1. Grade 6 Module 1 Lesson 17
From Rates to Ratios

2. Classwork
Given a rate, you can calculate the unit rate and associated ratios. Recognize that all ratios associated to a given rate are equivalent because they have the same value.

3. Example 1
Write each ratio as a rate. a. The ratio of miles to hours is 434 to 7.

4. Example 1 Write each ratio as a rate.
The ratio of miles to hours is 434 to 7.
Miles to hour – 434:7

5. Example 1 Write each ratio as a rate.
The ratio of miles to hours is 434 to 7.
Miles to hour – 434:7
Rate = 434 ÷ 7 (Solve Quotient)

6. Example 1 Write each ratio as a rate.
The ratio of miles to hours is 434 to 7.
Miles to hour – 434:7
Rate = 434 ÷ 7 (Solve Quotient)
Rate = 62 miles / hour

7. Example 1 Write each ratio as a rate.
The ratio of laps to minutes is 5 to 4.

8. Example 1 Write each ratio as a rate.
The ratio of laps to minutes is 5 to 4.
Laps to minute – 5:4

9. Example 1 Write each ratio as a rate.
The ratio of laps to minutes is 5 to 4.
Laps to minute – 5:4
Rate = 5 laps ÷ 4 minutes =

10. Example 1 Write each ratio as a rate.
The ratio of laps to minutes is 5 to 4.
Laps to minute – 5:4
Rate = 5 laps ÷ 4 minutes =
Rate = 5/4 laps per minute

11. Example 2
Complete the model below using the ratio from Example 1, part (b).
Ratio Unit Rate Rate

12. Example 2
Complete the model below using the ratio from Example 1, part (b).
Ratio Unit Rate Rate
5: /4 5/4 laps/min

13. Example 2
b. Complete the model below using the ratio listed below. Ratio Unit Rate Rate 6 ft / sec

14. Example 2
Will everyone have the same exact ratio to represent the given rate? Why or why not?

15. Example 2
Will everyone have the same exact ratio to represent the given rate? Why or why not? Not everyone’s ratios will be exactly the same because there are many different equivalent ratios that could be used to represent the same rate.

16. Example 2
What are some different examples that could be represented in the ratio box?

17. Example 2
What are some different examples that could be represented in the ratio box? 12:2; 18:3; 24:4

18. Example 2
b. Complete the model below using the ratio listed below. Ratio Unit Rate Rate 6:1; 60:10; 12:2 6 ft / sec

19. Example 2
b. Complete the model below using the ratio listed below. Ratio Unit Rate Rate 6:1; 60:10; 12:2 6 6 ft / sec

20. Example 3
Dave can clean pools at a constant rate of 3/5 pools/hour. a. What is the ratio of pools to hour?

21. Example 3 Dave can clean pools at a constant rate of 3/5 pools/hour.
What is the ratio of pools to hour?
3:5

22. Example 3
Dave can clean pools at a constant rate of 3/5 pools/hour. b. How many pools can Dave clean in 10 hours?

23. Example 3 Dave can clean pools at a constant rate of 3/5 pools/hour.
How many pools can Dave clean in 10 hours?
Pools = ?
Hours = 10 hrs

24. Example 3 2 Dave can clean pools at a constant rate of 3/5 pools/hour.
How many pools can Dave clean in 10 hours?
Pools = ?
Hours = 10 hrs 2

25. Example 3
Dave can clean pools at a constant rate of 3/5 pools/hour.
How many pools can Dave clean in 10 hours?
Pools = 6 pools
Hours = 10 hrs 2 2

26. Example 3 Dave can clean pools at a constant rate of 3/5 pools/hour.
How many pools can Dave clean in 10 hours?
Dave can clean 6 pools in 10 hours.

