

SOLUTION:  The product of two integers with different signs is negative. So, 9 • (–14) = –126.

74. 54 ÷ (–6)

SOLUTION:  The quotient of two integers with different signs is negative. So, 54 ÷ (–6) = –9.

75. –14 • 2

SOLUTION:  The product of two integers with different signs is negative. So, –14 • 2 = –28.

76. –72 ÷ (–4)

SOLUTION:  The quotient of two integers with the same sign is positive. So, –72 ÷ (–4) = 18.

eSolutions Manual - Powered by Cognero Page 7

5-4 Converting Rates

Page 8: Crystal - Ms. Wilson's Math Classes · a. Crystal ran 10 kilometers in 64 minutes. Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming

1. In Brazil, about 20 acres of rainforest are destroyed each minute. At this rate, how much rainforest is destroyed per day?

SOLUTION:  

At the rate of 20 acres per minute, there are 28,800 acres of rainforest in Brazil destroyed per day.

2. Lexi can paint 5 yards of fencing in one hour. At this rate, how many inches does she paint per minute?

SOLUTION:  

At the rate of 5 yards per hour, Lexi can paint 3 inches per minute.

Complete each conversion. Round to the nearest hundredth, if necessary.3. 8 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

4. 5 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

5. 15 oz ≈ _ g

SOLUTION:  Use 1 oz ≈ 28.35 g.

6. 24 cm ≈ _ in.

SOLUTION:  Use 1 cm ≈ 0.394 in.

7. 9 pt ≈ _ L

SOLUTION:  Use 1 pt ≈ 0.473 L.

8. 3 m ≈ _ ft

SOLUTION:  Use 1 m ≈ 3.279 ft.

9. An elephant can eat up to 440 pounds of vegetation every day. How many grams per minute is this? Round to the nearest hundredth.

SOLUTION:  

An elephant can eat about 138.72 grams of vegetation per minute.

10. A candy company can produce 4800 sour lemon candies per minute. How many candies can they produce each hour?

SOLUTION:  

The company can produce 288,000 candies each hour.

11. In a recent year, 51.9 billion aluminum cans were recycled. About how many cans per week is this?

SOLUTION:  

About 1 billion aluminum cans were recycled per week.

12. The average American student spends almost 1500 hours per year watching television. To the nearest hundredth, how many minutes per day is this?

SOLUTION:  

The average American student spends 246.58 minutes per day watching television.

13. A thrill ride at an amusement park travels 55 miles per hour. To the nearest hundredth, how many feet per second is this?

SOLUTION:  

The thrill ride travels about 80.67 feet per second.

Complete each conversion. Round to the nearest hundredth, if necessary.14. 4 L ≈ _ qt

SOLUTION:  Use 1 L ≈ 1.057 qt.

15. 16 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

16. 13 m ≈ _ ft

SOLUTION:  Use 1 ft ≈ 0.305 m.

17. 8 yd ≈ _ m

SOLUTION:  Use 1 yd ≈ 0.914 m.

18. 18 lb ≈ _ kg

SOLUTION:  Use 1 lb ≈ 0.454 kg.

19. 7 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

20. 1500 g ≈ _ oz

SOLUTION:  Use 1 oz ≈ 28.35 g.

21. 15 ft ≈ _ m

SOLUTION:  Use 1 ft ≈ 0.305 m.

22. 28 fl oz ≈ _ mL

SOLUTION:  Use 1 fl oz ≈ 29.574 mL.

23. The velocity of sound through wood at 0° Celsius is 1454 meters per second. How many miles is this per hour? Round to the nearest hundredth.

SOLUTION:  

The velocity of sound through wood is approximately 3250.68 miles per hour.

24. A certain car in Canada can travel 15 kilometers per 1 liter of gasoline. How many miles per gallon is this? Round to the nearest hundredth.

SOLUTION:  

The car can travel approximately 35.28 miles per gallon.

Complete each conversion. Round to the nearest hundredth, if necessary.25. 8 in. ≈ _ mm

SOLUTION:  Use 1 in. ≈ 2.54 cm and 1 cm = 10 mm.

26. 16 L ≈ _ c

SOLUTION:  Use 1 L ≈ 2.114 pt and 1 pt = 2 cups.

27. 2 km ≈ _ yd

SOLUTION:  Use 1 km = 1000 m and 1 m ≈ 1.094 yd.

28. 250 fl oz ≈ _ L

SOLUTION:  Use 1 fl oz ≈ 29.574 mL and 1000 mL = 1 L.

29. 2750 g ≈ _ lb

SOLUTION:  Use 1 g ≈ 0.035 oz and 16 oz = 1 lb.

30. 5 gal ≈ _ mL

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 L = 1000 mL.

31. Crystal’s times for each portion of a triathlon are shown in the table. Round to the nearest hundredth.

a. How many meters per second did she run? b. What was her speed in miles per hour for the aquabike portion (swimming and biking)?

SOLUTION:  a. Crystal ran 10 kilometers in 64 minutes.

Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming and biking was 1.5 + 40 or 41.5 kilometers. Her time for theseportions was 40 + 86 or 126 minutes.

Crystal’s speed for the aquabike portion was about 12.27 miles per hour.

Order each group of rates from least to greatest.32. 100 oz/min, 2500 g/min, 10 lb/min

SOLUTION:  

5.51 lb/min < 6.25 lb/min < 10 lb/min Ordered from least to greatest, the rates are 2500 g/min, 100 oz/min, and 10 lb/min.

100 oz/min

2500 g/min

10 lb/min

33. 500 m/h, 7 yd/min, 6 in./s

SOLUTION:  

4.20 in./s < 5.47 in./s < 6 in./s Ordered from least to greatest, the rates are 7 yd/min, 500 m/h, and 6 in./s.

500 m/h

7 yd/min

6 in./s

34. 32 mi/gal, 15 m/mL, 6600 yd/qt

SOLUTION:  

6600 yd/qt < 14,080 yd/qt < 15,524 yd/qt Ordered from least to greatest, the rates are 6600 yd/qt, 32 mi/gal, and 15 m/mL.

32 mi/gal

15 m/mL

6600 yd/qt

35. 500 kg/h, 5 oz/s, 18 lb/min

SOLUTION:  

4.8 oz/s < 4.90 oz/s < 5 oz/s Ordered from least to greatest, the rates are 18 lb/min, 500 kg/h, and 5 oz/s.

500 kg/h

5 oz/s

18 lb/min

36. The sprinkler system in the Willis Tower pumps up to 1500 gallons of water per minute. How many liters of water

can the system pump in  minute? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L.

Divide the rate by 4 to find the amount of water pumped in  minute.

The water system in the Sears Tower can pump 1419.38 liters of water in  minute.

37. The average American consumes 20 gallons of ice cream in one year. At this rate, how many liters of ice cream will50 Americans consume in one week? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 yr = 52 wk.

Multiply the rate by 50 to find how many liters 50 Americans consume.

So, 50 Americans consume about 72.79 liters of ice cream per week.

Replace each _ with <, >, or = to make a true sentence.38. 10 m _ 390 in.

SOLUTION:  Use 1 m ≈ 3.279 ft and 1 ft = 12 in.

39. 520 oz _ 15 kg

SOLUTION:  Use 1 oz ≈ 28.35 g and 1000 g = 1 kg.

40. 14 pt _ 6622 mL

SOLUTION:  Use 1 pt ≈ 0.473 L and 1 L = 1000 mL.

Financial Literacy Use dimensional analysis and the table below to make each conversion. Round to the nearest hundredth, if necessary.

41. 150 dollars to euros

SOLUTION:  

So, 150 dollars is equal to 118.5 euros.

42. 275 dollars to pounds

SOLUTION:  

So, 275 dollars is equal to 175.18 pounds.

43. 570 yuan to dollars

SOLUTION:  

So, 570 yuan is equal to 89.41 dollars.

44. 500 pesos to dollars

SOLUTION:  

So, 500 pesos is approximately equal to 37.19 dollars.

45. Model with Mathematics Write and solve a real-world problem in which dimensional analysis is used to convert square feet to square yards. Hint: 1 square yard = 9 square feet

SOLUTION:  Sample answer: Macha needs 120 square feet of carpeting for her bedroom. How many square yards does she need?

Maria needs square yards.

46. Be Precise Give two examples of different measurements that are equivalent to 10 centimeters per second.

SOLUTION:  Sample answers:

Two measurements equivalent to 10 centimeters per second are 600 centimeters per minute and 360 meters per hour.

47. WHICH ONE DOESN’T BELONG? Select the rate that does not have the same value as the other three. Explain your reasoning.

SOLUTION:  Convert each rate to miles per hour and compare the values.

The rate that does not belong is 500 ft/min. All of the other rates are equal to 60 mi/h.

60 mi/h

88 ft/sec

500 ft/min

1440 mi/day

48. Persevere with Problems A recipe for fruit punch uses the ingredients shown. About how many cups of each ingredient are needed? Round to the nearest tenth.

SOLUTION:  Use 1000 mL = 1L, 1 L ≈ 2.114 pt, and 1 pt = 2 cups.  Cranberry juice:

  Apple juice:

  Pineapple juice:

  Lemon juice:

  Club soda:

49. Identify Structure What property of multiplication allows you to multiply a rate by a conversion factor without changing its value? Explain.

SOLUTION:  

The Identity Property of Multiplication allows you to multiply a rate by a conversion factor without changing its value

because the conversion factor is equal to 1. For example, multiplying by  is the same as multiplying by 1 

because 12 inches equals 1 foot.

50. Building on the Essential Question Explain how you would convert 10 miles per hour to meters per second.

SOLUTION:  Sample answer: Use dimensional analysis.

So, 10 miles per hour is approximately equal to 4.47 meters per second.

51. A speed of 55 miles per hour is the same rate as which of the following?

 

A  34 kilometers per hourB  50 kilometers per hourC  88 kilometers per hourD  98 kilometers per hour

SOLUTION:  Use 1 mi ≈ 1.609 kilometers.

55 miles per hour is approximately equal to 88 kilometers per hour. Choice C is correct.

52. A piece of notebook paper measures  inches by 11 inches. Which of the following metric approximations is the 

same?

 

F  2 m by 2.8 mG  3 cm by 4 cmH  22 cm by 28 cmJ  30 m by 40 m

SOLUTION:  Use 1 in. ≈ 2.54 centimeters.

The approximate metric dimensions of a piece of notebook paper are 22 cm by 28 cm. Choice H is correct.

53. A car’s mileage is registered at 29,345.5 miles. The driver sees a sign that warns of road work in 1000 feet. What will be the car’s mileage when the road work begins?

 

A  29,345.7B  29,345.9C  29,356.2D  29,356.5

SOLUTION:  To find the car’s mileage when the road work begins, find the sum of the current mileage and the distance to the

road work, in miles.

29,345.5 + 0.2 = 29,345.7 When the road work begins, the mileage will be 29,345.7. Choice A is correct.

54. SHORT RESPONSE Convert 565 miles per hour to feet per second. Show the procedure you used.

SOLUTION:  Use dimensional analysis and the following conversion facts to convert 565 miles per hour to feet per second.1 mile = 5280 feet 1 hour = 60 min = 3600 seconds

 or 828.67 feet per second

Express each rate as a unit rate. Round to the nearest tenth or to the nearest cent, if necessary.55. $183 for 4 concert tickets

SOLUTION:  

The unit rate is $45.75 per ticket.

56. 100 feet in 14.5 seconds

SOLUTION:  

The unit rate is about 6.9 feet per second.

57. 254.1 miles on 10.5 gallons

SOLUTION:  

The unit rate is 24.2 miles per gallon.

58. 9 inches of snow in 12 hours

SOLUTION:  

Rounded to the nearest tenth, the unit rate is 0.8 inches per hour.

59. Financial Literacy Mrs. Gallagher wants to buy the package of soda that is less expensive per can. Which pack of sodas shown should she buy? Explain your reasoning.

SOLUTION:  

The 6-pack of soda costs about $0.37 per can. The 12-pack of soda costs about $0.35 per can. So, the 12-pack is less expensive.

Express each ratio as a fraction in simplest form.60. 12 cars out of 30 vehicles

SOLUTION:  

61. 5 cups to 5 quarts

SOLUTION:  Convert 5 quarts to cups. There are 4 cups in 1 quart.

62. 15 soccer balls out of 35 balls

SOLUTION:  

63. 8 pencils to 20 crayons

SOLUTION:  

Simplify each expression.64. (x – 3) + 2

SOLUTION:  

65. (8 • y) • (–4)

SOLUTION:  

66. 25 + (d –8)

SOLUTION:  

67. 9(5m)

SOLUTION:  

68. (x + 1) – 9

SOLUTION:  

69. 5(3 • r)

SOLUTION:  

70. Clive is making hamburgers for a cookout. How many -pound hamburgers can he make from  pounds of 

ground beef?

SOLUTION:  Words: The amount of ground beef needed for each hamburger multiplied by the number of hamburgers equals the total amount of ground beef. Variable: Let h = the number of hamburgers

Equation:

Clive can make 11 hamburgers.

Find each product or quotient.71. –12 • (–10)

SOLUTION:  The product of two integers with the same sign is positive. So, –12 • (–10) = 120.

72. –18 ÷ 3

SOLUTION:  The quotient of two integers with different signs is negative. So, –18 ÷ 3 = –6.

73. 9 • (–14)

SOLUTION:  The product of two integers with different signs is negative. So, 9 • (–14) = –126.

74. 54 ÷ (–6)

SOLUTION:  The quotient of two integers with different signs is negative. So, 54 ÷ (–6) = –9.

75. –14 • 2

SOLUTION:  The product of two integers with different signs is negative. So, –14 • 2 = –28.

76. –72 ÷ (–4)

SOLUTION:  The quotient of two integers with the same sign is positive. So, –72 ÷ (–4) = 18.

eSolutions Manual - Powered by Cognero Page 8

5-4 Converting Rates

Page 9: Crystal - Ms. Wilson's Math Classes · a. Crystal ran 10 kilometers in 64 minutes. Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming

1. In Brazil, about 20 acres of rainforest are destroyed each minute. At this rate, how much rainforest is destroyed per day?

SOLUTION:  

At the rate of 20 acres per minute, there are 28,800 acres of rainforest in Brazil destroyed per day.

2. Lexi can paint 5 yards of fencing in one hour. At this rate, how many inches does she paint per minute?

SOLUTION:  

At the rate of 5 yards per hour, Lexi can paint 3 inches per minute.

Complete each conversion. Round to the nearest hundredth, if necessary.3. 8 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

4. 5 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

5. 15 oz ≈ _ g

SOLUTION:  Use 1 oz ≈ 28.35 g.

6. 24 cm ≈ _ in.

SOLUTION:  Use 1 cm ≈ 0.394 in.

7. 9 pt ≈ _ L

SOLUTION:  Use 1 pt ≈ 0.473 L.

8. 3 m ≈ _ ft

SOLUTION:  Use 1 m ≈ 3.279 ft.

9. An elephant can eat up to 440 pounds of vegetation every day. How many grams per minute is this? Round to the nearest hundredth.

SOLUTION:  

An elephant can eat about 138.72 grams of vegetation per minute.

10. A candy company can produce 4800 sour lemon candies per minute. How many candies can they produce each hour?

SOLUTION:  

The company can produce 288,000 candies each hour.

11. In a recent year, 51.9 billion aluminum cans were recycled. About how many cans per week is this?

SOLUTION:  

About 1 billion aluminum cans were recycled per week.

12. The average American student spends almost 1500 hours per year watching television. To the nearest hundredth, how many minutes per day is this?

SOLUTION:  

The average American student spends 246.58 minutes per day watching television.

13. A thrill ride at an amusement park travels 55 miles per hour. To the nearest hundredth, how many feet per second is this?

SOLUTION:  

The thrill ride travels about 80.67 feet per second.

Complete each conversion. Round to the nearest hundredth, if necessary.14. 4 L ≈ _ qt

SOLUTION:  Use 1 L ≈ 1.057 qt.

15. 16 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

16. 13 m ≈ _ ft

SOLUTION:  Use 1 ft ≈ 0.305 m.

17. 8 yd ≈ _ m

SOLUTION:  Use 1 yd ≈ 0.914 m.

18. 18 lb ≈ _ kg

SOLUTION:  Use 1 lb ≈ 0.454 kg.

19. 7 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

20. 1500 g ≈ _ oz

SOLUTION:  Use 1 oz ≈ 28.35 g.

21. 15 ft ≈ _ m

SOLUTION:  Use 1 ft ≈ 0.305 m.

22. 28 fl oz ≈ _ mL

SOLUTION:  Use 1 fl oz ≈ 29.574 mL.

23. The velocity of sound through wood at 0° Celsius is 1454 meters per second. How many miles is this per hour? Round to the nearest hundredth.

SOLUTION:  

The velocity of sound through wood is approximately 3250.68 miles per hour.

24. A certain car in Canada can travel 15 kilometers per 1 liter of gasoline. How many miles per gallon is this? Round to the nearest hundredth.

SOLUTION:  

The car can travel approximately 35.28 miles per gallon.

Complete each conversion. Round to the nearest hundredth, if necessary.25. 8 in. ≈ _ mm

SOLUTION:  Use 1 in. ≈ 2.54 cm and 1 cm = 10 mm.

26. 16 L ≈ _ c

SOLUTION:  Use 1 L ≈ 2.114 pt and 1 pt = 2 cups.

27. 2 km ≈ _ yd

SOLUTION:  Use 1 km = 1000 m and 1 m ≈ 1.094 yd.

28. 250 fl oz ≈ _ L

SOLUTION:  Use 1 fl oz ≈ 29.574 mL and 1000 mL = 1 L.

29. 2750 g ≈ _ lb

SOLUTION:  Use 1 g ≈ 0.035 oz and 16 oz = 1 lb.

30. 5 gal ≈ _ mL

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 L = 1000 mL.

31. Crystal’s times for each portion of a triathlon are shown in the table. Round to the nearest hundredth.

a. How many meters per second did she run? b. What was her speed in miles per hour for the aquabike portion (swimming and biking)?

SOLUTION:  a. Crystal ran 10 kilometers in 64 minutes.

Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming and biking was 1.5 + 40 or 41.5 kilometers. Her time for theseportions was 40 + 86 or 126 minutes.

Crystal’s speed for the aquabike portion was about 12.27 miles per hour.

Order each group of rates from least to greatest.32. 100 oz/min, 2500 g/min, 10 lb/min

SOLUTION:  

5.51 lb/min < 6.25 lb/min < 10 lb/min Ordered from least to greatest, the rates are 2500 g/min, 100 oz/min, and 10 lb/min.

100 oz/min

2500 g/min

10 lb/min

33. 500 m/h, 7 yd/min, 6 in./s

SOLUTION:  

4.20 in./s < 5.47 in./s < 6 in./s Ordered from least to greatest, the rates are 7 yd/min, 500 m/h, and 6 in./s.

500 m/h

7 yd/min

6 in./s

34. 32 mi/gal, 15 m/mL, 6600 yd/qt

SOLUTION:  

6600 yd/qt < 14,080 yd/qt < 15,524 yd/qt Ordered from least to greatest, the rates are 6600 yd/qt, 32 mi/gal, and 15 m/mL.

32 mi/gal

15 m/mL

6600 yd/qt

35. 500 kg/h, 5 oz/s, 18 lb/min

SOLUTION:  

4.8 oz/s < 4.90 oz/s < 5 oz/s Ordered from least to greatest, the rates are 18 lb/min, 500 kg/h, and 5 oz/s.

500 kg/h

5 oz/s

18 lb/min

36. The sprinkler system in the Willis Tower pumps up to 1500 gallons of water per minute. How many liters of water

can the system pump in  minute? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L.

Divide the rate by 4 to find the amount of water pumped in  minute.

The water system in the Sears Tower can pump 1419.38 liters of water in  minute.

37. The average American consumes 20 gallons of ice cream in one year. At this rate, how many liters of ice cream will50 Americans consume in one week? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 yr = 52 wk.

Multiply the rate by 50 to find how many liters 50 Americans consume.

So, 50 Americans consume about 72.79 liters of ice cream per week.

Replace each _ with <, >, or = to make a true sentence.38. 10 m _ 390 in.

SOLUTION:  Use 1 m ≈ 3.279 ft and 1 ft = 12 in.

39. 520 oz _ 15 kg

SOLUTION:  Use 1 oz ≈ 28.35 g and 1000 g = 1 kg.

40. 14 pt _ 6622 mL

SOLUTION:  Use 1 pt ≈ 0.473 L and 1 L = 1000 mL.

Financial Literacy Use dimensional analysis and the table below to make each conversion. Round to the nearest hundredth, if necessary.

41. 150 dollars to euros

SOLUTION:  

So, 150 dollars is equal to 118.5 euros.

42. 275 dollars to pounds

SOLUTION:  

So, 275 dollars is equal to 175.18 pounds.

43. 570 yuan to dollars

SOLUTION:  

So, 570 yuan is equal to 89.41 dollars.

44. 500 pesos to dollars

SOLUTION:  

So, 500 pesos is approximately equal to 37.19 dollars.

45. Model with Mathematics Write and solve a real-world problem in which dimensional analysis is used to convert square feet to square yards. Hint: 1 square yard = 9 square feet

SOLUTION:  Sample answer: Macha needs 120 square feet of carpeting for her bedroom. How many square yards does she need?

Maria needs square yards.

46. Be Precise Give two examples of different measurements that are equivalent to 10 centimeters per second.

SOLUTION:  Sample answers:

Two measurements equivalent to 10 centimeters per second are 600 centimeters per minute and 360 meters per hour.

47. WHICH ONE DOESN’T BELONG? Select the rate that does not have the same value as the other three. Explain your reasoning.

SOLUTION:  Convert each rate to miles per hour and compare the values.

The rate that does not belong is 500 ft/min. All of the other rates are equal to 60 mi/h.

60 mi/h

88 ft/sec

500 ft/min

1440 mi/day

48. Persevere with Problems A recipe for fruit punch uses the ingredients shown. About how many cups of each ingredient are needed? Round to the nearest tenth.

SOLUTION:  Use 1000 mL = 1L, 1 L ≈ 2.114 pt, and 1 pt = 2 cups.  Cranberry juice:

  Apple juice:

  Pineapple juice:

  Lemon juice:

  Club soda:

49. Identify Structure What property of multiplication allows you to multiply a rate by a conversion factor without changing its value? Explain.

SOLUTION:  

The Identity Property of Multiplication allows you to multiply a rate by a conversion factor without changing its value

because the conversion factor is equal to 1. For example, multiplying by  is the same as multiplying by 1 

because 12 inches equals 1 foot.

50. Building on the Essential Question Explain how you would convert 10 miles per hour to meters per second.

SOLUTION:  Sample answer: Use dimensional analysis.

So, 10 miles per hour is approximately equal to 4.47 meters per second.

51. A speed of 55 miles per hour is the same rate as which of the following?

 

A  34 kilometers per hourB  50 kilometers per hourC  88 kilometers per hourD  98 kilometers per hour

SOLUTION:  Use 1 mi ≈ 1.609 kilometers.

55 miles per hour is approximately equal to 88 kilometers per hour. Choice C is correct.

52. A piece of notebook paper measures  inches by 11 inches. Which of the following metric approximations is the 

same?

