1. Name Numeracy Skill Builder: Long Division
Write any remainders as fractions and reduce.
Date
3 25 8 506 6 1227 4 8030
Objectives
1. Find a Unit Rate
2. Compare by using Unit 1 1 1 1
Rates 8 63 204 2007
3 4 2 2
Concept 1: Find a Unit Rate
Basic Proficient Advanced
I need 24 dollars for 6 sandwiches. I need 18 cups of flour for 8 loaves of I need 2 teaspoons of salt for 60
Find and reduce the unit rate. bread. Find and reduce the unit rate. cookies. Find and reduce the unit rate.
1 1
4 dollars per sandwich 2 cups per loaf teaspoon per cookie
4 30
Concept 2: Compare by using Unit Rates
Basic Proficient Advanced
Andrew drives 150 miles in 4 hours. Andrew drives 120 miles in 2 hours. Andrew drives 228 miles in 4 hours.
How fast does he drive? Erika drives 196 miles in 3 hours. Erika drives 281 miles in 5 hours.
Who drives faster? Who drives faster and by how much?
1 1 1
A : 60 mph E : 65 mph A : 57 mph E : 56 mph
37 miles per hour 3 5
2 4
Erika drives faster. Andrew drives faster by mph
5

2. How fast does he drive? Erika drives 196 miles in 3 hours. Erika drives 281 miles in 5 hours.
Who drives faster? Who drives faster and by how much?
Test Prep
3 Work / Explanation
1. Which number is the additive inverse of - ?
5
A 5 C 3 Additive inverse = opposite.
-
3 5 ( )+( )=0
B
-
5 D 3 Change the sign.
3 5
3
2. Which number is the multiplicative inverse of - ?
5
Multiplicative inverse = reciprocal.
A 5 C 3
3
-
5
( )•( )=1
B 5 D 3 Flip the fraction.
-
3 5

3. How fast does he drive? Erika drives 196 miles in 3 hours. Erika drives 281 miles in 5 hours.
Who drives faster? Who drives faster and by how much?
Test Prep
3 Work / Explanation
1. Which number is the additive inverse of - ?
5
A 5 C 3 Additive inverse = opposite.
-
3 5 ( )+( )=0
B
-
5 D 3 Change the sign.
3 5
3
2. Which number is the multiplicative inverse of - ?
5
Multiplicative inverse = reciprocal.
A 5 C 3
3
-
5
( )•( )=1
B 5 D 3 Flip the fraction.
-
3 5

4. How fast does he drive? Erika drives 196 miles in 3 hours. Erika drives 281 miles in 5 hours.
Who drives faster? Who drives faster and by how much?
Test Prep
3 Work / Explanation
1. Which number is the additive inverse of - ?
5
A 5 C 3 Additive inverse = opposite.
-
3 5 ( )+( )=0
B
-
5 D 3 Change the sign.
3 5
3
2. Which number is the multiplicative inverse of - ?
5
Multiplicative inverse = reciprocal.
A 5 C 3
3
-
5
( )•( )=1
B 5 D 3 Flip the fraction.
-
3 5

5. Which one
should I buy?

7. 24.12 ounces 36.5 ounces

8. 24.12 ounces 36.5 ounces
.331
24.12 7.99

9. 24.12 ounces 36.5 ounces
.331
24.12 7.99
Each ounce costs 33.1 cents

10. 24.12 ounces 36.5 ounces
.331 .247
24.12 7.99 36.5 8.99
Each ounce costs 33.1 cents

11. 24.12 ounces 36.5 ounces
.331 .247
24.12 7.99 36.5 8.99
Each ounce costs 33.1 cents Each ounce costs 24.7 cents

12. 24.12 ounces 36.5 ounces
.331 .247
24.12 7.99 36.5 8.99
Each ounce costs 33.1 cents Each ounce costs 24.7 cents

13. 24.12 ounces 36.5 ounces
.331 .247
24.12 7.99 36.5 8.99
Each ounce costs 33.1 cents Each ounce costs 24.7 cents

