1. Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue.

2. 6 6 Multiplying and Dividing Decimals and Fractions Chapter Menu Lesson 6-1Lesson 6-1Multiplying Decimals by Whole Numbers Lesson 6-2Lesson 6-2Multiplying Decimals Lesson 6-3Lesson 6-3Problem-Solving Strategy: Reasonable Answers Lesson 6-4Lesson 6-4Dividing Decimals by Whole Numbers Lesson 6-5Lesson 6-5Dividing by Decimals Lesson 6-6Lesson 6-6Problem-Solving Investigation: Choose the Best Strategy Lesson 6-7Lesson 6-7Estimating Products of Fractions Lesson 6-8Lesson 6-8Multiplying Fractions Lesson 6-9Lesson 6-9Multiplying Mixed Numbers Lesson 6-10Lesson 6-10Dividing Fractions Lesson 6-11Lesson 6-11Dividing Mixed Numbers

3. Lesson 1 Menu Five-Minute Check (over Chapter 5) Main Idea and Vocabulary California Standards Example 1: Multiply Decimals Example 2: Multiply Decimals Example 3: Annex Zeros in the Product Example 4: Annex Zeros in the Product Example 5: Scientific Notation 6-1 Multiplying Decimals by Whole Numbers

4. 6-1 Multiplying Decimals by Whole Numbers Lesson 1 MI/Vocab I will estimate and find the product of decimals and whole numbers. scientific notation

5. 6-1 Multiplying Decimals by Whole Numbers Lesson 1 Standard 1 Standard 5NS2.1 Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of results.

6. Lesson 1 Ex1 6-1 Multiplying Decimals by Whole Numbers One Way: Use estimation. Round 18.9 to 19. 18.9 × 4 19 × 4 or 76 18.9 × 4 6 Since the estimate is 76, place the decimal point after the 5. 33 57. Find 18.9 × 4.

7. Lesson 1 Ex1 6-1 Multiplying Decimals by Whole Numbers Another Way: Count decimal places. 18.9 × 4 6 33 57. Answer: 75.6

8. Lesson 1 CYP1 6-1 Multiplying Decimals by Whole Numbers A.64 B.63.5 C.60.35 D.63.35 Find 12.7 × 5.

9. Lesson 1 Ex2 6-1 Multiplying Decimals by Whole Numbers One Way: Use estimation. Find 0.56 × 7. Round 0.56 to 1. 0.56 × 7 1 × 7 or 7 0.56 × 7 2 Since the estimate is 7, place the decimal point after the 3. 43 93.

10. Lesson 1 Ex2 6-1 Multiplying Decimals by Whole Numbers Another Way: Count decimal places. 0.56 × 7 2 43 93. Answer: 3.92

11. Lesson 1 CYP2 6-1 Multiplying Decimals by Whole Numbers A.8 B.5.76 C.3.76 D.0.392 Find 0.47 × 8.

12. Lesson 1 Ex3 6-1 Multiplying Decimals by Whole Numbers 0.016 × 3 8 1 4 0.0 Find 3 × 0.016. Answer: 0.048

13. Lesson 1 CYP3 6-1 Multiplying Decimals by Whole Numbers A.0.052 B.0.52 C.0.0052 D.0.502 Find 0.026 × 2.

14. Lesson 1 Ex4 ALGEBRA Evaluate 5g if g = 0.0091. 6-1 Multiplying Decimals by Whole Numbers 0.0091 × 5 5 4 5 04 5g = 5 × 0.0091 Replace g with 0.0091. 0. Answer: 0.0455

15. Lesson 1 CYP4 6-1 Multiplying Decimals by Whole Numbers ALGEBRA Evaluate 3h if h = 0.0054. A.1.62 B.0.162 C.0.00162 D.0.0162

16. Lesson 1 Ex5 6-1 Multiplying Decimals by Whole Numbers The average distance from Earth to the Sun is 1.5 × 10 8 kilometers. Write the distance in standard form.

17. Lesson 1 Ex5 6-1 Multiplying Decimals by Whole Numbers One Way: Use order of operations. Evaluate 10 8 first. Then multiply. 1.5 × 10 8 = 1.5 × 10,000,000 = 150,000,000 kilometers

18. Lesson 1 Ex5 6-1 Multiplying Decimals by Whole Numbers Another Way: Use mental math. Move the decimal point to the right the same number of places as the exponent of 10, or 8 places. 1.5 × 10 8 = 1.50000000 = 150,000,000

19. Lesson 1 Ex5 6-1 Multiplying Decimals by Whole Numbers Answer: The average distance from Earth to the Sun is 150,000,000 kilometers.

20. Lesson 1 CYP5 6-1 Multiplying Decimals by Whole Numbers A.588,000,000 kilometers B.58,000,000 kilometers C.5,880,000,000 kilometers D.5,800,000 kilometers The average distance from the Sun to the planet Jupiter is 58.8 × 10 7 kilometers. Choose the answer showing the distance written in standard form.

21. End of Lesson 1

22. Lesson 2 Menu Five-Minute Check (over Lesson 6-1) Main Idea California Standards Example 1: Multiply Decimals Example 2: Multiply Decimals Example 3: Evaluate an Expression Example 4: Real-World Example 6-2 Multiplying Decimals

23. 6-2 Multiplying Decimals Lesson 2 MI/Vocab I will multiply decimals by decimals.

