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3. Lesson 7-3 Solving Proportions Lesson 7-4 Scale Drawings
Lesson 7-1 Ratios
Lesson 7-2 Rates
Lesson 7-3 Solving Proportions
Lesson 7-4 Scale Drawings
Lesson 7-5 Fractions, Decimals, and Percents
Lesson 7-6 Percents Greater Than 100% and Percents Less than 1%
Lesson 7-7 Percent of a Number
Lesson 7-8 The Percent Proportion
Contents

4. Example 1 Write Ratios in Simplest Form
Example 3 Write a Ratio by Converting Units
Example 4 Compare Ratios
Example 5 Compare Ratios
Lesson 1 Contents

5. Write the ratio 30 to 9 as a fraction in simplest form.
Write the ratio as a fraction.
Simplify.
Answer: Written as a fraction in simplest form,
the ratio 30 to 9 is
Example 1-1a

6. Write the ratio 35 to 20 as a fraction in simplest form.
Answer:
Example 1-1b

7. Write the ratio 4:24 as a fraction in simplest form.
Simplify.
Answer: The ratio 4:24 is in simplest form.
Example 1-2a

8. Write the ratio 9:36 as a fraction in simplest form.
Answer:
Example 1-2b

9. Write the ratio 3 feet to 8 inches as a fraction in simplest form.
Convert 3 feet to inches. 9
Divide by the GCF, 4 inches. 2
Simplify.
Example 1-3a

10. Answer: The ratio 3 feet to 8 inches can be written as
Example 1-3a

11. Write the ratio 4 feet to 20 inches as a fraction in simplest form.
Answer:
Example 1-3b

12. Determine whether 12:15 and 32:40 are equivalent.
Write each ratio as a fraction in simplest form.
The GCF of 12 and 15 is 3.
The GCF of 32 and 40 is 8.
Answer: The ratios in simplest form both equal
So, 12:15 and 32:40 are equivalent ratios.
Example 1-4a

13. Determine whether 8:24 and 14:42 are equivalent.
Answer: yes
Example 1-4b

14. POOLS It is recommended that no more than one person be allowed into the shallow end of an outdoor public pool for every 15 square feet of surface area. If a local pool’s shallow end has a surface area of 1,800 square feet, are the lifeguards correct to allow 120 people into that part of the pool?
Recommended ratio
1 to 15 or
Actual ratio
120 to 1,800 or
Answer: Since the ratios are equivalent, the lifeguards are correct to allow 120 people into the shallow end of the pool.
Example 1-5a

15. WALLPAPER The instructions on a particular brand of wallpaper suggest using 1 quart of wallpaper paste for every 32 square feet of wallpaper hung. Bill purchases 8 quarts of wallpaper paste to complete a job that requires hanging 256 square feet of wallpaper. Is Bill using the proper amount of paste?
Answer: yes
Example 1-5b

16. End of Lesson 1

17. Example 1 Find a Unit Rate Example 2 Find Unit Rates
Example 4 Choose the Best Buy
Lesson 2 Contents

18. Write the rate as a fraction.
READING Julia read 52 pages in 2 hours. What is the average number of pages she read per hour?
Write the rate as a fraction. Then find an equivalent rate with a denominator of 1.
Write the rate as a fraction.
Divide the numerator and denominator by 2.
Simplify.
Example 2-1a

19. Answer: The average number of pages Julia reads, or unit rate, is 26 pages per hour.
Example 2-1a

20. Answer: 4 laps per minute
SKATING Kyle skated 16 laps around the ice rink in 4 minutes. What is the average number of laps he skated per minute?
Answer: 4 laps per minute
Example 2-1b

21. Write the rate as a fraction.
GRID-IN TEST ITEM Write 440 miles in 8 hours as a unit rate in miles per hour.
Read the Test Item Write the ratio as a fraction. Then divide to get a denominator of 1.
Solve the Test Item
440 miles in 8 hours
Write the rate as a fraction.
Example 2-2a