 

F  2 m by 2.8 mG  3 cm by 4 cmH  22 cm by 28 cmJ  30 m by 40 m

SOLUTION:  Use 1 in. ≈ 2.54 centimeters.

The approximate metric dimensions of a piece of notebook paper are 22 cm by 28 cm. Choice H is correct.

53. A car’s mileage is registered at 29,345.5 miles. The driver sees a sign that warns of road work in 1000 feet. What will be the car’s mileage when the road work begins?

 

A  29,345.7B  29,345.9C  29,356.2D  29,356.5

SOLUTION:  To find the car’s mileage when the road work begins, find the sum of the current mileage and the distance to the

road work, in miles.

29,345.5 + 0.2 = 29,345.7 When the road work begins, the mileage will be 29,345.7. Choice A is correct.

54. SHORT RESPONSE Convert 565 miles per hour to feet per second. Show the procedure you used.

SOLUTION:  Use dimensional analysis and the following conversion facts to convert 565 miles per hour to feet per second.1 mile = 5280 feet 1 hour = 60 min = 3600 seconds

 or 828.67 feet per second

Express each rate as a unit rate. Round to the nearest tenth or to the nearest cent, if necessary.55. $183 for 4 concert tickets

SOLUTION:  

The unit rate is $45.75 per ticket.

56. 100 feet in 14.5 seconds

SOLUTION:  

The unit rate is about 6.9 feet per second.

57. 254.1 miles on 10.5 gallons

SOLUTION:  

The unit rate is 24.2 miles per gallon.

58. 9 inches of snow in 12 hours

SOLUTION:  

Rounded to the nearest tenth, the unit rate is 0.8 inches per hour.

59. Financial Literacy Mrs. Gallagher wants to buy the package of soda that is less expensive per can. Which pack of sodas shown should she buy? Explain your reasoning.

SOLUTION:  

The 6-pack of soda costs about $0.37 per can. The 12-pack of soda costs about $0.35 per can. So, the 12-pack is less expensive.

Express each ratio as a fraction in simplest form.60. 12 cars out of 30 vehicles

SOLUTION:  

61. 5 cups to 5 quarts

SOLUTION:  Convert 5 quarts to cups. There are 4 cups in 1 quart.

62. 15 soccer balls out of 35 balls

SOLUTION:  

63. 8 pencils to 20 crayons

SOLUTION:  

Simplify each expression.64. (x – 3) + 2

SOLUTION:  

65. (8 • y) • (–4)

SOLUTION:  

66. 25 + (d –8)

SOLUTION:  

67. 9(5m)

SOLUTION:  

68. (x + 1) – 9

SOLUTION:  

69. 5(3 • r)

SOLUTION:  

70. Clive is making hamburgers for a cookout. How many -pound hamburgers can he make from  pounds of 

ground beef?

SOLUTION:  Words: The amount of ground beef needed for each hamburger multiplied by the number of hamburgers equals the total amount of ground beef. Variable: Let h = the number of hamburgers

Equation:

Clive can make 11 hamburgers.

Find each product or quotient.71. –12 • (–10)

SOLUTION:  The product of two integers with the same sign is positive. So, –12 • (–10) = 120.

72. –18 ÷ 3

SOLUTION:  The quotient of two integers with different signs is negative. So, –18 ÷ 3 = –6.

73. 9 • (–14)

SOLUTION:  The product of two integers with different signs is negative. So, 9 • (–14) = –126.

74. 54 ÷ (–6)

SOLUTION:  The quotient of two integers with different signs is negative. So, 54 ÷ (–6) = –9.

75. –14 • 2

SOLUTION:  The product of two integers with different signs is negative. So, –14 • 2 = –28.

76. –72 ÷ (–4)

SOLUTION:  The quotient of two integers with the same sign is positive. So, –72 ÷ (–4) = 18.

eSolutions Manual - Powered by Cognero Page 9

5-4 Converting Rates

Page 10: Crystal - Ms. Wilson's Math Classes · a. Crystal ran 10 kilometers in 64 minutes. Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming

1. In Brazil, about 20 acres of rainforest are destroyed each minute. At this rate, how much rainforest is destroyed per day?

SOLUTION:  

At the rate of 20 acres per minute, there are 28,800 acres of rainforest in Brazil destroyed per day.

2. Lexi can paint 5 yards of fencing in one hour. At this rate, how many inches does she paint per minute?

SOLUTION:  

At the rate of 5 yards per hour, Lexi can paint 3 inches per minute.

Complete each conversion. Round to the nearest hundredth, if necessary.3. 8 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

4. 5 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

5. 15 oz ≈ _ g

SOLUTION:  Use 1 oz ≈ 28.35 g.

6. 24 cm ≈ _ in.

SOLUTION:  Use 1 cm ≈ 0.394 in.

7. 9 pt ≈ _ L

SOLUTION:  Use 1 pt ≈ 0.473 L.

8. 3 m ≈ _ ft

SOLUTION:  Use 1 m ≈ 3.279 ft.

9. An elephant can eat up to 440 pounds of vegetation every day. How many grams per minute is this? Round to the nearest hundredth.

SOLUTION:  

An elephant can eat about 138.72 grams of vegetation per minute.

10. A candy company can produce 4800 sour lemon candies per minute. How many candies can they produce each hour?

SOLUTION:  

The company can produce 288,000 candies each hour.

11. In a recent year, 51.9 billion aluminum cans were recycled. About how many cans per week is this?

SOLUTION:  

About 1 billion aluminum cans were recycled per week.

12. The average American student spends almost 1500 hours per year watching television. To the nearest hundredth, how many minutes per day is this?

SOLUTION:  

The average American student spends 246.58 minutes per day watching television.

13. A thrill ride at an amusement park travels 55 miles per hour. To the nearest hundredth, how many feet per second is this?

SOLUTION:  

The thrill ride travels about 80.67 feet per second.

Complete each conversion. Round to the nearest hundredth, if necessary.14. 4 L ≈ _ qt

SOLUTION:  Use 1 L ≈ 1.057 qt.

15. 16 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

16. 13 m ≈ _ ft

SOLUTION:  Use 1 ft ≈ 0.305 m.

17. 8 yd ≈ _ m

SOLUTION:  Use 1 yd ≈ 0.914 m.

18. 18 lb ≈ _ kg

SOLUTION:  Use 1 lb ≈ 0.454 kg.

19. 7 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

20. 1500 g ≈ _ oz

SOLUTION:  Use 1 oz ≈ 28.35 g.

21. 15 ft ≈ _ m

SOLUTION:  Use 1 ft ≈ 0.305 m.

22. 28 fl oz ≈ _ mL

SOLUTION:  Use 1 fl oz ≈ 29.574 mL.

23. The velocity of sound through wood at 0° Celsius is 1454 meters per second. How many miles is this per hour? Round to the nearest hundredth.

SOLUTION:  

The velocity of sound through wood is approximately 3250.68 miles per hour.

24. A certain car in Canada can travel 15 kilometers per 1 liter of gasoline. How many miles per gallon is this? Round to the nearest hundredth.

SOLUTION:  

The car can travel approximately 35.28 miles per gallon.

Complete each conversion. Round to the nearest hundredth, if necessary.25. 8 in. ≈ _ mm

SOLUTION:  Use 1 in. ≈ 2.54 cm and 1 cm = 10 mm.

26. 16 L ≈ _ c

SOLUTION:  Use 1 L ≈ 2.114 pt and 1 pt = 2 cups.

27. 2 km ≈ _ yd

SOLUTION:  Use 1 km = 1000 m and 1 m ≈ 1.094 yd.

28. 250 fl oz ≈ _ L

SOLUTION:  Use 1 fl oz ≈ 29.574 mL and 1000 mL = 1 L.

29. 2750 g ≈ _ lb

SOLUTION:  Use 1 g ≈ 0.035 oz and 16 oz = 1 lb.

30. 5 gal ≈ _ mL

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 L = 1000 mL.

31. Crystal’s times for each portion of a triathlon are shown in the table. Round to the nearest hundredth.

a. How many meters per second did she run? b. What was her speed in miles per hour for the aquabike portion (swimming and biking)?

SOLUTION:  a. Crystal ran 10 kilometers in 64 minutes.

Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming and biking was 1.5 + 40 or 41.5 kilometers. Her time for theseportions was 40 + 86 or 126 minutes.

Crystal’s speed for the aquabike portion was about 12.27 miles per hour.

Order each group of rates from least to greatest.32. 100 oz/min, 2500 g/min, 10 lb/min

SOLUTION:  

5.51 lb/min < 6.25 lb/min < 10 lb/min Ordered from least to greatest, the rates are 2500 g/min, 100 oz/min, and 10 lb/min.

100 oz/min

2500 g/min

10 lb/min

33. 500 m/h, 7 yd/min, 6 in./s

SOLUTION:  

4.20 in./s < 5.47 in./s < 6 in./s Ordered from least to greatest, the rates are 7 yd/min, 500 m/h, and 6 in./s.

500 m/h

7 yd/min

6 in./s

34. 32 mi/gal, 15 m/mL, 6600 yd/qt

SOLUTION:  

6600 yd/qt < 14,080 yd/qt < 15,524 yd/qt Ordered from least to greatest, the rates are 6600 yd/qt, 32 mi/gal, and 15 m/mL.

32 mi/gal

15 m/mL

6600 yd/qt

35. 500 kg/h, 5 oz/s, 18 lb/min

SOLUTION:  

4.8 oz/s < 4.90 oz/s < 5 oz/s Ordered from least to greatest, the rates are 18 lb/min, 500 kg/h, and 5 oz/s.

500 kg/h

5 oz/s

18 lb/min

36. The sprinkler system in the Willis Tower pumps up to 1500 gallons of water per minute. How many liters of water

can the system pump in  minute? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L.

Divide the rate by 4 to find the amount of water pumped in  minute.

The water system in the Sears Tower can pump 1419.38 liters of water in  minute.

37. The average American consumes 20 gallons of ice cream in one year. At this rate, how many liters of ice cream will50 Americans consume in one week? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 yr = 52 wk.

Multiply the rate by 50 to find how many liters 50 Americans consume.

So, 50 Americans consume about 72.79 liters of ice cream per week.

Replace each _ with <, >, or = to make a true sentence.38. 10 m _ 390 in.

SOLUTION:  Use 1 m ≈ 3.279 ft and 1 ft = 12 in.

39. 520 oz _ 15 kg

SOLUTION:  Use 1 oz ≈ 28.35 g and 1000 g = 1 kg.

40. 14 pt _ 6622 mL

SOLUTION:  Use 1 pt ≈ 0.473 L and 1 L = 1000 mL.

Financial Literacy Use dimensional analysis and the table below to make each conversion. Round to the nearest hundredth, if necessary.

41. 150 dollars to euros

SOLUTION:  

So, 150 dollars is equal to 118.5 euros.

42. 275 dollars to pounds

SOLUTION:  

So, 275 dollars is equal to 175.18 pounds.

43. 570 yuan to dollars

SOLUTION:  

So, 570 yuan is equal to 89.41 dollars.

44. 500 pesos to dollars

SOLUTION:  

So, 500 pesos is approximately equal to 37.19 dollars.

45. Model with Mathematics Write and solve a real-world problem in which dimensional analysis is used to convert square feet to square yards. Hint: 1 square yard = 9 square feet

SOLUTION:  Sample answer: Macha needs 120 square feet of carpeting for her bedroom. How many square yards does she need?

Maria needs square yards.

46. Be Precise Give two examples of different measurements that are equivalent to 10 centimeters per second.

SOLUTION:  Sample answers:

Two measurements equivalent to 10 centimeters per second are 600 centimeters per minute and 360 meters per hour.

47. WHICH ONE DOESN’T BELONG? Select the rate that does not have the same value as the other three. Explain your reasoning.

SOLUTION:  Convert each rate to miles per hour and compare the values.

The rate that does not belong is 500 ft/min. All of the other rates are equal to 60 mi/h.

60 mi/h

88 ft/sec

500 ft/min

1440 mi/day

48. Persevere with Problems A recipe for fruit punch uses the ingredients shown. About how many cups of each ingredient are needed? Round to the nearest tenth.

SOLUTION:  Use 1000 mL = 1L, 1 L ≈ 2.114 pt, and 1 pt = 2 cups.  Cranberry juice:

  Apple juice:

  Pineapple juice:

  Lemon juice:

  Club soda:

49. Identify Structure What property of multiplication allows you to multiply a rate by a conversion factor without changing its value? Explain.

SOLUTION:  

The Identity Property of Multiplication allows you to multiply a rate by a conversion factor without changing its value

because the conversion factor is equal to 1. For example, multiplying by  is the same as multiplying by 1 

because 12 inches equals 1 foot.

50. Building on the Essential Question Explain how you would convert 10 miles per hour to meters per second.

SOLUTION:  Sample answer: Use dimensional analysis.

So, 10 miles per hour is approximately equal to 4.47 meters per second.

51. A speed of 55 miles per hour is the same rate as which of the following?

 

A  34 kilometers per hourB  50 kilometers per hourC  88 kilometers per hourD  98 kilometers per hour

SOLUTION:  Use 1 mi ≈ 1.609 kilometers.

55 miles per hour is approximately equal to 88 kilometers per hour. Choice C is correct.

52. A piece of notebook paper measures  inches by 11 inches. Which of the following metric approximations is the 

same?

 

F  2 m by 2.8 mG  3 cm by 4 cmH  22 cm by 28 cmJ  30 m by 40 m

SOLUTION:  Use 1 in. ≈ 2.54 centimeters.

The approximate metric dimensions of a piece of notebook paper are 22 cm by 28 cm. Choice H is correct.

53. A car’s mileage is registered at 29,345.5 miles. The driver sees a sign that warns of road work in 1000 feet. What will be the car’s mileage when the road work begins?

 

A  29,345.7B  29,345.9C  29,356.2D  29,356.5

SOLUTION:  To find the car’s mileage when the road work begins, find the sum of the current mileage and the distance to the

road work, in miles.

29,345.5 + 0.2 = 29,345.7 When the road work begins, the mileage will be 29,345.7. Choice A is correct.

54. SHORT RESPONSE Convert 565 miles per hour to feet per second. Show the procedure you used.

SOLUTION:  Use dimensional analysis and the following conversion facts to convert 565 miles per hour to feet per second.1 mile = 5280 feet 1 hour = 60 min = 3600 seconds

 or 828.67 feet per second

Express each rate as a unit rate. Round to the nearest tenth or to the nearest cent, if necessary.55. $183 for 4 concert tickets

SOLUTION:  

The unit rate is $45.75 per ticket.

56. 100 feet in 14.5 seconds

SOLUTION:  

The unit rate is about 6.9 feet per second.

57. 254.1 miles on 10.5 gallons

SOLUTION:  

The unit rate is 24.2 miles per gallon.

58. 9 inches of snow in 12 hours

SOLUTION:  

Rounded to the nearest tenth, the unit rate is 0.8 inches per hour.

59. Financial Literacy Mrs. Gallagher wants to buy the package of soda that is less expensive per can. Which pack of sodas shown should she buy? Explain your reasoning.

SOLUTION:  

The 6-pack of soda costs about $0.37 per can. The 12-pack of soda costs about $0.35 per can. So, the 12-pack is less expensive.

Express each ratio as a fraction in simplest form.60. 12 cars out of 30 vehicles

SOLUTION:  

61. 5 cups to 5 quarts

SOLUTION:  Convert 5 quarts to cups. There are 4 cups in 1 quart.

62. 15 soccer balls out of 35 balls

SOLUTION:  

63. 8 pencils to 20 crayons

SOLUTION:  

Simplify each expression.64. (x – 3) + 2

SOLUTION:  

65. (8 • y) • (–4)

SOLUTION:  

66. 25 + (d –8)

SOLUTION:  

67. 9(5m)

SOLUTION:  

68. (x + 1) – 9

SOLUTION:  

69. 5(3 • r)

SOLUTION:  

70. Clive is making hamburgers for a cookout. How many -pound hamburgers can he make from  pounds of 

ground beef?

SOLUTION:  Words: The amount of ground beef needed for each hamburger multiplied by the number of hamburgers equals the total amount of ground beef. Variable: Let h = the number of hamburgers

Equation:

Clive can make 11 hamburgers.

Find each product or quotient.71. –12 • (–10)

SOLUTION:  The product of two integers with the same sign is positive. So, –12 • (–10) = 120.

72. –18 ÷ 3

SOLUTION:  The quotient of two integers with different signs is negative. So, –18 ÷ 3 = –6.

73. 9 • (–14)

SOLUTION:  The product of two integers with different signs is negative. So, 9 • (–14) = –126.

74. 54 ÷ (–6)

SOLUTION:  The quotient of two integers with different signs is negative. So, 54 ÷ (–6) = –9.

75. –14 • 2

SOLUTION:  The product of two integers with different signs is negative. So, –14 • 2 = –28.

76. –72 ÷ (–4)

SOLUTION:  The quotient of two integers with the same sign is positive. So, –72 ÷ (–4) = 18.

eSolutions Manual - Powered by Cognero Page 10

5-4 Converting Rates

Page 11: Crystal - Ms. Wilson's Math Classes · a. Crystal ran 10 kilometers in 64 minutes. Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming

1. In Brazil, about 20 acres of rainforest are destroyed each minute. At this rate, how much rainforest is destroyed per day?

SOLUTION:  

At the rate of 20 acres per minute, there are 28,800 acres of rainforest in Brazil destroyed per day.

2. Lexi can paint 5 yards of fencing in one hour. At this rate, how many inches does she paint per minute?

SOLUTION:  

At the rate of 5 yards per hour, Lexi can paint 3 inches per minute.

Complete each conversion. Round to the nearest hundredth, if necessary.3. 8 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

4. 5 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

5. 15 oz ≈ _ g

SOLUTION:  Use 1 oz ≈ 28.35 g.

6. 24 cm ≈ _ in.

SOLUTION:  Use 1 cm ≈ 0.394 in.

7. 9 pt ≈ _ L

SOLUTION:  Use 1 pt ≈ 0.473 L.

8. 3 m ≈ _ ft

SOLUTION:  Use 1 m ≈ 3.279 ft.

9. An elephant can eat up to 440 pounds of vegetation every day. How many grams per minute is this? Round to the nearest hundredth.

SOLUTION:  

An elephant can eat about 138.72 grams of vegetation per minute.

10. A candy company can produce 4800 sour lemon candies per minute. How many candies can they produce each hour?

SOLUTION:  

The company can produce 288,000 candies each hour.

11. In a recent year, 51.9 billion aluminum cans were recycled. About how many cans per week is this?

SOLUTION:  

About 1 billion aluminum cans were recycled per week.

12. The average American student spends almost 1500 hours per year watching television. To the nearest hundredth, how many minutes per day is this?

SOLUTION:  

The average American student spends 246.58 minutes per day watching television.

13. A thrill ride at an amusement park travels 55 miles per hour. To the nearest hundredth, how many feet per second is this?

SOLUTION:  

The thrill ride travels about 80.67 feet per second.

Complete each conversion. Round to the nearest hundredth, if necessary.14. 4 L ≈ _ qt

SOLUTION:  Use 1 L ≈ 1.057 qt.

15. 16 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

16. 13 m ≈ _ ft

SOLUTION:  Use 1 ft ≈ 0.305 m.

17. 8 yd ≈ _ m

SOLUTION:  Use 1 yd ≈ 0.914 m.

18. 18 lb ≈ _ kg

SOLUTION:  Use 1 lb ≈ 0.454 kg.

19. 7 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

20. 1500 g ≈ _ oz

SOLUTION:  Use 1 oz ≈ 28.35 g.

21. 15 ft ≈ _ m

SOLUTION:  Use 1 ft ≈ 0.305 m.

22. 28 fl oz ≈ _ mL

SOLUTION:  Use 1 fl oz ≈ 29.574 mL.

23. The velocity of sound through wood at 0° Celsius is 1454 meters per second. How many miles is this per hour? Round to the nearest hundredth.

SOLUTION:  

The velocity of sound through wood is approximately 3250.68 miles per hour.

24. A certain car in Canada can travel 15 kilometers per 1 liter of gasoline. How many miles per gallon is this? Round to the nearest hundredth.

SOLUTION:  

The car can travel approximately 35.28 miles per gallon.

Complete each conversion. Round to the nearest hundredth, if necessary.25. 8 in. ≈ _ mm

SOLUTION:  Use 1 in. ≈ 2.54 cm and 1 cm = 10 mm.

26. 16 L ≈ _ c

SOLUTION:  Use 1 L ≈ 2.114 pt and 1 pt = 2 cups.

27. 2 km ≈ _ yd

SOLUTION:  Use 1 km = 1000 m and 1 m ≈ 1.094 yd.

28. 250 fl oz ≈ _ L

SOLUTION:  Use 1 fl oz ≈ 29.574 mL and 1000 mL = 1 L.

29. 2750 g ≈ _ lb

SOLUTION:  Use 1 g ≈ 0.035 oz and 16 oz = 1 lb.

30. 5 gal ≈ _ mL

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 L = 1000 mL.

31. Crystal’s times for each portion of a triathlon are shown in the table. Round to the nearest hundredth.

a. How many meters per second did she run? b. What was her speed in miles per hour for the aquabike portion (swimming and biking)?

SOLUTION:  a. Crystal ran 10 kilometers in 64 minutes.

Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming and biking was 1.5 + 40 or 41.5 kilometers. Her time for theseportions was 40 + 86 or 126 minutes.

Crystal’s speed for the aquabike portion was about 12.27 miles per hour.

Order each group of rates from least to greatest.32. 100 oz/min, 2500 g/min, 10 lb/min

SOLUTION:  

5.51 lb/min < 6.25 lb/min < 10 lb/min Ordered from least to greatest, the rates are 2500 g/min, 100 oz/min, and 10 lb/min.

100 oz/min

2500 g/min

10 lb/min

33. 500 m/h, 7 yd/min, 6 in./s

SOLUTION:  

4.20 in./s < 5.47 in./s < 6 in./s Ordered from least to greatest, the rates are 7 yd/min, 500 m/h, and 6 in./s.

500 m/h

7 yd/min

6 in./s

34. 32 mi/gal, 15 m/mL, 6600 yd/qt

SOLUTION:  

6600 yd/qt < 14,080 yd/qt < 15,524 yd/qt Ordered from least to greatest, the rates are 6600 yd/qt, 32 mi/gal, and 15 m/mL.

32 mi/gal

15 m/mL

6600 yd/qt

35. 500 kg/h, 5 oz/s, 18 lb/min

SOLUTION:  

4.8 oz/s < 4.90 oz/s < 5 oz/s Ordered from least to greatest, the rates are 18 lb/min, 500 kg/h, and 5 oz/s.

500 kg/h

5 oz/s

18 lb/min

36. The sprinkler system in the Willis Tower pumps up to 1500 gallons of water per minute. How many liters of water

can the system pump in  minute? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L.

Divide the rate by 4 to find the amount of water pumped in  minute.

The water system in the Sears Tower can pump 1419.38 liters of water in  minute.

37. The average American consumes 20 gallons of ice cream in one year. At this rate, how many liters of ice cream will50 Americans consume in one week? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 yr = 52 wk.

Multiply the rate by 50 to find how many liters 50 Americans consume.

So, 50 Americans consume about 72.79 liters of ice cream per week.