24. 6-2 Multiplying Decimals Lesson 2 Standard 1 Standard 5NS2.1 Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of results. Standard 5MR2.1 Use estimation to verify the reasonableness of calculated results.

25. Lesson 2 Ex1 6-2 Multiplying Decimals Estimate 8.3 × 2.9 8 × 3 or 24 × 8.3 2.9 747 +166 24.07 Find 8.3 × 2.9. one decimal place two decimal places Answer: So, the product is 24.07.

26. Lesson 2 Ex1 6-2 Multiplying Decimals Check for Reasonableness Compare 24.07 to the estimate. 24.07 is about 24.

27. Lesson 2 CYP1 6-2 Multiplying Decimals Find 4.5 × 3.9. A.17.55 B.20 C.18.44 D.19.45

28. Lesson 2 Ex2 Find 0.12 × 5.3. 6-2 Multiplying Decimals Estimate 0.12 × 5.3 0 × 5 or 0 × 0.12 5.3 36 +60 0.636 two decimal places one decimal place three decimal places Answer: So, the product is 0.636.

29. Lesson 2 Ex2 6-2 Multiplying Decimals Check for Reasonableness Compare 0.636 to the estimate. 0.636 is about 0.

30. Lesson 2 CYP2 6-2 Multiplying Decimals Find 0.14 × 3.3. A.0.636 B.0.543 C.0.462 D.0.723

31. Lesson 2 Ex3 ALGEBRA Evaluate 1.8r if r = 0.029. 6-2 Multiplying Decimals 1.8r = 1.8 × 0.029 Replace r with 0.029. × 0.029 1.8 232 +29 0.0522 one decimal place Annex a zero to make four decimal places. Answer: So, the product is 0.0522. three decimal places

32. Lesson 2 CYP3 6-2 Multiplying Decimals ALGEBRA Evaluate 2.7x if x = 0.038. A.2.738 B.0.1026 C.0.0126 D.0.2106

33. Lesson 2 Ex4 Carmen earns $14.60 per hour as a painter’s helper. She worked a total of 15.75 hours one week. How much money did she earn? 6-2 Multiplying Decimals × $14.60 15.75 7300 10220 229.9500 two decimal places 7300 1460 + Estimate 14.60 × 15.75 15 × 16 or 240

34. Compare $229.95 to the estimate. $229.95 is about $240. Lesson 2 Ex4 Answer: So, Carmen earned $229.95. 6-2 Multiplying Decimals Check for Reasonableness

35. Lesson 2 CYP4 6-2 Multiplying Decimals Alex went shopping for 6.5 hours and spent $32.50 per hour. How much did she spend? A.$211.25 B.$225 C.$250.25 D.$211.50

36. End of Lesson 2

37. Lesson 3 Menu Five-Minute Check (over Lesson 6-2) Main Idea California Standards Example 1: Problem-Solving Strategy 6-3 Problem-Solving Strategy: Reasonable Answers

38. 6-3 Problem-Solving Strategy: Reasonable Answers Lesson 3 MI/Vocab I will solve problems by determining reasonable answers.

39. 6-3 Problem-Solving Strategy: Reasonable Answers Lesson 3 Standard 1 Standard 5MR3.1 Evaluate the reasonableness of the solution in the context of the original situation. Standard 5NS2.1 Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of results.

40. Lesson 3 Ex 1 6-3 Problem-Solving Strategy: Reasonable Answers For their science project, Stephanie and Angel need to know about how much more a blue whale weighs in pounds than a humpback whale. They have learned that there are 2,000 pounds in one ton. While doing research, they found a table that shows the weights of whales in tons.

41. Lesson 3 Ex1 Understand What facts do you know? There are 2,000 pounds in one ton. A blue whale weighs 151.0 tons. A humpback whale weighs 38.1 tons. What do you need to find? A reasonable estimate of the difference in the weight of a blue whale and a humpback whale. 6-3 Problem-Solving Strategy: Reasonable Answers

42. Lesson 3 Ex1 Plan Estimate to find the weight of each whale in pounds and then subtract to find a reasonable estimate of the difference. 6-3 Problem-Solving Strategy: Reasonable Answers

43. Lesson 3 Ex1 Solve 6-3 Problem-Solving Strategy: Reasonable Answers Blue whale: Answer: A reasonable estimate for the difference in the weight of a blue whale and a humpback whale is 220,000 pounds. Humpback whale: 2,000 × 151 2,000 × 38.1 2,000 × 150 2,000 × 40 300,000 80,000 300,000 – 80,000 = 220,000

44. Lesson 3 Ex1 Check 6-3 Problem-Solving Strategy: Reasonable Answers Look back at the problem. A blue whale weighs about 150 – 40 or 110 more tons than a humpback whale. This is equal to 110 × 2,000 or 220,000 pounds. So the answer is reasonable.

45. End of Lesson 3

46. Lesson 4 Menu Five-Minute Check (over Lesson 6-3) Main Idea and Vocabulary California Standards Example 1: Divide a Decimal by a 1-Digit Number Example 2: Divide a Decimal by a 2-Digit Number Example 3: Real-World Example 6-4 Dividing Decimals by Whole Numbers

47. 6-4 Dividing Decimals by Whole Numbers Lesson 4 MI/Vocab I will divide decimals by whole numbers. quotient

48. 6-4 Dividing Decimals by Whole Numbers Lesson 4 Standard 1 Standard 5NS2.1 Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of results.

49. 6-4 Dividing Decimals by Whole Numbers Lesson 4 Standard 1 Standard 5NS2.2 Demonstrate proficiency with division, including division with positive decimals and long division with multidigit divisors.