14. Main Concept
Unit Rates

15. Find Unit Rate
I need 8 feet of wrapping paper to wrap 5 presents.
=

16. Find Unit Rate
I need 8 feet of wrapping paper to wrap 5 presents.
8 feet
=

17. Find Unit Rate
I need 8 feet of wrapping paper to wrap 5 presents.
8 feet
=
5 presents

18. Find Unit Rate
I need 8 feet of wrapping paper to wrap 5 presents.
8 feet
=
5 presents

19. Find Unit Rate
I need 8 feet of wrapping paper to wrap 5 presents.
8 feet
=
5 presents
more or less than 1 whole?

20. Find Unit Rate
I need 8 feet of wrapping paper to wrap 5 presents.
8 feet
=
5 presents
more or less than 1 whole?
5 8

21. Find Unit Rate
I need 8 feet of wrapping paper to wrap 5 presents.
8 feet
=
5 presents
more or less than 1 whole?
1
5 8

22. Find Unit Rate
I need 8 feet of wrapping paper to wrap 5 presents.
8 feet
=
5 presents
more or less than 1 whole?
1
5 8
−5

23. Find Unit Rate
I need 8 feet of wrapping paper to wrap 5 presents.
8 feet
=
5 presents
more or less than 1 whole?
1
5 8
−5
3

24. Find Unit Rate
I need 8 feet of wrapping paper to wrap 5 presents.
8 feet
=
5 presents
more or less than 1 whole?
3
1
5 8
−5
3

25. Find Unit Rate
I need 8 feet of wrapping paper to wrap 5 presents.
8 feet
=
5 presents
more or less than 1 whole?
3
15
5 8
−5
3

26. Find Unit Rate
I need 8 feet of wrapping paper to wrap 5 presents.
8 feet 3
= 1
5 presents 5
more or less than 1 whole?
3
15
5 8
−5
3

27. Find Unit Rate
I need 8 feet of wrapping paper to wrap 5 presents.
8 feet 3 feet
= 1
5 presents 5 present
more or less than 1 whole?
3
15
5 8
−5
3

28. Find Unit Rate
I need 8 feet of wrapping paper to wrap 5 presents.
8 feet 3 feet 3
= 1 = 1
5 presents 5 present 5
more or less than 1 whole?
3
15
5 8
−5
3

29. Find Unit Rate
I need 8 feet of wrapping paper to wrap 5 presents.
8 feet 3 feet 3
= 1 = 1 feet per present
5 presents 5 present 5
more or less than 1 whole?
3
15
5 8
−5
3

30. Find Unit Rate
I run 3 miles in 21 minutes.
=

31. Find Unit Rate
I run 3 miles in 21 minutes.
3 miles
=

32. Find Unit Rate
I run 3 miles in 21 minutes.
3 miles
=
21 minutes

33. Find Unit Rate
I run 3 miles in 21 minutes.
3 miles
=
21 minutes

34. Find Unit Rate
I run 3 miles in 21 minutes.
3 miles
=
21 minutes
more or less than 1 whole?

35. Find Unit Rate
I run 3 miles in 21 minutes.
3 miles
=
21 minutes
more or less than 1 whole?
3
21

36. Find Unit Rate
I run 3 miles in 21 minutes.
3 miles
=
21 minutes
more or less than 1 whole?
3 ÷3
21

37. Find Unit Rate
I run 3 miles in 21 minutes.
3 miles
=
21 minutes
more or less than 1 whole?
3 ÷3
21 ÷3

38. Find Unit Rate
I run 3 miles in 21 minutes.
3 miles
=
21 minutes
more or less than 1 whole?
3 ÷3 1
=
21 ÷3 7

39. Find Unit Rate
I run 3 miles in 21 minutes.
3 miles 1
=
21 minutes 7
more or less than 1 whole?
3 ÷3 1
=
21 ÷3 7

40. Find Unit Rate
I run 3 miles in 21 minutes.
3 miles 1 mile
=
21 minutes 7 minute
more or less than 1 whole?
3 ÷3 1
=
21 ÷3 7

41. Find Unit Rate
I run 3 miles in 21 minutes.
3 miles 1 mile 1
= =
21 minutes 7 minute 7
more or less than 1 whole?
3 ÷3 1
=
21 ÷3 7

42. Find Unit Rate
I run 3 miles in 21 minutes.
3 miles 1 mile 1
= = mile per minute
21 minutes 7 minute 7
more or less than 1 whole?
3 ÷3 1
=
21 ÷3 7

