# How do you simplify 7/9 div (3/4 - 1/3)?

Apr 16, 2015

The answer is $\frac{28}{15}$.

Firstly, subtract $\frac{3}{4}$ and $\frac{1}{3}$. To do that, find a common denominator, convert the fractions, and do the subtraction. Common denominator for 4 and 3 is 12.

$\frac{3}{4} - \frac{1}{3} = \frac{9}{12} - \frac{4}{12} = \frac{5}{12}$

Plug your result into the original equation:

$\frac{7}{9} \div \left(\frac{3}{4} - \frac{1}{3}\right) = \frac{7}{9} \div \frac{5}{12}$

To divide fractions, turn the second fraction into its reciprocal and multiple the two fractions. Reciprocal of $\frac{5}{12}$ is $\frac{12}{5}$ (just flip the fraction upside down).

$\frac{7}{9} \div \frac{5}{12} = \frac{7}{9} \cdot \frac{12}{5} = \frac{7}{\cancel{9} 3} \cdot \frac{\cancel{12} 4}{5} = \frac{28}{15}$