###### Example1.2.15

We could also use multiplication to decrease amounts. Suppose we needed to cut the recipe down to just one fifth. Instead of four of the $$\frac{2}{3}$$ cup milk, we need one fifth of the $$\frac{2}{3}$$ cup milk. So instead of multiplying by $$4\text{,}$$ we multiply by $$\frac{1}{5}\text{.}$$ But how much is $$\frac{1}{5}$$ of $$\frac{2}{3}$$ cup?

If we cut the measuring cup into five equal vertical strips along with the three equal horizontal strips, then in total there are $$3\cdot5=15$$ subdivisions of the cup. Two of those sections represent $$\frac{1}{5}$$ of the $$\frac{2}{3}$$ cup.

In the end, we have $$\frac{2}{15}$$ of a cup. The denominator $$15$$ came from multiplying $$5$$ and $$3\text{,}$$ the denominators of the fractions we had to multiply. The numerator $$2$$ came from multiplying $$1$$ and $$2\text{,}$$ the numerators of the fractions we had to multiply.

\begin{align*} \frac{1}{5}\cdot\frac{2}{3}\amp=\frac{1\cdot2}{5\cdot3}\\ \amp=\frac{2}{15} \end{align*}
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