43. Find Unit Rate
To answer a “how fast” question, use a unit rate.
I save 400 dollars every 3 months. How fast is my
bank account growing?
=

44. Find Unit Rate
To answer a “how fast” question, use a unit rate.
I save 400 dollars every 3 months. How fast is my
bank account growing?
400 dollars
=

45. Find Unit Rate
To answer a “how fast” question, use a unit rate.
I save 400 dollars every 3 months. How fast is my
bank account growing?
400 dollars
=
3 months

46. Find Unit Rate
To answer a “how fast” question, use a unit rate.
I save 400 dollars every 3 months. How fast is my
bank account growing?
400 dollars
=
3 months

47. Find Unit Rate
To answer a “how fast” question, use a unit rate.
I save 400 dollars every 3 months. How fast is my
bank account growing?
400 dollars
=
3 months
more or less than 1 whole?

48. Find Unit Rate
To answer a “how fast” question, use a unit rate.
I save 400 dollars every 3 months. How fast is my
bank account growing?
400 dollars
=
3 months
more or less than 1 whole? 3 400

49. Find Unit Rate
To answer a “how fast” question, use a unit rate.
I save 400 dollars every 3 months. How fast is my
bank account growing?
400 dollars
=
3 months
1
more or less than 1 whole? 3 400

50. Find Unit Rate
To answer a “how fast” question, use a unit rate.
I save 400 dollars every 3 months. How fast is my
bank account growing?
400 dollars
=
3 months
1
more or less than 1 whole? 3 400
−3

51. Find Unit Rate
To answer a “how fast” question, use a unit rate.
I save 400 dollars every 3 months. How fast is my
bank account growing?
400 dollars
=
3 months
1
more or less than 1 whole? 3 400
−3
1

52. Find Unit Rate
To answer a “how fast” question, use a unit rate.
I save 400 dollars every 3 months. How fast is my
bank account growing?
400 dollars
=
3 months
1
more or less than 1 whole? 3 400
−3
10

53. Find Unit Rate
To answer a “how fast” question, use a unit rate.
I save 400 dollars every 3 months. How fast is my
bank account growing?
400 dollars
=
3 months
13
more or less than 1 whole? 3 400
−3
10

54. Find Unit Rate
To answer a “how fast” question, use a unit rate.
I save 400 dollars every 3 months. How fast is my
bank account growing?
400 dollars
=
3 months
13
more or less than 1 whole? 3 400
−3
10
−9

55. Find Unit Rate
To answer a “how fast” question, use a unit rate.
I save 400 dollars every 3 months. How fast is my
bank account growing?
400 dollars
=
3 months
13
more or less than 1 whole? 3 400
−3
10
−9
1

56. Find Unit Rate
To answer a “how fast” question, use a unit rate.
I save 400 dollars every 3 months. How fast is my
bank account growing?
400 dollars
=
3 months
13
more or less than 1 whole? 3 400
−3
10
−9
10

57. Find Unit Rate
To answer a “how fast” question, use a unit rate.
I save 400 dollars every 3 months. How fast is my
bank account growing?
400 dollars
=
3 months
13 3
more or less than 1 whole? 3 400
−3
10
−9
10

58. Find Unit Rate
To answer a “how fast” question, use a unit rate.
I save 400 dollars every 3 months. How fast is my
bank account growing?
400 dollars
=
3 months
13 3
more or less than 1 whole? 3 400
−3
10
−9
10
−9

59. Find Unit Rate
To answer a “how fast” question, use a unit rate.
I save 400 dollars every 3 months. How fast is my
bank account growing?
400 dollars
=
3 months
13 3
more or less than 1 whole? 3 400
−3
10
−9
10
−9
1

60. Find Unit Rate
To answer a “how fast” question, use a unit rate.
I save 400 dollars every 3 months. How fast is my
bank account growing?
400 dollars
=
3 months
1
13 3 3
more or less than 1 whole? 3 400
−3
10
−9
10
−9
1

61. Find Unit Rate
To answer a “how fast” question, use a unit rate.
I save 400 dollars every 3 months. How fast is my
bank account growing?
400 dollars 133 1
=
3 months 3 1
13 3 3
more or less than 1 whole? 3 400
−3
10
−9
10
−9
1

