2. Welcome to Interactive Chalkboard Mathematics: Applications and Concepts, Course 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240

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

5. Lesson 1 Contents Example 1Write Ratios in Simplest Form Example 2Write Ratios in Simplest Form Example 3Write a Ratio by Converting Units Example 4Compare Ratios Example 5Compare Ratios

6. Example 1-1a 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

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

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

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

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

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

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

13. Example 1-4a 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.

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

15. Example 1-5a 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 Answer: Since the ratios are equivalent, the lifeguards are correct to allow 120 people into the shallow end of the pool. Actual ratio 120 to 1,800 or

16. Example 1-5b 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

17. End of Lesson 1

18. Lesson 2 Contents Example 1Find a Unit Rate Example 2Find Unit Rates Example 3Find Unit Rates Example 4Choose the Best Buy

19. Example 2-1a 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. Simplify. Write the rate as a fraction. Divide the numerator and denominator by 2.

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

21. Example 2-1b 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

22. Example 2-2a 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.

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

24. Example 2-2c Answer:

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

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

27. Example 2-3b 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

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

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

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

31. End of Lesson 2

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

33. Example 3-1a 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.

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

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

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

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

38. Example 3-3b Answer: 25 Solve

39. Example 3-4a 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. Answer: The length of a U.S. flag having a width of 2.5 feet must be 4.75 feet. Multiply.

40. Example 3-4b 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

41. End of Lesson 3

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

43. Example 4-1a 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.

44. Example 4-1a ScalePortland to Olympia map → actual → ← map ← actual Multiply. Cross products Simplify. Multiply both sides by

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

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

47. Example 4-2a 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?

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

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

50. Example 4-2b 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

51. Example 4-3a 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.

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

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

54. Example 4-4a Write a proportion using the scale. Scale Length of Model model → actual → ← model ← actual 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?

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

56. Example 4-4b 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.

57. End of Lesson 4

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

59. Example 5-1a 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. Simplify. Multiply byto eliminate the decimal in the numerator.

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

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

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

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

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

65. Example 5-3a 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.

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

67. Example 5-3b 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%

68. Example 5-4a Write as a percent. Round to the nearest hundredth.Estimate is about which equals or 50%. Write a proportion using Answer: So, is about 41.67%. This result is close to the estimate. Find the cross products. ENTER 41.66666667 Use a calculator to simplify.

69. Example 5-4b Write as a percent. Round to the nearest hundredth. Answer: 73.33%

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

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

72. Example 5-6a Answer: 42.86% Write as a percent. Round to the nearest hundredth.Write as a decimal. Multiply by 100 and add the %.

73. Example 5-6b Write as a percent. Round to the nearest hundredth. Answer: 81.82%

74. End of Lesson 5

75. Lesson 6 Contents Example 1Percents as Decimals or Fractions Example 2Percents as Decimals or Fractions Example 3Real-Life Percents as Decimals Example 4Decimals as Percents

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

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

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

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

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

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

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

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

84. Example 6-5a Write 0.0015 as a percent. Answer: 0.15% Multiply by 100.

85. Example 6-5b Write 0.0096 as a percent. Answer: 0.96%

86. End of Lesson 6

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

88. Example 7-1a 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 →

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

90. Example 7-1b 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

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

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

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

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

95. End of Lesson 7

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

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

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

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

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

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

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

103. Example 8-3a 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.

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

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

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

107. End of Lesson 8

108. Online Explore online information about the information introduced in this chapter. Click on the Connect button to launch your browser and go to the Mathematics: Applications and Concepts, Course 2 Web site. At this site, you will find extra examples for each lesson in the Student Edition of your textbook. When you finish exploring, exit the browser program to return to this presentation. If you experience difficulty connecting to the Web site, manually launch your Web browser and go to www.msmath2.net/extra_examples.

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125. Help To navigate within this Interactive Chalkboard product: Click the Forward button to go to the next slide. Click the Previous button to return to the previous slide. Click the Section Back button to return to the beginning of the lesson you are working on. If you accessed a feature, this button will return you to the slide from where you accessed the feature. Click the Main Menu button to return to the presentation main menu. Click the Help button to access this screen. Click the Exit button or press the Escape key [Esc] to end the current slide show. Click the Extra Examples button to access additional examples on the Internet. Click the 5-Minute Check button to access the specific 5-Minute Check transparency that corresponds to each lesson.

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