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4. Contents Lesson 10-1Ratios Lesson 10-2Solving Proportions Lesson 10-3Scale Drawings and Models Lesson 10-4Modeling Percents Lesson 10-5Percents and Fractions Lesson 10-6Percents and Decimals Lesson 10-7Percent of a Number Lesson 10-8Estimating with Percents

5. Lesson 1 Contents Example 1Write a Ratio in Simplest Form Example 2Use Ratios to Compare Parts of a Whole Example 3Find Unit Rate

6. Example 1-1a RECREATION Write the ratio that compares the number of unicycles to the number of scooters. Answer: The ratio of unicycles to scooters is 11 to 5, or 11:5. For every 11 unicycles, there are 5 scooters.

7. Example 1-1b FRUIT Write the ratio that compares the number of apples to the number of oranges. Answer:

8. Example 1-2a BOOKS Write the ratio that compares the number of books about sports to the total number of books. Answer: The ratio of books about sports to the total number of books is 5 to 8, or 5:8. For every five sports books, there are eight total books.

9. Example 1-2b SPORTS Write the ratio that compares the number of basketballs to the total number of sports balls. Answer:

10. Example 1-3a FOOD Find the cost per ounce of a 16-ounce jar of salsa that costs $2.88. Divide the numerator and denominator by 16 to get a denominator of 1. Answer: So, the cost per ounce of the salsa is $0.18.

11. Example 1-3b TEMPERATURE The outside temperature rises 32 degrees in four hours. Find the temperature increase for one hour. Answer:

12. End of Lesson 1

13. Lesson 2 Contents Example 1Solve a Proportion Example 2Solve a Proportion Example 3Use a Proportion to Solve a Problem

14. Example 2-1a Cross products Multiply. Solve Answer: The solution is 35. Divide each side by 4.

15. Example 2-1b Answer: 24 Solve

16. Example 2-2a Solve Cross products Multiply. Divide each side by 1.2. Answer: The solution is 0.5.

17. Example 2-2b Answer: 3 Solve

18. Example 2-3a SPORTS Out of the 40 students in a gym class, 12 rate soccer as their favorite sport. Based on this result, how many of the 4,200 students in the community will rate soccer as their favorite sport? Write and solve a proportion. Let s represent the number of students who can be expected to rate soccer as their favorite sport. soccer as favorite sport  total students in class   total students in community  soccer as favorite sport

19. Example 2-3b Cross products Multiply. Divide. Answer: So, 1,260 of the students in the community can be expected to rate soccer as their favorite sport.

20. Example 2-3c BUSINESS Out of 50 people in one department of a large corporation, 35 stated that they enjoy their job. Based on this result, how many of the 2,400 employees of this corporation can be expected to say that they enjoy their job? Answer: 1,680 employees

21. End of Lesson 2

22. Lesson 3 Contents Example 1Find Actual Measurements Example 2Find Actual Measurements

23. Example 3-1a Answer: The actual height of the monument is 555 feet. Let x represent the actual height. Find the cross products. Multiply.  model height  actual height Monument model height  actual height  Scale Model MONUMENTS A scale model of the Washington Monument has a scale of If the height of the model is 5.55 feet, what is the actual height of the monument?

24. CARS A scale model of a car has a scale of inches. If the length of the car model is 5 inches, what is the actual length of the car? Example 3-1b Answer: 120 in.

25. Example 3-2a STATES On a map of Pennsylvania, the distance between Pittsburgh and Harrisburg is 2.5 inches. If the scale on the map is what is the actual distance between Pittsburgh and Harrisburg? Let d represent the actual distance. Find the cross products. Multiply. Answer: The actual distance is 155 miles. map distance  actual distance   map distance  actual distance Actual DistanceMap Scale

26. MAPS On a map, the distance between two small towns is 8.5 inches. If the scale on the map is what is the actual distance between the two small towns? Example 3-2b Answer: 340 mi

27. End of Lesson 3

28. Lesson 4 Contents Example 1Model a Percent Example 2Identify a Percent Example 3Identify a Percent

29. Example 4-1a 60% means 60 out of 100. So, shade 60 of the 100 squares. Answer:

30. Example 4-1b Answer:

31. Example 4-2a Identify the percent that is modeled. There are 75 out of 100 squares shaded. Answer: So, the model shows 75%.

32. Example 4-2b Identify the percent that is modeled. Answer: 45%

33. Example 4-3a Identify the percent that is modeled. There are 30 out of 100 squares shaded. Answer: So, the model shows 30%.

34. Example 4-3b Identify the percent that is modeled. Answer: 5%

35. End of Lesson 4

36. Lesson 5 Contents Example 1Write a Percent as a Fraction Example 2Write a Percent as a Fraction Example 3Write a Percent as a Fraction Example 4Write a Fraction as a Percent Example 5Write a Fraction as a Percent

37. Example 5-1a Write 60% as a fraction in simplest form. 60% means 60 out of 100. Write the percent as a fraction with a denominator of 100. Simplify. Divide the numerator and denominator by the GCF, 20. 5 3 Answer:

38. Example 5-1b Write 30% as a fraction in simplest form. Answer:

39. Example 5-2a Write 140% as a fraction in simplest form. 140% means 140 for every 100.

40. Example 5-2b Write the percent as a fraction with a denominator of 100. Answer: Simplify. Divide the numerator and denominator by the GCF, 20. 5 2

41. Example 5-2c Write 180% as a fraction in simplest form. Answer:

42. Example 5-3a LUNCH Use the table below. What fraction of the class members preferred spaghetti for the school lunch? School Lunch Choices LunchPercent pizza30% spaghetti25% hamburger20% chicken strips15% soup10%

43. Example 5-3b The table shows that 25% of the class members preferred spaghetti. Write the percent as a fraction with a denominator of 100. Simplify. Answer: So, of the class members preferred spaghetti for the school lunch.