Replace each _ with <, >, or = to make a true sentence.38. 10 m _ 390 in.

SOLUTION:  Use 1 m ≈ 3.279 ft and 1 ft = 12 in.

39. 520 oz _ 15 kg

SOLUTION:  Use 1 oz ≈ 28.35 g and 1000 g = 1 kg.

40. 14 pt _ 6622 mL

SOLUTION:  Use 1 pt ≈ 0.473 L and 1 L = 1000 mL.

Financial Literacy Use dimensional analysis and the table below to make each conversion. Round to the nearest hundredth, if necessary.

41. 150 dollars to euros

SOLUTION:  

So, 150 dollars is equal to 118.5 euros.

42. 275 dollars to pounds

SOLUTION:  

So, 275 dollars is equal to 175.18 pounds.

43. 570 yuan to dollars

SOLUTION:  

So, 570 yuan is equal to 89.41 dollars.

44. 500 pesos to dollars

SOLUTION:  

So, 500 pesos is approximately equal to 37.19 dollars.

45. Model with Mathematics Write and solve a real-world problem in which dimensional analysis is used to convert square feet to square yards. Hint: 1 square yard = 9 square feet

SOLUTION:  Sample answer: Macha needs 120 square feet of carpeting for her bedroom. How many square yards does she need?

Maria needs square yards.

46. Be Precise Give two examples of different measurements that are equivalent to 10 centimeters per second.

SOLUTION:  Sample answers:

Two measurements equivalent to 10 centimeters per second are 600 centimeters per minute and 360 meters per hour.

47. WHICH ONE DOESN’T BELONG? Select the rate that does not have the same value as the other three. Explain your reasoning.

SOLUTION:  Convert each rate to miles per hour and compare the values.

The rate that does not belong is 500 ft/min. All of the other rates are equal to 60 mi/h.

60 mi/h

88 ft/sec

500 ft/min

1440 mi/day

48. Persevere with Problems A recipe for fruit punch uses the ingredients shown. About how many cups of each ingredient are needed? Round to the nearest tenth.

SOLUTION:  Use 1000 mL = 1L, 1 L ≈ 2.114 pt, and 1 pt = 2 cups.  Cranberry juice:

  Apple juice:

  Pineapple juice:

  Lemon juice:

  Club soda:

49. Identify Structure What property of multiplication allows you to multiply a rate by a conversion factor without changing its value? Explain.

SOLUTION:  

The Identity Property of Multiplication allows you to multiply a rate by a conversion factor without changing its value

because the conversion factor is equal to 1. For example, multiplying by  is the same as multiplying by 1 

because 12 inches equals 1 foot.

50. Building on the Essential Question Explain how you would convert 10 miles per hour to meters per second.

SOLUTION:  Sample answer: Use dimensional analysis.

So, 10 miles per hour is approximately equal to 4.47 meters per second.

51. A speed of 55 miles per hour is the same rate as which of the following?

 

A  34 kilometers per hourB  50 kilometers per hourC  88 kilometers per hourD  98 kilometers per hour

SOLUTION:  Use 1 mi ≈ 1.609 kilometers.

55 miles per hour is approximately equal to 88 kilometers per hour. Choice C is correct.

52. A piece of notebook paper measures  inches by 11 inches. Which of the following metric approximations is the 

same?

 

F  2 m by 2.8 mG  3 cm by 4 cmH  22 cm by 28 cmJ  30 m by 40 m

SOLUTION:  Use 1 in. ≈ 2.54 centimeters.

The approximate metric dimensions of a piece of notebook paper are 22 cm by 28 cm. Choice H is correct.

53. A car’s mileage is registered at 29,345.5 miles. The driver sees a sign that warns of road work in 1000 feet. What will be the car’s mileage when the road work begins?

 

A  29,345.7B  29,345.9C  29,356.2D  29,356.5

SOLUTION:  To find the car’s mileage when the road work begins, find the sum of the current mileage and the distance to the

road work, in miles.

29,345.5 + 0.2 = 29,345.7 When the road work begins, the mileage will be 29,345.7. Choice A is correct.

54. SHORT RESPONSE Convert 565 miles per hour to feet per second. Show the procedure you used.

SOLUTION:  Use dimensional analysis and the following conversion facts to convert 565 miles per hour to feet per second.1 mile = 5280 feet 1 hour = 60 min = 3600 seconds

 or 828.67 feet per second

Express each rate as a unit rate. Round to the nearest tenth or to the nearest cent, if necessary.55. $183 for 4 concert tickets

SOLUTION:  

The unit rate is $45.75 per ticket.

56. 100 feet in 14.5 seconds

SOLUTION:  

The unit rate is about 6.9 feet per second.

57. 254.1 miles on 10.5 gallons

SOLUTION:  

The unit rate is 24.2 miles per gallon.

58. 9 inches of snow in 12 hours

SOLUTION:  

Rounded to the nearest tenth, the unit rate is 0.8 inches per hour.

59. Financial Literacy Mrs. Gallagher wants to buy the package of soda that is less expensive per can. Which pack of sodas shown should she buy? Explain your reasoning.

SOLUTION:  

The 6-pack of soda costs about $0.37 per can. The 12-pack of soda costs about $0.35 per can. So, the 12-pack is less expensive.

Express each ratio as a fraction in simplest form.60. 12 cars out of 30 vehicles

SOLUTION:  

61. 5 cups to 5 quarts

SOLUTION:  Convert 5 quarts to cups. There are 4 cups in 1 quart.

62. 15 soccer balls out of 35 balls

SOLUTION:  

63. 8 pencils to 20 crayons

SOLUTION:  

Simplify each expression.64. (x – 3) + 2

SOLUTION:  

65. (8 • y) • (–4)

SOLUTION:  

66. 25 + (d –8)

SOLUTION:  

67. 9(5m)

SOLUTION:  

68. (x + 1) – 9

SOLUTION:  

69. 5(3 • r)

SOLUTION:  

70. Clive is making hamburgers for a cookout. How many -pound hamburgers can he make from  pounds of 

ground beef?

SOLUTION:  Words: The amount of ground beef needed for each hamburger multiplied by the number of hamburgers equals the total amount of ground beef. Variable: Let h = the number of hamburgers

Equation:

Clive can make 11 hamburgers.

Find each product or quotient.71. –12 • (–10)

SOLUTION:  The product of two integers with the same sign is positive. So, –12 • (–10) = 120.

72. –18 ÷ 3

SOLUTION:  The quotient of two integers with different signs is negative. So, –18 ÷ 3 = –6.

73. 9 • (–14)

SOLUTION:  The product of two integers with different signs is negative. So, 9 • (–14) = –126.

74. 54 ÷ (–6)

SOLUTION:  The quotient of two integers with different signs is negative. So, 54 ÷ (–6) = –9.

75. –14 • 2

SOLUTION:  The product of two integers with different signs is negative. So, –14 • 2 = –28.

76. –72 ÷ (–4)

SOLUTION:  The quotient of two integers with the same sign is positive. So, –72 ÷ (–4) = 18.

eSolutions Manual - Powered by Cognero Page 11

5-4 Converting Rates

Page 12: Crystal - Ms. Wilson's Math Classes · a. Crystal ran 10 kilometers in 64 minutes. Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming

1. In Brazil, about 20 acres of rainforest are destroyed each minute. At this rate, how much rainforest is destroyed per day?

SOLUTION:  

At the rate of 20 acres per minute, there are 28,800 acres of rainforest in Brazil destroyed per day.

2. Lexi can paint 5 yards of fencing in one hour. At this rate, how many inches does she paint per minute?

SOLUTION:  

At the rate of 5 yards per hour, Lexi can paint 3 inches per minute.

Complete each conversion. Round to the nearest hundredth, if necessary.3. 8 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

4. 5 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

5. 15 oz ≈ _ g

SOLUTION:  Use 1 oz ≈ 28.35 g.

6. 24 cm ≈ _ in.

SOLUTION:  Use 1 cm ≈ 0.394 in.

7. 9 pt ≈ _ L

SOLUTION:  Use 1 pt ≈ 0.473 L.

8. 3 m ≈ _ ft

SOLUTION:  Use 1 m ≈ 3.279 ft.

9. An elephant can eat up to 440 pounds of vegetation every day. How many grams per minute is this? Round to the nearest hundredth.

SOLUTION:  

An elephant can eat about 138.72 grams of vegetation per minute.

10. A candy company can produce 4800 sour lemon candies per minute. How many candies can they produce each hour?

SOLUTION:  

The company can produce 288,000 candies each hour.

11. In a recent year, 51.9 billion aluminum cans were recycled. About how many cans per week is this?

SOLUTION:  

About 1 billion aluminum cans were recycled per week.

12. The average American student spends almost 1500 hours per year watching television. To the nearest hundredth, how many minutes per day is this?

SOLUTION:  

The average American student spends 246.58 minutes per day watching television.

13. A thrill ride at an amusement park travels 55 miles per hour. To the nearest hundredth, how many feet per second is this?

SOLUTION:  

The thrill ride travels about 80.67 feet per second.

Complete each conversion. Round to the nearest hundredth, if necessary.14. 4 L ≈ _ qt

SOLUTION:  Use 1 L ≈ 1.057 qt.

15. 16 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

16. 13 m ≈ _ ft

SOLUTION:  Use 1 ft ≈ 0.305 m.

17. 8 yd ≈ _ m

SOLUTION:  Use 1 yd ≈ 0.914 m.

18. 18 lb ≈ _ kg

SOLUTION:  Use 1 lb ≈ 0.454 kg.

19. 7 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

20. 1500 g ≈ _ oz

SOLUTION:  Use 1 oz ≈ 28.35 g.

21. 15 ft ≈ _ m

SOLUTION:  Use 1 ft ≈ 0.305 m.

22. 28 fl oz ≈ _ mL

SOLUTION:  Use 1 fl oz ≈ 29.574 mL.

23. The velocity of sound through wood at 0° Celsius is 1454 meters per second. How many miles is this per hour? Round to the nearest hundredth.

SOLUTION:  

The velocity of sound through wood is approximately 3250.68 miles per hour.

24. A certain car in Canada can travel 15 kilometers per 1 liter of gasoline. How many miles per gallon is this? Round to the nearest hundredth.

SOLUTION:  

The car can travel approximately 35.28 miles per gallon.

Complete each conversion. Round to the nearest hundredth, if necessary.25. 8 in. ≈ _ mm

SOLUTION:  Use 1 in. ≈ 2.54 cm and 1 cm = 10 mm.

26. 16 L ≈ _ c

SOLUTION:  Use 1 L ≈ 2.114 pt and 1 pt = 2 cups.

27. 2 km ≈ _ yd

SOLUTION:  Use 1 km = 1000 m and 1 m ≈ 1.094 yd.

28. 250 fl oz ≈ _ L

SOLUTION:  Use 1 fl oz ≈ 29.574 mL and 1000 mL = 1 L.

29. 2750 g ≈ _ lb

SOLUTION:  Use 1 g ≈ 0.035 oz and 16 oz = 1 lb.

30. 5 gal ≈ _ mL

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 L = 1000 mL.

31. Crystal’s times for each portion of a triathlon are shown in the table. Round to the nearest hundredth.

a. How many meters per second did she run? b. What was her speed in miles per hour for the aquabike portion (swimming and biking)?

SOLUTION:  a. Crystal ran 10 kilometers in 64 minutes.

Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming and biking was 1.5 + 40 or 41.5 kilometers. Her time for theseportions was 40 + 86 or 126 minutes.

Crystal’s speed for the aquabike portion was about 12.27 miles per hour.

Order each group of rates from least to greatest.32. 100 oz/min, 2500 g/min, 10 lb/min

SOLUTION:  

5.51 lb/min < 6.25 lb/min < 10 lb/min Ordered from least to greatest, the rates are 2500 g/min, 100 oz/min, and 10 lb/min.

100 oz/min

2500 g/min

10 lb/min

33. 500 m/h, 7 yd/min, 6 in./s

SOLUTION:  

4.20 in./s < 5.47 in./s < 6 in./s Ordered from least to greatest, the rates are 7 yd/min, 500 m/h, and 6 in./s.

500 m/h

7 yd/min

6 in./s

34. 32 mi/gal, 15 m/mL, 6600 yd/qt

SOLUTION:  

6600 yd/qt < 14,080 yd/qt < 15,524 yd/qt Ordered from least to greatest, the rates are 6600 yd/qt, 32 mi/gal, and 15 m/mL.

32 mi/gal

15 m/mL

6600 yd/qt

35. 500 kg/h, 5 oz/s, 18 lb/min

SOLUTION:  

4.8 oz/s < 4.90 oz/s < 5 oz/s Ordered from least to greatest, the rates are 18 lb/min, 500 kg/h, and 5 oz/s.

500 kg/h

5 oz/s

18 lb/min

36. The sprinkler system in the Willis Tower pumps up to 1500 gallons of water per minute. How many liters of water

can the system pump in  minute? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L.

Divide the rate by 4 to find the amount of water pumped in  minute.

The water system in the Sears Tower can pump 1419.38 liters of water in  minute.

37. The average American consumes 20 gallons of ice cream in one year. At this rate, how many liters of ice cream will50 Americans consume in one week? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 yr = 52 wk.

Multiply the rate by 50 to find how many liters 50 Americans consume.

So, 50 Americans consume about 72.79 liters of ice cream per week.

Replace each _ with <, >, or = to make a true sentence.38. 10 m _ 390 in.

SOLUTION:  Use 1 m ≈ 3.279 ft and 1 ft = 12 in.

39. 520 oz _ 15 kg

SOLUTION:  Use 1 oz ≈ 28.35 g and 1000 g = 1 kg.

40. 14 pt _ 6622 mL

SOLUTION:  Use 1 pt ≈ 0.473 L and 1 L = 1000 mL.

Financial Literacy Use dimensional analysis and the table below to make each conversion. Round to the nearest hundredth, if necessary.

41. 150 dollars to euros

SOLUTION:  

So, 150 dollars is equal to 118.5 euros.

42. 275 dollars to pounds

SOLUTION:  

So, 275 dollars is equal to 175.18 pounds.

43. 570 yuan to dollars

SOLUTION:  

So, 570 yuan is equal to 89.41 dollars.

44. 500 pesos to dollars

SOLUTION:  

So, 500 pesos is approximately equal to 37.19 dollars.

45. Model with Mathematics Write and solve a real-world problem in which dimensional analysis is used to convert square feet to square yards. Hint: 1 square yard = 9 square feet

SOLUTION:  Sample answer: Macha needs 120 square feet of carpeting for her bedroom. How many square yards does she need?

Maria needs square yards.

46. Be Precise Give two examples of different measurements that are equivalent to 10 centimeters per second.

SOLUTION:  Sample answers:

Two measurements equivalent to 10 centimeters per second are 600 centimeters per minute and 360 meters per hour.

47. WHICH ONE DOESN’T BELONG? Select the rate that does not have the same value as the other three. Explain your reasoning.

SOLUTION:  Convert each rate to miles per hour and compare the values.

The rate that does not belong is 500 ft/min. All of the other rates are equal to 60 mi/h.

60 mi/h

88 ft/sec

500 ft/min

1440 mi/day

48. Persevere with Problems A recipe for fruit punch uses the ingredients shown. About how many cups of each ingredient are needed? Round to the nearest tenth.

SOLUTION:  Use 1000 mL = 1L, 1 L ≈ 2.114 pt, and 1 pt = 2 cups.  Cranberry juice:

  Apple juice:

  Pineapple juice:

  Lemon juice:

  Club soda:

49. Identify Structure What property of multiplication allows you to multiply a rate by a conversion factor without changing its value? Explain.

SOLUTION:  

The Identity Property of Multiplication allows you to multiply a rate by a conversion factor without changing its value

because the conversion factor is equal to 1. For example, multiplying by  is the same as multiplying by 1 

because 12 inches equals 1 foot.

50. Building on the Essential Question Explain how you would convert 10 miles per hour to meters per second.

SOLUTION:  Sample answer: Use dimensional analysis.

So, 10 miles per hour is approximately equal to 4.47 meters per second.

51. A speed of 55 miles per hour is the same rate as which of the following?

 

A  34 kilometers per hourB  50 kilometers per hourC  88 kilometers per hourD  98 kilometers per hour

SOLUTION:  Use 1 mi ≈ 1.609 kilometers.

55 miles per hour is approximately equal to 88 kilometers per hour. Choice C is correct.

52. A piece of notebook paper measures  inches by 11 inches. Which of the following metric approximations is the 

same?

 

F  2 m by 2.8 mG  3 cm by 4 cmH  22 cm by 28 cmJ  30 m by 40 m

SOLUTION:  Use 1 in. ≈ 2.54 centimeters.

The approximate metric dimensions of a piece of notebook paper are 22 cm by 28 cm. Choice H is correct.

53. A car’s mileage is registered at 29,345.5 miles. The driver sees a sign that warns of road work in 1000 feet. What will be the car’s mileage when the road work begins?

 

A  29,345.7B  29,345.9C  29,356.2D  29,356.5

SOLUTION:  To find the car’s mileage when the road work begins, find the sum of the current mileage and the distance to the

road work, in miles.

29,345.5 + 0.2 = 29,345.7 When the road work begins, the mileage will be 29,345.7. Choice A is correct.

54. SHORT RESPONSE Convert 565 miles per hour to feet per second. Show the procedure you used.

SOLUTION:  Use dimensional analysis and the following conversion facts to convert 565 miles per hour to feet per second.1 mile = 5280 feet 1 hour = 60 min = 3600 seconds

 or 828.67 feet per second

Express each rate as a unit rate. Round to the nearest tenth or to the nearest cent, if necessary.55. $183 for 4 concert tickets

SOLUTION:  

The unit rate is $45.75 per ticket.

56. 100 feet in 14.5 seconds

SOLUTION:  

The unit rate is about 6.9 feet per second.

57. 254.1 miles on 10.5 gallons

SOLUTION:  

The unit rate is 24.2 miles per gallon.

58. 9 inches of snow in 12 hours

SOLUTION:  

Rounded to the nearest tenth, the unit rate is 0.8 inches per hour.

59. Financial Literacy Mrs. Gallagher wants to buy the package of soda that is less expensive per can. Which pack of sodas shown should she buy? Explain your reasoning.

SOLUTION:  

The 6-pack of soda costs about $0.37 per can. The 12-pack of soda costs about $0.35 per can. So, the 12-pack is less expensive.

Express each ratio as a fraction in simplest form.60. 12 cars out of 30 vehicles

SOLUTION:  

61. 5 cups to 5 quarts

SOLUTION:  Convert 5 quarts to cups. There are 4 cups in 1 quart.

62. 15 soccer balls out of 35 balls

SOLUTION:  

63. 8 pencils to 20 crayons

SOLUTION:  

Simplify each expression.64. (x – 3) + 2

SOLUTION:  

65. (8 • y) • (–4)

SOLUTION:  

66. 25 + (d –8)

SOLUTION:  

67. 9(5m)

SOLUTION:  

68. (x + 1) – 9

SOLUTION:  

69. 5(3 • r)

SOLUTION:  

70. Clive is making hamburgers for a cookout. How many -pound hamburgers can he make from  pounds of 

ground beef?

SOLUTION:  Words: The amount of ground beef needed for each hamburger multiplied by the number of hamburgers equals the total amount of ground beef. Variable: Let h = the number of hamburgers

Equation:

Clive can make 11 hamburgers.

Find each product or quotient.71. –12 • (–10)

SOLUTION:  The product of two integers with the same sign is positive. So, –12 • (–10) = 120.

72. –18 ÷ 3

SOLUTION:  The quotient of two integers with different signs is negative. So, –18 ÷ 3 = –6.

73. 9 • (–14)

SOLUTION:  The product of two integers with different signs is negative. So, 9 • (–14) = –126.

74. 54 ÷ (–6)

SOLUTION:  The quotient of two integers with different signs is negative. So, 54 ÷ (–6) = –9.

75. –14 • 2

SOLUTION:  The product of two integers with different signs is negative. So, –14 • 2 = –28.

76. –72 ÷ (–4)

SOLUTION:  The quotient of two integers with the same sign is positive. So, –72 ÷ (–4) = 18.

eSolutions Manual - Powered by Cognero Page 12

5-4 Converting Rates

Page 13: Crystal - Ms. Wilson's Math Classes · a. Crystal ran 10 kilometers in 64 minutes. Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming

1. In Brazil, about 20 acres of rainforest are destroyed each minute. At this rate, how much rainforest is destroyed per day?

SOLUTION:  

At the rate of 20 acres per minute, there are 28,800 acres of rainforest in Brazil destroyed per day.

2. Lexi can paint 5 yards of fencing in one hour. At this rate, how many inches does she paint per minute?

SOLUTION:  

At the rate of 5 yards per hour, Lexi can paint 3 inches per minute.

Complete each conversion. Round to the nearest hundredth, if necessary.3. 8 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

4. 5 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

5. 15 oz ≈ _ g

SOLUTION:  Use 1 oz ≈ 28.35 g.

6. 24 cm ≈ _ in.

SOLUTION:  Use 1 cm ≈ 0.394 in.

7. 9 pt ≈ _ L

SOLUTION:  Use 1 pt ≈ 0.473 L.

8. 3 m ≈ _ ft

SOLUTION:  Use 1 m ≈ 3.279 ft.

9. An elephant can eat up to 440 pounds of vegetation every day. How many grams per minute is this? Round to the nearest hundredth.

SOLUTION:  

An elephant can eat about 138.72 grams of vegetation per minute.

10. A candy company can produce 4800 sour lemon candies per minute. How many candies can they produce each hour?

SOLUTION:  

The company can produce 288,000 candies each hour.

11. In a recent year, 51.9 billion aluminum cans were recycled. About how many cans per week is this?

SOLUTION:  

About 1 billion aluminum cans were recycled per week.

12. The average American student spends almost 1500 hours per year watching television. To the nearest hundredth, how many minutes per day is this?

SOLUTION:  

The average American student spends 246.58 minutes per day watching television.

13. A thrill ride at an amusement park travels 55 miles per hour. To the nearest hundredth, how many feet per second is this?

SOLUTION:  

The thrill ride travels about 80.67 feet per second.

Complete each conversion. Round to the nearest hundredth, if necessary.14. 4 L ≈ _ qt

SOLUTION:  Use 1 L ≈ 1.057 qt.

15. 16 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

16. 13 m ≈ _ ft

SOLUTION:  Use 1 ft ≈ 0.305 m.

17. 8 yd ≈ _ m

SOLUTION:  Use 1 yd ≈ 0.914 m.

18. 18 lb ≈ _ kg

SOLUTION:  Use 1 lb ≈ 0.454 kg.

19. 7 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

20. 1500 g ≈ _ oz

SOLUTION:  Use 1 oz ≈ 28.35 g.

21. 15 ft ≈ _ m

SOLUTION:  Use 1 ft ≈ 0.305 m.

22. 28 fl oz ≈ _ mL

SOLUTION:  Use 1 fl oz ≈ 29.574 mL.

23. The velocity of sound through wood at 0° Celsius is 1454 meters per second. How many miles is this per hour? Round to the nearest hundredth.

SOLUTION:  

The velocity of sound through wood is approximately 3250.68 miles per hour.

24. A certain car in Canada can travel 15 kilometers per 1 liter of gasoline. How many miles per gallon is this? Round to the nearest hundredth.

