Question

Francine uses 2/3 cup of pineapple juice for every 1/3 cup of orange juice to make a smoothie. Enter the number of cups of pineapple juice Francine uses for 1 cup of orange juice.

Answer 1

$\bf \begin{array}{ccllll} pineapple&orange\\ \textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\ \frac{2}{3}&\frac{1}{3}\\\\ x&1 \end{array}\implies \cfrac{\frac{2}{3}}{x}=\cfrac{\frac{1}{3}}{1}\implies \cfrac{\frac{2}{3}}{\frac{x}{1}}=\cfrac{\frac{1}{3}}{\frac{1}{1}}\\\\ -----------------------------$

$\bf \textit{now recall that }\qquad \cfrac{\frac{a}{b}}{\frac{c}{{{ d}}}}\implies \cfrac{a}{b}\cdot \cfrac{{{ d}}}{c}\\\\ -----------------------------\\\\ \cfrac{2}{3}\cdot \cfrac{1}{x}=\cfrac{1}{3}\cdot \cfrac{1}{1}\implies \cfrac{2}{3x}=\cfrac{1}{3}\implies 2\cdot 3=1\cdot 3x\implies 6=3x \\\\\\ \cfrac{6}{3}=x$

and surely, you know how much that is