# How do you simplify 1/5 div 3/5?

Mar 16, 2018

The simplified answer is $\frac{1}{3}$.

#### Explanation:

You can use this nifty property when diving by fractions:

$\frac{a}{b} \div \frac{\textcolor{red}{c}}{\textcolor{b l u e}{d}} q \quad \implies q \quad \frac{a}{b} \times \frac{\textcolor{b l u e}{d}}{\textcolor{red}{c}}$

Just flip the fraction, and change it to multiplication. Here's this property applied to our problem:

$\textcolor{w h i t e}{=} \frac{1}{5} \div \frac{\textcolor{red}{3}}{\textcolor{b l u e}{5}}$

$= \frac{1}{5} \times \frac{\textcolor{b l u e}{5}}{\textcolor{red}{3}}$

$= \frac{1 \times \textcolor{b l u e}{5}}{5 \times \textcolor{red}{3}}$

$= \frac{1 \times \textcolor{red}{\cancel{\textcolor{b l u e}{5}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} \times \textcolor{red}{3}}$

$= \frac{1}{\textcolor{red}{3}}$

That's the most simplified it gets. Hope this helped!