Question

A recipe requires 1/3 cup of milk for each 1/4 cup of water. How many cups of water are needed for each cup of milk?

Answer 1

D) 1 1/3

(1/3) x reciprocal of 1/4 so (4/1) = 4/3 which simplifies to 1 1/3 

Answer 2

$\bf \begin{array}{ccllll} milk&water\\ \textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\ \frac{1}{3}&\frac{1}{4}\\ 1&x \end{array}\implies \cfrac{\frac{1}{3}}{1}=\cfrac{\frac{1}{4}}{x}\implies \cfrac{\frac{1}{3}}{\frac{1}{1}}=\cfrac{\frac{1}{4}}{\frac{x}{1}} \\\\\\ \cfrac{1}{3}\cdot \cfrac{1}{1}=\cfrac{1}{4}\cdot \cfrac{1}{x}\implies \cfrac{1}{3}=\cfrac{1}{4x}\implies 4x=3\implies x=\cfrac{3}{4}$