How do you divide 6\frac { 7} { 15} \div 2\frac { 9} { 14}?

May 9, 2017

See a solution process below:

Explanation:

First, convert each mixed fraction to an improper fraction:

$6 \frac{7}{15} \div 2 \frac{9}{14} \implies \left(\left(\frac{15}{15} \times 6\right) + \frac{7}{15}\right) \div \left(\left(\frac{14}{14} \times 2\right) + \frac{9}{14}\right)$

$\implies \left(\frac{90}{15} + \frac{7}{15}\right) \div \left(\frac{28}{14} + \frac{9}{14}\right) \implies \frac{97}{15} \div \frac{37}{14}$

We can rewrite this as:

$\frac{\frac{97}{15}}{\frac{37}{14}}$

Now, we can use this rule for dividing fractions to complete the division:

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

$\frac{\frac{\textcolor{red}{97}}{\textcolor{b l u e}{15}}}{\frac{\textcolor{g r e e n}{37}}{\textcolor{p u r p \le}{14}}} \implies \frac{\textcolor{red}{97} \times \textcolor{p u r p \le}{14}}{\textcolor{b l u e}{15} \times \textcolor{g r e e n}{37}} \implies \frac{1358}{555} \implies \frac{1110 + 248}{555} \implies \frac{1110}{555} + \frac{248}{555} \implies$

$2 + \frac{248}{555} \implies 2 \frac{248}{555}$