27. Example 3
Dave can clean pools at a constant rate of 3/5 pools/hour. c. How long does it take Dave to clean 15 pools? Pools = 15 pools Hours

28. Example 3
Dave can clean pools at a constant rate of 3/5 pools/hour. c. How long does it take Dave to clean 15 pools? Pools = 15 pools Hours 5

29. Example 3
Dave can clean pools at a constant rate of 3/5 pools/hour. c. How long does it take Dave to clean 15 pools? Pools = 15 pools Hours 25 hrs 5 5

30. Example 3
Dave can clean pools at a constant rate of 3/5 pools/hour. c. How long does it take Dave to clean 15 pools? It will take Dave 25 hours to clean 15 pools.

31. Example 4
Emeline can type at a constant rate of ¼ pages/minute. a. What is the ratio of pages to minutes?

32. Example 4 Emeline can type at a constant rate of ¼ pages/minute.
What is the ratio of pages to minutes?
1:4

33. Example 4
Emeline can type at a constant rate of ¼ pages/minute. b. Emeline has to type a 5-page article but only has 18 minutes until she reaches the deadline. Does Emeline have enough time to type the article? Why or why not?

34. Example 4
Emeline has to type a 5-page article but only has 18 minutes until she reaches the deadline. Does Emeline have enough time to type the article? Why or why not?
Pages
Minutes 1 2 3 4 5

35. Example 4
Emeline has to type a 5-page article but only has 18 minutes until she reaches the deadline. Does Emeline have enough time to type the article? Why or why not?
Pages
Minutes 1 4 2 3 5

36. Example 4
Emeline has to type a 5-page article but only has 18 minutes until she reaches the deadline. Does Emeline have enough time to type the article? Why or why not?
Pages
Minutes 1 4 2 8 3 5

37. Example 4
Emeline has to type a 5-page article but only has 18 minutes until she reaches the deadline. Does Emeline have enough time to type the article? Why or why not?
Pages
Minutes 1 4 2 8 3 12 5

38. Example 4
Emeline has to type a 5-page article but only has 18 minutes until she reaches the deadline. Does Emeline have enough time to type the article? Why or why not?
Pages
Minutes 1 4 2 8 3 12 16 5

39. Example 4
Emeline has to type a 5-page article but only has 18 minutes until she reaches the deadline. Does Emeline have enough time to type the article? Why or why not?
Pages
Minutes 1 4 2 8 3 12 16 5 20

40. Example 4
Emeline has to type a 5-page article but only has 18 minutes until she reaches the deadline. Does Emeline have enough time to type the article? Why or why not? No, Emeline will not have enough time because it will take her 20 minutes to type a 5-page article.

41. Example 4
Emeline has to type a 7-page article. How much time will it take her?
Pages
Minutes 5 6 7

42. Example 4
Emeline has to type a 7-page article. How much time will it take her?
Pages
Minutes 5 20 6 7

43. Example 4
Emeline has to type a 7-page article. How much time will it take her?
Pages
Minutes 5 20 6 24 7

44. Example 4
Emeline has to type a 7-page article. How much time will it take her?
Pages
Minutes 5 20 6 24 7 28

45. Example 4
Emeline has to type a 7-page article. How much time will it take her?
It will take Emeline 28 minutes to type a 7-page article.

46. Example 5
Xavier can swim at a constant speed of 5/3 meters/second. a. What is the ratio of meters to seconds?

47. Example 5 Xavier can swim at a constant speed of 5/3 meters/second.
What is the ratio of meters to seconds?
5:3

48. Example 5 Xavier can swim at a constant speed of 5/3 meters/second.
Xavier is trying to qualify for the National Swim Meet. To qualify, he must complete a 100 meter race in 55 seconds. Will Xavier be able to qualify? Why or why not?

