# How do you simplify (4/5)/(6 2/3)?

Apr 6, 2017

When you see a mixed number, get rid of it!

#### Explanation:

$6 \frac{2}{3} = \frac{20}{3}$.

Therefore, your complex fraction is equivalent to

$\frac{\frac{4}{5}}{\frac{20}{3}}$.

Now you are simply dividing two ordinary fractions. "Invert and multiply."

Apr 6, 2017

$\frac{3}{25}$

#### Explanation:

To simplify $\frac{4}{5} \div 6 \frac{2}{3}$ follow the steps shown, changing any

$\textcolor{b l u e}{\text{ mixed numbers to improper fractions}}$

$\Rightarrow 6 \frac{2}{3} = \frac{20}{3}$

• " leave the first fraction"

• " change division to multiplication"

• " invert (turn upside down) the second fraction"

• " cancel, if possible, and simplify"

$\Rightarrow \frac{4}{5} \times \frac{3}{20} \leftarrow \textcolor{red}{\text{ multiply and invert}}$

$= {\cancel{4}}^{1} / 5 \times \frac{3}{\cancel{20}} ^ 5 \leftarrow \textcolor{red}{\text{ cancelling by 4}}$

Multiply remaining values on numerator/denominator.

$= \frac{1 \times 3}{5 \times 5}$

$= \frac{3}{25}$

Apr 6, 2017

$\frac{3}{25}$

#### Explanation:

The complex fraction $\frac{\frac{4}{5}}{6 \frac{2}{3}}$ can also be written as:

$\left(\frac{4}{5}\right) \div \left(6 \frac{2}{3}\right) \text{ }$ change to improper fractions

$= \frac{4}{5} \div \frac{20}{3} \text{ } \leftarrow$ multiply by the reciprocal

$= \frac{\cancel{4}}{5} \times \frac{3}{\cancel{20}} ^ 5$

$= \frac{3}{25}$