# How do you write your answer in simplest form given 7/12 div 2/9?

Nov 16, 2016

$\frac{21}{8}$

#### Explanation:

First we perform the arithmetic functions to arrive at a single fraction. Then we simplify it to the smallest numerical values possible.

$\frac{\frac{7}{12}}{\frac{2}{9}} = \left(\frac{7}{12}\right) \cdot \left(\frac{9}{2}\right) = \frac{63}{24}$ Divide this fraction by 3 to get $\frac{21}{8}$.

This cannot be simplified further as 21 and 8 have no more common factors.

Nov 16, 2016

$\frac{21}{8} = 2 \frac{5}{8}$

#### Explanation:

Dividing by a fraction is the same as multiplying by its reciprocal.

$\frac{7}{12} \div \frac{2}{9}$
$\textcolor{w h i t e}{\times .} \downarrow$
=$\frac{7}{12} \times \frac{9}{2} \text{ } \leftarrow$ cancel wherever possible through x.

$\frac{7}{\cancel{12}} ^ 4 \times {\cancel{9}}^{3} / 2$

Dividing first makes the numbers smaller.
Now multiply straight across..

$\frac{21}{8}$

=$2 \frac{5}{8}$