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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.