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Published byBetty Carroll Modified over 9 years ago

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Dividing Fractions

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To Divide Fractions: Rewrite the first fraction. Change the division sign to a multiplication sign. Flip the second fraction upside down. Multiply.

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Reciprocal When you flip the second fraction, you are writing that fraction’s reciprocal. 3 5 5 3

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Finding Reciprocals 2 5 = 5 2 6 13 = 6

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Example 1 1 3 ÷ 1 2 Rewrite: 1 3 x 2 1 = 2 3

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Example 2 4 5 ÷ 4 9 Rewrite: 4 5 x 9 4 1 1 = 9 5 = 1 4 5

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Example 3 12 ÷ 3 5 1 Rewrite: 12 1 x 5 3 4 1 = 20 1 =

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Example 4 1 6 ÷ 2 1 Rewrite: 1 6 x 1 2 = 1 12

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Classwork: Try these Visual models to help you learn Division with fractions. See if you can guess with whole numbers!Visual models

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Dividing Mixed Numbers

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Strategy: Change mixed numbers into improper fractions. Instead of dividing, multiply by the reciprocal. Factor when possible, multiply, and put your answer in simplest form.

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Example 1 6 2 5 ÷ 2 2 7 ÷ 32 5 16 7 32 5 x 7 16 2 1 = 14 5 = 2 4 5

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Example 2 1 1 9 ÷ 6 2 3 ÷ 10 9 20 3 x 10 9 3 20 1 2 3 1 = 1 6

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Example 3 8 1 13 ÷ 5 ÷ 105 13 5 1 105 13 x 1 5 21 1 = 13 = 1 8

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Classwork: Visit the Visual Fractions modeling mixed number site.Visual Fractions

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Solving Fraction Equations by Multiplying

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If the variable is in the fraction… When the variable is the numerator of the fraction, then it suggests a division problem. To solve a division problem, the inverse operation is multiplying.

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Example y 8 = 20 This equation reads “y divided by 8 equals 20.” The opposite of dividing by 8 is multiplying by 8. Multiply both sides by 8.

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y 8 = 20 8 1 · 1 1 y 1 = · 8 160 y=

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Example 2 m 2 = 3 · 2 1 1 1 m 1 = · 2 6 m = 6

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Check answers in the original equation. m 2 =3 6 2 =3 3 =3

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If the variable is being multiplied by a fraction… To isolate a variable that is being multiplied by a fraction, multiply by the reciprocal. Perform the same operation on the other side of the equation.

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Example 2 3 r= 10 · 3 2 1 11 1 1 r = · 3 2 1 5 1 15 1 r =

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Classwork: Try this interactive site that reminds us to balance equations! Next Play Connect 4 with a partner and solve equations Homework Time-Dividing Fractions HOinteractive site Connect 4

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