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4. Contents Lesson 6-1Estimating with Fractions Lesson 6-2Adding and Subtracting Fractions Lesson 6-3Adding and Subtracting Mixed Numbers Lesson 6-4Multiplying Fractions and Mixed Numbers Lesson 6-5Algebra: Solving Equations Lesson 6-6Dividing Fractions and Mixed Numbers Lesson 6-7Measurement: Changing Customary Units Lesson 6-8Geometry: Perimeter and Area Lesson 6-9Geometry: Circles and Circumference

5. Lesson 1 Contents Example 1Estimate with Mixed Numbers Example 2Estimate with Mixed Numbers Example 3Estimate with Fractions Example 4Estimate with Fractions Example 5Estimate with Fractions Example 6Use Compatible Numbers Example 7Use Compatible Numbers

6. Example 1-1a Estimate Answer: The sum is about 9.

7. Example 1-1b Estimate Answer: 8

8. Example 1-2a Answer: The product is about 16. Estimate

9. Example 1-2b Answer: 15 Estimate

10. Example 1-3a Answer: The sum is about 1. Estimate

11. Example 1-3b Answer: 1 Estimate

12. Example 1-4a Answer: The difference is about Estimate

13. Example 1-4b Answer: 1 Estimate

14. Example 1-5a Answer: The quotient is about 2. Estimate

15. Example 1-5b Estimate Answer:

16. Example 1-6a Answer: The product is about 15. Estimate THINK What is Round 21 to 20, since 20 is divisible by 4.

17. Example 1-6b Estimate Answer: 12

18. Example 1-7a Answer: The quotient is about 4. Estimate

19. Example 1-7b Estimate Answer: 5

20. End of Lesson 1

21. Lesson 2 Contents Example 1Add and Subtract Like Fractions Example 2Add and Subtract Like Fractions Example 3Add and Subtract Unlike Fractions Example 4Add and Subtract Unlike Fractions Example 5Add and Subtract Unlike Fractions

22. Example 2-1a Find Write in simplest form. Add the numerators. Write the sum over the denominator. Answer:

23. Example 2-1b Answer: Find

24. Example 2-2a Subtract the numerators. Write the difference over the denominator. Simplify. Find Write in simplest form. Answer:

25. Example 2-2b Answer: Find

26. Example 2-3a The least common multiple of 3 and 9 is 9. Find Write in simplest form. Rename using the LCD. Estimate

27. Example 2-3b Answer: is close to the estimate.

28. Example 2-3c Answer: Find Write in simplest form.

29. Example 2-4a The LCM of 4 and 6 is 12. Estimate Find Write in simplest form.

30. Example 2-4b Answer: So, Compare to the estimate.

31. Example 2-4c Answer: Find Write in simplest form.

32. Example 2-5a ART A picture is mounted on art board that is inch thick. The frame selected for the picture is inch thick. The thickness of the picture is so small that it can be ignored. What thickness of cardboard is needed to hold the picture in place?

33. Example 2-5b The LCM of 2 and 8 is 8. Rename the fractions with the LCD. Subtract the numerators. Answer: The thickness of the cardboard needed to hold the picture in place is inch.

34. Example 2-5c WEATHER Over the weekend inch of rain fell on Saturday and inch of rain fell on Sunday. What was the total rainfall for the weekend? Answer:

35. End of Lesson 2

36. Lesson 3 Contents Example 1Add and Subtract Mixed Numbers Example 2Add and Subtract Mixed Numbers Example 3Use Mixed Numbers to Solve a Problem Example 4Rename Mixed Numbers to Subtract Example 5Rename Mixed Numbers to Subtract

37. Example 3-1a Find Write in simplest form. Answer: Estimate Add the whole numbers and fractions separately. Simplify. Compare the sum to the estimate.

38. Example 3-1b Find Answer:

39. Example 3-2a Answer: Estimate Simplify. Compare the sum to the estimate. Find Write in simplest form. Rename the fraction using the LCD.