50. Lesson 4 Ex1 6-4 Dividing Decimals by Whole Numbers Find 7.2 ÷ 3. Estimate 7.2 ÷ 3 6 ÷ 3 or about 2 3 7.2 24. – 6 12 –12 0

51. Lesson 4 Ex1 6-4 Dividing Decimals by Whole Numbers Answer: 7.2 ÷ 3 = 2.4 Check Compared to the estimate, the quotient is reasonable.

52. Lesson 4 CYP1 6-4 Dividing Decimals by Whole Numbers A.8 B.16 C.1.6 D.0.8 Find 6.4 ÷ 4.

53. Lesson 4 Ex2 6-4 Dividing Decimals by Whole Numbers Find 6.6 ÷ 15. Estimate 6.6 ÷ 15 8 ÷ 16 or about 0.5 15 6.6 04. – 0 66 –60 6 4 0 0 –60 0

54. Lesson 4 Ex2 6-4 Dividing Decimals by Whole Numbers Answer: 6.6 ÷ 15 = 0.44 Check Compared to the estimate, the quotient is reasonable.

55. Lesson 4 CYP2 6-4 Dividing Decimals by Whole Numbers A.5.5 B.0.55 C.0.22 D.2.2 Find 8.8 ÷ 16.

56. Lesson 4 Ex3 During a science experiment, Nita measured the mass of four unknown samples. Her data is shown below. 6-4 Dividing Decimals by Whole Numbers

57. Lesson 4 Ex3 First, add all the data together. Answer: So, the mean mass of Nita’s samples is 6.11 grams. 6-4 Dividing Decimals by Whole Numbers + 6.23 5.81 5.93 6.47 24.44 Divide by the number of addends to find the mean mass. 4 24.44 6.11

58. Lesson 4 CYP3 6-4 Dividing Decimals by Whole Numbers Greta bought 4 pairs of socks for $25.36. If each pair of socks costs the same amount, how much was each pair? A.$6.34 B.$6.00 C.$4.63 D.$3.64

59. End of Lesson 4

60. Lesson 5 Menu Five-Minute Check (over Lesson 6-4) Main Idea and Vocabulary California Standards Example 1: Divide by Decimals Example 2: Zeros in the Quotient and Dividend Example 3: Zeros in the Quotient and Dividend Example 4: Round Quotients 6-5 Dividing by Decimals Dividing Decimals

61. 6-5 Dividing by Decimals Lesson 5 MI/Vocab I will divide decimals by decimals. power

62. 6-5 Dividing by Decimals Lesson 5 Standard 1 Standard 5NS2.1 Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of results.

63. 6-5 Dividing by Decimals Lesson 5 Standard 1 Standard 5NS2.2 Demonstrate proficiency with division, including division with positive decimals and long division with multidigit divisors.

64. Lesson 5 Ex1 6-5 Dividing by Decimals Find 21.44 ÷ 6.4. Estimate 21 ÷ 7 = 3 64 214.4 33. – 192 22 4 – 0 32 – 0 6.4 21.44 5 19 2 0 320 Divide as with whole numbers. Annex a zero to continue. Place the decimal point.

65. Lesson 5 Ex1 Answer: 21.44 divided by 6.4 is 3.35. 6-5 Dividing by Decimals Compare 3.35 to the estimate. Check 3.35 × 6.4 = 21.44

66. Lesson 5 CYP1 6-5 Dividing by Decimals Find 32.45 ÷ 5.5. A.5.9 B.5.09 C.5.90 D.50.9

67. Lesson 5 Ex2 6-5 Dividing by Decimals Find 72 ÷ 0.4. 4 720. 18. – 4 3 2 – 00 – 0 0.4 72.0 0 32 0 Place the decimal point. Answer: So, 72 ÷ 0.4 = 180. Check 180 × 0.4 = 72

68. Lesson 5 CYP2 6-5 Dividing by Decimals Find 45 ÷ 0.9. A.0.50 B.50 C.5 D.5.0

69. Lesson 5 Ex3 6-5 Dividing by Decimals Find 0.024 ÷ 2.4. 24 0.24 00. – 0 0 2 – 24 – 0 2.4 0.024 1 0 24 Place the decimal point. Answer: So, 0.024 ÷ 2.4 = 0.01. Check 0.01 × 2.4 = 0.024 24 does not go into 2, so write a 0 in the tenths place.

70. Lesson 5 CYP3 6-5 Dividing by Decimals A.0.03 B.3 C.0.3 D.1.2 Find 0.036 ÷ 1.2.

71. Lesson 5 Ex4 6-5 Dividing by Decimals Ioviano bought a stock at $42.88 per share. If he spent $786.85, how many shares did he buy? Round to the nearest tenth. 42.88 786.85 Find 786.85 ÷ 42.88.

72. Lesson 5 Ex4 6-5 Dividing by Decimals 42.88 78685.00 83. – 4288 3580 5 – 15010 5 34304 To the nearest tenth, 786.85 ÷ 42.88 = 18.4. 1 12864– 21460 21440 – 20 Answer: So, Ioviano bought about 18.4 shares.

