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

Jul 16, 2017

See a solution process below:

#### Explanation:

Step 1) Convert the mixed numbers into improper fractions:

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

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

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

$\frac{7}{5} \div \frac{5}{4}$

Step 2) Rewrite the expression as:

$\frac{\frac{7}{5}}{\frac{5}{4}}$

Step 3) Use this rule for dividing fractions to evaluate the expression:

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

$\frac{\frac{\textcolor{red}{7}}{\textcolor{b l u e}{5}}}{\frac{\textcolor{g r e e n}{5}}{\textcolor{p u r p \le}{4}}} \implies \frac{\textcolor{red}{7} \times \textcolor{p u r p \le}{4}}{\textcolor{b l u e}{5} \times \textcolor{g r e e n}{5}} \implies \frac{28}{25}$