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

Feb 1, 2017

See the entire simplification process below:

#### Explanation:

First, convert the compound fractions to improper fractions:

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

$\left(\frac{15}{5} + \frac{2}{5}\right) \div \left(\frac{6}{2} + \frac{1}{2}\right) \to$

$\frac{17}{5} \div \frac{7}{2}$

We can now rewrite this expression as:

$\frac{\frac{17}{5}}{\frac{7}{2}}$

We can now use this rule for dividing fractions:

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

Substituting and calculating gives:

$\frac{\frac{\textcolor{red}{17}}{\textcolor{b l u e}{5}}}{\frac{\textcolor{g r e e n}{7}}{\textcolor{p u r p \le}{2}}} = \frac{\textcolor{red}{17} \times \textcolor{p u r p \le}{2}}{\textcolor{b l u e}{5} \times \textcolor{g r e e n}{7}} = \frac{34}{35}$