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. 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 6-1 Multiplying Decimals by Whole Numbers

5. 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 6-1 Multiplying Decimals by Whole Numbers

6. 5Min 1-3 (over Chapter 5) A.1 3 5 C.2 3 5 Find 5 – 3. 2 5 4 5 B.2 2 5 D.8 4 5 6-1 Multiplying Decimals by Whole Numbers

7. 5Min 1-4 (over Chapter 5) A.6 6 8 C.5 3 8 Find 15 – 9. 1 4 7 8 B.6 5 8 D.23 3 8 6-1 Multiplying Decimals by Whole Numbers

8. 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

9. 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.

10. 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.

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

12. 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.

13. 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.

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

15. 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.

16. 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

17. 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.

18. 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

19. 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

20. 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.

21. 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 × 100,000,000 = 150,000,000 kilometers

22. 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

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

24. 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 5.88 × 10 8 kilometers. Choose the answer showing the distance written in standard form.

25. End of Lesson 1

26. 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

27. 5Min 2-1 (over Lesson 6-1) Find 3.8 × 2. A.5.8 B.7.6 C.5.6 D.5 6-2 Multiplying Decimals

28. 5Min 2-2 Find 0.6 × 25. A.15 B.25 C.10 D.4 (over Lesson 6-1) 6-2 Multiplying Decimals

29. 5Min 2-3 Find 0.038 × 15. A.0.63 B.1.35 C.0.57 D.1 (over Lesson 6-1) 6-2 Multiplying Decimals

30. 5Min 2-4 Find 0.0003 × 17. A.0.0021 B.0.0034 C.0.0051 D.0.21 (over Lesson 6-1) 6-2 Multiplying Decimals

31. 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) 6-2 Multiplying Decimals

32. 6-2 Multiplying Decimals Lesson 2 MI/Vocab I will multiply decimals by decimals.

33. 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.

34. 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.

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

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

37. 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.

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

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

40. 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

41. 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

42. 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

43. 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

44. 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

45. End of Lesson 2

46. 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

47. 5Min 3-1 (over Lesson 6-2) Find 75.4 × 2.9. A.150.36 B.77.36 C.125 D.218.66 6-3 Problem-Solving Strategy: Reasonable Answers

48. 5Min 3-2 (over Lesson 6-2) Find 0.05 × 0.123. A.0.15 B.0.00615 C.0.00506 D.1 6-3 Problem-Solving Strategy: Reasonable Answers

49. 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 6-3 Problem-Solving Strategy: Reasonable Answers

50. 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 6-3 Problem-Solving Strategy: Reasonable Answers

51. 6-3 Problem-Solving Strategy: Reasonable Answers Lesson 3 MI/Vocab I will solve problems by determining reasonable answers.

52. 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.

53. 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.

54. 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

55. 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

56. 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

57. 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.

58. End of Lesson 3

59. 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

60. 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 6-4 Dividing Decimals by Whole Numbers

61. 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) 6-4 Dividing Decimals by Whole Numbers

62. 6-4 Dividing Decimals by Whole Numbers Lesson 4 MI/Vocab I will divide decimals by whole numbers. quotient

63. 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.

64. 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.

65. 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

66. 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.

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

68. 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

69. 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.

70. 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.

71. 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 What is the mean mass in grams of the four samples?

72. 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

73. 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

74. End of Lesson 4

75. 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

76. 5Min 5-1 (over Lesson 6-4) Find 27.09 ÷ 9. Round to the nearest tenth if necessary. A.7.1 B.4 C.3 D.7 6-5 Dividing by Decimals

77. 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 6-5 Dividing by Decimals

78. 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 6-5 Dividing by Decimals

79. 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 6-5 Dividing by Decimals

80. 6-5 Dividing by Decimals Lesson 5 MI/Vocab I will divide decimals by decimals. power

81. 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.

82. 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.

83. 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.

84. 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

85. Lesson 5 CYP1 6-5 Dividing by Decimals Find 32.45 ÷ 5.5. A.59 B.5.09 C.5.90 D.50.9

86. 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

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

88. 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.

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

90. 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.

91. 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.

