# How do you divide 1\frac { 1} { 2} \div 1\frac { 4} { 5}?

Jul 14, 2017

See a solution process below:

#### Explanation:

First we need to convert the two mixed numbers into improper fractions:

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

$\left(\left[\frac{2}{2} \times 1\right] + \frac{1}{2}\right) \div \left(\left[\frac{5}{5} \times 1\right] + \frac{4}{5}\right) \implies$

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

$\frac{3}{2} \div \frac{9}{5}$

We can next rewrite this expression as:

$\frac{3}{2} \div \frac{9}{5} \implies \frac{\frac{3}{2}}{\frac{9}{5}}$

We can now use this rule for dividing fractions to evaluate the expression:

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

$\frac{\frac{\textcolor{red}{3}}{\textcolor{b l u e}{2}}}{\frac{\textcolor{g r e e n}{9}}{\textcolor{p u r p \le}{5}}} \implies \frac{\textcolor{red}{3} \times \textcolor{p u r p \le}{5}}{\textcolor{b l u e}{2} \times \textcolor{g r e e n}{9}} \implies \frac{\cancel{\textcolor{red}{3}} \times \textcolor{p u r p \le}{5}}{\textcolor{b l u e}{2} \times \cancel{\textcolor{g r e e n}{9}} 3} \implies$

$\frac{5}{6}$