SOLUTION:  

The car can travel approximately 35.28 miles per gallon.

Complete each conversion. Round to the nearest hundredth, if necessary.25. 8 in. ≈ _ mm

SOLUTION:  Use 1 in. ≈ 2.54 cm and 1 cm = 10 mm.

26. 16 L ≈ _ c

SOLUTION:  Use 1 L ≈ 2.114 pt and 1 pt = 2 cups.

27. 2 km ≈ _ yd

SOLUTION:  Use 1 km = 1000 m and 1 m ≈ 1.094 yd.

28. 250 fl oz ≈ _ L

SOLUTION:  Use 1 fl oz ≈ 29.574 mL and 1000 mL = 1 L.

29. 2750 g ≈ _ lb

SOLUTION:  Use 1 g ≈ 0.035 oz and 16 oz = 1 lb.

30. 5 gal ≈ _ mL

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 L = 1000 mL.

31. Crystal’s times for each portion of a triathlon are shown in the table. Round to the nearest hundredth.

a. How many meters per second did she run? b. What was her speed in miles per hour for the aquabike portion (swimming and biking)?

SOLUTION:  a. Crystal ran 10 kilometers in 64 minutes.

Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming and biking was 1.5 + 40 or 41.5 kilometers. Her time for theseportions was 40 + 86 or 126 minutes.

Crystal’s speed for the aquabike portion was about 12.27 miles per hour.

Order each group of rates from least to greatest.32. 100 oz/min, 2500 g/min, 10 lb/min

SOLUTION:  

5.51 lb/min < 6.25 lb/min < 10 lb/min Ordered from least to greatest, the rates are 2500 g/min, 100 oz/min, and 10 lb/min.

100 oz/min

2500 g/min

10 lb/min

33. 500 m/h, 7 yd/min, 6 in./s

SOLUTION:  

4.20 in./s < 5.47 in./s < 6 in./s Ordered from least to greatest, the rates are 7 yd/min, 500 m/h, and 6 in./s.

500 m/h

7 yd/min

6 in./s

34. 32 mi/gal, 15 m/mL, 6600 yd/qt

SOLUTION:  

6600 yd/qt < 14,080 yd/qt < 15,524 yd/qt Ordered from least to greatest, the rates are 6600 yd/qt, 32 mi/gal, and 15 m/mL.

32 mi/gal

15 m/mL

6600 yd/qt

35. 500 kg/h, 5 oz/s, 18 lb/min

SOLUTION:  

4.8 oz/s < 4.90 oz/s < 5 oz/s Ordered from least to greatest, the rates are 18 lb/min, 500 kg/h, and 5 oz/s.

500 kg/h

5 oz/s

18 lb/min

36. The sprinkler system in the Willis Tower pumps up to 1500 gallons of water per minute. How many liters of water

can the system pump in  minute? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L.

Divide the rate by 4 to find the amount of water pumped in  minute.

The water system in the Sears Tower can pump 1419.38 liters of water in  minute.

37. The average American consumes 20 gallons of ice cream in one year. At this rate, how many liters of ice cream will50 Americans consume in one week? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 yr = 52 wk.

Multiply the rate by 50 to find how many liters 50 Americans consume.

So, 50 Americans consume about 72.79 liters of ice cream per week.

Replace each _ with <, >, or = to make a true sentence.38. 10 m _ 390 in.

SOLUTION:  Use 1 m ≈ 3.279 ft and 1 ft = 12 in.

39. 520 oz _ 15 kg

SOLUTION:  Use 1 oz ≈ 28.35 g and 1000 g = 1 kg.

40. 14 pt _ 6622 mL

SOLUTION:  Use 1 pt ≈ 0.473 L and 1 L = 1000 mL.

Financial Literacy Use dimensional analysis and the table below to make each conversion. Round to the nearest hundredth, if necessary.

41. 150 dollars to euros

SOLUTION:  

So, 150 dollars is equal to 118.5 euros.

42. 275 dollars to pounds

SOLUTION:  

So, 275 dollars is equal to 175.18 pounds.

43. 570 yuan to dollars

SOLUTION:  

So, 570 yuan is equal to 89.41 dollars.

44. 500 pesos to dollars

SOLUTION:  

So, 500 pesos is approximately equal to 37.19 dollars.

45. Model with Mathematics Write and solve a real-world problem in which dimensional analysis is used to convert square feet to square yards. Hint: 1 square yard = 9 square feet

SOLUTION:  Sample answer: Macha needs 120 square feet of carpeting for her bedroom. How many square yards does she need?

Maria needs square yards.

46. Be Precise Give two examples of different measurements that are equivalent to 10 centimeters per second.

SOLUTION:  Sample answers:

Two measurements equivalent to 10 centimeters per second are 600 centimeters per minute and 360 meters per hour.

47. WHICH ONE DOESN’T BELONG? Select the rate that does not have the same value as the other three. Explain your reasoning.

SOLUTION:  Convert each rate to miles per hour and compare the values.

The rate that does not belong is 500 ft/min. All of the other rates are equal to 60 mi/h.

60 mi/h

88 ft/sec

500 ft/min

1440 mi/day

48. Persevere with Problems A recipe for fruit punch uses the ingredients shown. About how many cups of each ingredient are needed? Round to the nearest tenth.

SOLUTION:  Use 1000 mL = 1L, 1 L ≈ 2.114 pt, and 1 pt = 2 cups.  Cranberry juice:

  Apple juice:

  Pineapple juice:

  Lemon juice:

  Club soda:

49. Identify Structure What property of multiplication allows you to multiply a rate by a conversion factor without changing its value? Explain.

SOLUTION:  

The Identity Property of Multiplication allows you to multiply a rate by a conversion factor without changing its value

because the conversion factor is equal to 1. For example, multiplying by  is the same as multiplying by 1 

because 12 inches equals 1 foot.

50. Building on the Essential Question Explain how you would convert 10 miles per hour to meters per second.

SOLUTION:  Sample answer: Use dimensional analysis.

So, 10 miles per hour is approximately equal to 4.47 meters per second.

51. A speed of 55 miles per hour is the same rate as which of the following?

 

A  34 kilometers per hourB  50 kilometers per hourC  88 kilometers per hourD  98 kilometers per hour

SOLUTION:  Use 1 mi ≈ 1.609 kilometers.

55 miles per hour is approximately equal to 88 kilometers per hour. Choice C is correct.

52. A piece of notebook paper measures  inches by 11 inches. Which of the following metric approximations is the 

same?

 

F  2 m by 2.8 mG  3 cm by 4 cmH  22 cm by 28 cmJ  30 m by 40 m

SOLUTION:  Use 1 in. ≈ 2.54 centimeters.

The approximate metric dimensions of a piece of notebook paper are 22 cm by 28 cm. Choice H is correct.

53. A car’s mileage is registered at 29,345.5 miles. The driver sees a sign that warns of road work in 1000 feet. What will be the car’s mileage when the road work begins?

 

A  29,345.7B  29,345.9C  29,356.2D  29,356.5

SOLUTION:  To find the car’s mileage when the road work begins, find the sum of the current mileage and the distance to the

road work, in miles.

29,345.5 + 0.2 = 29,345.7 When the road work begins, the mileage will be 29,345.7. Choice A is correct.

54. SHORT RESPONSE Convert 565 miles per hour to feet per second. Show the procedure you used.

SOLUTION:  Use dimensional analysis and the following conversion facts to convert 565 miles per hour to feet per second.1 mile = 5280 feet 1 hour = 60 min = 3600 seconds

 or 828.67 feet per second

Express each rate as a unit rate. Round to the nearest tenth or to the nearest cent, if necessary.55. $183 for 4 concert tickets

SOLUTION:  

The unit rate is $45.75 per ticket.

56. 100 feet in 14.5 seconds

SOLUTION:  

The unit rate is about 6.9 feet per second.

57. 254.1 miles on 10.5 gallons

SOLUTION:  

The unit rate is 24.2 miles per gallon.

58. 9 inches of snow in 12 hours

SOLUTION:  

Rounded to the nearest tenth, the unit rate is 0.8 inches per hour.

59. Financial Literacy Mrs. Gallagher wants to buy the package of soda that is less expensive per can. Which pack of sodas shown should she buy? Explain your reasoning.

SOLUTION:  

The 6-pack of soda costs about $0.37 per can. The 12-pack of soda costs about $0.35 per can. So, the 12-pack is less expensive.

Express each ratio as a fraction in simplest form.60. 12 cars out of 30 vehicles

SOLUTION:  

61. 5 cups to 5 quarts

SOLUTION:  Convert 5 quarts to cups. There are 4 cups in 1 quart.

62. 15 soccer balls out of 35 balls

SOLUTION:  

63. 8 pencils to 20 crayons

SOLUTION:  

Simplify each expression.64. (x – 3) + 2

SOLUTION:  

65. (8 • y) • (–4)

SOLUTION:  

66. 25 + (d –8)

SOLUTION:  

67. 9(5m)

SOLUTION:  

68. (x + 1) – 9

SOLUTION:  

69. 5(3 • r)

SOLUTION:  

70. Clive is making hamburgers for a cookout. How many -pound hamburgers can he make from  pounds of 

ground beef?

SOLUTION:  Words: The amount of ground beef needed for each hamburger multiplied by the number of hamburgers equals the total amount of ground beef. Variable: Let h = the number of hamburgers

Equation:

Clive can make 11 hamburgers.

Find each product or quotient.71. –12 • (–10)

SOLUTION:  The product of two integers with the same sign is positive. So, –12 • (–10) = 120.

72. –18 ÷ 3

SOLUTION:  The quotient of two integers with different signs is negative. So, –18 ÷ 3 = –6.

73. 9 • (–14)

SOLUTION:  The product of two integers with different signs is negative. So, 9 • (–14) = –126.

74. 54 ÷ (–6)

SOLUTION:  The quotient of two integers with different signs is negative. So, 54 ÷ (–6) = –9.

75. –14 • 2

SOLUTION:  The product of two integers with different signs is negative. So, –14 • 2 = –28.

76. –72 ÷ (–4)

SOLUTION:  The quotient of two integers with the same sign is positive. So, –72 ÷ (–4) = 18.

eSolutions Manual - Powered by Cognero Page 13

5-4 Converting Rates

Page 14: Crystal - Ms. Wilson's Math Classes · a. Crystal ran 10 kilometers in 64 minutes. Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming

1. In Brazil, about 20 acres of rainforest are destroyed each minute. At this rate, how much rainforest is destroyed per day?

SOLUTION:  

At the rate of 20 acres per minute, there are 28,800 acres of rainforest in Brazil destroyed per day.

2. Lexi can paint 5 yards of fencing in one hour. At this rate, how many inches does she paint per minute?

SOLUTION:  

At the rate of 5 yards per hour, Lexi can paint 3 inches per minute.

Complete each conversion. Round to the nearest hundredth, if necessary.3. 8 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

4. 5 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

5. 15 oz ≈ _ g

SOLUTION:  Use 1 oz ≈ 28.35 g.

6. 24 cm ≈ _ in.

SOLUTION:  Use 1 cm ≈ 0.394 in.

7. 9 pt ≈ _ L

SOLUTION:  Use 1 pt ≈ 0.473 L.

8. 3 m ≈ _ ft

SOLUTION:  Use 1 m ≈ 3.279 ft.

9. An elephant can eat up to 440 pounds of vegetation every day. How many grams per minute is this? Round to the nearest hundredth.

SOLUTION:  

An elephant can eat about 138.72 grams of vegetation per minute.

10. A candy company can produce 4800 sour lemon candies per minute. How many candies can they produce each hour?

SOLUTION:  

The company can produce 288,000 candies each hour.

11. In a recent year, 51.9 billion aluminum cans were recycled. About how many cans per week is this?

SOLUTION:  

About 1 billion aluminum cans were recycled per week.

12. The average American student spends almost 1500 hours per year watching television. To the nearest hundredth, how many minutes per day is this?

SOLUTION:  

The average American student spends 246.58 minutes per day watching television.

13. A thrill ride at an amusement park travels 55 miles per hour. To the nearest hundredth, how many feet per second is this?

SOLUTION:  

The thrill ride travels about 80.67 feet per second.

Complete each conversion. Round to the nearest hundredth, if necessary.14. 4 L ≈ _ qt

SOLUTION:  Use 1 L ≈ 1.057 qt.

15. 16 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

16. 13 m ≈ _ ft

SOLUTION:  Use 1 ft ≈ 0.305 m.

17. 8 yd ≈ _ m

SOLUTION:  Use 1 yd ≈ 0.914 m.

18. 18 lb ≈ _ kg

SOLUTION:  Use 1 lb ≈ 0.454 kg.

19. 7 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

20. 1500 g ≈ _ oz

SOLUTION:  Use 1 oz ≈ 28.35 g.

21. 15 ft ≈ _ m

SOLUTION:  Use 1 ft ≈ 0.305 m.

22. 28 fl oz ≈ _ mL

SOLUTION:  Use 1 fl oz ≈ 29.574 mL.

23. The velocity of sound through wood at 0° Celsius is 1454 meters per second. How many miles is this per hour? Round to the nearest hundredth.

SOLUTION:  

The velocity of sound through wood is approximately 3250.68 miles per hour.

24. A certain car in Canada can travel 15 kilometers per 1 liter of gasoline. How many miles per gallon is this? Round to the nearest hundredth.

SOLUTION:  

The car can travel approximately 35.28 miles per gallon.

Complete each conversion. Round to the nearest hundredth, if necessary.25. 8 in. ≈ _ mm

SOLUTION:  Use 1 in. ≈ 2.54 cm and 1 cm = 10 mm.

26. 16 L ≈ _ c

SOLUTION:  Use 1 L ≈ 2.114 pt and 1 pt = 2 cups.

27. 2 km ≈ _ yd

SOLUTION:  Use 1 km = 1000 m and 1 m ≈ 1.094 yd.

28. 250 fl oz ≈ _ L

SOLUTION:  Use 1 fl oz ≈ 29.574 mL and 1000 mL = 1 L.

29. 2750 g ≈ _ lb

SOLUTION:  Use 1 g ≈ 0.035 oz and 16 oz = 1 lb.

30. 5 gal ≈ _ mL

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 L = 1000 mL.

31. Crystal’s times for each portion of a triathlon are shown in the table. Round to the nearest hundredth.

a. How many meters per second did she run? b. What was her speed in miles per hour for the aquabike portion (swimming and biking)?

SOLUTION:  a. Crystal ran 10 kilometers in 64 minutes.

Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming and biking was 1.5 + 40 or 41.5 kilometers. Her time for theseportions was 40 + 86 or 126 minutes.

Crystal’s speed for the aquabike portion was about 12.27 miles per hour.

Order each group of rates from least to greatest.32. 100 oz/min, 2500 g/min, 10 lb/min

SOLUTION:  

5.51 lb/min < 6.25 lb/min < 10 lb/min Ordered from least to greatest, the rates are 2500 g/min, 100 oz/min, and 10 lb/min.

100 oz/min

2500 g/min

10 lb/min

33. 500 m/h, 7 yd/min, 6 in./s

SOLUTION:  

4.20 in./s < 5.47 in./s < 6 in./s Ordered from least to greatest, the rates are 7 yd/min, 500 m/h, and 6 in./s.

500 m/h

7 yd/min

6 in./s

34. 32 mi/gal, 15 m/mL, 6600 yd/qt

SOLUTION:  

6600 yd/qt < 14,080 yd/qt < 15,524 yd/qt Ordered from least to greatest, the rates are 6600 yd/qt, 32 mi/gal, and 15 m/mL.

32 mi/gal

15 m/mL

6600 yd/qt

35. 500 kg/h, 5 oz/s, 18 lb/min

SOLUTION:  

4.8 oz/s < 4.90 oz/s < 5 oz/s Ordered from least to greatest, the rates are 18 lb/min, 500 kg/h, and 5 oz/s.

500 kg/h

5 oz/s

18 lb/min

36. The sprinkler system in the Willis Tower pumps up to 1500 gallons of water per minute. How many liters of water

can the system pump in  minute? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L.

Divide the rate by 4 to find the amount of water pumped in  minute.

The water system in the Sears Tower can pump 1419.38 liters of water in  minute.

37. The average American consumes 20 gallons of ice cream in one year. At this rate, how many liters of ice cream will50 Americans consume in one week? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 yr = 52 wk.

Multiply the rate by 50 to find how many liters 50 Americans consume.

So, 50 Americans consume about 72.79 liters of ice cream per week.

Replace each _ with <, >, or = to make a true sentence.38. 10 m _ 390 in.

SOLUTION:  Use 1 m ≈ 3.279 ft and 1 ft = 12 in.

39. 520 oz _ 15 kg

SOLUTION:  Use 1 oz ≈ 28.35 g and 1000 g = 1 kg.

40. 14 pt _ 6622 mL

SOLUTION:  Use 1 pt ≈ 0.473 L and 1 L = 1000 mL.

Financial Literacy Use dimensional analysis and the table below to make each conversion. Round to the nearest hundredth, if necessary.

41. 150 dollars to euros

SOLUTION:  

So, 150 dollars is equal to 118.5 euros.

42. 275 dollars to pounds

SOLUTION:  

So, 275 dollars is equal to 175.18 pounds.

43. 570 yuan to dollars

SOLUTION:  

So, 570 yuan is equal to 89.41 dollars.

44. 500 pesos to dollars

SOLUTION:  

So, 500 pesos is approximately equal to 37.19 dollars.

45. Model with Mathematics Write and solve a real-world problem in which dimensional analysis is used to convert square feet to square yards. Hint: 1 square yard = 9 square feet

SOLUTION:  Sample answer: Macha needs 120 square feet of carpeting for her bedroom. How many square yards does she need?

Maria needs square yards.

46. Be Precise Give two examples of different measurements that are equivalent to 10 centimeters per second.

SOLUTION:  Sample answers:

Two measurements equivalent to 10 centimeters per second are 600 centimeters per minute and 360 meters per hour.

47. WHICH ONE DOESN’T BELONG? Select the rate that does not have the same value as the other three. Explain your reasoning.

SOLUTION:  Convert each rate to miles per hour and compare the values.

The rate that does not belong is 500 ft/min. All of the other rates are equal to 60 mi/h.

60 mi/h

88 ft/sec

500 ft/min

1440 mi/day

48. Persevere with Problems A recipe for fruit punch uses the ingredients shown. About how many cups of each ingredient are needed? Round to the nearest tenth.

SOLUTION:  Use 1000 mL = 1L, 1 L ≈ 2.114 pt, and 1 pt = 2 cups.  Cranberry juice:

  Apple juice:

  Pineapple juice:

  Lemon juice:

  Club soda:

49. Identify Structure What property of multiplication allows you to multiply a rate by a conversion factor without changing its value? Explain.

SOLUTION:  

The Identity Property of Multiplication allows you to multiply a rate by a conversion factor without changing its value

because the conversion factor is equal to 1. For example, multiplying by  is the same as multiplying by 1 

because 12 inches equals 1 foot.

50. Building on the Essential Question Explain how you would convert 10 miles per hour to meters per second.

SOLUTION:  Sample answer: Use dimensional analysis.

So, 10 miles per hour is approximately equal to 4.47 meters per second.

51. A speed of 55 miles per hour is the same rate as which of the following?

 

A  34 kilometers per hourB  50 kilometers per hourC  88 kilometers per hourD  98 kilometers per hour

SOLUTION:  Use 1 mi ≈ 1.609 kilometers.

55 miles per hour is approximately equal to 88 kilometers per hour. Choice C is correct.

52. A piece of notebook paper measures  inches by 11 inches. Which of the following metric approximations is the 

same?

 

F  2 m by 2.8 mG  3 cm by 4 cmH  22 cm by 28 cmJ  30 m by 40 m

SOLUTION:  Use 1 in. ≈ 2.54 centimeters.

The approximate metric dimensions of a piece of notebook paper are 22 cm by 28 cm. Choice H is correct.

53. A car’s mileage is registered at 29,345.5 miles. The driver sees a sign that warns of road work in 1000 feet. What will be the car’s mileage when the road work begins?

 

A  29,345.7B  29,345.9C  29,356.2D  29,356.5

SOLUTION:  To find the car’s mileage when the road work begins, find the sum of the current mileage and the distance to the

road work, in miles.

29,345.5 + 0.2 = 29,345.7 When the road work begins, the mileage will be 29,345.7. Choice A is correct.

54. SHORT RESPONSE Convert 565 miles per hour to feet per second. Show the procedure you used.

SOLUTION:  Use dimensional analysis and the following conversion facts to convert 565 miles per hour to feet per second.1 mile = 5280 feet 1 hour = 60 min = 3600 seconds

 or 828.67 feet per second

Express each rate as a unit rate. Round to the nearest tenth or to the nearest cent, if necessary.55. $183 for 4 concert tickets

SOLUTION:  

The unit rate is $45.75 per ticket.

56. 100 feet in 14.5 seconds

SOLUTION:  

The unit rate is about 6.9 feet per second.

57. 254.1 miles on 10.5 gallons

SOLUTION:  

The unit rate is 24.2 miles per gallon.

58. 9 inches of snow in 12 hours

SOLUTION:  

Rounded to the nearest tenth, the unit rate is 0.8 inches per hour.

59. Financial Literacy Mrs. Gallagher wants to buy the package of soda that is less expensive per can. Which pack of sodas shown should she buy? Explain your reasoning.

SOLUTION:  

The 6-pack of soda costs about $0.37 per can. The 12-pack of soda costs about $0.35 per can. So, the 12-pack is less expensive.

Express each ratio as a fraction in simplest form.60. 12 cars out of 30 vehicles

SOLUTION:  

61. 5 cups to 5 quarts

SOLUTION:  Convert 5 quarts to cups. There are 4 cups in 1 quart.

62. 15 soccer balls out of 35 balls

SOLUTION:  

63. 8 pencils to 20 crayons

SOLUTION:  

Simplify each expression.64. (x – 3) + 2

SOLUTION:  

65. (8 • y) • (–4)

SOLUTION:  

66. 25 + (d –8)

SOLUTION:  

67. 9(5m)

SOLUTION:  

68. (x + 1) – 9

SOLUTION:  

69. 5(3 • r)

SOLUTION:  

70. Clive is making hamburgers for a cookout. How many -pound hamburgers can he make from  pounds of 

ground beef?

SOLUTION:  Words: The amount of ground beef needed for each hamburger multiplied by the number of hamburgers equals the total amount of ground beef. Variable: Let h = the number of hamburgers

Equation:

Clive can make 11 hamburgers.

Find each product or quotient.71. –12 • (–10)

SOLUTION:  The product of two integers with the same sign is positive. So, –12 • (–10) = 120.

72. –18 ÷ 3

SOLUTION:  The quotient of two integers with different signs is negative. So, –18 ÷ 3 = –6.

73. 9 • (–14)

SOLUTION:  The product of two integers with different signs is negative. So, 9 • (–14) = –126.

74. 54 ÷ (–6)

SOLUTION:  The quotient of two integers with different signs is negative. So, 54 ÷ (–6) = –9.

75. –14 • 2

SOLUTION:  The product of two integers with different signs is negative. So, –14 • 2 = –28.

