## Basic College Mathematics (9th Edition)

Let's take a look on an example. $\frac{5}{4} \cdot \frac{2}{5}$. We can see that both fractions share the common factor $5$, one in the denominator and one in the numerator. So can divide $5$ and get as a result $\frac{5}{4} \cdot \frac{2}{5} = \frac{1}{4} \cdot \frac{2}{1}$. Rewriting the nominator of the first fraction $\frac{1}{2 \cdot 2} \cdot \frac{2}{1}$ shows us that both fractions share the common factor $2$ and we can divide by $2$ and get $\frac{1}{2 \cdot 2} \cdot \frac{2}{1} = \frac{1}{1 \cdot 2} \cdot \frac{1}{1} = \frac{1 \cdot 1}{2 \cdot 1} = \frac{1}{2 }$. Because of the short cut by all possible common factors the result is in lowest term.