# How do you simplify 3 3/5 div 2 1/2?

Feb 15, 2017

See the entire simplification process below:

#### Explanation:

First, we need to convert these mixed fractions to improper fractions by multiplying the integer portion of the mixed fraction by the appropriate form of $1$ and then adding the result to the fraction portion of the mixed fraction:

$3 \frac{3}{5} \div 2 \frac{1}{2}$ becomes:

$\left(\left(3 \times \frac{5}{5}\right) + \frac{3}{5}\right) \div \left(\left(2 \times \frac{2}{2}\right) + \frac{1}{2}\right)$

$\left(\frac{15}{5} + \frac{3}{5}\right) \div \left(\frac{4}{2} + \frac{1}{2}\right)$

$\frac{18}{5} \div \frac{5}{2}$

We can rewrite this as:

$\frac{\frac{18}{5}}{\frac{5}{2}}$

Now, we can use this rule for dividing fractions to obtain the result:

$\frac{\frac{\textcolor{red}{a}}{\textcolor{b l u e}{b}}}{\frac{\textcolor{g r e e n}{c}}{\textcolor{p u r p \le}{d}}} = \frac{\textcolor{red}{a} \times \textcolor{p u r p \le}{d}}{\textcolor{b l u e}{b} \times \textcolor{g r e e n}{c}}$

$\frac{\frac{\textcolor{red}{18}}{\textcolor{b l u e}{5}}}{\frac{\textcolor{g r e e n}{5}}{\textcolor{p u r p \le}{2}}} = \frac{\textcolor{red}{18} \times \textcolor{p u r p \le}{2}}{\textcolor{b l u e}{5} \times \textcolor{g r e e n}{5}} = \frac{36}{25}$

Or

$\frac{25 + 11}{25} = \frac{25}{25} + \frac{11}{25} = 1 + \frac{11}{25} = 1 \frac{11}{25}$