62. Find Unit Rate
To answer a “how fast” question, use a unit rate.
I save 400 dollars every 3 months. How fast is my
bank account growing?
400 dollars 133 1 dollars
=
3 months 3 month 1
13 3 3
more or less than 1 whole? 3 400
−3
10
−9
10
−9
1

63. Find Unit Rate
To answer a “how fast” question, use a unit rate.
I save 400 dollars every 3 months. How fast is my
bank account growing?
400 dollars 133 1 dollars 1
= = 133
3 months 3 month 1 3
13 3 3
more or less than 1 whole? 3 400
−3
10
−9
10
−9
1

64. Find Unit Rate
To answer a “how fast” question, use a unit rate.
I save 400 dollars every 3 months. How fast is my
bank account growing?
400 dollars 133 1 dollars 1 dollars per
= = 133
3 months 3 month 1 3 month
13 3 3
more or less than 1 whole? 3 400
−3
10
−9
10
−9
1

65. Find Unit Rate
I need 3 cups of sugar for 2 cakes. Find the unit rate.
I spend $265 every 4 weeks. Find the unit rate.
A tree grows 4 inches in 12 years. How fast is it growing?
I drive 228 miles in 5 hours. How fast am I driving?

66. Find Unit Rate
I need 3 cups of sugar for 2 cakes. Find the unit rate.
1
1 cups per cake
2
I spend $265 every 4 weeks. Find the unit rate.
A tree grows 4 inches in 12 years. How fast is it growing?
I drive 228 miles in 5 hours. How fast am I driving?

67. Find Unit Rate
I need 3 cups of sugar for 2 cakes. Find the unit rate.
1
1 cups per cake
2
I spend $265 every 4 weeks. Find the unit rate.
1
66 dollars per week
4
A tree grows 4 inches in 12 years. How fast is it growing?
I drive 228 miles in 5 hours. How fast am I driving?

68. Find Unit Rate
I need 3 cups of sugar for 2 cakes. Find the unit rate.
1
1 cups per cake
2
I spend $265 every 4 weeks. Find the unit rate.
1
66 dollars per week
4
A tree grows 4 inches in 12 years. How fast is it growing?
1
inch per year
3
I drive 228 miles in 5 hours. How fast am I driving?

69. Find Unit Rate
I need 3 cups of sugar for 2 cakes. Find the unit rate.
1
1 cups per cake
2
I spend $265 every 4 weeks. Find the unit rate.
1
66 dollars per week
4
A tree grows 4 inches in 12 years. How fast is it growing?
1
inch per year
3
I drive 228 miles in 5 hours. How fast am I driving?
3
45 miles per hour
5

70. Comparing Quantities
Samantha ran 96 meters in 40 seconds. Juan ran 110
meters in 50 seconds. Who ran faster?

71. Comparing Quantities
Samantha ran 96 meters in 40 seconds. Juan ran 110
meters in 50 seconds. Who ran faster?
Samantha

72. Comparing Quantities
Samantha ran 96 meters in 40 seconds. Juan ran 110
meters in 50 seconds. Who ran faster?
Samantha
96 meters
=
40 seconds

73. Comparing Quantities
Samantha ran 96 meters in 40 seconds. Juan ran 110
meters in 50 seconds. Who ran faster?
Samantha
96 meters 2
= 2
40 seconds 5

74. Comparing Quantities
Samantha ran 96 meters in 40 seconds. Juan ran 110
meters in 50 seconds. Who ran faster?
Samantha
96 meters 2
= 2 meters per second
40 seconds 5

75. Comparing Quantities
Samantha ran 96 meters in 40 seconds. Juan ran 110
meters in 50 seconds. Who ran faster?
Samantha
96 meters 2
= 2 meters per second
40 seconds 5
Juan

76. Comparing Quantities
Samantha ran 96 meters in 40 seconds. Juan ran 110
meters in 50 seconds. Who ran faster?
Samantha
96 meters 2
= 2 meters per second
40 seconds 5
Juan
110 meters
=
50 seconds

77. Comparing Quantities
Samantha ran 96 meters in 40 seconds. Juan ran 110
meters in 50 seconds. Who ran faster?
Samantha
96 meters 2
= 2 meters per second
40 seconds 5
Juan
110 meters 1
= 2
50 seconds 5