73. Lesson 5 CYP4 6-5 Dividing by Decimals A department store had one of their televisions on sale for $245.75. If sales of the televisions totaled $21,773.45, about how many televisions were sold? A.88.6 televisions B.88 televisions C.89 televisions D.90 televisions

74. End of Lesson 5

75. Lesson 6 Menu Five-Minute Check (over Lesson 6-5) Main Idea California Standards Example 1: Problem-Solving Investigation 6-6 Problem-Solving Investigation: Choose the Best Strategy

76. 6-6 Problem-Solving Investigation: Choose the Best Strategy Lesson 6 MI/Vocab/Standard 1 I will choose the best strategy to solve a problem.

77. 6-6 Problem-Solving Investigation: Choose the Best Strategy Lesson 6 Standard 1 Standard 5MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns. Standard 5NS2.1 Add, subtract, multiply, and divide with decimals;... and verify the reasonableness of results.

78. Lesson 6 Ex1 MIGUEL: At the store, I saw the following items: a batting glove for $8.95, roller blades for $39.75, a can of tennis balls for $2.75, and weights for $5.50. I have $15 and I would like to buy more than one item. YOUR MISSION: Find which items Miguel can buy and spend about $15. 6-6 Problem-Solving Investigation: Choose the Best Strategy

79. Lesson 6 Ex1 Understand What facts do you know? You know the cost of the items and that Miguel has $15 to spend. What do you need to find? You need to find which items Miguel can buy. 6-6 Problem-Solving Investigation: Choose the Best Strategy

80. Lesson 6 Ex1 Plan Make an organized list to see the different possibilities and use estimation to be sure he spends about $15. 6-6 Problem-Solving Investigation: Choose the Best Strategy

81. Lesson 6 Ex1 Solve 6-6 Problem-Solving Investigation: Choose the Best Strategy Since the roller blades cost more than $15, you can eliminate the roller blades. The batting glove is about $9, the weights are about $6, and the can of tennis balls is about $3. Start with the batting glove: 1 glove + 1 weights ≈ $9 + $6 or $15 1 glove + 2 cans of tennis balls ≈ $9 + $6 or $15

82. Lesson 6 Ex1 Solve 6-6 Problem-Solving Investigation: Choose the Best Strategy List other combinations that contain the weights: 2 weights + 1 can of tennis balls ≈ $12 + $3 or $15 1 weights + 3 cans of tennis balls ≈ $6 + $9 or $15 List the remaining combinations that contain only tennis balls: 5 cans of tennis balls ≈ $15

83. Lesson 6 Ex1 Check 6-6 Problem-Solving Investigation: Choose the Best Strategy Check the list to be sure that all of the possible combinations of sporting good items that total no more than $15 are included.

84. End of Lesson 6

85. Lesson 7 Menu Five-Minute Check (over Lesson 6-6) Main Idea and Vocabulary California Standards Example 1: Estimate Using Compatible Numbers Example 2: Estimate Using Compatible Numbers 6-7 Estimating Products of Fractions Example 4: Estimate With Mixed Numbers Example 3: Estimate by Rounding to 0,, or 1 1 2

86. 6-7 Estimating Products of Fractions Lesson 7 MI/Vocab I will estimate products of fractions using compatible numbers and rounding. compatible numbers

87. 6-7 Estimating Products of Fractions Lesson 7 Standard 1 Standard 5MR2.5 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy. Standard 5NS2.5 Compute and perform simple multiplication and division of fractions and apply these procedures to solving problems.

88. Lesson 7 Ex1 6-7 Estimating Products of Fractions Find a multiple of 5 that is close to 16. × 16 1 5 × 16 means of 16. 1 5 1 5 Estimate × 16. 1 5 × 15 1 5 × 15 = 3 1 5 Answer: So, × 16 is about 3. 1 5 15 and 5 are compatible numbers since 15 ÷ 5 = 3. 15 ÷ 5 = 3

89. Lesson 7 CYP1 6-7 Estimating Products of Fractions A.2 Estimate × 19. 1 9 B.3 C.2 1 2 D.2 1 4

90. Lesson 7 Ex2 6-7 Estimating Products of Fractions Find a multiple of 4 that is close to 23. × 23 1 4 Estimate × 23 first. 1 4 Estimate × 23. 3 4 × 24 1 4 × 24 = 6 1 4 Use 24 since 24 and 4 are compatible numbers. 24 ÷ 4 = 6

91. Lesson 7 Ex2 6-7 Estimating Products of Fractions Answer: So, of 23 is about 18. 3 4 If of 24 is 6, then of 24 is 6 × 3 or 18. 3 4 1 4

92. Lesson 7 CYP2 6-7 Estimating Products of Fractions Estimate × 29. 3 5 B.18 C.17 A.17 2 5 D.20

93. Lesson 7 Ex3 6-7 Estimating Products of Fractions × 4 5 1 × 1 6 Estimate ×. 4 5 1 6 1 6 1 × 1 6 = 1 6 Answer: So, × is about. 4 5 1 6 1 6

94. Lesson 7 CYP3 6-7 Estimating Products of Fractions Estimate ×. 5 6 3 8 B.2 A.1 3 8 D.2 1 6 C. 1 2

95. Lesson 7 Ex4 6-7 Estimating Products of Fractions Estimate the area of the rectangle. Round each mixed number to the nearest whole number.