49. Example 5
Xavier can swim at a constant speed of 5/3 meters/second.
Meters
Second 5 3

50. Example 5
Xavier can swim at a constant speed of 5/3 meters/second.
Meters
Second 5 3 10 6

51. Example 5
Xavier can swim at a constant speed of 5/3 meters/second.
Meters
Second 5 3 10 6
100 60

52. Example 5 Xavier can swim at a constant speed of 5/3 meters/second.
Xavier is trying to qualify for the National Swim Meet. To qualify, he must complete a 100 meter race in 55 seconds. Will Xavier be able to qualify? Why or why not?
Xavier will not qualify for the meet because he would complete the race in 60 seconds.

53. Example 5 Xavier can swim at a constant speed of 5/3 meters/second.
Xavier is also attempting to qualify for the same meet in the 200 meter event. To qualify, Xavier would have to complete the race in 130 seconds. Will Xavier be able to qualify in this race? Why or why not?

54. Example 5 Xavier can swim at a constant speed of 5/3 meters/second.
Xavier is also attempting to qualify for the same meet in the 200 meter event. To qualify, Xavier would have to complete the race in 130 seconds. Will Xavier be able to qualify in this race? Why or why not?

55. Example 5
Xavier can swim at a constant speed of 5/3 meters/second. c.
Meters
second

56. Example 5
Xavier can swim at a constant speed of 5/3 meters/second. c.
Meters
second
100 60

57. Example 5
Xavier can swim at a constant speed of 5/3 meters/second. c.
Meters
second
100 60
200
120

58. Example 5 Xavier can swim at a constant speed of 5/3 meters/second.
Xavier is also attempting to qualify for the same meet in the 200 meter event. To qualify, Xavier would have to complete the race in 130 seconds. Will Xavier be able to qualify in this race? Why or why not?
Xavier will qualify for the meet in the 200 meter race because he would complete the race in 120 seconds.

59. Example 6
The corner store sells apples at a rate of 1.25 dollars per apple. a. What is the ratio of dollars to apples?

60. Example 6
The corner store sells apples at a rate of 1.25 dollars per apple.
What is the ratio of dollars to apples?
1.25 : 1

61. Example 6
The corner store sells apples at a rate of 1.25 dollars per apple. b. Akia is only able to spend $10 on apples. How many apples can she buy?

62. Example 6
The corner store sells apples at a rate of 1.25 dollars per apple. b. Akia is only able to spend $10 on apples. How many apples can she buy?

63. Example 6
Dollars
Apples
1.25 1

64. Example 6
Dollars
Apples
1.25 1
2.50 2

65. Example 6
Dollars
Apples
1.25 1
2.50 2
3.75 3

66. Example 6
Dollars
Apples
1.25 1
2.50 2
3.75 3
5.00 4

67. Example 6
Dollars
Apples
1.25 1
2.50 2
3.75 3
5.00 4
6.25 5

68. Example 6
Dollars
Apples
1.25 1
2.50 2
3.75 3
5.00 4
6.25 5
7.50 6

69. Example 6 Dollars Apples 1.25 1 2.50 2 3.75 3 5.00 4 6.25 5 7.50 6
8.75 7

70. Example 6 Dollars Apples 1.25 1 2.50 2 3.75 3 5.00 4 6.25 5 7.50 6
8.75 7
10.00 8

71. Example 6
The corner store sells apples at a rate of 1.25 dollars per apple. b. Akia is only able to spend $10 on apples. How many apples can she buy? 8 apples

72. Example 6
The corner store sells apples at a rate of 1.25 dollars per apple.
Christian has $6 in his wallet and wants to spend it on apples. How many apples can Christian buy?

73. Example 6
The corner store sells apples at a rate of 1.25 dollars per apple.
Christian has $6 in his wallet and wants to spend it on apples. How many apples can Christian buy?
Christian can buy 4 apples and would spend $ Christian cannot buy a 5th apple because it would cost $6.25 for 5 apples, and he only has $6.00.

74. Closing
Lesson Summary A rate of 2/3 gallon per minute corresponds to the unit rate of 2/3 and also corresponds to the ratio 2:3. All ratios associated to a given rate are equivalent because they have the same value.