76. –72 ÷ (–4)

SOLUTION:  The quotient of two integers with the same sign is positive. So, –72 ÷ (–4) = 18.

eSolutions Manual - Powered by Cognero Page 14

5-4 Converting Rates

Page 15: Crystal - Ms. Wilson's Math Classes · a. Crystal ran 10 kilometers in 64 minutes. Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming

1. In Brazil, about 20 acres of rainforest are destroyed each minute. At this rate, how much rainforest is destroyed per day?

SOLUTION:  

At the rate of 20 acres per minute, there are 28,800 acres of rainforest in Brazil destroyed per day.

2. Lexi can paint 5 yards of fencing in one hour. At this rate, how many inches does she paint per minute?

SOLUTION:  

At the rate of 5 yards per hour, Lexi can paint 3 inches per minute.

Complete each conversion. Round to the nearest hundredth, if necessary.3. 8 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

4. 5 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

5. 15 oz ≈ _ g

SOLUTION:  Use 1 oz ≈ 28.35 g.

6. 24 cm ≈ _ in.

SOLUTION:  Use 1 cm ≈ 0.394 in.

7. 9 pt ≈ _ L

SOLUTION:  Use 1 pt ≈ 0.473 L.

8. 3 m ≈ _ ft

SOLUTION:  Use 1 m ≈ 3.279 ft.

9. An elephant can eat up to 440 pounds of vegetation every day. How many grams per minute is this? Round to the nearest hundredth.

SOLUTION:  

An elephant can eat about 138.72 grams of vegetation per minute.

10. A candy company can produce 4800 sour lemon candies per minute. How many candies can they produce each hour?

SOLUTION:  

The company can produce 288,000 candies each hour.

11. In a recent year, 51.9 billion aluminum cans were recycled. About how many cans per week is this?

SOLUTION:  

About 1 billion aluminum cans were recycled per week.

12. The average American student spends almost 1500 hours per year watching television. To the nearest hundredth, how many minutes per day is this?

SOLUTION:  

The average American student spends 246.58 minutes per day watching television.

13. A thrill ride at an amusement park travels 55 miles per hour. To the nearest hundredth, how many feet per second is this?

SOLUTION:  

The thrill ride travels about 80.67 feet per second.

Complete each conversion. Round to the nearest hundredth, if necessary.14. 4 L ≈ _ qt

SOLUTION:  Use 1 L ≈ 1.057 qt.

15. 16 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

16. 13 m ≈ _ ft

SOLUTION:  Use 1 ft ≈ 0.305 m.

17. 8 yd ≈ _ m

SOLUTION:  Use 1 yd ≈ 0.914 m.

18. 18 lb ≈ _ kg

SOLUTION:  Use 1 lb ≈ 0.454 kg.

19. 7 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

20. 1500 g ≈ _ oz

SOLUTION:  Use 1 oz ≈ 28.35 g.

21. 15 ft ≈ _ m

SOLUTION:  Use 1 ft ≈ 0.305 m.

22. 28 fl oz ≈ _ mL

SOLUTION:  Use 1 fl oz ≈ 29.574 mL.

23. The velocity of sound through wood at 0° Celsius is 1454 meters per second. How many miles is this per hour? Round to the nearest hundredth.

SOLUTION:  

The velocity of sound through wood is approximately 3250.68 miles per hour.

24. A certain car in Canada can travel 15 kilometers per 1 liter of gasoline. How many miles per gallon is this? Round to the nearest hundredth.

SOLUTION:  

The car can travel approximately 35.28 miles per gallon.

Complete each conversion. Round to the nearest hundredth, if necessary.25. 8 in. ≈ _ mm

SOLUTION:  Use 1 in. ≈ 2.54 cm and 1 cm = 10 mm.

26. 16 L ≈ _ c

SOLUTION:  Use 1 L ≈ 2.114 pt and 1 pt = 2 cups.

27. 2 km ≈ _ yd

SOLUTION:  Use 1 km = 1000 m and 1 m ≈ 1.094 yd.

28. 250 fl oz ≈ _ L

SOLUTION:  Use 1 fl oz ≈ 29.574 mL and 1000 mL = 1 L.

29. 2750 g ≈ _ lb

SOLUTION:  Use 1 g ≈ 0.035 oz and 16 oz = 1 lb.

30. 5 gal ≈ _ mL

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 L = 1000 mL.

31. Crystal’s times for each portion of a triathlon are shown in the table. Round to the nearest hundredth.

a. How many meters per second did she run? b. What was her speed in miles per hour for the aquabike portion (swimming and biking)?

SOLUTION:  a. Crystal ran 10 kilometers in 64 minutes.

Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming and biking was 1.5 + 40 or 41.5 kilometers. Her time for theseportions was 40 + 86 or 126 minutes.

Crystal’s speed for the aquabike portion was about 12.27 miles per hour.

Order each group of rates from least to greatest.32. 100 oz/min, 2500 g/min, 10 lb/min

SOLUTION:  

5.51 lb/min < 6.25 lb/min < 10 lb/min Ordered from least to greatest, the rates are 2500 g/min, 100 oz/min, and 10 lb/min.

100 oz/min

2500 g/min

10 lb/min

33. 500 m/h, 7 yd/min, 6 in./s

SOLUTION:  

4.20 in./s < 5.47 in./s < 6 in./s Ordered from least to greatest, the rates are 7 yd/min, 500 m/h, and 6 in./s.

500 m/h

7 yd/min

6 in./s

34. 32 mi/gal, 15 m/mL, 6600 yd/qt

SOLUTION:  

6600 yd/qt < 14,080 yd/qt < 15,524 yd/qt Ordered from least to greatest, the rates are 6600 yd/qt, 32 mi/gal, and 15 m/mL.

32 mi/gal

15 m/mL

6600 yd/qt

35. 500 kg/h, 5 oz/s, 18 lb/min

SOLUTION:  

4.8 oz/s < 4.90 oz/s < 5 oz/s Ordered from least to greatest, the rates are 18 lb/min, 500 kg/h, and 5 oz/s.

500 kg/h

5 oz/s

18 lb/min

36. The sprinkler system in the Willis Tower pumps up to 1500 gallons of water per minute. How many liters of water

can the system pump in  minute? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L.

Divide the rate by 4 to find the amount of water pumped in  minute.

The water system in the Sears Tower can pump 1419.38 liters of water in  minute.

37. The average American consumes 20 gallons of ice cream in one year. At this rate, how many liters of ice cream will50 Americans consume in one week? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 yr = 52 wk.

Multiply the rate by 50 to find how many liters 50 Americans consume.

So, 50 Americans consume about 72.79 liters of ice cream per week.

Replace each _ with <, >, or = to make a true sentence.38. 10 m _ 390 in.

SOLUTION:  Use 1 m ≈ 3.279 ft and 1 ft = 12 in.

39. 520 oz _ 15 kg

SOLUTION:  Use 1 oz ≈ 28.35 g and 1000 g = 1 kg.

40. 14 pt _ 6622 mL

SOLUTION:  Use 1 pt ≈ 0.473 L and 1 L = 1000 mL.

Financial Literacy Use dimensional analysis and the table below to make each conversion. Round to the nearest hundredth, if necessary.

41. 150 dollars to euros

SOLUTION:  

So, 150 dollars is equal to 118.5 euros.

42. 275 dollars to pounds

SOLUTION:  

So, 275 dollars is equal to 175.18 pounds.

43. 570 yuan to dollars

SOLUTION:  

So, 570 yuan is equal to 89.41 dollars.

44. 500 pesos to dollars

SOLUTION:  

So, 500 pesos is approximately equal to 37.19 dollars.

45. Model with Mathematics Write and solve a real-world problem in which dimensional analysis is used to convert square feet to square yards. Hint: 1 square yard = 9 square feet

SOLUTION:  Sample answer: Macha needs 120 square feet of carpeting for her bedroom. How many square yards does she need?

Maria needs square yards.

46. Be Precise Give two examples of different measurements that are equivalent to 10 centimeters per second.

SOLUTION:  Sample answers:

Two measurements equivalent to 10 centimeters per second are 600 centimeters per minute and 360 meters per hour.

47. WHICH ONE DOESN’T BELONG? Select the rate that does not have the same value as the other three. Explain your reasoning.

SOLUTION:  Convert each rate to miles per hour and compare the values.

The rate that does not belong is 500 ft/min. All of the other rates are equal to 60 mi/h.

60 mi/h

88 ft/sec

500 ft/min

1440 mi/day

48. Persevere with Problems A recipe for fruit punch uses the ingredients shown. About how many cups of each ingredient are needed? Round to the nearest tenth.

SOLUTION:  Use 1000 mL = 1L, 1 L ≈ 2.114 pt, and 1 pt = 2 cups.  Cranberry juice:

  Apple juice:

  Pineapple juice:

  Lemon juice:

  Club soda:

49. Identify Structure What property of multiplication allows you to multiply a rate by a conversion factor without changing its value? Explain.

SOLUTION:  

The Identity Property of Multiplication allows you to multiply a rate by a conversion factor without changing its value

because the conversion factor is equal to 1. For example, multiplying by  is the same as multiplying by 1 

because 12 inches equals 1 foot.

50. Building on the Essential Question Explain how you would convert 10 miles per hour to meters per second.

SOLUTION:  Sample answer: Use dimensional analysis.

So, 10 miles per hour is approximately equal to 4.47 meters per second.

51. A speed of 55 miles per hour is the same rate as which of the following?

 

A  34 kilometers per hourB  50 kilometers per hourC  88 kilometers per hourD  98 kilometers per hour

SOLUTION:  Use 1 mi ≈ 1.609 kilometers.

55 miles per hour is approximately equal to 88 kilometers per hour. Choice C is correct.

52. A piece of notebook paper measures  inches by 11 inches. Which of the following metric approximations is the 

same?

 

F  2 m by 2.8 mG  3 cm by 4 cmH  22 cm by 28 cmJ  30 m by 40 m

SOLUTION:  Use 1 in. ≈ 2.54 centimeters.

The approximate metric dimensions of a piece of notebook paper are 22 cm by 28 cm. Choice H is correct.

53. A car’s mileage is registered at 29,345.5 miles. The driver sees a sign that warns of road work in 1000 feet. What will be the car’s mileage when the road work begins?

 

A  29,345.7B  29,345.9C  29,356.2D  29,356.5

SOLUTION:  To find the car’s mileage when the road work begins, find the sum of the current mileage and the distance to the

road work, in miles.

29,345.5 + 0.2 = 29,345.7 When the road work begins, the mileage will be 29,345.7. Choice A is correct.

54. SHORT RESPONSE Convert 565 miles per hour to feet per second. Show the procedure you used.

SOLUTION:  Use dimensional analysis and the following conversion facts to convert 565 miles per hour to feet per second.1 mile = 5280 feet 1 hour = 60 min = 3600 seconds

 or 828.67 feet per second

Express each rate as a unit rate. Round to the nearest tenth or to the nearest cent, if necessary.55. $183 for 4 concert tickets

SOLUTION:  

The unit rate is $45.75 per ticket.

56. 100 feet in 14.5 seconds

SOLUTION:  

The unit rate is about 6.9 feet per second.

57. 254.1 miles on 10.5 gallons

SOLUTION:  

The unit rate is 24.2 miles per gallon.

58. 9 inches of snow in 12 hours

SOLUTION:  

Rounded to the nearest tenth, the unit rate is 0.8 inches per hour.

59. Financial Literacy Mrs. Gallagher wants to buy the package of soda that is less expensive per can. Which pack of sodas shown should she buy? Explain your reasoning.

SOLUTION:  

The 6-pack of soda costs about $0.37 per can. The 12-pack of soda costs about $0.35 per can. So, the 12-pack is less expensive.

Express each ratio as a fraction in simplest form.60. 12 cars out of 30 vehicles

SOLUTION:  

61. 5 cups to 5 quarts

SOLUTION:  Convert 5 quarts to cups. There are 4 cups in 1 quart.

62. 15 soccer balls out of 35 balls

SOLUTION:  

63. 8 pencils to 20 crayons

SOLUTION:  

Simplify each expression.64. (x – 3) + 2

SOLUTION:  

65. (8 • y) • (–4)

SOLUTION:  

66. 25 + (d –8)

SOLUTION:  

67. 9(5m)

SOLUTION:  

68. (x + 1) – 9

SOLUTION:  

69. 5(3 • r)

SOLUTION:  

70. Clive is making hamburgers for a cookout. How many -pound hamburgers can he make from  pounds of 

ground beef?

SOLUTION:  Words: The amount of ground beef needed for each hamburger multiplied by the number of hamburgers equals the total amount of ground beef. Variable: Let h = the number of hamburgers

Equation:

Clive can make 11 hamburgers.

Find each product or quotient.71. –12 • (–10)

SOLUTION:  The product of two integers with the same sign is positive. So, –12 • (–10) = 120.

72. –18 ÷ 3

SOLUTION:  The quotient of two integers with different signs is negative. So, –18 ÷ 3 = –6.

73. 9 • (–14)

SOLUTION:  The product of two integers with different signs is negative. So, 9 • (–14) = –126.

74. 54 ÷ (–6)

SOLUTION:  The quotient of two integers with different signs is negative. So, 54 ÷ (–6) = –9.

75. –14 • 2

SOLUTION:  The product of two integers with different signs is negative. So, –14 • 2 = –28.

76. –72 ÷ (–4)

SOLUTION:  The quotient of two integers with the same sign is positive. So, –72 ÷ (–4) = 18.

eSolutions Manual - Powered by Cognero Page 15

5-4 Converting Rates

Page 16: Crystal - Ms. Wilson's Math Classes · a. Crystal ran 10 kilometers in 64 minutes. Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming

1. In Brazil, about 20 acres of rainforest are destroyed each minute. At this rate, how much rainforest is destroyed per day?

SOLUTION:  

At the rate of 20 acres per minute, there are 28,800 acres of rainforest in Brazil destroyed per day.

2. Lexi can paint 5 yards of fencing in one hour. At this rate, how many inches does she paint per minute?

SOLUTION:  

At the rate of 5 yards per hour, Lexi can paint 3 inches per minute.

Complete each conversion. Round to the nearest hundredth, if necessary.3. 8 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

4. 5 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

5. 15 oz ≈ _ g

SOLUTION:  Use 1 oz ≈ 28.35 g.

6. 24 cm ≈ _ in.

SOLUTION:  Use 1 cm ≈ 0.394 in.

7. 9 pt ≈ _ L

SOLUTION:  Use 1 pt ≈ 0.473 L.

8. 3 m ≈ _ ft

SOLUTION:  Use 1 m ≈ 3.279 ft.

9. An elephant can eat up to 440 pounds of vegetation every day. How many grams per minute is this? Round to the nearest hundredth.

SOLUTION:  

An elephant can eat about 138.72 grams of vegetation per minute.

10. A candy company can produce 4800 sour lemon candies per minute. How many candies can they produce each hour?

SOLUTION:  

The company can produce 288,000 candies each hour.

11. In a recent year, 51.9 billion aluminum cans were recycled. About how many cans per week is this?

SOLUTION:  

About 1 billion aluminum cans were recycled per week.

12. The average American student spends almost 1500 hours per year watching television. To the nearest hundredth, how many minutes per day is this?

SOLUTION:  

The average American student spends 246.58 minutes per day watching television.

13. A thrill ride at an amusement park travels 55 miles per hour. To the nearest hundredth, how many feet per second is this?

SOLUTION:  

The thrill ride travels about 80.67 feet per second.

Complete each conversion. Round to the nearest hundredth, if necessary.14. 4 L ≈ _ qt

SOLUTION:  Use 1 L ≈ 1.057 qt.

15. 16 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

16. 13 m ≈ _ ft

SOLUTION:  Use 1 ft ≈ 0.305 m.

17. 8 yd ≈ _ m

SOLUTION:  Use 1 yd ≈ 0.914 m.

18. 18 lb ≈ _ kg

SOLUTION:  Use 1 lb ≈ 0.454 kg.

19. 7 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

20. 1500 g ≈ _ oz

SOLUTION:  Use 1 oz ≈ 28.35 g.

21. 15 ft ≈ _ m

SOLUTION:  Use 1 ft ≈ 0.305 m.

22. 28 fl oz ≈ _ mL

SOLUTION:  Use 1 fl oz ≈ 29.574 mL.

23. The velocity of sound through wood at 0° Celsius is 1454 meters per second. How many miles is this per hour? Round to the nearest hundredth.

SOLUTION:  

The velocity of sound through wood is approximately 3250.68 miles per hour.

24. A certain car in Canada can travel 15 kilometers per 1 liter of gasoline. How many miles per gallon is this? Round to the nearest hundredth.

SOLUTION:  

The car can travel approximately 35.28 miles per gallon.

Complete each conversion. Round to the nearest hundredth, if necessary.25. 8 in. ≈ _ mm

SOLUTION:  Use 1 in. ≈ 2.54 cm and 1 cm = 10 mm.

26. 16 L ≈ _ c

SOLUTION:  Use 1 L ≈ 2.114 pt and 1 pt = 2 cups.

27. 2 km ≈ _ yd

SOLUTION:  Use 1 km = 1000 m and 1 m ≈ 1.094 yd.

28. 250 fl oz ≈ _ L

SOLUTION:  Use 1 fl oz ≈ 29.574 mL and 1000 mL = 1 L.

29. 2750 g ≈ _ lb

SOLUTION:  Use 1 g ≈ 0.035 oz and 16 oz = 1 lb.

30. 5 gal ≈ _ mL

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 L = 1000 mL.

31. Crystal’s times for each portion of a triathlon are shown in the table. Round to the nearest hundredth.

a. How many meters per second did she run? b. What was her speed in miles per hour for the aquabike portion (swimming and biking)?

SOLUTION:  a. Crystal ran 10 kilometers in 64 minutes.

Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming and biking was 1.5 + 40 or 41.5 kilometers. Her time for theseportions was 40 + 86 or 126 minutes.

Crystal’s speed for the aquabike portion was about 12.27 miles per hour.

Order each group of rates from least to greatest.32. 100 oz/min, 2500 g/min, 10 lb/min

SOLUTION:  

5.51 lb/min < 6.25 lb/min < 10 lb/min Ordered from least to greatest, the rates are 2500 g/min, 100 oz/min, and 10 lb/min.

100 oz/min

2500 g/min

10 lb/min

33. 500 m/h, 7 yd/min, 6 in./s

SOLUTION:  

4.20 in./s < 5.47 in./s < 6 in./s Ordered from least to greatest, the rates are 7 yd/min, 500 m/h, and 6 in./s.

500 m/h

7 yd/min

6 in./s

34. 32 mi/gal, 15 m/mL, 6600 yd/qt

SOLUTION:  

6600 yd/qt < 14,080 yd/qt < 15,524 yd/qt Ordered from least to greatest, the rates are 6600 yd/qt, 32 mi/gal, and 15 m/mL.

32 mi/gal

15 m/mL

6600 yd/qt

35. 500 kg/h, 5 oz/s, 18 lb/min

SOLUTION:  

4.8 oz/s < 4.90 oz/s < 5 oz/s Ordered from least to greatest, the rates are 18 lb/min, 500 kg/h, and 5 oz/s.

500 kg/h

5 oz/s

18 lb/min

36. The sprinkler system in the Willis Tower pumps up to 1500 gallons of water per minute. How many liters of water

can the system pump in  minute? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L.

Divide the rate by 4 to find the amount of water pumped in  minute.

The water system in the Sears Tower can pump 1419.38 liters of water in  minute.

37. The average American consumes 20 gallons of ice cream in one year. At this rate, how many liters of ice cream will50 Americans consume in one week? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 yr = 52 wk.

Multiply the rate by 50 to find how many liters 50 Americans consume.

So, 50 Americans consume about 72.79 liters of ice cream per week.

Replace each _ with <, >, or = to make a true sentence.38. 10 m _ 390 in.

SOLUTION:  Use 1 m ≈ 3.279 ft and 1 ft = 12 in.

39. 520 oz _ 15 kg

SOLUTION:  Use 1 oz ≈ 28.35 g and 1000 g = 1 kg.

40. 14 pt _ 6622 mL

SOLUTION:  Use 1 pt ≈ 0.473 L and 1 L = 1000 mL.

Financial Literacy Use dimensional analysis and the table below to make each conversion. Round to the nearest hundredth, if necessary.

41. 150 dollars to euros

SOLUTION:  

So, 150 dollars is equal to 118.5 euros.

42. 275 dollars to pounds

SOLUTION:  

So, 275 dollars is equal to 175.18 pounds.

43. 570 yuan to dollars

SOLUTION:  

So, 570 yuan is equal to 89.41 dollars.

44. 500 pesos to dollars

SOLUTION:  

So, 500 pesos is approximately equal to 37.19 dollars.

45. Model with Mathematics Write and solve a real-world problem in which dimensional analysis is used to convert square feet to square yards. Hint: 1 square yard = 9 square feet

SOLUTION:  Sample answer: Macha needs 120 square feet of carpeting for her bedroom. How many square yards does she need?

Maria needs square yards.

46. Be Precise Give two examples of different measurements that are equivalent to 10 centimeters per second.

SOLUTION:  Sample answers:

Two measurements equivalent to 10 centimeters per second are 600 centimeters per minute and 360 meters per hour.

47. WHICH ONE DOESN’T BELONG? Select the rate that does not have the same value as the other three. Explain your reasoning.

SOLUTION:  Convert each rate to miles per hour and compare the values.

The rate that does not belong is 500 ft/min. All of the other rates are equal to 60 mi/h.

60 mi/h

88 ft/sec

500 ft/min

1440 mi/day

48. Persevere with Problems A recipe for fruit punch uses the ingredients shown. About how many cups of each ingredient are needed? Round to the nearest tenth.

SOLUTION:  Use 1000 mL = 1L, 1 L ≈ 2.114 pt, and 1 pt = 2 cups.  Cranberry juice:

  Apple juice:

  Pineapple juice:

  Lemon juice:

  Club soda:

49. Identify Structure What property of multiplication allows you to multiply a rate by a conversion factor without changing its value? Explain.

SOLUTION:  

The Identity Property of Multiplication allows you to multiply a rate by a conversion factor without changing its value

because the conversion factor is equal to 1. For example, multiplying by  is the same as multiplying by 1 

because 12 inches equals 1 foot.

50. Building on the Essential Question Explain how you would convert 10 miles per hour to meters per second.

SOLUTION:  Sample answer: Use dimensional analysis.

So, 10 miles per hour is approximately equal to 4.47 meters per second.

51. A speed of 55 miles per hour is the same rate as which of the following?

 

A  34 kilometers per hourB  50 kilometers per hourC  88 kilometers per hourD  98 kilometers per hour

SOLUTION:  Use 1 mi ≈ 1.609 kilometers.

55 miles per hour is approximately equal to 88 kilometers per hour. Choice C is correct.

52. A piece of notebook paper measures  inches by 11 inches. Which of the following metric approximations is the 

same?

 

F  2 m by 2.8 mG  3 cm by 4 cmH  22 cm by 28 cmJ  30 m by 40 m

SOLUTION:  Use 1 in. ≈ 2.54 centimeters.

The approximate metric dimensions of a piece of notebook paper are 22 cm by 28 cm. Choice H is correct.

53. A car’s mileage is registered at 29,345.5 miles. The driver sees a sign that warns of road work in 1000 feet. What will be the car’s mileage when the road work begins?