96. Lesson 7 Ex4 6-7 Estimating Products of Fractions × 7 × 2 = 14 Answer: So, the area is about 14 square inches. 7 8 6 1 4 2

97. Lesson 7 CYP4 6-7 Estimating Products of Fractions Estimate the area of a rectangle with a width of 9 in. and a length of 3 in. 4 5 1 8 A.30 in 2 B.27 in 2 C.40 in 2 D.36 in 2

98. End of Lesson 7

99. Lesson 8 Menu Five-Minute Check (over Lesson 6-7) Main Idea California Standards Key Concept: Multiply Fractions Click here to continue the Lesson Menu 6-8 Multiplying Fractions

100. Lesson 8 Menu Example 1: Multiply Fractions Example 2: Multiply Fractions and Whole Numbers Example 3: Simplify Before Multiplying Example 4: Evaluate Expressions 6-8 Multiplying Fractions

101. 6-8 Multiplying Fractions Lesson 8 MI/Vocab I will multiply fractions.

102. 6-8 Multiplying Fractions Lesson 8 Standard 1 Standard 5NS2.5 Compute and perform simple multiplication and division of fractions and apply these procedures to solving problems.

103. Lesson 8 Key Concept 6-8 Multiplying Fractions

104. Lesson 8 Ex1 6-8 Multiplying Fractions Find ×. 1 5 1 6 1 5 × 1 6 = 1 × 1 5 × 6 Multiply the numerators. Multiply the denominators. = 1 30 Simplify.

105. Lesson 8 CYP1 6-8 Multiplying Fractions Find ×. 1 7 1 2 C. 1 2 A. 2 14 D. 1 14 B. 1 7

106. Lesson 8 Ex2 6-8 Multiplying Fractions Find × 7. 5 8 Estimate × 7 = 3 1 2 1 2 5 8 × 7 = 5 8 × 7 1 Write 7 as. 7 1 = 5 × 7 8 × 1 Multiply. = 35 8 or 4 3 8 Simplify.

107. Lesson 8 Ex2 6-8 Multiplying Fractions Check for Reasonableness 4 is about 3. 3 8 1 2

108. Lesson 8 CYP2 6-8 Multiplying Fractions Find × 9. 7 8 C.9 A.8 B.7 7 9 D.8 1 9

109. Lesson 8 Ex3 6-8 Multiplying Fractions Find ×. 3 7 2 9 Estimate × 0 = 0 1 2 3 7 × 2 9 = 3 × 2 7 × 9 Multiply. = 6 63 or 2 21 Simplify.

110. Lesson 8 Ex3 6-8 Multiplying Fractions Check for Reasonableness is about 0. 2 21

111. Lesson 8 CYP3 6-8 Multiplying Fractions Find ×. 4 6 3 7 D.1 A. 4 13 B. 2 7 C. 6 26

112. Lesson 8 Ex4 6-8 Multiplying Fractions ALGEBRA Evaluate pq if p = and q =. 3 4 8 9 pq = × 3 4 8 9 Replace p with and q with. 3 4 8 9 = 3 × 8 4 × 9 The GCF of 3 and 9 is 3. The GCF of 4 and 8 is 4. Divide the numerator and the denominator by 3 and 4. 1 3 2 1 = 2 3 Simplify. Answer: So, × =. 3 4 8 9 2 3

113. Lesson 8 CYP4 6-8 Multiplying Fractions ALGEBRA Evaluate gh if g = and h =. 2 5 5 10 B. 1 5 A. 1 2 C. 10 50 D. 5 50

114. End of Lesson 8

115. Lesson 9 Menu Five-Minute Check (over Lesson 6-8) Main Idea California Standards Key Concept: Multiply Mixed Numbers Example 1: Multiply a Fraction and a Mixed Number Example 2: Multiply Mixed Numbers Example 3: Evaluate Expressions 6-9 Multiplying Mixed Numbers

116. 6-9 Multiplying Mixed Numbers Lesson 9 MI/Vocab I will multiply mixed numbers.

117. 6-9 Multiplying Mixed Numbers Lesson 9 Standard 1 Standard 5NS2.5 Compute and perform simple multiplication and division of fractions and apply these procedures to solving problems.

118. Lesson 9 Key Concept 6-9 Multiplying Mixed Numbers

119. Lesson 9 Ex1 6-9 Multiplying Mixed Numbers Find × 3. 3 8 1 3 3 8 × 3 1 3 Estimate × 3 = 1 1 2 1 2 3 × 10 8 × 3 = Write 3 as. 1 3 10 3 = 3 8 × 3 = 5 4 or 1 1 4 Divide 10 and 8 by their GCF, 2. Divide 3 and 3 by their GCF, 3. Simplify. Compare to the estimate. 5 41 1 Answer: 1 1 4

120. Lesson 9 CYP1 6-9 Multiplying Mixed Numbers Find × 2. 4 5 2 3 C.3 A.2 2 15 1 2 D.3 B.2 1 2

121. Lesson 9 Ex2 6-9 Multiplying Mixed Numbers Belinda lives 1 times farther from school than Elena does. If Elena lives 4 miles from school, how far from school does Belinda live? 1 2 1 5 Elena lives 4 miles from school. Multiply 4 × 1. 1 5 1 2 1 5

122. Lesson 9 Ex2 6-9 Multiplying Mixed Numbers 4 × 1 1 5 1 2 21 × 3 5 × 2 = First, write mixed numbers as improper fractions. = 3 2 × 21 5 Then, multiply the numerators and multiply the denominators. Simplify. = or 6 63 10 3 Answer: So, Belinda lives 6 miles from school. 3 10

123. Lesson 9 CYP2 6-9 Multiplying Mixed Numbers Mariah is making 4 times the recipe for crispy treats. If the recipe calls for 1 cups of butter, how much butter will she need? 1 4 1 4 A. cups 85 16 B.5 cups 1 5 C.5 cups 5 16 D. cups 25 16

