134 Chapter 2 Fractions and Mixed Numbers: Multiplication and Division Example 2 Divide and simplify, if possible. Write the answer as a fraction. 35 14 a. b. c. d. 12 Solution: a. Dividing Fractions 8 3 7 Multiply numerators. Multiply denominators. b. Simplify. Multiply. c. Multiply by the reciprocal of the divisor. Simplify. Multiply. d. Write the whole number 12 as an improper fraction. Multiply by the reciprocal of the divisor. Simplify. 5 12 1 3 12 1 9 2 3 8 3 82 5 Multiply. 2 5 2 27 35 14 12 8 3 12 1 8 3 5 14 35 14 1 71 35 14 1 7 7 35 14 7 1 5 36 2 1 27 9 15 84 Multiply by the reciprocal of the divisor (“second” fraction). 8 15 2 27 15 8 8 35 2 4 5 7 Multiply by the reciprocal of the divisor (“second” fraction). 7 4 2 5 4 7 Write the whole number 7 as an improper fraction before multiplying by the reciprocal. 2 27 8 15 2 5 7 4 3. Order of Operations When simplifying fractional expressions with more than one operation, be sure to follow the order of operations. Simplify within parentheses first. Then simplify expressions with exponents, followed by multiplication or division in the order of appearance from left to right. Skill Practice Divide and simplify.Write the answer as a fraction. 8. 9. 10. 11. 20 Answers 8. 9. 10. 11. 25 3 3 8 5 12 5 8 12 5 15 4 10 3 8 9 10 1 4 2 5 Avoiding Mistakes Do not try to simplify until after taking the reciprocal of the divisor. In Example 2(a) it would be incorrect to “cancel” the 2 and the 4 in the expression 25 74 .
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