Example 1.2.13

Suppose a recipe calls for \(\frac{2}{3}\) cup of milk, but we’d like to quadruple the recipe (make it four times as big). We'll need four times as much milk, and one way to measure this out is to fill a measuring cup to \(\frac{2}{3}\) full, four times:

When you count up the shaded thirds, there are eight of them. So multiplying \(\frac{2}{3}\) by the whole number \(4\text{,}\) the result is \(\frac{8}{3}\text{.}\) Mathematically:

\begin{align*} 4\cdot\frac{2}{3}\amp=\frac{4\cdot2}{3}\\ \amp=\frac{8}{3} \end{align*}