###### Example1.2.12

Say a recipe calls for $$\frac{2}{3}$$ cup of milk, but we’d like to double the recipe. One way to measure this out is to fill a measuring cup to $$\frac{2}{3}\text{,}$$ two times:

Altogether there are four thirds of a whole here. So $$\frac{2}{3} \cdot 2 = \frac{4}{3}\text{.}$$ The figure shows $$\frac{2}{3}$$ of two wholes. Two wholes can be written as $$2\text{,}$$ or as the fraction $$\frac{2}{1}\text{.}$$ So mathematically, our figure says

\begin{equation*} \frac{2}{3} \cdot 2 = \frac{2}{3} \cdot \frac{2}{1} = \frac{4}{3}\text{.} \end{equation*}
in-context