## Basic College Mathematics (9th Edition)

Published by Pearson

# Chapter 3 - Adding and Subtracting Fractions - Test - Page 260: 16

#### Answer

Addition/subtraction requires forming a least common denominator, while multiplication/division does not.

#### Work Step by Step

When working with fractions, people often find addition and subtraction more difficult than division and multiplication because addition/subtractions requires forming the least common denominator, while multiplication/division does not. For example, consider adding vs multiplying the following fractions: $\displaystyle \frac{1}{2}+\frac{1}{3}=\frac{3}{6}+\frac{2}{6}=\frac{5}{6}$ $\displaystyle \frac{1}{2}*\frac{1}{3}=\frac{1}{2*3}+\frac{1}{6}$ Multiplication took fewer steps and there was less "thinking" involved -- all one had to do was multiply the numbers across. Similarly, division can be turned into multiplication by simply taking the reciprocal of the second fraction. Thus subtraction/addition tend to "feel" harder for most students.

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