Question

Convert 6 2/3 cups to pints. Express your answer in simplest form.

Answer 1

First off, let's convert the mixed fraction to "improper", keeping in mind that, there are 2 cups in 1 pint.

$\bf \stackrel{mixed}{6\frac{2}{3}}\implies \cfrac{6\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{20}{3}} \\\\\\ \begin{array}{ccll} cups&pints\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 2&1\\\\ \frac{20}{3}&p \end{array}\implies \cfrac{\quad 2\quad }{\frac{20}{3}}=\cfrac{1}{p}\implies \cfrac{\quad \frac{2}{1}\quad }{\frac{20}{3}}=\cfrac{1}{p}$

$\bf \cfrac{2}{1}\cdot \cfrac{3}{20}=\cfrac{1}{p}\implies \cfrac{3}{10}=\cfrac{1}{p}\implies p=\cfrac{10\cdot 1}{3}\implies p=\cfrac{10}{3}\implies p=3\frac{1}{3}$