Question

A teapot is 1/3 full of tea. When all of the tea is poured into an empty container, the container ie 2/3 full. What fraction of the tea from a full teapot is needed to fill 1 entire container?

Answer 1

so.. we took 1/3 that was in the teapot, dumped it into the container, and the container ended up 2/3 of the way, now, to fill the container, all we need is really 1/3, because 2/3 + 1/3 is 3/3 or 1 whole

so.. how much is 1/3 of the container, in teapot's terms?

well     $\bf \begin{array}{ccllll} teapot&container\\ \textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\ \frac{1}{3}&\frac{2}{3}\\\\ x&\frac{1}{3} \end{array}\implies \cfrac{\frac{1}{3}}{x}=\cfrac{\frac{2}{3}}{\frac{1}{3}} \\\\\\ \cfrac{\frac{1}{3}\cdot \frac{1}{3}}{\frac{2}{3}}=x\implies \cfrac{\frac{1}{9}}{\frac{2}{3}}=x\implies \cfrac{1}{9}\cdot \cfrac{3}{2}=x\implies \cfrac{1}{4}=x$