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3-6 Dividing by Decimals Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

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3-6 Dividing by Decimals Warm Up Divide. 1. 4.8 ÷ 2 2. 16.1 ÷ 7 3. 0.36 ÷ 3 4. 25.28 ÷ 4 2.4 2.3 0.12 6.32

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3-6 Dividing by Decimals Problem of the Day In the following magic square, 3.375 is the product of the numbers in every row, column, and diagonal. Fill in the missing numbers. 4.50.25 0.5 3 11.5 2.25 0.75 9

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3-6 Dividing by Decimals Learn to divide whole numbers and decimals by decimals.

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3-6 Dividing by Decimals Multiplying the divisor and the dividend by the same number does not change the quotient. 42 ÷ 6 = 7 10 10 420 ÷ 60 = 7 10 10 4,200 ÷ 600 = 7 Helpful Hint

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3-6 Dividing by Decimals Additional Example 1A: Dividing a Decimal by a Decimal Find the quotient. 5.2 ÷ 1.3 1.3 5.2 Multiply the divisor and dividend by the same power of ten. There is one decimal place in the divisor. Multiply by 10 1, or 10. Think: 1.3 x 10 = 135.2 x 10 = 52 Divide. 13 52 4 –52 0 5.2 ÷ 1.3 = 4

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3-6 Dividing by Decimals Additional Example 1B: Dividing a Decimal by a Decimal 61.3 ÷ 0.36 0.36 61.30 Think: 0.36 x 100 = 36 61.3 x 100 = 6,130 Make the divisor a whole number by multiplying the divisor and dividend by 10 2, or 100. 36 6,130.000

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3-6 Dividing by Decimals Additional Example 1B Continued Place the decimal point in the quotient. Divide. 36 6,130.000 7 -36 1 253 -252 10 -0 0 100.2 -72 -252 7 280 -252 280 7 28 61.3 ÷ 0.36 = 170.27 __ When a repeating pattern occurs, show three dots or draw a bar over the repeating part of the quotient.

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3-6 Dividing by Decimals Check It Out: Example 1A Find the quotient. 6.6 ÷ 1.1 1.1 6.6 Multiply the divisor and dividend by the same power of ten. There is one decimal place in the divisor. Multiply by 10, or 10. Think: 1.1 x 10 = 116.6 x 10 = 66 1 Divide. 11 66 6 -66 0 6.6 ÷ 1.1 = 6

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3-6 Dividing by Decimals Check It Out: Example 1B 51.2 ÷ 0.24 0.24 51.2 Think: 0.24 x 100 = 24 51.2 x 100 = 5,120 Make the divisor a whole number by multiplying the divisor and dividend by 10 2, or 100. 24 5120.00 0

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3-6 Dividing by Decimals Check It Out: Example 1B Continued Divide. 24 5,120.00 1 -48 2 32 -24 80 -72 3 80.3 -72 80 3 51.2 ÷ 0.24 = 213.3 __ When a repeating pattern occurs, show three dots or draw a bar over the repeating part of the quotient. 8

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3-6 Dividing by Decimals Additional Example 2: Problem Solving Application After driving 216.3 miles, the York’s filled up with 10.5 gallons of gas. On average, how many miles did they drive per gallon of gas? 1 Understand the Problem The answer will be the average number of miles per gallon. List the important information: They drove 216.3 miles. They used 10.5 gallons of gas.

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3-6 Dividing by Decimals 2 Make a Plan Solve a simpler problem by replacing the decimals in the problem with whole numbers. If they drove 10 miles using 2 gallons of gas, they averaged 5 miles per gallon. You need to divide miles by gallons to solve the problem. Solve 3 First estimate the answer. You can use compatible numbers. 216.3 ÷ 10.5 200 ÷ 10 = 20

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3-6 Dividing by Decimals The York family averaged 20.6 miles per gallon. 105 2163.0 -210 2 63 -0 630 -630 0 0.6 Solve Continued 3 10.5 216.3 Multiply the divisor and dividend by 10. Think: 10.5 x 10 = 105 216.3 x 10 = 2,163 Place the decimal point in the quotient. Divide.

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3-6 Dividing by Decimals Look Back4 The answer is reasonable since 20.6 is close to the estimate of 20.

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3-6 Dividing by Decimals Check It Out: Example 2 After driving 191.1 miles, the Chang’s filled up with 10.5 gallons of gas. On average, how many miles did they drive per gallon of gas? 1 Understand the Problem The answer will be the average number of miles per gallon. List the important information: They drove 191.1 miles. They used 10.5 gallons of gas.

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3-6 Dividing by Decimals 2 Make a Plan Solve a simpler problem by replacing the decimals in the problem with whole numbers. If they drove 10 miles using 2 gallons of gas, they averaged 5 miles per gallon. You need to divide miles by gallons to solve the problem. Solve 3 First estimate the answer. You can use compatible numbers. 191.1 ÷ 10.5 190 ÷ 10 = 19

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3-6 Dividing by Decimals 105 1911.0 -105 1 861 -840 210 -210 8 0.2 The Chang family averaged 18.2 miles per gallon. Solve Continued 3 10.5 191.1 Multiply the divisor and dividend by 10. Think: 10.5 x 10 = 105 191.1 x 10 = 1,911 Place the decimal point in the quotient. Divide.

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3-6 Dividing by Decimals Look Back4 The answer is reasonable since 18.2 is close to the estimate of 19.

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3-6 Dividing by Decimals Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

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3-6 Dividing by Decimals Lesson Quiz Find each quotient. 1. 49 ÷ 0.7 2. 21.63 ÷ 2.1 3. 38.43 ÷ 6.1 4. 16.9 ÷ 5.2 5. John spent $13.44 renting 4 videos for the weekend. What was the cost per video? 10.3 70 6.3 3.25 $3.36

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3-6 Dividing by Decimals 1. Identify the quotient. 72 0.9 A. 70 B. 79 C. 80 D. 90 Lesson Quiz for Student Response Systems

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3-6 Dividing by Decimals 2. Identify the quotient. 36.12 4.2 A. 8.6 B. 8.8 C. 9.5 D. 9.6 Lesson Quiz for Student Response Systems

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3-6 Dividing by Decimals 3. Identify the quotient. 51.51 5.1 A. 10.1 B. 10 C. 5.1 D. 5 Lesson Quiz for Student Response Systems

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3-6 Dividing by Decimals 4. Identify the quotient. 26.35 6.2 A. 4.25 B. 4.5 C. 4.75 D. 5 Lesson Quiz for Student Response Systems

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3-6 Dividing by Decimals 5. Dee bought 5 cups of iced tea for $4.85. What was the cost per cup? A. $0.66 B. $0.69 C. $0.95 D. $0.97 Lesson Quiz for Student Response Systems

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