 

A  29,345.7B  29,345.9C  29,356.2D  29,356.5

SOLUTION:  To find the car’s mileage when the road work begins, find the sum of the current mileage and the distance to the

road work, in miles.

29,345.5 + 0.2 = 29,345.7 When the road work begins, the mileage will be 29,345.7. Choice A is correct.

54. SHORT RESPONSE Convert 565 miles per hour to feet per second. Show the procedure you used.

SOLUTION:  Use dimensional analysis and the following conversion facts to convert 565 miles per hour to feet per second.1 mile = 5280 feet 1 hour = 60 min = 3600 seconds

 or 828.67 feet per second

Express each rate as a unit rate. Round to the nearest tenth or to the nearest cent, if necessary.55. $183 for 4 concert tickets

SOLUTION:  

The unit rate is $45.75 per ticket.

56. 100 feet in 14.5 seconds

SOLUTION:  

The unit rate is about 6.9 feet per second.

57. 254.1 miles on 10.5 gallons

SOLUTION:  

The unit rate is 24.2 miles per gallon.

58. 9 inches of snow in 12 hours

SOLUTION:  

Rounded to the nearest tenth, the unit rate is 0.8 inches per hour.

59. Financial Literacy Mrs. Gallagher wants to buy the package of soda that is less expensive per can. Which pack of sodas shown should she buy? Explain your reasoning.

SOLUTION:  

The 6-pack of soda costs about $0.37 per can. The 12-pack of soda costs about $0.35 per can. So, the 12-pack is less expensive.

Express each ratio as a fraction in simplest form.60. 12 cars out of 30 vehicles

SOLUTION:  

61. 5 cups to 5 quarts

SOLUTION:  Convert 5 quarts to cups. There are 4 cups in 1 quart.

62. 15 soccer balls out of 35 balls

SOLUTION:  

63. 8 pencils to 20 crayons

SOLUTION:  

Simplify each expression.64. (x – 3) + 2

SOLUTION:  

65. (8 • y) • (–4)

SOLUTION:  

66. 25 + (d –8)

SOLUTION:  

67. 9(5m)

SOLUTION:  

68. (x + 1) – 9

SOLUTION:  

69. 5(3 • r)

SOLUTION:  

70. Clive is making hamburgers for a cookout. How many -pound hamburgers can he make from  pounds of 

ground beef?

SOLUTION:  Words: The amount of ground beef needed for each hamburger multiplied by the number of hamburgers equals the total amount of ground beef. Variable: Let h = the number of hamburgers

Equation:

Clive can make 11 hamburgers.

Find each product or quotient.71. –12 • (–10)

SOLUTION:  The product of two integers with the same sign is positive. So, –12 • (–10) = 120.

72. –18 ÷ 3

SOLUTION:  The quotient of two integers with different signs is negative. So, –18 ÷ 3 = –6.

73. 9 • (–14)

SOLUTION:  The product of two integers with different signs is negative. So, 9 • (–14) = –126.

74. 54 ÷ (–6)

SOLUTION:  The quotient of two integers with different signs is negative. So, 54 ÷ (–6) = –9.

75. –14 • 2

SOLUTION:  The product of two integers with different signs is negative. So, –14 • 2 = –28.

76. –72 ÷ (–4)

SOLUTION:  The quotient of two integers with the same sign is positive. So, –72 ÷ (–4) = 18.

eSolutions Manual - Powered by Cognero Page 16

5-4 Converting Rates

Page 17: Crystal - Ms. Wilson's Math Classes · a. Crystal ran 10 kilometers in 64 minutes. Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming

1. In Brazil, about 20 acres of rainforest are destroyed each minute. At this rate, how much rainforest is destroyed per day?

SOLUTION:  

At the rate of 20 acres per minute, there are 28,800 acres of rainforest in Brazil destroyed per day.

2. Lexi can paint 5 yards of fencing in one hour. At this rate, how many inches does she paint per minute?

SOLUTION:  

At the rate of 5 yards per hour, Lexi can paint 3 inches per minute.

Complete each conversion. Round to the nearest hundredth, if necessary.3. 8 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

4. 5 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

5. 15 oz ≈ _ g

SOLUTION:  Use 1 oz ≈ 28.35 g.

6. 24 cm ≈ _ in.

SOLUTION:  Use 1 cm ≈ 0.394 in.

7. 9 pt ≈ _ L

SOLUTION:  Use 1 pt ≈ 0.473 L.

8. 3 m ≈ _ ft

SOLUTION:  Use 1 m ≈ 3.279 ft.

9. An elephant can eat up to 440 pounds of vegetation every day. How many grams per minute is this? Round to the nearest hundredth.

SOLUTION:  

An elephant can eat about 138.72 grams of vegetation per minute.

10. A candy company can produce 4800 sour lemon candies per minute. How many candies can they produce each hour?

SOLUTION:  

The company can produce 288,000 candies each hour.

11. In a recent year, 51.9 billion aluminum cans were recycled. About how many cans per week is this?

SOLUTION:  

About 1 billion aluminum cans were recycled per week.

12. The average American student spends almost 1500 hours per year watching television. To the nearest hundredth, how many minutes per day is this?

SOLUTION:  

The average American student spends 246.58 minutes per day watching television.

13. A thrill ride at an amusement park travels 55 miles per hour. To the nearest hundredth, how many feet per second is this?

SOLUTION:  

The thrill ride travels about 80.67 feet per second.

Complete each conversion. Round to the nearest hundredth, if necessary.14. 4 L ≈ _ qt

SOLUTION:  Use 1 L ≈ 1.057 qt.

15. 16 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

16. 13 m ≈ _ ft

SOLUTION:  Use 1 ft ≈ 0.305 m.

17. 8 yd ≈ _ m

SOLUTION:  Use 1 yd ≈ 0.914 m.

18. 18 lb ≈ _ kg

SOLUTION:  Use 1 lb ≈ 0.454 kg.

19. 7 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

20. 1500 g ≈ _ oz

SOLUTION:  Use 1 oz ≈ 28.35 g.

21. 15 ft ≈ _ m

SOLUTION:  Use 1 ft ≈ 0.305 m.

22. 28 fl oz ≈ _ mL

SOLUTION:  Use 1 fl oz ≈ 29.574 mL.

23. The velocity of sound through wood at 0° Celsius is 1454 meters per second. How many miles is this per hour? Round to the nearest hundredth.

SOLUTION:  

The velocity of sound through wood is approximately 3250.68 miles per hour.

24. A certain car in Canada can travel 15 kilometers per 1 liter of gasoline. How many miles per gallon is this? Round to the nearest hundredth.

SOLUTION:  

The car can travel approximately 35.28 miles per gallon.

Complete each conversion. Round to the nearest hundredth, if necessary.25. 8 in. ≈ _ mm

SOLUTION:  Use 1 in. ≈ 2.54 cm and 1 cm = 10 mm.

26. 16 L ≈ _ c

SOLUTION:  Use 1 L ≈ 2.114 pt and 1 pt = 2 cups.

27. 2 km ≈ _ yd

SOLUTION:  Use 1 km = 1000 m and 1 m ≈ 1.094 yd.

28. 250 fl oz ≈ _ L

SOLUTION:  Use 1 fl oz ≈ 29.574 mL and 1000 mL = 1 L.

29. 2750 g ≈ _ lb

SOLUTION:  Use 1 g ≈ 0.035 oz and 16 oz = 1 lb.

30. 5 gal ≈ _ mL

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 L = 1000 mL.

31. Crystal’s times for each portion of a triathlon are shown in the table. Round to the nearest hundredth.

a. How many meters per second did she run? b. What was her speed in miles per hour for the aquabike portion (swimming and biking)?

SOLUTION:  a. Crystal ran 10 kilometers in 64 minutes.

Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming and biking was 1.5 + 40 or 41.5 kilometers. Her time for theseportions was 40 + 86 or 126 minutes.

Crystal’s speed for the aquabike portion was about 12.27 miles per hour.

Order each group of rates from least to greatest.32. 100 oz/min, 2500 g/min, 10 lb/min

SOLUTION:  

5.51 lb/min < 6.25 lb/min < 10 lb/min Ordered from least to greatest, the rates are 2500 g/min, 100 oz/min, and 10 lb/min.

100 oz/min

2500 g/min

10 lb/min

33. 500 m/h, 7 yd/min, 6 in./s

SOLUTION:  

4.20 in./s < 5.47 in./s < 6 in./s Ordered from least to greatest, the rates are 7 yd/min, 500 m/h, and 6 in./s.

500 m/h

7 yd/min

6 in./s

34. 32 mi/gal, 15 m/mL, 6600 yd/qt

SOLUTION:  

6600 yd/qt < 14,080 yd/qt < 15,524 yd/qt Ordered from least to greatest, the rates are 6600 yd/qt, 32 mi/gal, and 15 m/mL.

32 mi/gal

15 m/mL

6600 yd/qt

35. 500 kg/h, 5 oz/s, 18 lb/min

SOLUTION:  

4.8 oz/s < 4.90 oz/s < 5 oz/s Ordered from least to greatest, the rates are 18 lb/min, 500 kg/h, and 5 oz/s.

500 kg/h

5 oz/s

18 lb/min

36. The sprinkler system in the Willis Tower pumps up to 1500 gallons of water per minute. How many liters of water

can the system pump in  minute? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L.

Divide the rate by 4 to find the amount of water pumped in  minute.

The water system in the Sears Tower can pump 1419.38 liters of water in  minute.

37. The average American consumes 20 gallons of ice cream in one year. At this rate, how many liters of ice cream will50 Americans consume in one week? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 yr = 52 wk.

Multiply the rate by 50 to find how many liters 50 Americans consume.

So, 50 Americans consume about 72.79 liters of ice cream per week.

Replace each _ with <, >, or = to make a true sentence.38. 10 m _ 390 in.

SOLUTION:  Use 1 m ≈ 3.279 ft and 1 ft = 12 in.

39. 520 oz _ 15 kg

SOLUTION:  Use 1 oz ≈ 28.35 g and 1000 g = 1 kg.

40. 14 pt _ 6622 mL

SOLUTION:  Use 1 pt ≈ 0.473 L and 1 L = 1000 mL.

Financial Literacy Use dimensional analysis and the table below to make each conversion. Round to the nearest hundredth, if necessary.

41. 150 dollars to euros

SOLUTION:  

So, 150 dollars is equal to 118.5 euros.

42. 275 dollars to pounds

SOLUTION:  

So, 275 dollars is equal to 175.18 pounds.

43. 570 yuan to dollars

SOLUTION:  

So, 570 yuan is equal to 89.41 dollars.

44. 500 pesos to dollars

SOLUTION:  

So, 500 pesos is approximately equal to 37.19 dollars.

45. Model with Mathematics Write and solve a real-world problem in which dimensional analysis is used to convert square feet to square yards. Hint: 1 square yard = 9 square feet

SOLUTION:  Sample answer: Macha needs 120 square feet of carpeting for her bedroom. How many square yards does she need?

Maria needs square yards.

46. Be Precise Give two examples of different measurements that are equivalent to 10 centimeters per second.

SOLUTION:  Sample answers:

Two measurements equivalent to 10 centimeters per second are 600 centimeters per minute and 360 meters per hour.

47. WHICH ONE DOESN’T BELONG? Select the rate that does not have the same value as the other three. Explain your reasoning.

SOLUTION:  Convert each rate to miles per hour and compare the values.

The rate that does not belong is 500 ft/min. All of the other rates are equal to 60 mi/h.

60 mi/h

88 ft/sec

500 ft/min

1440 mi/day

48. Persevere with Problems A recipe for fruit punch uses the ingredients shown. About how many cups of each ingredient are needed? Round to the nearest tenth.

SOLUTION:  Use 1000 mL = 1L, 1 L ≈ 2.114 pt, and 1 pt = 2 cups.  Cranberry juice:

  Apple juice:

  Pineapple juice:

  Lemon juice:

  Club soda:

49. Identify Structure What property of multiplication allows you to multiply a rate by a conversion factor without changing its value? Explain.

SOLUTION:  

The Identity Property of Multiplication allows you to multiply a rate by a conversion factor without changing its value

because the conversion factor is equal to 1. For example, multiplying by  is the same as multiplying by 1 

because 12 inches equals 1 foot.

50. Building on the Essential Question Explain how you would convert 10 miles per hour to meters per second.

SOLUTION:  Sample answer: Use dimensional analysis.

So, 10 miles per hour is approximately equal to 4.47 meters per second.

51. A speed of 55 miles per hour is the same rate as which of the following?

 

A  34 kilometers per hourB  50 kilometers per hourC  88 kilometers per hourD  98 kilometers per hour

SOLUTION:  Use 1 mi ≈ 1.609 kilometers.

55 miles per hour is approximately equal to 88 kilometers per hour. Choice C is correct.

52. A piece of notebook paper measures  inches by 11 inches. Which of the following metric approximations is the 

same?

 

F  2 m by 2.8 mG  3 cm by 4 cmH  22 cm by 28 cmJ  30 m by 40 m

SOLUTION:  Use 1 in. ≈ 2.54 centimeters.

The approximate metric dimensions of a piece of notebook paper are 22 cm by 28 cm. Choice H is correct.

53. A car’s mileage is registered at 29,345.5 miles. The driver sees a sign that warns of road work in 1000 feet. What will be the car’s mileage when the road work begins?

 

A  29,345.7B  29,345.9C  29,356.2D  29,356.5

SOLUTION:  To find the car’s mileage when the road work begins, find the sum of the current mileage and the distance to the

road work, in miles.

29,345.5 + 0.2 = 29,345.7 When the road work begins, the mileage will be 29,345.7. Choice A is correct.

54. SHORT RESPONSE Convert 565 miles per hour to feet per second. Show the procedure you used.

SOLUTION:  Use dimensional analysis and the following conversion facts to convert 565 miles per hour to feet per second.1 mile = 5280 feet 1 hour = 60 min = 3600 seconds

 or 828.67 feet per second

Express each rate as a unit rate. Round to the nearest tenth or to the nearest cent, if necessary.55. $183 for 4 concert tickets

SOLUTION:  

The unit rate is $45.75 per ticket.

56. 100 feet in 14.5 seconds

SOLUTION:  

The unit rate is about 6.9 feet per second.

57. 254.1 miles on 10.5 gallons

SOLUTION:  

The unit rate is 24.2 miles per gallon.

58. 9 inches of snow in 12 hours

SOLUTION:  

Rounded to the nearest tenth, the unit rate is 0.8 inches per hour.

59. Financial Literacy Mrs. Gallagher wants to buy the package of soda that is less expensive per can. Which pack of sodas shown should she buy? Explain your reasoning.

SOLUTION:  

The 6-pack of soda costs about $0.37 per can. The 12-pack of soda costs about $0.35 per can. So, the 12-pack is less expensive.

Express each ratio as a fraction in simplest form.60. 12 cars out of 30 vehicles

SOLUTION:  

61. 5 cups to 5 quarts

SOLUTION:  Convert 5 quarts to cups. There are 4 cups in 1 quart.

62. 15 soccer balls out of 35 balls

SOLUTION:  

63. 8 pencils to 20 crayons

SOLUTION:  

Simplify each expression.64. (x – 3) + 2

SOLUTION:  

65. (8 • y) • (–4)

SOLUTION:  

66. 25 + (d –8)

SOLUTION:  

67. 9(5m)

SOLUTION:  

68. (x + 1) – 9

SOLUTION:  

69. 5(3 • r)

SOLUTION:  

70. Clive is making hamburgers for a cookout. How many -pound hamburgers can he make from  pounds of 

ground beef?

SOLUTION:  Words: The amount of ground beef needed for each hamburger multiplied by the number of hamburgers equals the total amount of ground beef. Variable: Let h = the number of hamburgers

Equation:

Clive can make 11 hamburgers.

Find each product or quotient.71. –12 • (–10)

SOLUTION:  The product of two integers with the same sign is positive. So, –12 • (–10) = 120.

72. –18 ÷ 3

SOLUTION:  The quotient of two integers with different signs is negative. So, –18 ÷ 3 = –6.

73. 9 • (–14)

SOLUTION:  The product of two integers with different signs is negative. So, 9 • (–14) = –126.

74. 54 ÷ (–6)

SOLUTION:  The quotient of two integers with different signs is negative. So, 54 ÷ (–6) = –9.

75. –14 • 2

SOLUTION:  The product of two integers with different signs is negative. So, –14 • 2 = –28.

76. –72 ÷ (–4)

SOLUTION:  The quotient of two integers with the same sign is positive. So, –72 ÷ (–4) = 18.

eSolutions Manual - Powered by Cognero Page 17

5-4 Converting Rates

Page 18: Crystal - Ms. Wilson's Math Classes · a. Crystal ran 10 kilometers in 64 minutes. Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming

1. In Brazil, about 20 acres of rainforest are destroyed each minute. At this rate, how much rainforest is destroyed per day?

SOLUTION:  

At the rate of 20 acres per minute, there are 28,800 acres of rainforest in Brazil destroyed per day.

2. Lexi can paint 5 yards of fencing in one hour. At this rate, how many inches does she paint per minute?

SOLUTION:  

At the rate of 5 yards per hour, Lexi can paint 3 inches per minute.

Complete each conversion. Round to the nearest hundredth, if necessary.3. 8 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

4. 5 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

5. 15 oz ≈ _ g

SOLUTION:  Use 1 oz ≈ 28.35 g.

6. 24 cm ≈ _ in.

SOLUTION:  Use 1 cm ≈ 0.394 in.

7. 9 pt ≈ _ L

SOLUTION:  Use 1 pt ≈ 0.473 L.

8. 3 m ≈ _ ft

SOLUTION:  Use 1 m ≈ 3.279 ft.

9. An elephant can eat up to 440 pounds of vegetation every day. How many grams per minute is this? Round to the nearest hundredth.

SOLUTION:  

An elephant can eat about 138.72 grams of vegetation per minute.

10. A candy company can produce 4800 sour lemon candies per minute. How many candies can they produce each hour?

SOLUTION:  

The company can produce 288,000 candies each hour.

11. In a recent year, 51.9 billion aluminum cans were recycled. About how many cans per week is this?

SOLUTION:  

About 1 billion aluminum cans were recycled per week.

12. The average American student spends almost 1500 hours per year watching television. To the nearest hundredth, how many minutes per day is this?

SOLUTION:  

The average American student spends 246.58 minutes per day watching television.

13. A thrill ride at an amusement park travels 55 miles per hour. To the nearest hundredth, how many feet per second is this?

SOLUTION:  

The thrill ride travels about 80.67 feet per second.

Complete each conversion. Round to the nearest hundredth, if necessary.14. 4 L ≈ _ qt

SOLUTION:  Use 1 L ≈ 1.057 qt.

15. 16 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

16. 13 m ≈ _ ft

SOLUTION:  Use 1 ft ≈ 0.305 m.

17. 8 yd ≈ _ m

SOLUTION:  Use 1 yd ≈ 0.914 m.

18. 18 lb ≈ _ kg

SOLUTION:  Use 1 lb ≈ 0.454 kg.

19. 7 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

20. 1500 g ≈ _ oz

SOLUTION:  Use 1 oz ≈ 28.35 g.

21. 15 ft ≈ _ m

SOLUTION:  Use 1 ft ≈ 0.305 m.

22. 28 fl oz ≈ _ mL

SOLUTION:  Use 1 fl oz ≈ 29.574 mL.

23. The velocity of sound through wood at 0° Celsius is 1454 meters per second. How many miles is this per hour? Round to the nearest hundredth.

SOLUTION:  

The velocity of sound through wood is approximately 3250.68 miles per hour.

24. A certain car in Canada can travel 15 kilometers per 1 liter of gasoline. How many miles per gallon is this? Round to the nearest hundredth.

SOLUTION:  

The car can travel approximately 35.28 miles per gallon.

Complete each conversion. Round to the nearest hundredth, if necessary.25. 8 in. ≈ _ mm

SOLUTION:  Use 1 in. ≈ 2.54 cm and 1 cm = 10 mm.

26. 16 L ≈ _ c

SOLUTION:  Use 1 L ≈ 2.114 pt and 1 pt = 2 cups.

27. 2 km ≈ _ yd

SOLUTION:  Use 1 km = 1000 m and 1 m ≈ 1.094 yd.

28. 250 fl oz ≈ _ L

SOLUTION:  Use 1 fl oz ≈ 29.574 mL and 1000 mL = 1 L.

29. 2750 g ≈ _ lb

SOLUTION:  Use 1 g ≈ 0.035 oz and 16 oz = 1 lb.

30. 5 gal ≈ _ mL

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 L = 1000 mL.

31. Crystal’s times for each portion of a triathlon are shown in the table. Round to the nearest hundredth.

a. How many meters per second did she run? b. What was her speed in miles per hour for the aquabike portion (swimming and biking)?

SOLUTION:  a. Crystal ran 10 kilometers in 64 minutes.

Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming and biking was 1.5 + 40 or 41.5 kilometers. Her time for theseportions was 40 + 86 or 126 minutes.

Crystal’s speed for the aquabike portion was about 12.27 miles per hour.

Order each group of rates from least to greatest.32. 100 oz/min, 2500 g/min, 10 lb/min

SOLUTION:  

5.51 lb/min < 6.25 lb/min < 10 lb/min Ordered from least to greatest, the rates are 2500 g/min, 100 oz/min, and 10 lb/min.

100 oz/min

2500 g/min

10 lb/min

33. 500 m/h, 7 yd/min, 6 in./s

SOLUTION:  

4.20 in./s < 5.47 in./s < 6 in./s Ordered from least to greatest, the rates are 7 yd/min, 500 m/h, and 6 in./s.

500 m/h

7 yd/min

6 in./s

34. 32 mi/gal, 15 m/mL, 6600 yd/qt

SOLUTION:  

6600 yd/qt < 14,080 yd/qt < 15,524 yd/qt Ordered from least to greatest, the rates are 6600 yd/qt, 32 mi/gal, and 15 m/mL.

32 mi/gal

15 m/mL

6600 yd/qt

35. 500 kg/h, 5 oz/s, 18 lb/min

SOLUTION:  

4.8 oz/s < 4.90 oz/s < 5 oz/s Ordered from least to greatest, the rates are 18 lb/min, 500 kg/h, and 5 oz/s.

500 kg/h

5 oz/s

18 lb/min

36. The sprinkler system in the Willis Tower pumps up to 1500 gallons of water per minute. How many liters of water

can the system pump in  minute? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L.

Divide the rate by 4 to find the amount of water pumped in  minute.

The water system in the Sears Tower can pump 1419.38 liters of water in  minute.

37. The average American consumes 20 gallons of ice cream in one year. At this rate, how many liters of ice cream will50 Americans consume in one week? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 yr = 52 wk.

Multiply the rate by 50 to find how many liters 50 Americans consume.

So, 50 Americans consume about 72.79 liters of ice cream per week.

Replace each _ with <, >, or = to make a true sentence.38. 10 m _ 390 in.

SOLUTION:  Use 1 m ≈ 3.279 ft and 1 ft = 12 in.

39. 520 oz _ 15 kg

SOLUTION:  Use 1 oz ≈ 28.35 g and 1000 g = 1 kg.

40. 14 pt _ 6622 mL

SOLUTION:  Use 1 pt ≈ 0.473 L and 1 L = 1000 mL.