22. Divide the numerator and the denominator by 8.
Simplify.
The unit rate is 55 miles per hour.
Example 2-2b

23. Answer:
Example 2-2c

24. GRID-IN TEST ITEM Write 455 miles in 7 hours as a unit rate in miles per hour.
Answer:
Example 2-2d

25. Write the rate as a fraction.
Find the unit price per can if it costs $3 for 6 cans of soda. Round to the nearest hundredth if necessary.
Write the rate as a fraction.
Divide the numerator and the denominator by 6.
Simplify.
Answer: The unit price is $0.50 per can.
Example 2-3a

26. Find the unit price per cookie if it costs $3 for one dozen cookies
Find the unit price per cookie if it costs $3 for one dozen cookies. Round to the nearest hundredth if necessary.
Answer: $0.25 per cookie
Example 2-3b

27. The costs of different sizes of orange juice are shown in the table
The costs of different sizes of orange juice are shown in the table. Which container costs the least per ounce?
Amount
Total Cost
16 oz
$1.28
32 oz
$1.92
64 oz
$2.56
96 oz
$3.36
Example 2-4a

28. Find the unit price, or the cost per ounce, of each size of orange juice. Divide the price by the number of ounces.
16-ounce container
32-ounce container
64-ounce container
96-ounce container
Answer: The 96-ounce container of orange juice costs the least per ounce.
Example 2-4b

29. The costs of different sizes of bottles of laundry detergent are shown below. Which bottle costs the least per ounce?
Amount
Total Cost
16 oz
$3.12
32 oz
$5.04
64 oz
$7.04
96 oz
$11.52
Answer: 64-ounce bottle
Example 2-4c

30. End of Lesson 2

31. Example 1 Identify a Proportion Example 2 Identify a Proportion
Example 3 Solve Proportions
Example 4 Solve Proportions
Lesson 3 Contents

32. Determine whether and form a proportion.
Write a proportion.
Find the cross products.
Multiply.
Answer: The cross products are equal, so the ratios form a proportion.
Example 3-1a

33. Determine whether and form a proportion.
Answer: no
Example 3-1b

34. Determine whether and form a proportion.
Write a proportion.
Find the cross products.
Multiply.
Answer: The cross products are not equal, so the ratios do not form a proportion.
Example 3-2a

35. Determine whether and form a proportion.
Answer: yes
Example 3-2b

36. Find the cross products.
Solve
Write the proportion.
Find the cross products.
Multiply.
Divide each side by 3.5.
Simplify.
Answer: The solution is 24.
Example 3-3a

37. Solve
Answer: 25
Example 3-3b

38. Find the cross products.
FLAGS According to specifications, the ratio of the length of the U.S. flag to its width must be 1.9 to 1. How long must a U.S. flag be if it is designed to have a width of 2.5 feet?
length → width →
Write a proportion.
Find the cross products.
Multiply.
Answer: The length of a U.S. flag having a width of 2.5 feet must be 4.75 feet.
Example 3-4a

39. SCHOOL The ratio of boys to girls at Blue Hills Middle School is 4 to 5. How many girls attend the school if there are 96 boys?
Answer: 120 girls
Example 3-4b

40. End of Lesson 3

41. Example 1 Use a Scale Drawing Example 2 Read a Scale Drawing
Example 3 Find the Scale Factor
Example 4 Make a Scale Model
Lesson 4 Contents

42. MAPS On the map below, the distance between
Portland and Olympia is about inches.
What is the actual distance?
Let d the actual distance between the cities. Write and solve a proportion. Use the scale written as a fraction.
Example 4-1a

43. Scale Portland to Olympia map → actual → ← map ← actual Cross products
Multiply.
Multiply both sides by
Simplify.
Example 4-1a

44. Answer: The distance between Portland and Olympia is about 125 miles.
Example 4-1a

45. MAPS On a map, the scale is given as 2 inches 100 miles
MAPS On a map, the scale is given as 2 inches miles. If the distance on the map between two cities is 15 inches, what is the actual distance between the two cities?
Answer: 750 miles
Example 4-1b

46. bedroom on the blueprint is inches, what is the
ARCHITECTURE On the blueprint of a new house, one-quarter inch represents feet. If the length of a
bedroom on the blueprint is inches, what is the
actual length of the room?
Example 4-2a

47. Simplify. Multiply each side by 4.
Scale
Length of Room
blueprint →
actual →
← blueprint
← actual
Cross products
Multiply.
Simplify. Multiply each side by 4.
Example 4-2a

