## Basic College Mathematics (10th Edition)

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.