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\\ (1)/(3)&(2)/(3)\\\\ x&(1)/(3) \end{array}\implies \cfrac{(1)/(3)}{x}=\cfrac{(2)/(3)}{(1)/(3)} \\\\\\ \cfrac{(1)/(3)\cdot (1)/(3)}{(2)/(3)}=x\implies \cfrac{(1)/(9)}{(2)/(3)}=x\implies \cfrac{1}{9}\cdot \cfrac{3}{2}=x\implies \cfrac{1}{4}=x`