Financial Literacy Use dimensional analysis and the table below to make each conversion. Round to the nearest hundredth, if necessary.

41. 150 dollars to euros

SOLUTION:  

So, 150 dollars is equal to 118.5 euros.

42. 275 dollars to pounds

SOLUTION:  

So, 275 dollars is equal to 175.18 pounds.

43. 570 yuan to dollars

SOLUTION:  

So, 570 yuan is equal to 89.41 dollars.

44. 500 pesos to dollars

SOLUTION:  

So, 500 pesos is approximately equal to 37.19 dollars.

45. Model with Mathematics Write and solve a real-world problem in which dimensional analysis is used to convert square feet to square yards. Hint: 1 square yard = 9 square feet

SOLUTION:  Sample answer: Macha needs 120 square feet of carpeting for her bedroom. How many square yards does she need?

Maria needs square yards.

46. Be Precise Give two examples of different measurements that are equivalent to 10 centimeters per second.

SOLUTION:  Sample answers:

Two measurements equivalent to 10 centimeters per second are 600 centimeters per minute and 360 meters per hour.

47. WHICH ONE DOESN’T BELONG? Select the rate that does not have the same value as the other three. Explain your reasoning.

SOLUTION:  Convert each rate to miles per hour and compare the values.

The rate that does not belong is 500 ft/min. All of the other rates are equal to 60 mi/h.

60 mi/h

88 ft/sec

500 ft/min

1440 mi/day

48. Persevere with Problems A recipe for fruit punch uses the ingredients shown. About how many cups of each ingredient are needed? Round to the nearest tenth.

SOLUTION:  Use 1000 mL = 1L, 1 L ≈ 2.114 pt, and 1 pt = 2 cups.  Cranberry juice:

  Apple juice:

  Pineapple juice:

  Lemon juice:

  Club soda:

49. Identify Structure What property of multiplication allows you to multiply a rate by a conversion factor without changing its value? Explain.

SOLUTION:  

The Identity Property of Multiplication allows you to multiply a rate by a conversion factor without changing its value

because the conversion factor is equal to 1. For example, multiplying by  is the same as multiplying by 1 

because 12 inches equals 1 foot.

50. Building on the Essential Question Explain how you would convert 10 miles per hour to meters per second.

SOLUTION:  Sample answer: Use dimensional analysis.

So, 10 miles per hour is approximately equal to 4.47 meters per second.

51. A speed of 55 miles per hour is the same rate as which of the following?

 

A  34 kilometers per hourB  50 kilometers per hourC  88 kilometers per hourD  98 kilometers per hour

SOLUTION:  Use 1 mi ≈ 1.609 kilometers.

55 miles per hour is approximately equal to 88 kilometers per hour. Choice C is correct.

52. A piece of notebook paper measures  inches by 11 inches. Which of the following metric approximations is the 

same?

 

F  2 m by 2.8 mG  3 cm by 4 cmH  22 cm by 28 cmJ  30 m by 40 m

SOLUTION:  Use 1 in. ≈ 2.54 centimeters.

The approximate metric dimensions of a piece of notebook paper are 22 cm by 28 cm. Choice H is correct.

53. A car’s mileage is registered at 29,345.5 miles. The driver sees a sign that warns of road work in 1000 feet. What will be the car’s mileage when the road work begins?

 

A  29,345.7B  29,345.9C  29,356.2D  29,356.5

SOLUTION:  To find the car’s mileage when the road work begins, find the sum of the current mileage and the distance to the

road work, in miles.

29,345.5 + 0.2 = 29,345.7 When the road work begins, the mileage will be 29,345.7. Choice A is correct.

54. SHORT RESPONSE Convert 565 miles per hour to feet per second. Show the procedure you used.

SOLUTION:  Use dimensional analysis and the following conversion facts to convert 565 miles per hour to feet per second.1 mile = 5280 feet 1 hour = 60 min = 3600 seconds

 or 828.67 feet per second

Express each rate as a unit rate. Round to the nearest tenth or to the nearest cent, if necessary.55. $183 for 4 concert tickets

SOLUTION:  

The unit rate is $45.75 per ticket.

56. 100 feet in 14.5 seconds

SOLUTION:  

The unit rate is about 6.9 feet per second.

57. 254.1 miles on 10.5 gallons

SOLUTION:  

The unit rate is 24.2 miles per gallon.

58. 9 inches of snow in 12 hours

SOLUTION:  

Rounded to the nearest tenth, the unit rate is 0.8 inches per hour.

59. Financial Literacy Mrs. Gallagher wants to buy the package of soda that is less expensive per can. Which pack of sodas shown should she buy? Explain your reasoning.

SOLUTION:  

The 6-pack of soda costs about $0.37 per can. The 12-pack of soda costs about $0.35 per can. So, the 12-pack is less expensive.

Express each ratio as a fraction in simplest form.60. 12 cars out of 30 vehicles

SOLUTION:  

61. 5 cups to 5 quarts

SOLUTION:  Convert 5 quarts to cups. There are 4 cups in 1 quart.

62. 15 soccer balls out of 35 balls

SOLUTION:  

63. 8 pencils to 20 crayons

SOLUTION:  

Simplify each expression.64. (x – 3) + 2

SOLUTION:  

65. (8 • y) • (–4)

SOLUTION:  

66. 25 + (d –8)

SOLUTION:  

67. 9(5m)

SOLUTION:  

68. (x + 1) – 9

SOLUTION:  

69. 5(3 • r)

SOLUTION:  

70. Clive is making hamburgers for a cookout. How many -pound hamburgers can he make from  pounds of 

ground beef?

SOLUTION:  Words: The amount of ground beef needed for each hamburger multiplied by the number of hamburgers equals the total amount of ground beef. Variable: Let h = the number of hamburgers

Equation:

Clive can make 11 hamburgers.

Find each product or quotient.71. –12 • (–10)

SOLUTION:  The product of two integers with the same sign is positive. So, –12 • (–10) = 120.

72. –18 ÷ 3

SOLUTION:  The quotient of two integers with different signs is negative. So, –18 ÷ 3 = –6.

73. 9 • (–14)

SOLUTION:  The product of two integers with different signs is negative. So, 9 • (–14) = –126.

74. 54 ÷ (–6)

SOLUTION:  The quotient of two integers with different signs is negative. So, 54 ÷ (–6) = –9.

75. –14 • 2

SOLUTION:  The product of two integers with different signs is negative. So, –14 • 2 = –28.

76. –72 ÷ (–4)

SOLUTION:  The quotient of two integers with the same sign is positive. So, –72 ÷ (–4) = 18.

eSolutions Manual - Powered by Cognero Page 18

5-4 Converting Rates

Page 19: Crystal - Ms. Wilson's Math Classes · a. Crystal ran 10 kilometers in 64 minutes. Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming

1. In Brazil, about 20 acres of rainforest are destroyed each minute. At this rate, how much rainforest is destroyed per day?

SOLUTION:  

At the rate of 20 acres per minute, there are 28,800 acres of rainforest in Brazil destroyed per day.

2. Lexi can paint 5 yards of fencing in one hour. At this rate, how many inches does she paint per minute?

SOLUTION:  

At the rate of 5 yards per hour, Lexi can paint 3 inches per minute.

Complete each conversion. Round to the nearest hundredth, if necessary.3. 8 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

4. 5 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

5. 15 oz ≈ _ g

SOLUTION:  Use 1 oz ≈ 28.35 g.

6. 24 cm ≈ _ in.

SOLUTION:  Use 1 cm ≈ 0.394 in.

7. 9 pt ≈ _ L

SOLUTION:  Use 1 pt ≈ 0.473 L.

8. 3 m ≈ _ ft

SOLUTION:  Use 1 m ≈ 3.279 ft.

9. An elephant can eat up to 440 pounds of vegetation every day. How many grams per minute is this? Round to the nearest hundredth.

SOLUTION:  

An elephant can eat about 138.72 grams of vegetation per minute.

10. A candy company can produce 4800 sour lemon candies per minute. How many candies can they produce each hour?

SOLUTION:  

The company can produce 288,000 candies each hour.

11. In a recent year, 51.9 billion aluminum cans were recycled. About how many cans per week is this?

SOLUTION:  

About 1 billion aluminum cans were recycled per week.

12. The average American student spends almost 1500 hours per year watching television. To the nearest hundredth, how many minutes per day is this?

SOLUTION:  

The average American student spends 246.58 minutes per day watching television.

13. A thrill ride at an amusement park travels 55 miles per hour. To the nearest hundredth, how many feet per second is this?

SOLUTION:  

The thrill ride travels about 80.67 feet per second.

Complete each conversion. Round to the nearest hundredth, if necessary.14. 4 L ≈ _ qt

SOLUTION:  Use 1 L ≈ 1.057 qt.

15. 16 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

16. 13 m ≈ _ ft

SOLUTION:  Use 1 ft ≈ 0.305 m.

17. 8 yd ≈ _ m

SOLUTION:  Use 1 yd ≈ 0.914 m.

18. 18 lb ≈ _ kg

SOLUTION:  Use 1 lb ≈ 0.454 kg.

19. 7 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

20. 1500 g ≈ _ oz

SOLUTION:  Use 1 oz ≈ 28.35 g.

21. 15 ft ≈ _ m

SOLUTION:  Use 1 ft ≈ 0.305 m.

22. 28 fl oz ≈ _ mL

SOLUTION:  Use 1 fl oz ≈ 29.574 mL.

23. The velocity of sound through wood at 0° Celsius is 1454 meters per second. How many miles is this per hour? Round to the nearest hundredth.

SOLUTION:  

The velocity of sound through wood is approximately 3250.68 miles per hour.

24. A certain car in Canada can travel 15 kilometers per 1 liter of gasoline. How many miles per gallon is this? Round to the nearest hundredth.

SOLUTION:  

The car can travel approximately 35.28 miles per gallon.

Complete each conversion. Round to the nearest hundredth, if necessary.25. 8 in. ≈ _ mm

SOLUTION:  Use 1 in. ≈ 2.54 cm and 1 cm = 10 mm.

26. 16 L ≈ _ c

SOLUTION:  Use 1 L ≈ 2.114 pt and 1 pt = 2 cups.

27. 2 km ≈ _ yd

SOLUTION:  Use 1 km = 1000 m and 1 m ≈ 1.094 yd.

28. 250 fl oz ≈ _ L

SOLUTION:  Use 1 fl oz ≈ 29.574 mL and 1000 mL = 1 L.

29. 2750 g ≈ _ lb

SOLUTION:  Use 1 g ≈ 0.035 oz and 16 oz = 1 lb.

30. 5 gal ≈ _ mL

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 L = 1000 mL.

31. Crystal’s times for each portion of a triathlon are shown in the table. Round to the nearest hundredth.

a. How many meters per second did she run? b. What was her speed in miles per hour for the aquabike portion (swimming and biking)?

SOLUTION:  a. Crystal ran 10 kilometers in 64 minutes.

Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming and biking was 1.5 + 40 or 41.5 kilometers. Her time for theseportions was 40 + 86 or 126 minutes.

Crystal’s speed for the aquabike portion was about 12.27 miles per hour.

Order each group of rates from least to greatest.32. 100 oz/min, 2500 g/min, 10 lb/min

SOLUTION:  

5.51 lb/min < 6.25 lb/min < 10 lb/min Ordered from least to greatest, the rates are 2500 g/min, 100 oz/min, and 10 lb/min.

100 oz/min

2500 g/min

10 lb/min

33. 500 m/h, 7 yd/min, 6 in./s

SOLUTION:  

4.20 in./s < 5.47 in./s < 6 in./s Ordered from least to greatest, the rates are 7 yd/min, 500 m/h, and 6 in./s.

500 m/h

7 yd/min

6 in./s

34. 32 mi/gal, 15 m/mL, 6600 yd/qt

SOLUTION:  

6600 yd/qt < 14,080 yd/qt < 15,524 yd/qt Ordered from least to greatest, the rates are 6600 yd/qt, 32 mi/gal, and 15 m/mL.

32 mi/gal

15 m/mL

6600 yd/qt

35. 500 kg/h, 5 oz/s, 18 lb/min

SOLUTION:  

4.8 oz/s < 4.90 oz/s < 5 oz/s Ordered from least to greatest, the rates are 18 lb/min, 500 kg/h, and 5 oz/s.

500 kg/h

5 oz/s

18 lb/min

36. The sprinkler system in the Willis Tower pumps up to 1500 gallons of water per minute. How many liters of water

can the system pump in  minute? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L.

Divide the rate by 4 to find the amount of water pumped in  minute.

The water system in the Sears Tower can pump 1419.38 liters of water in  minute.

37. The average American consumes 20 gallons of ice cream in one year. At this rate, how many liters of ice cream will50 Americans consume in one week? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 yr = 52 wk.

Multiply the rate by 50 to find how many liters 50 Americans consume.

So, 50 Americans consume about 72.79 liters of ice cream per week.

Replace each _ with <, >, or = to make a true sentence.38. 10 m _ 390 in.

SOLUTION:  Use 1 m ≈ 3.279 ft and 1 ft = 12 in.

39. 520 oz _ 15 kg

SOLUTION:  Use 1 oz ≈ 28.35 g and 1000 g = 1 kg.

40. 14 pt _ 6622 mL

SOLUTION:  Use 1 pt ≈ 0.473 L and 1 L = 1000 mL.

Financial Literacy Use dimensional analysis and the table below to make each conversion. Round to the nearest hundredth, if necessary.

41. 150 dollars to euros

SOLUTION:  

So, 150 dollars is equal to 118.5 euros.

42. 275 dollars to pounds

SOLUTION:  

So, 275 dollars is equal to 175.18 pounds.

43. 570 yuan to dollars

SOLUTION:  

So, 570 yuan is equal to 89.41 dollars.

44. 500 pesos to dollars

SOLUTION:  

So, 500 pesos is approximately equal to 37.19 dollars.

45. Model with Mathematics Write and solve a real-world problem in which dimensional analysis is used to convert square feet to square yards. Hint: 1 square yard = 9 square feet

SOLUTION:  Sample answer: Macha needs 120 square feet of carpeting for her bedroom. How many square yards does she need?

Maria needs square yards.

46. Be Precise Give two examples of different measurements that are equivalent to 10 centimeters per second.

SOLUTION:  Sample answers:

Two measurements equivalent to 10 centimeters per second are 600 centimeters per minute and 360 meters per hour.

47. WHICH ONE DOESN’T BELONG? Select the rate that does not have the same value as the other three. Explain your reasoning.

SOLUTION:  Convert each rate to miles per hour and compare the values.

The rate that does not belong is 500 ft/min. All of the other rates are equal to 60 mi/h.

60 mi/h

88 ft/sec

500 ft/min

1440 mi/day

48. Persevere with Problems A recipe for fruit punch uses the ingredients shown. About how many cups of each ingredient are needed? Round to the nearest tenth.

SOLUTION:  Use 1000 mL = 1L, 1 L ≈ 2.114 pt, and 1 pt = 2 cups.  Cranberry juice:

  Apple juice:

  Pineapple juice:

  Lemon juice:

  Club soda:

49. Identify Structure What property of multiplication allows you to multiply a rate by a conversion factor without changing its value? Explain.

SOLUTION:  

The Identity Property of Multiplication allows you to multiply a rate by a conversion factor without changing its value

because the conversion factor is equal to 1. For example, multiplying by  is the same as multiplying by 1 

because 12 inches equals 1 foot.

50. Building on the Essential Question Explain how you would convert 10 miles per hour to meters per second.

SOLUTION:  Sample answer: Use dimensional analysis.

So, 10 miles per hour is approximately equal to 4.47 meters per second.

51. A speed of 55 miles per hour is the same rate as which of the following?

 

A  34 kilometers per hourB  50 kilometers per hourC  88 kilometers per hourD  98 kilometers per hour

SOLUTION:  Use 1 mi ≈ 1.609 kilometers.

55 miles per hour is approximately equal to 88 kilometers per hour. Choice C is correct.

52. A piece of notebook paper measures  inches by 11 inches. Which of the following metric approximations is the 

same?

 

F  2 m by 2.8 mG  3 cm by 4 cmH  22 cm by 28 cmJ  30 m by 40 m

SOLUTION:  Use 1 in. ≈ 2.54 centimeters.

The approximate metric dimensions of a piece of notebook paper are 22 cm by 28 cm. Choice H is correct.

53. A car’s mileage is registered at 29,345.5 miles. The driver sees a sign that warns of road work in 1000 feet. What will be the car’s mileage when the road work begins?

 

A  29,345.7B  29,345.9C  29,356.2D  29,356.5

SOLUTION:  To find the car’s mileage when the road work begins, find the sum of the current mileage and the distance to the

road work, in miles.

29,345.5 + 0.2 = 29,345.7 When the road work begins, the mileage will be 29,345.7. Choice A is correct.

54. SHORT RESPONSE Convert 565 miles per hour to feet per second. Show the procedure you used.

SOLUTION:  Use dimensional analysis and the following conversion facts to convert 565 miles per hour to feet per second.1 mile = 5280 feet 1 hour = 60 min = 3600 seconds

 or 828.67 feet per second

Express each rate as a unit rate. Round to the nearest tenth or to the nearest cent, if necessary.55. $183 for 4 concert tickets

SOLUTION:  

The unit rate is $45.75 per ticket.

56. 100 feet in 14.5 seconds

SOLUTION:  

The unit rate is about 6.9 feet per second.

57. 254.1 miles on 10.5 gallons

SOLUTION:  

The unit rate is 24.2 miles per gallon.

58. 9 inches of snow in 12 hours

SOLUTION:  

Rounded to the nearest tenth, the unit rate is 0.8 inches per hour.

59. Financial Literacy Mrs. Gallagher wants to buy the package of soda that is less expensive per can. Which pack of sodas shown should she buy? Explain your reasoning.

SOLUTION:  

The 6-pack of soda costs about $0.37 per can. The 12-pack of soda costs about $0.35 per can. So, the 12-pack is less expensive.

Express each ratio as a fraction in simplest form.60. 12 cars out of 30 vehicles

SOLUTION:  

61. 5 cups to 5 quarts

SOLUTION:  Convert 5 quarts to cups. There are 4 cups in 1 quart.

62. 15 soccer balls out of 35 balls

SOLUTION:  

63. 8 pencils to 20 crayons

SOLUTION:  

Simplify each expression.64. (x – 3) + 2

SOLUTION:  

65. (8 • y) • (–4)

SOLUTION:  

66. 25 + (d –8)

SOLUTION:  

67. 9(5m)

SOLUTION:  

68. (x + 1) – 9

SOLUTION:  

69. 5(3 • r)

SOLUTION:  

70. Clive is making hamburgers for a cookout. How many -pound hamburgers can he make from  pounds of 

ground beef?

SOLUTION:  Words: The amount of ground beef needed for each hamburger multiplied by the number of hamburgers equals the total amount of ground beef. Variable: Let h = the number of hamburgers

Equation:

Clive can make 11 hamburgers.

Find each product or quotient.71. –12 • (–10)

SOLUTION:  The product of two integers with the same sign is positive. So, –12 • (–10) = 120.

72. –18 ÷ 3

SOLUTION:  The quotient of two integers with different signs is negative. So, –18 ÷ 3 = –6.

73. 9 • (–14)

SOLUTION:  The product of two integers with different signs is negative. So, 9 • (–14) = –126.

74. 54 ÷ (–6)

SOLUTION:  The quotient of two integers with different signs is negative. So, 54 ÷ (–6) = –9.

75. –14 • 2

SOLUTION:  The product of two integers with different signs is negative. So, –14 • 2 = –28.

76. –72 ÷ (–4)

SOLUTION:  The quotient of two integers with the same sign is positive. So, –72 ÷ (–4) = 18.

eSolutions Manual - Powered by Cognero Page 19

5-4 Converting Rates

Page 20: Crystal - Ms. Wilson's Math Classes · a. Crystal ran 10 kilometers in 64 minutes. Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming

1. In Brazil, about 20 acres of rainforest are destroyed each minute. At this rate, how much rainforest is destroyed per day?

SOLUTION:  

At the rate of 20 acres per minute, there are 28,800 acres of rainforest in Brazil destroyed per day.

2. Lexi can paint 5 yards of fencing in one hour. At this rate, how many inches does she paint per minute?

SOLUTION:  

At the rate of 5 yards per hour, Lexi can paint 3 inches per minute.

Complete each conversion. Round to the nearest hundredth, if necessary.3. 8 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

4. 5 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

5. 15 oz ≈ _ g

SOLUTION:  Use 1 oz ≈ 28.35 g.

6. 24 cm ≈ _ in.

SOLUTION:  Use 1 cm ≈ 0.394 in.

7. 9 pt ≈ _ L

SOLUTION:  Use 1 pt ≈ 0.473 L.

8. 3 m ≈ _ ft

SOLUTION:  Use 1 m ≈ 3.279 ft.

9. An elephant can eat up to 440 pounds of vegetation every day. How many grams per minute is this? Round to the nearest hundredth.

SOLUTION:  

An elephant can eat about 138.72 grams of vegetation per minute.

10. A candy company can produce 4800 sour lemon candies per minute. How many candies can they produce each hour?

SOLUTION:  

The company can produce 288,000 candies each hour.

11. In a recent year, 51.9 billion aluminum cans were recycled. About how many cans per week is this?

SOLUTION:  

About 1 billion aluminum cans were recycled per week.

12. The average American student spends almost 1500 hours per year watching television. To the nearest hundredth, how many minutes per day is this?

SOLUTION:  

The average American student spends 246.58 minutes per day watching television.

13. A thrill ride at an amusement park travels 55 miles per hour. To the nearest hundredth, how many feet per second is this?

SOLUTION:  

The thrill ride travels about 80.67 feet per second.

Complete each conversion. Round to the nearest hundredth, if necessary.14. 4 L ≈ _ qt

SOLUTION:  Use 1 L ≈ 1.057 qt.

15. 16 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

16. 13 m ≈ _ ft

SOLUTION:  Use 1 ft ≈ 0.305 m.

17. 8 yd ≈ _ m

SOLUTION:  Use 1 yd ≈ 0.914 m.

18. 18 lb ≈ _ kg

SOLUTION:  Use 1 lb ≈ 0.454 kg.

19. 7 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

20. 1500 g ≈ _ oz

SOLUTION:  Use 1 oz ≈ 28.35 g.

21. 15 ft ≈ _ m

SOLUTION:  Use 1 ft ≈ 0.305 m.

22. 28 fl oz ≈ _ mL

SOLUTION:  Use 1 fl oz ≈ 29.574 mL.

23. The velocity of sound through wood at 0° Celsius is 1454 meters per second. How many miles is this per hour? Round to the nearest hundredth.

SOLUTION:  

The velocity of sound through wood is approximately 3250.68 miles per hour.

24. A certain car in Canada can travel 15 kilometers per 1 liter of gasoline. How many miles per gallon is this? Round to the nearest hundredth.

SOLUTION:  

The car can travel approximately 35.28 miles per gallon.

Complete each conversion. Round to the nearest hundredth, if necessary.25. 8 in. ≈ _ mm

SOLUTION:  Use 1 in. ≈ 2.54 cm and 1 cm = 10 mm.

26. 16 L ≈ _ c

SOLUTION:  Use 1 L ≈ 2.114 pt and 1 pt = 2 cups.