40. Example 3-2b Find Write in simplest form. Answer:

41. Example 3-3a COOKING A quiche recipe calls for cups of grated cheese. A recipe for quesadillas requires cups of grated cheese. What is the total amount of grated cheese needed for both recipes? Rename the fractions. Add the whole numbers and add the fractions.

42. Example 3-3b Simplify. Answer: The total amount of grated cheese needed for both recipes is cups. Rename as.

43. Example 3-3c Answer: cups BAKING A recipe for chocolate chip cookies calls for cups of sugar. A recipe for muffins requires cups of sugar. What is the total amount of sugar needed for both recipes?

44. Example 3-4a Find Answer: First subtract the whole numbers and then the fractions. Rename

45. Example 3-4b Answer: Find.

46. Example 3-5a Estimate Answer: Subtract. The difference is close to the estimate. Find.

47. Example 3-5b Answer: Find.

48. End of Lesson 3

49. Lesson 4 Contents Example 1Multiply Fractions Example 2Multiply Fractions Example 3Simplify Before Multiplying Example 4Multiply Mixed Numbers

50. Example 4-1a Multiply. Write in simplest form.

51. Example 4-1a Answer: Multiply the denominators. Multiply the numerators. Simplify.

52. Example 4-1b Answer: Multiply Write in simplest form.

53. Example 4-2a Simplify. Multiply the numerators and multiply the denominators. Answer: 2 Multiply Write in simplest form.

54. Example 4-2b Answer: 2 Multiply Write in simplest form.

55. Example 4-3a Multiply the numerators and multiply the denominators. Divide 4 and 12 by their GCF, 4. Simplify. Answer: 3 1 Multiply Write in simplest form.

56. Example 4-3b Answer: Multiply. Write in simplest form.

57. Example 4-4a Estimate Method 1 Rename the mixed number. 1 16 Multiply Write in simplest form.

58. Example 4-4b Multiply. Simplify. The product is close to the estimate.

59. Example 4-4c Method 2 Use mental math.

60. Example 4-4c Distributive Property Multiply. Compare this product to the model shown on the previous slide. Answer:

61. Example 4-4b Answer: Multiply Write in simplest form.

62. End of Lesson 4

63. Lesson 5 Contents Example 1Find Multiplicative Inverses Example 2Find Multiplicative Inverses Example 3Solve a Division Equation Example 4Use a Reciprocal to Solve an Equation

64. Example 5-1a Answer: The multiplicative inverse of Find the multiplicative inverse of

65. Example 5-1b Answer: Find the multiplicative inverse of

66. Example 5-2a Answer: The multiplicative inverse of Rename the mixed number as an improper fraction. Find the multiplicative inverse of

67. Example 5-2b Answer: Find the multiplicative inverse of

68. Example 5-3a Write the equation. Multiply each side of the equation by 6. Simplify. Answer: The solution is 66. Solve Check your solution.

69. Example 5-3b Answer: 36 Solve Check your solution.

70. Example 5-4a MULTIPLE-CHOICE TEST ITEM What value of a true sentence? A B C D Read the Test Item To find the value of y, solve the equation.

71. Example 5-4b Solve the Test Item Answer: D Write the equation. Simplify.

72. Example 5-4c MULTIPLE-CHOICE TEST ITEM What value of a true sentence? A B C D Answer: C

73. End of Lesson 5

74. Lesson 6 Contents Example 1Divide by a Fraction Example 2Divide by Mixed Numbers Example 3Divide by Mixed Numbers Example 4Divide by Mixed Numbers

75. Example 6-1a Divide out common factors. Multiply and simplify. Answer: 1 3 2 1 Find Write in simplest form. Multiply the reciprocal of

76. Example 6-1b Answer: Find Write in simplest form.

77. Example 6-2a JETS An Air Force unit has 34 million dollars to spend on new jets. Each jet costs million dollars. How many jets can be bought? Estimate