48. Answer: The length of the room is 15 feet.
Example 4-2a

49. ARCHITECTURE On a blueprint of a new house, one-quarter inch represents 3 feet. If the width of the kitchen on the blueprint is 2 inches, what is the actual width of the room?
Answer: 24 feet
Example 4-2b

50. Find the scale factor of a blueprint if the scale is
Write the ratio of in simplest form.
Convert 3 feet to inches.
Multiply by to eliminate
the fraction in the numerator.
Cancel the units.
Example 4-3a

51. Answer: The scale factor is That is, each measure on the blueprint is the actual measure.
Example 4-3a

52. Find the scale factor of a blueprint if the scale is 1 inch 4 feet.
Answer:
Example 4-3b

53. Write a proportion using the scale.
PHOTOGRAPHY A model is being created from a picture frame which has a length of inches. If the scale to be used is 8 inches 1 inch, what is the length of the model?
Write a proportion using the scale.
Scale
Length of Model
model →
actual →
← model
← actual
Example 4-4a

54. Find the cross products.
Multiply.
Answer: The scale model is 38 inches long.
Example 4-4a

55. FURNITURE A model is being created from a child-sized rocking chair which has a height of 8 inches. If the scale to be used is 12 inches 1 inch, what is the height of the model?
Answer: 96 in.
Example 4-4b

56. End of Lesson 4

57. Example 1 Percents as Fractions Example 2 Percents as Fractions
Example 3 Fractions as Percents
Example 4 Fractions as Percents
Example 5 Fractions as Percents
Example 6 Fractions as Percents
Lesson 5 Contents

58. Write a fraction with a denominator of 100.
NUTRITION In a recent consumer poll, 41.8% of the people surveyed said they gained nutrition knowledge from family and friends. What fraction is this? Write in simplest form.
Write a fraction with a denominator of 100.
Multiply by to eliminate the
decimal in the numerator.
Simplify.
Example 5-1a

59. Answer: So, of the people gained nutrition
knowledge from family and friends.
Example 5-1a

60. ELECTION In a recent election, 64
ELECTION In a recent election, 64.8% of registered voters actually voted. What fraction is this? Write in simplest form.
Answer:
Example 5-1b

61. Write as a fraction in simplest form.
Write a fraction.
Divide.
Write as an improper fraction.
Example 5-2a

62. Multiply by the reciprocal of 100, which is
Simplify.
Answer:
Example 5-2a

63. Write as a fraction in simplest form.
Answer:
Example 5-2b

64. To find the percent of green bananas, write as a percent.
PRODUCE In one shipment of fruit to a grocery store, 5 out of 8 bananas were still green. Find this amount as a percent.
To find the percent of green bananas, write as a percent.
Estimate is greater than or greater than 50%.
Write a proportion using
Find the cross products.
Example 5-3a

65. Answer: So, This is greater than 50%, which was the estimate.
Divide each side by 8.
Simplify.
Answer: So, This is greater than 50%, which was the estimate.
Example 5-3a

66. HOCKEY During a hockey game, the forward on one of the teams scored 3 goals out of 8 shots taken. Find this amount as a percent.
Answer: 37.5%
Example 5-3b

67. Write as a percent. Round to the nearest hundredth.
Estimate is about which equals or 50%.
Write a proportion using
Find the cross products.
ENTER
Use a calculator to simplify.
Answer: So, is about 41.67%. This result is close to the estimate.
Example 5-4a

68. Write as a percent. Round to the nearest hundredth.
Answer: %
Example 5-4b

69. Multiply by 100 and add the %.
Write as a percent.
Write as a decimal.
Multiply by 100 and add the %.
Answer: 45%
Example 5-5a

70. Write as a percent.
Answer: 52%
Example 5-5b

71. Write as a percent. Round to the nearest hundredth.
Write as a decimal.
Multiply by 100 and add the %.
Answer: %
Example 5-6a

72. Write as a percent. Round to the nearest hundredth.
Answer: %
Example 5-6b

73. End of Lesson 5

74. Example 1 Percents as Decimals or Fractions
Example 3 Real-Life Percents as Decimals
Example 4 Decimals as Percents
Lesson 6 Contents

75. Write 220% as a decimal and as a mixed number or fraction in simplest form.
Definition of percent
Simplify.
Answer:
Example 6-1a

