# How do you find the quotient of a number and 4 is 6?

Sep 7, 2015

The number is either $24$ or $\frac{2}{3}$

#### Explanation:

Let the number be designated by $n$

quotient: number obtained by division (definition)

"quotient of a number and 4" $\leftrightarrow \textcolor{red}{\frac{n}{4}} \mathmr{and} \textcolor{b l u e}{\frac{4}{n}}$

"quotient of a number and 4 is 6"
$\leftrightarrow \textcolor{red}{\frac{n}{4} = 6} \mathmr{and} \textcolor{b l u e}{\frac{4}{n} = 6}$

$\textcolor{red}{n = 24} \mathmr{and} \textcolor{b l u e}{n = \frac{4}{6} = \frac{2}{3}}$