27. 2 km ≈ _ yd

SOLUTION:  Use 1 km = 1000 m and 1 m ≈ 1.094 yd.

28. 250 fl oz ≈ _ L

SOLUTION:  Use 1 fl oz ≈ 29.574 mL and 1000 mL = 1 L.

29. 2750 g ≈ _ lb

SOLUTION:  Use 1 g ≈ 0.035 oz and 16 oz = 1 lb.

30. 5 gal ≈ _ mL

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 L = 1000 mL.

31. Crystal’s times for each portion of a triathlon are shown in the table. Round to the nearest hundredth.

a. How many meters per second did she run? b. What was her speed in miles per hour for the aquabike portion (swimming and biking)?

SOLUTION:  a. Crystal ran 10 kilometers in 64 minutes.

Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming and biking was 1.5 + 40 or 41.5 kilometers. Her time for theseportions was 40 + 86 or 126 minutes.

Crystal’s speed for the aquabike portion was about 12.27 miles per hour.

Order each group of rates from least to greatest.32. 100 oz/min, 2500 g/min, 10 lb/min

SOLUTION:  

5.51 lb/min < 6.25 lb/min < 10 lb/min Ordered from least to greatest, the rates are 2500 g/min, 100 oz/min, and 10 lb/min.

100 oz/min

2500 g/min

10 lb/min

33. 500 m/h, 7 yd/min, 6 in./s

SOLUTION:  

4.20 in./s < 5.47 in./s < 6 in./s Ordered from least to greatest, the rates are 7 yd/min, 500 m/h, and 6 in./s.

500 m/h

7 yd/min

6 in./s

34. 32 mi/gal, 15 m/mL, 6600 yd/qt

SOLUTION:  

6600 yd/qt < 14,080 yd/qt < 15,524 yd/qt Ordered from least to greatest, the rates are 6600 yd/qt, 32 mi/gal, and 15 m/mL.

32 mi/gal

15 m/mL

6600 yd/qt

35. 500 kg/h, 5 oz/s, 18 lb/min

SOLUTION:  

4.8 oz/s < 4.90 oz/s < 5 oz/s Ordered from least to greatest, the rates are 18 lb/min, 500 kg/h, and 5 oz/s.

500 kg/h

5 oz/s

18 lb/min

36. The sprinkler system in the Willis Tower pumps up to 1500 gallons of water per minute. How many liters of water

can the system pump in  minute? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L.

Divide the rate by 4 to find the amount of water pumped in  minute.

The water system in the Sears Tower can pump 1419.38 liters of water in  minute.

37. The average American consumes 20 gallons of ice cream in one year. At this rate, how many liters of ice cream will50 Americans consume in one week? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 yr = 52 wk.

Multiply the rate by 50 to find how many liters 50 Americans consume.

So, 50 Americans consume about 72.79 liters of ice cream per week.

Replace each _ with <, >, or = to make a true sentence.38. 10 m _ 390 in.

SOLUTION:  Use 1 m ≈ 3.279 ft and 1 ft = 12 in.

39. 520 oz _ 15 kg

SOLUTION:  Use 1 oz ≈ 28.35 g and 1000 g = 1 kg.

40. 14 pt _ 6622 mL

SOLUTION:  Use 1 pt ≈ 0.473 L and 1 L = 1000 mL.

Financial Literacy Use dimensional analysis and the table below to make each conversion. Round to the nearest hundredth, if necessary.

41. 150 dollars to euros

SOLUTION:  

So, 150 dollars is equal to 118.5 euros.

42. 275 dollars to pounds

SOLUTION:  

So, 275 dollars is equal to 175.18 pounds.

43. 570 yuan to dollars

SOLUTION:  

So, 570 yuan is equal to 89.41 dollars.

44. 500 pesos to dollars

SOLUTION:  

So, 500 pesos is approximately equal to 37.19 dollars.

45. Model with Mathematics Write and solve a real-world problem in which dimensional analysis is used to convert square feet to square yards. Hint: 1 square yard = 9 square feet

SOLUTION:  Sample answer: Macha needs 120 square feet of carpeting for her bedroom. How many square yards does she need?

Maria needs square yards.

46. Be Precise Give two examples of different measurements that are equivalent to 10 centimeters per second.

SOLUTION:  Sample answers:

Two measurements equivalent to 10 centimeters per second are 600 centimeters per minute and 360 meters per hour.

47. WHICH ONE DOESN’T BELONG? Select the rate that does not have the same value as the other three. Explain your reasoning.

SOLUTION:  Convert each rate to miles per hour and compare the values.

The rate that does not belong is 500 ft/min. All of the other rates are equal to 60 mi/h.

60 mi/h

88 ft/sec

500 ft/min

1440 mi/day

48. Persevere with Problems A recipe for fruit punch uses the ingredients shown. About how many cups of each ingredient are needed? Round to the nearest tenth.

SOLUTION:  Use 1000 mL = 1L, 1 L ≈ 2.114 pt, and 1 pt = 2 cups.  Cranberry juice:

  Apple juice:

  Pineapple juice:

  Lemon juice:

  Club soda:

49. Identify Structure What property of multiplication allows you to multiply a rate by a conversion factor without changing its value? Explain.

SOLUTION:  

The Identity Property of Multiplication allows you to multiply a rate by a conversion factor without changing its value

because the conversion factor is equal to 1. For example, multiplying by  is the same as multiplying by 1 

because 12 inches equals 1 foot.

50. Building on the Essential Question Explain how you would convert 10 miles per hour to meters per second.

SOLUTION:  Sample answer: Use dimensional analysis.

So, 10 miles per hour is approximately equal to 4.47 meters per second.

51. A speed of 55 miles per hour is the same rate as which of the following?

 

A  34 kilometers per hourB  50 kilometers per hourC  88 kilometers per hourD  98 kilometers per hour

SOLUTION:  Use 1 mi ≈ 1.609 kilometers.

55 miles per hour is approximately equal to 88 kilometers per hour. Choice C is correct.

52. A piece of notebook paper measures  inches by 11 inches. Which of the following metric approximations is the 

same?

 

F  2 m by 2.8 mG  3 cm by 4 cmH  22 cm by 28 cmJ  30 m by 40 m

SOLUTION:  Use 1 in. ≈ 2.54 centimeters.

The approximate metric dimensions of a piece of notebook paper are 22 cm by 28 cm. Choice H is correct.

53. A car’s mileage is registered at 29,345.5 miles. The driver sees a sign that warns of road work in 1000 feet. What will be the car’s mileage when the road work begins?

 

A  29,345.7B  29,345.9C  29,356.2D  29,356.5

SOLUTION:  To find the car’s mileage when the road work begins, find the sum of the current mileage and the distance to the

road work, in miles.

29,345.5 + 0.2 = 29,345.7 When the road work begins, the mileage will be 29,345.7. Choice A is correct.

54. SHORT RESPONSE Convert 565 miles per hour to feet per second. Show the procedure you used.

SOLUTION:  Use dimensional analysis and the following conversion facts to convert 565 miles per hour to feet per second.1 mile = 5280 feet 1 hour = 60 min = 3600 seconds

 or 828.67 feet per second

Express each rate as a unit rate. Round to the nearest tenth or to the nearest cent, if necessary.55. $183 for 4 concert tickets

SOLUTION:  

The unit rate is $45.75 per ticket.

56. 100 feet in 14.5 seconds

SOLUTION:  

The unit rate is about 6.9 feet per second.

57. 254.1 miles on 10.5 gallons

SOLUTION:  

The unit rate is 24.2 miles per gallon.

58. 9 inches of snow in 12 hours

SOLUTION:  

Rounded to the nearest tenth, the unit rate is 0.8 inches per hour.

59. Financial Literacy Mrs. Gallagher wants to buy the package of soda that is less expensive per can. Which pack of sodas shown should she buy? Explain your reasoning.

SOLUTION:  

The 6-pack of soda costs about $0.37 per can. The 12-pack of soda costs about $0.35 per can. So, the 12-pack is less expensive.

Express each ratio as a fraction in simplest form.60. 12 cars out of 30 vehicles

SOLUTION:  

61. 5 cups to 5 quarts

SOLUTION:  Convert 5 quarts to cups. There are 4 cups in 1 quart.

62. 15 soccer balls out of 35 balls

SOLUTION:  

63. 8 pencils to 20 crayons

SOLUTION:  

Simplify each expression.64. (x – 3) + 2

SOLUTION:  

65. (8 • y) • (–4)

SOLUTION:  

66. 25 + (d –8)

SOLUTION:  

67. 9(5m)

SOLUTION:  

68. (x + 1) – 9

SOLUTION:  

69. 5(3 • r)

SOLUTION:  

70. Clive is making hamburgers for a cookout. How many -pound hamburgers can he make from  pounds of 

ground beef?

SOLUTION:  Words: The amount of ground beef needed for each hamburger multiplied by the number of hamburgers equals the total amount of ground beef. Variable: Let h = the number of hamburgers

Equation:

Clive can make 11 hamburgers.

Find each product or quotient.71. –12 • (–10)

SOLUTION:  The product of two integers with the same sign is positive. So, –12 • (–10) = 120.

72. –18 ÷ 3

SOLUTION:  The quotient of two integers with different signs is negative. So, –18 ÷ 3 = –6.

73. 9 • (–14)

SOLUTION:  The product of two integers with different signs is negative. So, 9 • (–14) = –126.

74. 54 ÷ (–6)

SOLUTION:  The quotient of two integers with different signs is negative. So, 54 ÷ (–6) = –9.

75. –14 • 2

SOLUTION:  The product of two integers with different signs is negative. So, –14 • 2 = –28.

76. –72 ÷ (–4)

SOLUTION:  The quotient of two integers with the same sign is positive. So, –72 ÷ (–4) = 18.

eSolutions Manual - Powered by Cognero Page 20

5-4 Converting Rates

Page 21: Crystal - Ms. Wilson's Math Classes · a. Crystal ran 10 kilometers in 64 minutes. Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming

1. In Brazil, about 20 acres of rainforest are destroyed each minute. At this rate, how much rainforest is destroyed per day?

SOLUTION:  

At the rate of 20 acres per minute, there are 28,800 acres of rainforest in Brazil destroyed per day.

2. Lexi can paint 5 yards of fencing in one hour. At this rate, how many inches does she paint per minute?

SOLUTION:  

At the rate of 5 yards per hour, Lexi can paint 3 inches per minute.

Complete each conversion. Round to the nearest hundredth, if necessary.3. 8 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

4. 5 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

5. 15 oz ≈ _ g

SOLUTION:  Use 1 oz ≈ 28.35 g.

6. 24 cm ≈ _ in.

SOLUTION:  Use 1 cm ≈ 0.394 in.

7. 9 pt ≈ _ L

SOLUTION:  Use 1 pt ≈ 0.473 L.

8. 3 m ≈ _ ft

SOLUTION:  Use 1 m ≈ 3.279 ft.

9. An elephant can eat up to 440 pounds of vegetation every day. How many grams per minute is this? Round to the nearest hundredth.

SOLUTION:  

An elephant can eat about 138.72 grams of vegetation per minute.

10. A candy company can produce 4800 sour lemon candies per minute. How many candies can they produce each hour?

SOLUTION:  

The company can produce 288,000 candies each hour.

11. In a recent year, 51.9 billion aluminum cans were recycled. About how many cans per week is this?

SOLUTION:  

About 1 billion aluminum cans were recycled per week.

12. The average American student spends almost 1500 hours per year watching television. To the nearest hundredth, how many minutes per day is this?

SOLUTION:  

The average American student spends 246.58 minutes per day watching television.

13. A thrill ride at an amusement park travels 55 miles per hour. To the nearest hundredth, how many feet per second is this?

SOLUTION:  

The thrill ride travels about 80.67 feet per second.

Complete each conversion. Round to the nearest hundredth, if necessary.14. 4 L ≈ _ qt

SOLUTION:  Use 1 L ≈ 1.057 qt.

15. 16 in. ≈ _ cm

SOLUTION:  Use 1 in. ≈ 2.54 cm.

16. 13 m ≈ _ ft

SOLUTION:  Use 1 ft ≈ 0.305 m.

17. 8 yd ≈ _ m

SOLUTION:  Use 1 yd ≈ 0.914 m.

18. 18 lb ≈ _ kg

SOLUTION:  Use 1 lb ≈ 0.454 kg.

19. 7 L ≈ _ gal

SOLUTION:  Use 1 L ≈ 0.264 gal.

20. 1500 g ≈ _ oz

SOLUTION:  Use 1 oz ≈ 28.35 g.

21. 15 ft ≈ _ m

SOLUTION:  Use 1 ft ≈ 0.305 m.

22. 28 fl oz ≈ _ mL

SOLUTION:  Use 1 fl oz ≈ 29.574 mL.

23. The velocity of sound through wood at 0° Celsius is 1454 meters per second. How many miles is this per hour? Round to the nearest hundredth.

SOLUTION:  

The velocity of sound through wood is approximately 3250.68 miles per hour.

24. A certain car in Canada can travel 15 kilometers per 1 liter of gasoline. How many miles per gallon is this? Round to the nearest hundredth.

SOLUTION:  

The car can travel approximately 35.28 miles per gallon.

Complete each conversion. Round to the nearest hundredth, if necessary.25. 8 in. ≈ _ mm

SOLUTION:  Use 1 in. ≈ 2.54 cm and 1 cm = 10 mm.

26. 16 L ≈ _ c

SOLUTION:  Use 1 L ≈ 2.114 pt and 1 pt = 2 cups.

27. 2 km ≈ _ yd

SOLUTION:  Use 1 km = 1000 m and 1 m ≈ 1.094 yd.

28. 250 fl oz ≈ _ L

SOLUTION:  Use 1 fl oz ≈ 29.574 mL and 1000 mL = 1 L.

29. 2750 g ≈ _ lb

SOLUTION:  Use 1 g ≈ 0.035 oz and 16 oz = 1 lb.

30. 5 gal ≈ _ mL

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 L = 1000 mL.

31. Crystal’s times for each portion of a triathlon are shown in the table. Round to the nearest hundredth.

a. How many meters per second did she run? b. What was her speed in miles per hour for the aquabike portion (swimming and biking)?

SOLUTION:  a. Crystal ran 10 kilometers in 64 minutes.

Crystal ran about 2.60 meters per second. b. The total distance Crystal traveled while swimming and biking was 1.5 + 40 or 41.5 kilometers. Her time for theseportions was 40 + 86 or 126 minutes.

Crystal’s speed for the aquabike portion was about 12.27 miles per hour.

Order each group of rates from least to greatest.32. 100 oz/min, 2500 g/min, 10 lb/min

SOLUTION:  

5.51 lb/min < 6.25 lb/min < 10 lb/min Ordered from least to greatest, the rates are 2500 g/min, 100 oz/min, and 10 lb/min.

100 oz/min

2500 g/min

10 lb/min

33. 500 m/h, 7 yd/min, 6 in./s

SOLUTION:  

4.20 in./s < 5.47 in./s < 6 in./s Ordered from least to greatest, the rates are 7 yd/min, 500 m/h, and 6 in./s.

500 m/h

7 yd/min

6 in./s

34. 32 mi/gal, 15 m/mL, 6600 yd/qt

SOLUTION:  

6600 yd/qt < 14,080 yd/qt < 15,524 yd/qt Ordered from least to greatest, the rates are 6600 yd/qt, 32 mi/gal, and 15 m/mL.

32 mi/gal

15 m/mL

6600 yd/qt

35. 500 kg/h, 5 oz/s, 18 lb/min

SOLUTION:  

4.8 oz/s < 4.90 oz/s < 5 oz/s Ordered from least to greatest, the rates are 18 lb/min, 500 kg/h, and 5 oz/s.

500 kg/h

5 oz/s

18 lb/min

36. The sprinkler system in the Willis Tower pumps up to 1500 gallons of water per minute. How many liters of water

can the system pump in  minute? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L.

Divide the rate by 4 to find the amount of water pumped in  minute.

The water system in the Sears Tower can pump 1419.38 liters of water in  minute.

37. The average American consumes 20 gallons of ice cream in one year. At this rate, how many liters of ice cream will50 Americans consume in one week? Round to the nearest hundredth.

SOLUTION:  Use 1 gal ≈ 3.785 L and 1 yr = 52 wk.

Multiply the rate by 50 to find how many liters 50 Americans consume.

So, 50 Americans consume about 72.79 liters of ice cream per week.

Replace each _ with <, >, or = to make a true sentence.38. 10 m _ 390 in.

SOLUTION:  Use 1 m ≈ 3.279 ft and 1 ft = 12 in.

39. 520 oz _ 15 kg

SOLUTION:  Use 1 oz ≈ 28.35 g and 1000 g = 1 kg.

40. 14 pt _ 6622 mL

SOLUTION:  Use 1 pt ≈ 0.473 L and 1 L = 1000 mL.

Financial Literacy Use dimensional analysis and the table below to make each conversion. Round to the nearest hundredth, if necessary.

41. 150 dollars to euros

SOLUTION:  

So, 150 dollars is equal to 118.5 euros.

42. 275 dollars to pounds

SOLUTION:  

So, 275 dollars is equal to 175.18 pounds.

43. 570 yuan to dollars

SOLUTION:  

So, 570 yuan is equal to 89.41 dollars.

44. 500 pesos to dollars

SOLUTION:  

So, 500 pesos is approximately equal to 37.19 dollars.

45. Model with Mathematics Write and solve a real-world problem in which dimensional analysis is used to convert square feet to square yards. Hint: 1 square yard = 9 square feet

SOLUTION:  Sample answer: Macha needs 120 square feet of carpeting for her bedroom. How many square yards does she need?

Maria needs square yards.

46. Be Precise Give two examples of different measurements that are equivalent to 10 centimeters per second.

SOLUTION:  Sample answers:

Two measurements equivalent to 10 centimeters per second are 600 centimeters per minute and 360 meters per hour.

47. WHICH ONE DOESN’T BELONG? Select the rate that does not have the same value as the other three. Explain your reasoning.

SOLUTION:  Convert each rate to miles per hour and compare the values.

The rate that does not belong is 500 ft/min. All of the other rates are equal to 60 mi/h.

60 mi/h

88 ft/sec

500 ft/min

1440 mi/day

48. Persevere with Problems A recipe for fruit punch uses the ingredients shown. About how many cups of each ingredient are needed? Round to the nearest tenth.

SOLUTION:  Use 1000 mL = 1L, 1 L ≈ 2.114 pt, and 1 pt = 2 cups.  Cranberry juice:

  Apple juice:

  Pineapple juice:

  Lemon juice:

  Club soda:

49. Identify Structure What property of multiplication allows you to multiply a rate by a conversion factor without changing its value? Explain.

SOLUTION:  

The Identity Property of Multiplication allows you to multiply a rate by a conversion factor without changing its value

because the conversion factor is equal to 1. For example, multiplying by  is the same as multiplying by 1 

because 12 inches equals 1 foot.

50. Building on the Essential Question Explain how you would convert 10 miles per hour to meters per second.

SOLUTION:  Sample answer: Use dimensional analysis.

So, 10 miles per hour is approximately equal to 4.47 meters per second.

51. A speed of 55 miles per hour is the same rate as which of the following?

 

A  34 kilometers per hourB  50 kilometers per hourC  88 kilometers per hourD  98 kilometers per hour

SOLUTION:  Use 1 mi ≈ 1.609 kilometers.

55 miles per hour is approximately equal to 88 kilometers per hour. Choice C is correct.

52. A piece of notebook paper measures  inches by 11 inches. Which of the following metric approximations is the 

same?

 

F  2 m by 2.8 mG  3 cm by 4 cmH  22 cm by 28 cmJ  30 m by 40 m

SOLUTION:  Use 1 in. ≈ 2.54 centimeters.

The approximate metric dimensions of a piece of notebook paper are 22 cm by 28 cm. Choice H is correct.

53. A car’s mileage is registered at 29,345.5 miles. The driver sees a sign that warns of road work in 1000 feet. What will be the car’s mileage when the road work begins?

 

A  29,345.7B  29,345.9C  29,356.2D  29,356.5

SOLUTION:  To find the car’s mileage when the road work begins, find the sum of the current mileage and the distance to the

road work, in miles.

29,345.5 + 0.2 = 29,345.7 When the road work begins, the mileage will be 29,345.7. Choice A is correct.

54. SHORT RESPONSE Convert 565 miles per hour to feet per second. Show the procedure you used.

SOLUTION:  Use dimensional analysis and the following conversion facts to convert 565 miles per hour to feet per second.1 mile = 5280 feet 1 hour = 60 min = 3600 seconds

 or 828.67 feet per second

Express each rate as a unit rate. Round to the nearest tenth or to the nearest cent, if necessary.55. $183 for 4 concert tickets

SOLUTION:  

The unit rate is $45.75 per ticket.

56. 100 feet in 14.5 seconds

SOLUTION:  

The unit rate is about 6.9 feet per second.

57. 254.1 miles on 10.5 gallons

SOLUTION:  

The unit rate is 24.2 miles per gallon.

58. 9 inches of snow in 12 hours

SOLUTION:  

Rounded to the nearest tenth, the unit rate is 0.8 inches per hour.

59. Financial Literacy Mrs. Gallagher wants to buy the package of soda that is less expensive per can. Which pack of sodas shown should she buy? Explain your reasoning.

SOLUTION:  

The 6-pack of soda costs about $0.37 per can. The 12-pack of soda costs about $0.35 per can. So, the 12-pack is less expensive.

Express each ratio as a fraction in simplest form.60. 12 cars out of 30 vehicles

SOLUTION:  

61. 5 cups to 5 quarts

SOLUTION:  Convert 5 quarts to cups. There are 4 cups in 1 quart.

62. 15 soccer balls out of 35 balls

SOLUTION:  

63. 8 pencils to 20 crayons

SOLUTION:  

Simplify each expression.64. (x – 3) + 2

SOLUTION:  

65. (8 • y) • (–4)

SOLUTION:  

66. 25 + (d –8)

SOLUTION:  

67. 9(5m)

SOLUTION:  

68. (x + 1) – 9

SOLUTION:  

69. 5(3 • r)

SOLUTION:  

70. Clive is making hamburgers for a cookout. How many -pound hamburgers can he make from  pounds of 

ground beef?

SOLUTION:  Words: The amount of ground beef needed for each hamburger multiplied by the number of hamburgers equals the total amount of ground beef. Variable: Let h = the number of hamburgers

Equation:

Clive can make 11 hamburgers.

Find each product or quotient.71. –12 • (–10)

SOLUTION:  The product of two integers with the same sign is positive. So, –12 • (–10) = 120.

72. –18 ÷ 3

SOLUTION:  The quotient of two integers with different signs is negative. So, –18 ÷ 3 = –6.

73. 9 • (–14)

SOLUTION:  The product of two integers with different signs is negative. So, 9 • (–14) = –126.

74. 54 ÷ (–6)

SOLUTION:  The quotient of two integers with different signs is negative. So, 54 ÷ (–6) = –9.

75. –14 • 2

SOLUTION:  The product of two integers with different signs is negative. So, –14 • 2 = –28.

76. –72 ÷ (–4)

SOLUTION:  The quotient of two integers with the same sign is positive. So, –72 ÷ (–4) = 18.

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5-4 Converting Rates