44. Example 5-3c ICE CREAM Use the table below. What fraction of the students chose chocolate as their favorite flavor? Students Favorite Ice Cream Flavor FlavorPercent vanilla37% chocolate28% chocolate chip20% Strawberry8% Other7% Answer:

45. Example 5-4a Write as a percent. Multiply. Write the cross products. Set up a proportion. Divide each side by 10. Simplify. Answer: So, is equivalent to 70%.

46. Example 5-4b Write as a percent. Answer: 40%

47. Example 5-5a Write as a percent. Answer: So, is equivalent to 240%. Multiply. Write the cross products. Set up a proportion. Divide each side by 5. Simplify.

48. Example 5-5b Answer: 225% Write as a percent.

49. End of Lesson 5

50. Lesson 6 Contents Example 1Write a Percent as a Decimal Example 2Write a Percent as a Decimal Example 3Write a Percent as a Decimal Example 4Write a Decimal as a Percent Example 5Write a Decimal as a Percent

51. Example 6-1a Write 86% as a decimal. Rewrite the percent as a fraction with a denominator of 100. Write the fraction as a decimal. Answer: 0.86

52. Example 6-1b Write 34% as a decimal. Answer: 0.34

53. Example 6-2a Write 112% as a decimal. Rewrite the percent as a fraction with a denominator of 100. Write the fraction as a decimal. Answer: 1.12

54. Example 6-2b Write 154% as a decimal. Answer: 1.54

55. Example 6-3a Write 0.9% as a decimal. 0.9% means nine-tenths of one percent.

56. Example 6-3b Rewrite the percent as a fraction with a denominator of 100. Answer: 0.009 Write the fraction as a decimal. Multiply by to eliminate the decimal in the numerator.

57. Example 6-3c Write 0.2% as a decimal. Answer: 0.002

58. Example 6-4a Write 0.44 as a percent. Answer: 44% Write the decimal as a fraction. Write the fraction as a percent.

59. Example 6-4b Write 0.82 as a percent. Answer: 82%

60. Example 6-5a Write 0.254 as a percent. Answer: 25.4% Write the decimal as a fraction. Divide the numerator and denominator by 10. Write the fraction as a percent.

61. Example 6-5b Write 0.683 as a percent. Answer: 68.3%

62. End of Lesson 6

63. Lesson 7 Contents Example 1Find the Percent of a Number Example 2Find the Percent of a Number Example 3Find the Percent of a Number

64. Example 7-1a Find 8% of 125. Method 1 Write the percent as a fraction. Method 2 Write the percent as a decimal.

65. Example 7-1b So, 8% of 125 is 10. Use a model to check the answer. Answer: The model confirms that 8% of 125 is 10.

66. Example 7-1c Find 6% of 150. Answer: 9

67. Example 7-2a Find 125% of 64. Method 1 Write the percent as a fraction.

68. Example 7-2b Method 2 Write the percent as a decimal. So, 125% of 64 is 80. Use a model to check your answer. Answer: The model confirms that 125% of 64 is 80.

69. Example 7-2c Find 175% of 240. Answer: 420

70. Example 7-3a LANGUAGES The graph to the right shows that 30% of the people in a community speak Spanish as their first language. If a community has 800 people, how many people can be expected to speak Spanish as their first language? Answer: So, 240 people can be expected to speak Spanish as their first language.

71. Example 7-3b SPORTS The graph below shows that 22% of the students stated that baseball was their favorite sport. If the seventh grade class has 300 students, how many can be expected to consider baseball their favorite sport? Answer: 66

72. End of Lesson 7

73. Lesson 8 Contents Example 1Estimate the Percent of a Number Example 2Estimate the Percent of a Number Example 3Use Estimation to Solve a Problem Example 4Estimate the Percent of a Figure

74. Example 8-1a Estimate 49% of 302. Round 302 to 300. 49% is close to 50% or of 300 is 150. Answer: So, 49% of 302 is about 150.

75. Example 8-1b Estimate 26% of 122. Sample answer: 30

76. Example 8-2a Estimate 80% of 1,605. Answer: So, 80% of 1,605 is about 1,280. Round 1,605 to 1,600. 80% is 160 1

77. Example 8-2b Estimate 40% of 1,207. Sample answer: 480

78. Example 8-3a MONEY A CD that originally cost $11.90 is on sale for 30% off. If you have $7, would you have enough money to buy the CD? To determine whether you have enough money to buy the CD, you need to estimate 70% of $11.90. 70% of $11.90 Answer: Since $8.40 is $1.40 more than $7, you would not have enough money.

79. Example 8-3b MONEY A poster that originally cost $14.90 is on sale for 40% off. If you have $10, would you have enough to buy the poster? Answer: yes

80. Example 8-4a MULTIPLE-CHOICE TEST ITEM Which of the following is a reasonable percent for the percent of the figure that is shaded? A 30%B 50%C 60%D 75%

81. Example 8-4b Read the Test Item You need to find what percent of the circles are shaded. So, 75% of the circles are shaded. Solve the Test Item 12 out of 16 circles are shaded. Answer: D

82. Example 8-4c MULTIPLE-CHOICE TEST ITEM Which of the following is a reasonable percent for the percent of the figure that is shaded? A 75%B 40%C 20% D 9% Answer: B

83. End of Lesson 8

84. 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 1 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.msmath1.net/extra_examples.

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