78. Example 6-2b Multiply by the reciprocal of, which is. Divide out common factors. Multiply. Answer: The Air Force unit can buy 8 jets. 1 2

79. Example 6-2c BAKING Linda has 22 cups of flour. She is using a cookie recipe that requires cups of flour per batch. How many batches of cookies can Linda make? Answer: 8 batches

80. Example 6-3a Estimate Find Write in simplest form.

81. Example 6-3b 1 Divide out common factors. Multiply. 1 3 1 The quotient is close to the estimate. Answer:

82. Example 6-3c Answer:

83. Example 6-4a Estimate Rename the mixed numbers as improper fractions. Multiply by the reciprocal of, which is.

84. Example 6-4b Divide out common factors. Multiply. Answer: 1 1

85. Example 6-4c Answer:

86. End of Lesson 6

87. Lesson 7 Contents Example 1Convert Larger Units to Smaller Units Example 2Convert Larger Units to Smaller Units Example 3Convert Units to Solve a Problem Example 4Convert Smaller Units to Larger Units Example 5Convert Smaller Units to Larger Units

88. Example 7-1a Answer: ft. Complete

89. Example 7-1b Answer: 24 ft. Complete

90. Example 7-2a Answer: c. Complete

91. Example 7-2b Answer: 24 pt. Complete

92. Example 7-3a ELEVATOR The elevator in an office building has a weight limit posted of one and a half tons. How many pounds can the elevator safely hold? Multiply by 2,000 since there are 2,000 pounds in 1 ton. Answer: So, the elevator can safely hold 3,000 pounds.

93. Example 7-3b Answer: 60 ounces PRODUCE The label on a bag of potatoes states that the bag contains pounds of potatoes. How many ounces of potatoes does the bag hold?

94. Example 7-4a Answer: Since there are 12 inches in a 1 foot, divide by 12. ft. Complete

95. Example 7-4b Answer: 14 yd. Complete

96. Example 7-5a Since 4 quarts are in 1 gallon, divide by 4. Answer: gal. Complete

97. Example 7-5b Answer: 16 pt. Complete

98. End of Lesson 7

99. Lesson 8 Contents Example 1Find the Perimeter of a Rectangle Example 2Find the Perimeter of an Irregular Figure Example 3Find the Area of a Rectangle

100. Example 8-1a Find the perimeter of the figure. Perimeter of a rectangle Multiply. Add. Answer: The perimeter is 40 feet.

101. Example 8-1b Find the perimeter of the figure. Answer: 46 in.

102. Example 8-2a Find the perimeter of the figure. Estimate This is close to the Answer: estimate.

103. Example 8-2c Find the perimeter of the figure. Answer: 10 ft

104. Example 8-3a FRESHWATER Find the area of the surface of the reservoir shown below. Area of a rectangle

105. Example 8-3b Multiply and simplify. Answer: The area of the surface of the reservoir is square miles.

106. Example 8-3c Answer: PAINTING Sue is painting a wall that measures feet long and 8 feet high. Find the area of the surface Sue will be painting.

107. End of Lesson 8

108. Lesson 9 Contents Example 1Find Circumference Example 2Find Circumference

109. Example 9-1a PETS Find the circumference around the hamster’s running wheel shown below. Round to the nearest tenth. Circumference of a circle Multiply. Answer: The distance around the hamster’s running wheel is about 18.8 inches.

110. Example 9-1b SWIMMING POOL A new children’s swimming pool is being built at the local recreation center. The pool is circular in shape with a diameter of 18 feet. Find the circumference of the pool. Round to the nearest tenth. Answer:

111. Example 9-2a Find the circumference of a circle with a diameter of 49 centimeters. Answer: The circumference of the circle is about 154 centimeters. Circumference of a circle Multiply. Divide by the GCF, 7. 1 7

112. Example 9-2b Find the circumference of a circle with a radius of 35 feet. Answer: 220 ft

113. End of Lesson 9

114. 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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