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

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Dividing Fractions

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

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

Finding Reciprocals 2 5 = 5 2 6 13 = 6

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

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

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

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

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

Dividing Mixed Numbers

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.

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

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

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

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

Solving Fraction Equations by Multiplying

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.

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.

y 8 = 20 8 1 · 1 1 y 1 = · 8 160 y=

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

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

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.

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

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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