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The Number System Dividing Decimals 1 © 2013 Meredith S. Moody

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Objective: You will be able to… Divide decimals using two different methods 2 © 2013 Meredith S. Moody

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Vocabulary Dividend: A number that is to be divided Divisor: A number that divides another number Quotient: The result of division; the number of times one quantity is contained in another Division bracket: The “box” the dividend is placed inside and the divisor is placed outside 3 © 2013 Meredith S. Moody

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Method 1: Division without the decimal Step 1: Find the smallest place value of the divisor and dividend Find the smallest place value of the divisor and dividend Step 2: Multiply the divisor and dividend by the power of 10 that corresponds with the smallest place value Multiply the divisor and dividend by the power of 10 that corresponds with the smallest place value Step 3: Put the dividend in the box Put the dividend in the box Step 4: Put the divisor outside the box Put the divisor outside the box Step 5: Put a decimal after the last digit in the dividend and on the quotient line right after the last digit in the dividend Put a decimal after the last digit in the dividend and on the quotient line right after the last digit in the dividend Step 6: Divide normally, adding zeros to the dividend when necessary Divide normally, adding zeros to the dividend when necessary 4 © 2013 Meredith S. Moody

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Guided practice 1, method 1 Divide and round the quotient to the nearest hundredths: 30.2 ÷ 8.2 Smallest place value is tenths multiply both numbers by 10 Smallest place value is tenths multiply both numbers by 10 Divide 302 by 82 Divide 302 by 82 Quotient: 3.68 Quotient: 3.68 5 © 2013 Meredith S. Moody

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Guided practice 1, method 1 visual 6 © 2013 Meredith S. Moody

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Guided practice 2, method 1 Divide and round the quotient to the nearest hundredth 491 ÷ 1.3 Smallest place value is tenths multiply each number by 10 Smallest place value is tenths multiply each number by 10 Divide 4910 by 13 Divide 4910 by 13 Quotient: 377.69 Quotient: 377.69 7 © 2013 Meredith S. Moody

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Guided practice 2, method 1 visual 8 © 2013 Meredith S. Moody

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Guided practice 3, method 1 0.25 ÷ 0.05 Smallest place value is hundredths multiply both numbers by 100 Smallest place value is hundredths multiply both numbers by 100 Divide 25 by 5 Divide 25 by 5 Quotient: 5 Quotient: 5 9 © 2013 Meredith S. Moody

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Guided practice 3, method 1 visual 10 © 2013 Meredith S. Moody

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Method 2: Division with the decimal Step 1: Multiply the divisor by the value of 10 that corresponds with the smallest place value Multiply the divisor by the value of 10 that corresponds with the smallest place value Step 2: Multiply the dividend by the same value of 10 Multiply the dividend by the same value of 10 Step 3: Place a decimal on the quotient line directly above the decimal in the dividend Place a decimal on the quotient line directly above the decimal in the dividend Step 4: Divide normally, adding zeros to the dividend when necessary Divide normally, adding zeros to the dividend when necessary 11 © 2013 Meredith S. Moody

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Guided practice 1, method 2 Divide and round your answer to the nearest hundredth: 30.24 ÷ 8.2 Divisor is 8.2, smallest place value is tenths multiply 8.2 by 10 82 Divisor is 8.2, smallest place value is tenths multiply 8.2 by 10 82 Multiply 30.24 by 10 302.4 Multiply 30.24 by 10 302.4 Set up the problem; place a decimal on the quotient line directly above the decimal in the dividend Set up the problem; place a decimal on the quotient line directly above the decimal in the dividend Divide Divide Quotient = 3.69 Quotient = 3.69 12 © 2013 Meredith S. Moody

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Guided practice 1, method 2 visual 13 © 2013 Meredith S. Moody

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Guided practice 2, method 2 4.875 ÷ 1.3 Divisor is 1.3, smallest place value is tenths multiply 1.3 by 10 13 Divisor is 1.3, smallest place value is tenths multiply 1.3 by 10 13 Multiply 4.875 by 10 48.75 Multiply 4.875 by 10 48.75 Set up the problem; place a decimal on the quotient line directly above the decimal in the dividend Set up the problem; place a decimal on the quotient line directly above the decimal in the dividend Divide Divide Quotient: 3.75 Quotient: 3.75 14 © 2013 Meredith S. Moody

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Guided practice 2, method 2 visual 15 © 2013 Meredith S. Moody

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Guided practice 3, method 2 0.2575 ÷ 0.05 Divisor is.05, smallest place value is hundredths multiply.05 by 100 5 Divisor is.05, smallest place value is hundredths multiply.05 by 100 5 Multiply.2575 by 100 25.75 Multiply.2575 by 100 25.75 Set up the problem; place a decimal on the quotient line directly above the decimal in the dividend Set up the problem; place a decimal on the quotient line directly above the decimal in the dividend Divide Divide Quotient: 5.15 Quotient: 5.15 16 © 2013 Meredith S. Moody

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Guided practice 3, method 2 visual 17 © 2013 Meredith S. Moody

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You try! Divide using either method 3.096 ÷ 0.3 3.096 ÷ 0.310.32 0.0048 ÷ 1.2 0.0048 ÷ 1.20.004 20.5 ÷ 0.005 20.5 ÷ 0.0054100 18 © 2013 Meredith S. Moody

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