Simplifying a fraction is the opposite of expanding a fraction. You will get a lot of use out of this technique because of how handy it is, so be sure you master it!

Rule

You simplify a fraction with numerator $a$ and denominator $b$ like this:

$$\frac{a}{b}=\frac{a\xf7c}{b\xf7c}$$ |

Example 1

**Simplify the fraction $\frac{4}{6}$ by 2 **

$$\frac{4}{6}=\frac{4\xf72}{6\xf72}=\frac{2}{3}$$ |

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Here you will learn to simplify a fraction in a very nifty way. It’s also fun, because the calculation becomes much easier!

When simplifying a fraction by canceling, first factorize the numerator and denominator as much as possible. Then, cancel equal factors in the numerator and denominator. You can only cancel one factor against another factor. The reason you can do this is because the two factors you cancel out just become 1 when you divide them by one another. Remember that any number multiplied by 1 is equal to itself.

Example 2

**Simplify the fraction $\frac{3}{6}$ by canceling **

$$\begin{array}{llll}\hfill \frac{3}{6}& =\frac{\text{3}\times 1}{2\times \text{3}}=\frac{1}{2}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$$ because $$\begin{array}{llll}\hfill \frac{3}{6}& =\frac{3\times 1}{2\times 3}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\frac{3}{3}\times \frac{1}{2}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =1\times \frac{1}{2}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\frac{1}{2}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$$