124. Lesson 9 Ex3 6-9 Multiplying Mixed Numbers ALGEBRA If y = 3 and w = 2, what is the value of wy? 3 4 4 5 = Divide the numerator and denominator by 2 and 5. Simplify. 3 12 7 wy = 2 × 3 4 5 3 4 Replace w with 2 and y with 3. 4 5 3 4 14 5 × 15 4 = or 10 1 2 21 2

125. Lesson 9 CYP3 6-9 Multiplying Mixed Numbers ALGEBRA If m = 4 and n = 2, what is the value of mn? 5 8 6 7 C.13 3 14 D.13 A. 185 14 B. 180 14

126. End of Lesson 9

127. Lesson 10 Menu Five-Minute Check (over Lesson 6-9) Main Idea and Vocabulary California Standards Key Concept: Divide Fractions Example 1: Find Reciprocals Example 2: Find Reciprocals Example 3: Divide by a Fraction Example 4: Divide by a Fraction Example 5: Real-World Example 6-10 Dividing Fractions

128. 6-10 Dividing Fractions Lesson 10 MI/Vocab I will divide fractions. reciprocal

129. 6-10 Dividing Fractions Lesson 10 Standard 1 Standard 5NS2.5 Compute and perform simple multiplication and division of fractions and apply these procedures to solving problems.

130. Lesson 10 Key Concept 1 6-10 Dividing Fractions

131. Lesson 10 Ex1 Find the reciprocal of 8. 6-10 Dividing Fractions Answer: Since, 8 × = 1, the reciprocal of 8 is. 1 8 1 8

132. Lesson 10 CYP1 6-10 Dividing Fractions Find the reciprocal of 6. A.6 B.0.6 C. 6 1 D. 1 6

133. Lesson 10 Ex2 6-10 Dividing Fractions Find the reciprocal of. 3 5 Answer: Since, × = 1, the reciprocal of is. 3 5 5 3 3 5 5 3

134. Lesson 10 CYP2 6-10 Dividing Fractions C. 2 2 D. 3 3 Find the reciprocal of. 2 3 A. 3 2 B. 2 3

135. Lesson 10 Ex3 6-10 Dividing Fractions 1 3 ÷ 5 6 1 × 6 3 × 5 = Multiply by the reciprocal. 6 5 = 2 5 Divide 3 and 6 by the GCF, 3. Multiply numerators. Multiply denominators. 2 1 Find ÷. 1 3 5 6 = 1 3 × 6 5 2 5 Answer:

136. Lesson 10 CYP3 6-10 Dividing Fractions C. 7 9 D. 9 7 A. 4 7 B. 12 21 Find ÷. 2 3 6 7

137. Lesson 10 Ex4 6-10 Dividing Fractions Find 5 ÷. 1 6 5 ÷ 1 6 Multiply by the reciprocal. 6 1 Simplify. = 5 1 × 6 1 = or 30 30 1 Answer: 30

138. Lesson 10 CYP4 6-10 Dividing Fractions C. 3 4 D.14 A.48 Find 6 ÷. 1 8 B. 6 8

139. Lesson 10 Ex5 6-10 Dividing Fractions A relay race is of a mile long. There are 4 runners in the race. What portion of a mile will each racer run? 3 4 Divide into 4 equal parts. 3 4

140. Lesson 10 Ex5 6-10 Dividing Fractions Answer: So, each runner ran of a mile. 3 16 Simplify. = 3 16 ÷ 4 3 4 Multiply by the reciprocal. = 3 4 × 1 4

141. Lesson 10 CYP5 6-10 Dividing Fractions Three ladies decided to knit the world’s longest scarf. It was of a mile long. If each lady knit the same amount, what portion of a mile did each lady knit? 1 4 A. 3 4 mile B. 1 12 mile C. 1 8 mile D. 2 4 mile

142. End of Lesson 10

143. Lesson 11 Menu Five-Minute Check (over Lesson 6-10) Main Idea California Standards Key Concept: Dividing by Mixed Numbers Example 1: Divide by a Mixed Number Example 2: Evaluate Expressions Example 3: Real-World Example 6-11 Dividing Mixed Numbers

144. 6-11 Dividing Mixed Numbers Lesson 11 MI/Vocab I will divide mixed numbers.

145. 6-11 Dividing Mixed Numbers Lesson 11 Standard 1 Standard 5NS2.5 Compute and perform simple multiplication and division of fractions and apply these procedures to solving problems.

146. Lesson 11 Key Concept 1 6-11 Dividing Mixed Numbers

147. Lesson 11 Ex1 6-11 Dividing Mixed Numbers Find 6 ÷ 2. 1 4 1 2 6 ÷ 2 1 4 1 2 Estimate 6 ÷ 3 = 2 Write mixed numbers as improper fractions. = 25 4 ÷ 5 2 Multiply by the reciprocal. = 25 4 × 2 5

148. Lesson 11 Ex1 6-11 Dividing Mixed Numbers Divide 2 and 4 by the GCF, 2, and 25 and 5 by the GCF, 5. = 25 4 × 2 5 1 2 5 1 Simplify. = or 2 1 2 5 2 Check for Reasonableness 2 is about 3. 1 2 Answer: 2 1 2

