1. 1 Alan S. Tussy R. David Gustafson Prealgebra Second Edition Copyright © 2002 Wadsworth Group.

2. 2 4.1 The Fundamental Property of Fractions In this section, you will learn about Basic facts about fractions Equivalent fractions Simplifying a fraction Expressing a fraction in higher terms

3. 3 Numerator, a Denominator, and a Fraction Bar

4. 4 Proper or Improper

5. 5 EXAMPLE 1 Fractional parts of a whole. a. In Figure 4-1, what fractional part of the barrel is full? b. What fractional part is empty?

6. 6 Negative fractions

7. 7 Equivalent fractions

8. 8

9. 9 The fundamental property of fractions

10. 10 Simplifying and Lowest terms

11. 11 Simplifying a fraction

12. 12 Expressing a fraction in higher terms

13. 13 4.2 Multiplying Fractions In this section, you will learn about Multiplying fractions Simplifying when multiplying fractions Multiplying algebraic fractions Powers of a fraction Applications

14. 14 Multiplying fractions

15. 15 Multiplying fractions – Step 2

16. 16 Multiplying fractions – Step 3

17. 17 Multiplying fractions – Observations

18. 18 Multiplying fractions - Rule

19. 19 Powers of a fraction

20. 20 EXAMPLE 9 House of Representatives. In the United States House of Representatives, a bill was introduced that would require a 9/5 vote of the 435 members to authorize any tax increase. Under this requirement, how many representatives would have to vote for a tax increase before it could become law?

21. 21 Triangles

22. 22 Area of a triangle

23. 23 EXAMPLE 10 Geography. Approximate the area of the state of Virginia using the triangle in Figure 4-4.

24. 24 4.3 Dividing Fractions In this section, you will learn about Division with fractions Reciprocals A rule for dividing fractions Dividing algebraic fractions

25. 25 Division with fractions

26. 26 Reciprocals

27. 27 Reciprocals

28. 28 A rule for dividing fractions

29. 29 Dividing fractions

30. 30 EXAMPLE 4 Surfboard design. Most surfboards are made of polyurethane foam plastic covered with several layers of fiberglass to keep them water-tight. How many layers are needed to build up a finish three- eighths of an inch thick if each layer of fiberglass has a thickness of one-sixteenth of an inch?

31. 31 4.4 Adding and Subtracting Fractions In this section, you will learn about Fractions with the same denominator Fractions with different denominators Finding the LCD Comparing fractions

32. 32 Fractions with the same denominator

33. 33 Adding or subtracting fractions with the same denominators

34. 34 Fractions with different denominators

35. 35 Different denominators

36. 36 Adding or subtracting fractions with different denominators

37. 37 Finding the LCD

38. 38 Finding the LCD by finding multiples

39. 39 Finding the LCD using prime factorization

40. 40 EXAMPLE 9 Television viewing habits. Students on a college campus were asked to estimate to the nearest hour how much television they watched each day. The results are given in the pie chart in Figure 4- 8. For example, the chart tells us that ¼ of those responding watched 1 hour per day. Find the fraction of the student body watching from 0 to 2 hours daily.

41. 41 Comparing fractions

42. 42 THE LCM AND THE GCF

43. 43 Finding the greatest common factor

44. 44 4.5 Multiplying and Dividing Mixed Numbers In this section, you will learn about Mixed numbers Writing mixed numbers as improper fractions Writing improper fractions as mixed numbers Graphing fractions and mixed numbers Multiplying and dividing mixed numbers

45. 45 Mixed numbers

46. 46 Writing mixed numbers as improper fractions

47. 47 Writing a mixed number as an improper fraction

48. 48 Writing improper fractions as mixed numbers

49. 49 Writing an improper fraction as a mixed number

50. 50 Graphing fractions and mixed numbers

51. 51 Multiplying and dividing mixed numbers

52. 52 Multiplying mixed numbers

53. 53 Dividing mixed numbers

54. 54 EXAMPLE 6 Government grant. If $12 ½ million is to be divided equally among five cities to fund recreation programs, how much will each city receive?

55. 55 4.6 Adding and Subtracting Mixed Numbers In this section, you will learn about Adding mixed numbers Adding mixed numbers in vertical form Subtracting mixed numbers

56. 56 Adding mixed numbers: method 1

57. 57 Adding mixed numbers: method 2

58. 58 Adding mixed numbers in vertical form

59. 59 EXAMPLE 3 Suspension bridge.

60. 60 4.7 Order of Operations and Complex Fractions In this section, you will learn about Order of operations Evaluating algebraic expressions Complex fractions Simplifying complex fractions

61. 61 EXAMPLE 4 Masonry. To build a wall, a mason will use blocks that are 5 ¾ inches high, held together with ⅜-inch-thick layers of mortar. (See Figure 4-10.) If the plans call for 8 layers of blocks, what will be the height of the wall when completed?

62. 62 Complex fractions

63. 63 Simplifying a complex fraction: method 1 Write the numerator and the denominator of the complex fraction as single fractions. Then do the indicated division of the two fractions and simplify.

64. 64 Simplifying a complex fraction: method 2 Multiply the numerator and the denominator of the complex fraction by the LCD of all the fractions that appear in its numerator and denominator. Then simplify.

65. 65 4.8 Solving Equations Containing Fractions In this section, you will learn about Using reciprocals to solve equations An alternate method The addition and subtraction properties of equality Clearing an equation of fractions The steps to solve equations Problem solving with equations

66. 66 Using reciprocals to solve equations

67. 67 An alternate method

68. 68 Clearing an equation of fractions

69. 69 Strategy for solving equations Simplify the equation: 1. Clear the equation of fractions. 2. Use the distributive property to remove any parentheses. 3. Combine like terms on either side of the equation. Isolate the variable: 4. Use the addition and subtraction properties of equality to get the variables on one side and the constants on the other. 5. Combine like terms when necessary. 6. Undo the operations of multiplication and division to isolate the variable.

70. 70 EXAMPLE 6 Native Americans. The United States Constitution requires a population count, called a census, to be taken every ten years. In the 1990 census, the population of the Navaho tribe was 225,000. This was about three-fifths of the population of the largest Native American tribe, the Cherokee. What was the population of the Cherokee tribe in 1990?

71. 71 EXAMPLE 7 Filmmaking. A movie director has sketched out a “storyboard” for a film that is in the planning stages. On the storyboard, he estimates the amount of time in the film that will be devoted to scenes involving dialogue, action scenes, and scenes used to transition between the two. (See Figure 4-11.) From the information on the storyboard, how long will this film be, in minutes?

72. 72 Fundamental Property of Fractions