## Multiply/Divide Fractions

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#### Study Guide Multiply/Divide Fractions Mathematics, Grade 6

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MULTIPLYING AND DIVIDING FRACTIONS What Is Multiplying and Dividing Fractions with Unlike Denominators? When two fractions have unlike denominators, multiply the numerators and multiply the denominators to find the product. For example: 3/5 x 2/3 = 6/15 When two fractions have unlike denominators, invert the divisor and multiply the two fractions. For example: 2/9 ÷ 3/5 2/9 x 5/3 = 10/27 The denominators do not have to be the same in order to complete the multiplication or division. How to multiply and divide fractions with unlike denominators: To multiply two fractions with unlike denominators, multiply the numerators and multiply the denominators. It is unnecessary to change the denominators for this operation. 2/5 x 6/7 = 12/35 5/9 x 3/6 = 15/54 7/10 x 7/8 = 49/80 To divide two fractions with unlike denominators, o First invert the divisor. 1/3 ÷ ½ invert ½ to 2/1 o After inverting the divisor, multiply the fractions 1/3 ÷ ½ 1/3 x 2/1 = 2/3 Any number divided by 1 equals that number: 5 ÷ 1 = 5 34 ÷ 1 = 34 1/6 ÷ 1 = 1/6 © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
Sometimes, the product resulting from multiplication or division can be reduced. This means dividing by one to make the denominator a lower value. For example, 8/10 can be reduced to 4/5 by dividing by 2/2 (an equivalent of 1). 12/15 4/5 Divide both numerator and denominator by 3. 30/35 6/7 Divide both numerator and denominator by 5. When multiplying or dividing fractions with unlike denominators, perform the operation and then reduce the product to lowest terms. Try This! Multiply and reduce to lowest terms: 3/11 x 2/3 = _____________________________________ Multiply and reduce to lowest terms: 4/5 x 2/6 = _____________________________________ Multiply and reduce to lowest terms: 6/7 x 1/3 = _____________________________________ Divide and reduce to lowest terms: 3/5 ÷ 2/3 = _____________________________________ Divide and reduce to lowest terms: ½ ÷ 4/5 = _____________________________________ © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.