149. Lesson 11 CYP1 6-11 Dividing Mixed Numbers Find 3 ÷ 1. 3 4 1 2 C.2 3 4 D.2 B.2 1 2 A.2 6 12

150. Lesson 11 Ex2 6-11 Dividing Mixed Numbers ALGEBRA Find a ÷ b if a = 2 and b =. 5 8 2 3 a ÷ b Write the mixed number as an improper fraction. = 21 8 ÷ 2 3 = 2 ÷ 5 8 2 3 Multiply by the reciprocal. = 21 8 × 3 2 Replace a with 2 and b with. 5 8 2 3 Simplify. = 63 16 or 3 15 16

151. Lesson 11 CYP2 6-11 Dividing Mixed Numbers ALGEBRA Find f ÷ g if f = 3 and g =. 2 3 5 8 D.2 1 6 A.5 3 5 C.5 13 15 B.2 7 24

152. Lesson 11 Ex3 6-11 Dividing Mixed Numbers Estimate 180 ÷ 4 = 45 180 ÷ 3 3 4 Write mixed numbers as improper fractions. A team took 3 days to complete 180 miles of an adventure race consisting of hiking, biking, and river rafting. How many miles did they average each day? 3 4 = ÷ 180 1 15 4

153. Lesson 11 Ex3 6-11 Dividing Mixed Numbers = 48 Multiply by the reciprocal. = × 180 1 4 15 Divide 15 and 180 by the GCF, 15. Simplify. Compare to the estimate. Answer: So, the team averaged 48 miles each day. = × 180 1 4 15 12 1

154. Lesson 11 CYP3 6-11 Dividing Mixed Numbers A cross country skier took 4 days to travel 240 miles. How many miles did he average each day? 2 3 D.52 miles 1 2 A.51 miles 3 7 B.51 miles 6 14 C.50 miles 3 4

155. End of Lesson 11

156. 6 6 Multiplying and Dividing Decimals and Fractions 6 6 CR Menu Five-Minute Checks Math Tool Chest Image Bank Dividing Decimals Multiplying Fractions

157. 6 6 Multiplying and Dividing Decimals and Fractions IB Instructions To use the images that are on the following four slides in your own presentation: 1.Exit this presentation. 2.Open a chapter presentation using a full installation of Microsoft ® PowerPoint ® in editing mode and scroll to the Image Bank slides. 3.Select an image, copy it, and paste it into your presentation.

158. 6 6 Multiplying and Dividing Decimals and Fractions IB 1

159. 6 6 Multiplying and Dividing Decimals and Fractions IB 2

160. 6 6 Multiplying and Dividing Decimals and Fractions IB 3

161. 6 6 Multiplying and Dividing Decimals and Fractions IB 4

162. 6 6 Multiplying and Dividing Decimals and Fractions 6 6 5Min Menu Lesson 6-1Lesson 6-1(over Chapter 5) Lesson 6-2Lesson 6-2(over Lesson 6-1) Lesson 6-3Lesson 6-3(over Lesson 6-2) Lesson 6-4Lesson 6-4(over Lesson 6-3) Lesson 6-5Lesson 6-5(over Lesson 6-4) Lesson 6-6Lesson 6-6(over Lesson 6-5) Lesson 6-7Lesson 6-7(over Lesson 6-6) Lesson 6-8Lesson 6-8(over Lesson 6-7) Lesson 6-9Lesson 6-9(over Lesson 6-8) Lesson 6-10Lesson 6-10(over Lesson 6-9) Lesson 6-11Lesson 6-11(over Lesson 6-10)

163. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 1-1 (over Chapter 5) Find 6 – 2. 1 4 3 4 C.4 1 2 D.4 A.3 1 2 B.8 3 4

164. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 1-2 (over Chapter 5) Find 5 – 3. 1 3 5 9 C.8 6 9 A.2 4 9 B.1 7 9 D.2 6 9

165. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 1-3 (over Chapter 5) Find the value of n. n + 1 = 8 3 5 A.6 2 5 B.6 D.5 C.4 3 5

166. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 1-4 (over Chapter 5) Find the value of n. C. 2 5 A.3 B. 5 13 D.1 5 6 n + 10 = 12 1 2 1 3

167. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 2-1 (over Lesson 6-1) Find 3.8 × 2. A.5.8 B.7.6 C.5.6 D.5

168. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 2-2 Find 0.6 × 25. A.15 B.25 C.10 D.4 (over Lesson 6-1)

169. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 2-3 Find 0.038 × 15. A.0.63 B.1.35 C.0.57 D.1 (over Lesson 6-1)

170. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 2-4 Find 0.0003 × 17. A.0.0021 B.0.0034 C.0.0051 D.0.21 (over Lesson 6-1)

171. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 2-5 Mercury is approximately 3.6 × 10 7 miles from the Sun. How far is this? A.360 mi B.1,800,000 mi C.36,000,000 mi D.3,000,000 mi (over Lesson 6-1)

172. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 3-1 (over Lesson 6-2) Find 75.4 × 2.9. A.150.36 B.77.36 C.125 D.218.66

173. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 3-2 (over Lesson 6-2) Find 0.05 × 0.123. A.0.15 B.0.00615 C.0.00506 D.1

174. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 3-3 (over Lesson 6-2) Evaluate 2.5y if y = 4.8. A.4.8 B.10.48 C.8.5 D.12

175. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 3-4 (over Lesson 6-2) Selam makes $6.75 an hour. Last week, she worked 12.4 hours. How much did she earn? A.$36.75 B.$48.55 C.$48.50 D.$83.70

176. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 4-1 (over Lesson 6-3) Determine a reasonable answer. Mr. Nieto has 63.75 yards of fencing. How many feet of fencing is that? A.127.50 ft B.191.25 ft C.255 ft D.33.75 ft

177. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 4-2 Cafeteria workers made 23.5 gallons of punch for an awards banquet. They are serving the punch in 1-quart pitchers. How many containers do they need for all the punch? (1 gal = 4 qt) A.11.75 pitchers B.40 pitchers C.4 pitchers D.94 pitchers (over Lesson 6-3)

178. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 5-1 (over Lesson 6-4) Find 27.09 ÷ 9. Round to the nearest tenth if necessary. A.7.09 B.4 C.3.01 D.7

179. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 5-2 (over Lesson 6-4) Find 378.5 ÷ 5. Round to the nearest tenth if necessary. A.75.7 B.75 C.35.5 D.102

180. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 5-3 (over Lesson 6-4) Find 247.52 ÷ 7. Round to the nearest tenth if necessary. A.35.4 B.24 C.35.04 D.23.5

181. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 5-4 (over Lesson 6-4) Find the mean for the following set of data: 7.8, 9.02, 2.62. A.4.5 B.4.45 C.6.48 D.5.55

182. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 6-1 (over Lesson 6-5) Find 24.36 ÷ 4.2. A.5.8 B.5.66 C.4 D.6.18

183. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 6-2 (over Lesson 6-5) Find 15.39 ÷ 0.05. A.128.5 B.3 C.12 D.307.8

184. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 6-3 (over Lesson 6-5) Find 0.648 ÷ 0.12. A.0.85 B.1.48 C.5.4 D.5.6

185. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 6-4 (over Lesson 6-5) Find 0.782 ÷ 3.4. A.0.23 B.0.015 C.4 D.12

186. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 7-1 (over Lesson 6-6) Choose the best strategy to solve the problem. The sum of three consecutive numbers is 42. What are the three numbers? A.12, 14, 16 B.15, 12, 9 C.13, 14, 15 D.12, 13, 14

187. 6 6 Multiplying and Dividing Decimals and Fractions C.1 × 36 = 6 5Min 8-1 (over Lesson 6-7) Estimate the product. A. × 38 = 8 1 6 × 38 1 6 B. × 36 = 6 1 6 D. × 48 = 8 1 6

188. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 8-2 (over Lesson 6-7) Estimate the product. A.1 × 45 = 45 C. × 45 = 30 2 3 × 44 2 3 B. × 45 = 45 2 3 D. × 44 = 11 2 4

189. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 8-3 (over Lesson 6-7) Estimate the product. × 3 8 4 5 B. × 45 = 30 3 8 C. × 45 = 17 1 2 A. × 1 = 1 2 1 2 D. × 1 = 1 1 2 1 2

190. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 8-4 (over Lesson 6-7) B.25 × 40 = 1,000 ft 2 C.26 × 40 = 1,040 ft 2 A.25 × 40 = 975 ft 2 A pool is 25 feet wide and 39 feet long. Estimate the area. 1 4 5 6 D.25 × 4 = 100 ft 2

191. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 9-1 (over Lesson 6-8) Multiply. Write in simplest form. × 2 3 9 10 1 3 B. C. 9 10 D. 3 5 A. 4 5

192. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 9-2 (over Lesson 6-8) Multiply. Write in simplest form. × 4 5 5 6 4 5 B. D. 2 5 A. 2 3 C.1 1 3

193. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 9-3 (over Lesson 6-8) Evaluate n if n =. Write in simplest form. 8 9 3 4 B. 1 3 D. 3 9 A. 4 5 C. 2 3

194. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 9-4 (over Lesson 6-8) Evaluate 10n if n =. Write in simplest form. 3 4 B.4 2 3 D. 1 3 A.7 1 2 C. 7 9

195. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 10-1 (over Lesson 6-9) Multiply. Write in simplest form. × 1 2 3 9 10 B.2 2 3 D.2 C.1 1 2 A.3 3 5

196. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 10-2 (over Lesson 6-9) Multiply. Write in simplest form. B.24 1 2 C.21 1 2 A.10 1 5 5 × 4 5 6 1 5 D.31 1 2

197. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 10-3 (over Lesson 6-9) The length of a square sandbox is 4 feet. What is the area of the sandbox? 2 3 B.23 ft 2 5 9 C.21 ft 2 5 9 A.21 ft 2 7 9 D.9 ft 2 1 3

198. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 10-4 (over Lesson 6-9) ALGEBRA If a = 4 and t = 1, what is the value of at? 4 5 1 16 C.5 3 5 D.6 A.5 5 16 B. 3 16

199. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 11-1 (over Lesson 6-10) Divide. Write in simplest form. ÷ 4 5 1 10 D.8 C.4 B. 1 2 A. 5 10

200. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 11-2 (over Lesson 6-10) ÷ 7 8 1 4 Divide. Write in simplest form. B.4 D.2 C.3 A.3 1 2

201. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 11-3 (over Lesson 6-10) 6 ÷ 2 3 Divide. Write in simplest form. B.3 D.9 C.8 A. 2 3

202. 6 6 Multiplying and Dividing Decimals and Fractions 5Min 11-4 (over Lesson 6-10) ÷ 1 2 3 4 Divide. Write in simplest form. C.1 A. 2 3 B. 1 2 D. 1 3

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