92. Lesson 5 CYP4 6-5 Dividing by Decimals The Martin family drove 354.5 miles for a camping trip and used 12.3 gallons of gas. How many miles did they get per gallon of gas? Round to the nearest tenth. A.2.8 miles per gallon B.28.2 miles per gallon C.28.8 miles per gallon D.288.2 miles per gallon

93. End of Lesson 5

94. 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

95. 5Min 6-1 (over Lesson 6-5) Find 24.36 ÷ 4.2. A.5.8 B.5.66 C.4 D.6.18 6-6 Problem-Solving Investigation: Choose the Best Strategy

96. 5Min 6-2 (over Lesson 6-5) Find 15.39 ÷ 0.05. A.128.5 B.3 C.12 D.307.8 6-6 Problem-Solving Investigation: Choose the Best Strategy

97. 5Min 6-3 (over Lesson 6-5) Find 0.648 ÷ 0.12. A.0.85 B.1.48 C.5.4 D.5.6 6-6 Problem-Solving Investigation: Choose the Best Strategy

98. 5Min 6-4 (over Lesson 6-5) Find 0.782 ÷ 3.4. A.0.23 B.0.015 C.4 D.12 6-6 Problem-Solving Investigation: Choose the Best Strategy

99. 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.

100. 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.

101. 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

102. 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

103. 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

104. 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

105. 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

106. 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.

107. End of Lesson 6

108. 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

109. 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 6-7 Estimating Products of Fractions

110. 6-7 Estimating Products of Fractions Lesson 7 MI/Vocab I will estimate products of fractions using compatible numbers and rounding. compatible numbers

111. 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.

112. 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

113. 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

114. 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

115. 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

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

117. Lesson 7 Ex3 6-7 Estimating Products of Fractions × 4 5 1 × 0 Estimate ×. 4 5 1 6 1 6 1 × 0 = 0 Answer: So, × is about 0. 4 5 1 6

118. 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

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

120. 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

121. 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

122. End of Lesson 7

123. 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

124. 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

125. 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 6-8 Multiplying Fractions

126. 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 6-8 Multiplying Fractions

127. 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 6-8 Multiplying Fractions

128. 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 6-8 Multiplying Fractions

129. 6-8 Multiplying Fractions Lesson 8 MI/Vocab I will multiply fractions.

130. 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.

131. Lesson 8 Key Concept 6-8 Multiplying Fractions

132. 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. Answer: 1 30

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

134. Lesson 8 Ex2 6-8 Multiplying Fractions Find × 7. 5 8 Estimate × 8 = 4 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.

135. Lesson 8 Ex2 6-8 Multiplying Fractions Check for Reasonableness 4 is about 4. 3 8 Answer: 4 3 8

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

137. 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 = 2 21 Simplify. Divide both the numerator and denominator by 3. 1 3 Answer: 2 21 The numerator and denominator have a common factor, 3.

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

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

140. 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

141. 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

142. End of Lesson 8

143. 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

144. 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 6-9 Multiplying Mixed Numbers

145. 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 6-9 Multiplying Mixed Numbers

146. 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 6-9 Multiplying Mixed Numbers

147. 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 6-9 Multiplying Mixed Numbers

148. 6-9 Multiplying Mixed Numbers Lesson 9 MI/Vocab I will multiply mixed numbers.

149. 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.

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

151. 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

152. 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

153. 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

154. 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

155. 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

156. 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 Answer: 10 1 2

157. 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

158. End of Lesson 9

159. 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

160. 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 6-10 Dividing Fractions

161. 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 6-10 Dividing Fractions

162. 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 6-10 Dividing Fractions

163. 5Min 10-4 (over Lesson 6-9) ALGEBRA If a = 4 and t = 1, what is the value of at? 4 5 1 6 C.5 3 5 D.6 A.5 5 16 B. 3 16 6-10 Dividing Fractions

164. 6-10 Dividing Fractions Lesson 10 MI/Vocab I will divide fractions. reciprocal

165. 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.

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

167. 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

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

169. 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

170. 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

171. 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:

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

173. 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

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

175. 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

176. 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

177. 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

178. End of Lesson 10

179. 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

180. 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 6-11 Dividing Mixed Numbers

181. 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 6-11 Dividing Mixed Numbers

182. 5Min 11-3 (over Lesson 6-10) 6 ÷ 2 3 Divide. Write in simplest form. B.3 D.9 C.8 A. 2 3 6-11 Dividing Mixed Numbers

183. 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 6-11 Dividing Mixed Numbers

184. 6-11 Dividing Mixed Numbers Lesson 11 MI/Vocab I will divide mixed numbers.

185. 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.

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

187. 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

188. 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 2. 1 2 Answer: 2 1 2

189. 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

190. 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 15 16 Answer: 3

191. 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

192. Lesson 11 Ex3 6-11 Dividing Mixed Numbers Estimate 200 ÷ 4 = 50 180 ÷ 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

193. 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

194. 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

195. End of Lesson 11