How do you divide 1\frac { 2} { 7} \div 3\frac { 3} { 7}?

Jul 16, 2017

See a solution process below:

Explanation:

Step 1 First, convert each mixed number into an improper fraction:

$1 \frac{2}{7} \div 3 \frac{3}{7} \implies \left(1 + \frac{2}{7}\right) \div \left(3 + \frac{3}{7}\right) \implies$

$\left(\left[\frac{7}{7} \times 1\right] + \frac{2}{7}\right) \div \left(\left[\frac{7}{7} \times 3\right] + \frac{3}{7}\right) \implies$

$\left(\frac{7}{7} + \frac{2}{7}\right) \div \left(\frac{21}{7} + \frac{3}{7}\right) \implies$

$\frac{9}{7} \div \frac{24}{7}$

Step 2) Rewrite the expression as:

$\frac{\frac{9}{7}}{\frac{24}{7}}$

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

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

$\frac{\frac{\textcolor{red}{9}}{\textcolor{b l u e}{7}}}{\frac{\textcolor{g r e e n}{24}}{\textcolor{p u r p \le}{7}}} \implies \frac{\textcolor{red}{9} \times \textcolor{p u r p \le}{7}}{\textcolor{b l u e}{7} \times \textcolor{g r e e n}{24}} \implies \frac{\textcolor{red}{9} \times \cancel{\textcolor{p u r p \le}{7}}}{\cancel{\textcolor{b l u e}{7}} \times \textcolor{g r e e n}{24}} \implies \frac{\textcolor{red}{3} \times \textcolor{red}{3}}{\textcolor{g r e e n}{3} \times \textcolor{g r e e n}{8}} \implies \frac{\cancel{\textcolor{red}{3}} \times \textcolor{red}{3}}{\cancel{\textcolor{g r e e n}{3}} \times \textcolor{g r e e n}{8}} \implies$

$\frac{3}{8}$