# How do you simplify 1\frac{5}{8}\times 3\frac{1}{5}?

Nov 18, 2016

You first convert each mixed fraction to an improper fraction:

#### Explanation:

$1 + \frac{5}{8} = 1 \times \frac{8}{8} + \frac{5}{8} = \frac{8 + 5}{8} = \frac{13}{8}$

$3 + \frac{1}{5} = 3 \times \frac{5}{5} + \frac{1}{5} = \frac{15 + 1}{5} = \frac{16}{5}$

Now we multiply:
$\frac{13}{8} \times \frac{16}{5} = \frac{13 \times 16}{8 \times 5}$

We can cancel by factoring:
$\frac{13 \times 2 \times \cancel{8}}{5 \times \cancel{8}} = \frac{26}{5}$

Now take the $\frac{5}{5}$ 's out for the whole number:
$5 \times \frac{5}{5} + \frac{1}{5} = 5 \frac{1}{5}$

Nov 19, 2016

Very details working out so you can see all the steps.

$5 \frac{1}{5}$

#### Explanation:

$\textcolor{g r e e n}{\left[\textcolor{red}{1} + \frac{5}{8}\right] \times \left[\textcolor{red}{\left(3 \times 1\right)} + \frac{1}{5}\right]}$

$\textcolor{g r e e n}{\left[\textcolor{red}{\frac{8}{8}} + \frac{5}{8}\right] \times \left[\textcolor{red}{\left(3 \times \frac{5}{5}\right)} + \frac{1}{5}\right]}$

$\textcolor{g r e e n}{\left[\textcolor{red}{\frac{8}{8}} + \frac{5}{8}\right] \times \left[\textcolor{red}{\frac{15}{5}} + \frac{1}{5}\right]}$

$\left[\frac{13}{8}\right] \times \left[\frac{16}{5}\right]$

Cancelling out the 8's

$\frac{13 \times 16}{8 \times 5} = \frac{13 \times {\cancel{16}}^{2}}{{\cancel{8}}^{1} \times 5} = \frac{26}{5}$

Write $\frac{26}{5}$ as $\text{ } \frac{25}{5} + \frac{1}{5}$

Cancelling out the 5's

$= \frac{{\cancel{25}}^{5}}{{\cancel{5}}^{1}} + \frac{1}{5} \text{ " =" } 5 \frac{1}{5}$