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3-7 Dividing by Decimals Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

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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 Course 1 3-7 Dividing by Decimals 6.32

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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. Course 1 3-7 Dividing by Decimals 4.50.25 0.5 3 11.5 2.25 0.75 9

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Learn to divide whole numbers and decimals by decimals. Course 1 3-7 Dividing by Decimals TEKS 6.11.B: Underlying processes and mathematical tools: use a problem-solving model...

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Course 1 3-7 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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Course 1 3-7 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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Course 1 3-7 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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Course 1 3-7 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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Course 1 3-7 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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Course 1 3-7 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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Course 1 3-7 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 = 213.33 __ When a repeating pattern occurs, show three dots or draw a bar over the repeating part of the quotient. 8

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Course 1 3-7 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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Course 1 3-7 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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Course 1 3-7 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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Course 1 3-7 Dividing by Decimals Look Back4 The answer is reasonable since 20.6 is close to the estimate of 20.

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Course 1 3-7 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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Course 1 3-7 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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Course 1 3-7 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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Course 1 3-7 Dividing by Decimals Look Back4 The answer is reasonable since 18.2 is close to the estimate of 19.

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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 Insert Lesson Title Here 6.3 3.25 Course 1 3-7 Dividing by Decimals $3.36

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