78. Comparing Quantities
Samantha ran 96 meters in 40 seconds. Juan ran 110
meters in 50 seconds. Who ran faster?
Samantha
96 meters 2
= 2 meters per second
40 seconds 5
Juan
110 meters 1
= 2 meters per second
50 seconds 5

79. Comparing Quantities
Samantha ran 96 meters in 40 seconds. Juan ran 110
meters in 50 seconds. Who ran faster?
Samantha
96 meters 2
= 2 meters per second
40 seconds 5
Juan
110 meters 1
= 2 meters per second
50 seconds 5
They were very close, but Samantha ran faster
by 1/5 of a meter every second.

80. Comparing Quantities
Noemi ran 105 meters in 30 seconds. Mirian ran 112
meters in 40 seconds. Who ran faster?
My tomato plants grow 4 inches in 10 months. My pepper
plants grow 3 inches in 6 months. Which grows faster?
Francisco earned $74 in 8 hours. Jasmine earned $105 in
12 hours. Who has a better paying job?

81. Comparing Quantities
Noemi ran 105 meters in 30 seconds. Mirian ran 112
meters in 40 seconds. Who ran faster?
1 4
Noemi: 3 metersper second Mirian: 2 metersper second
2 5
My tomato plants grow 4 inches in 10 months. My pepper
plants grow 3 inches in 6 months. Which grows faster?
Francisco earned $74 in 8 hours. Jasmine earned $105 in
12 hours. Who has a better paying job?

82. Comparing Quantities
Noemi ran 105 meters in 30 seconds. Mirian ran 112
meters in 40 seconds. Who ran faster?
1 4
Noemi: 3 metersper second Mirian: 2 metersper second
2 5
My tomato plants grow 4 inches in 10 months. My pepper
plants grow 3 inches in 6 months. Which grows faster?
Francisco earned $74 in 8 hours. Jasmine earned $105 in
12 hours. Who has a better paying job?

83. Comparing Quantities
Noemi ran 105 meters in 30 seconds. Mirian ran 112
meters in 40 seconds. Who ran faster?
1 4
Noemi: 3 metersper second Mirian: 2 metersper second
2 5
My tomato plants grow 4 inches in 10 months. My pepper
plants grow 3 inches in 6 months. Which grows faster?
2 1
Tomato: inch per month Pepper: inch per month
5 2
Francisco earned $74 in 8 hours. Jasmine earned $105 in
12 hours. Who has a better paying job?

84. Comparing Quantities
Noemi ran 105 meters in 30 seconds. Mirian ran 112
meters in 40 seconds. Who ran faster?
1 4
Noemi: 3 metersper second Mirian: 2 metersper second
2 5
My tomato plants grow 4 inches in 10 months. My pepper
plants grow 3 inches in 6 months. Which grows faster?
2 1
Tomato: inch per month Pepper: inch per month
5 2
Francisco earned $74 in 8 hours. Jasmine earned $105 in
12 hours. Who has a better paying job?

85. Comparing Quantities
Noemi ran 105 meters in 30 seconds. Mirian ran 112
meters in 40 seconds. Who ran faster?
1 4
Noemi: 3 metersper second Mirian: 2 metersper second
2 5
My tomato plants grow 4 inches in 10 months. My pepper
plants grow 3 inches in 6 months. Which grows faster?
2 1
Tomato: inch per month Pepper: inch per month
5 2
Francisco earned $74 in 8 hours. Jasmine earned $105 in
12 hours. Who has a better paying job?
1 3
Francisco: 9 dollars per hour Jasmine: 8 dollars per hour
4 4

86. Comparing Quantities
Noemi ran 105 meters in 30 seconds. Mirian ran 112
meters in 40 seconds. Who ran faster?
1 4
Noemi: 3 metersper second Mirian: 2 metersper second
2 5
My tomato plants grow 4 inches in 10 months. My pepper
plants grow 3 inches in 6 months. Which grows faster?
2 1
Tomato: inch per month Pepper: inch per month
5 2
Francisco earned $74 in 8 hours. Jasmine earned $105 in
12 hours. Who has a better paying job?
1 3
Francisco: 9 dollars per hour Jasmine: 8 dollars per hour
4 4