# How do you simplify 7/8 div 3/4?

Aug 24, 2016

$\frac{7}{6}$

#### Explanation:

To make the division into a multiplication question, which are the easiest to solve, all you do is flip the right-hand fraction upside down and change the divide to a multiply. So it becomes:

$\frac{7}{8} \times \frac{4}{3}$

Cancel the 4 on the top with the eight on the bottom and you are left with:

$\frac{7}{\cancel{8}} ^ 2 \times \frac{\cancel{4}}{3} \rightarrow \frac{7}{2} \times \frac{1}{3}$

Multiply the top numbers together and the bottom numbers together, and you get the final answer:

$\frac{7}{6}$

Aug 24, 2016

Write the equation as a complex fraction. and then simply the problem.

#### Explanation:

$\frac{7}{8}$ is a division, it means 7 divided by 8.

$\frac{3}{4}$ is a division, it means 3 divided by 4

$\frac{7}{8}$ divided by $\frac{3}{4}$ can be written as one division.
$\frac{\frac{7}{8}}{\frac{3}{4}}$

Now use the multiplicative inverse to make the bottom fraction (the denominator) $\frac{3}{4}$ disappear

Multiply both the bottom fraction (denominator) and the top fraction($\frac{7}{8}$) (numerator) by the multiplicative inverse $\frac{4}{3}$

$\left(\frac{7}{8}\right) \times \frac{\frac{4}{3}}{\frac{3}{4} \times \frac{4}{3}}$

$\left(\frac{3}{4}\right) \times \left(\frac{4}{3}\right)$ = 1

leaving $\left(\frac{7}{8}\right) \times \left(\frac{4}{3}\right) = \frac{28}{24} = \frac{7}{6} = 1 \frac{1}{6}$