76. Write 375% as a decimal and as a mixed number or fraction in simplest form.
Answer:
Example 6-1b

77. Write 0.6% as a decimal and as a mixed number or fraction in simplest form.
Definition of percent
Simplify.
Answer:
Example 6-2a

78. Write 0.4% as a decimal and as a mixed number or fraction in simplest form.
Answer:
Example 6-2b

79. STOCKS During a stock market rally, a company’s stock increased in value by 200%. Write 200% as a decimal.
Divide by 100.
Answer: 2
Example 6-3a

80. Write 420% as a decimal.
Answer: 4.2
Example 6-3b

81. Write 5.12 as a percent.
Multiply by 100.
Answer: 512%
Example 6-4a

82. Write 9.35 as a percent.
Answer: 935%
Example 6-4b

83. Write as a percent.
Multiply by 100.
Answer: 0.15%
Example 6-5a

84. Write as a percent.
Answer: 0.96%
Example 6-5b

85. End of Lesson 6

86. Example 1 Use a Proportion to Find a Percent
Example 2 Use Multiplication to Find a Percent
Example 3 Use Multiplication to Find a Percent
Lesson 7 Contents

87. percent of people that knew name
SURVEYS Out of 1,423 adults surveyed, 30% said they knew the name of their mail carrier. How many of the people surveyed knew their mail carrier’s name?
30% means that 30 out of 100 people knew their mail carrier’s name. Find an equivalent ratio x out of 1,423 and write a proportion.
percent of people that knew name
number that knew name → total number in survey →
Example 7-1a

88. Now solve the proportion.
Write the proportion.
Find the cross products.
Multiply.
Divide each side by 100.
Simplify.
Answer: About 427 of the 1,423 adults surveyed knew their mail carrier’s name.
Example 7-1a

89. SURVEYS Out of 765 students surveyed, 42% said that they watch some television after school before doing their homework. How many of the students surveyed watch some television after school before doing their homework?
Answer: about 321
Example 7-1b

90. Write a multiplication expression.
What number is 120% of 24?
Write a multiplication expression.
Write 120% as a decimal.
Multiply.
Answer: 120% of 24 is 28.8.
Example 7-2a

91. What number is 160% of 44?
Answer: 70.4
Example 7-2b

92. Write a multiplication expression.
Find 25% of $600.
Write a multiplication expression.
Write 25% as a decimal.
Multiply.
Answer: 25% of $600 is $150.
Example 7-3a

93. Find 80% of $450.
Answer: $360
Example 7-3b

94. End of Lesson 7

95. Example 1 Find the Percent Example 2 Find the Part
Example 3 Find the Base
Lesson 8 Contents

96. 18 is the part, and 24 is the base. You need to find the percent p.
What percent of 24 is 18?
18 is the part, and 24 is the base. You need to find the percent p.
Example 8-1a

97. Replace a with 18 and b with 24.
Percent proportion
Replace a with 18 and b with 24.
Find the cross products.
Simplify.
Divide each side by 24.
Simplify.
Answer: 75% of 24 is 18. Compare the answer to the model.
Example 8-1a

98. What percent of 80 is 28?
Answer: 35%
Example 8-1b

99. 30 is the percent and 150 is the base. You need to find the part.
What number is 30% of 150?
30 is the percent and 150 is the base. You need to find the part.
Example 8-2a

100. Replace b with 150 and p with 30.
Percent proportion
Replace b with 150 and p with 30.
Find the cross products.
Simplify.
Divide each side by 100.
Simplify.
Answer: 30% of 150 is 45. Compare the answer to the model.
Example 8-2a

101. What number is 65% of 180?
Answer: 117
Example 8-2b

102. 12 is 80% of what number?
12 is the part and 80 is the percent. You need to find the base, or the whole quantity.
Example 8-3a

103. Replace a with 12 and p with 80.
Percent proportion 12
Replace a with 12 and p with 80.
Find the cross products.
Simplify.
Divide each side by 80.
Simplify.
Example 8-3a

104. Check In the model, the whole quantity is 12 3 or 15.
Answer: 12 is 80% of 15.
Example 8-3a

105. 36 is 40% of what number?
Answer: 90
Example 8-3b

106. End of Lesson 8

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