# How do you simplify 2/9 * 3/5 / (1/2 + 2/3)?

Jan 12, 2016

$\frac{4}{35}$

#### Explanation:

You need to solve the expression in the brackets first:

$\frac{1}{2} + \frac{2}{3}$

To do so, you must find the least common multiple (for $2$ and $3$, this is $6$) and extend the fractions to it:

$\frac{1}{2} + \frac{2}{3} = \frac{1 \cdot 3}{2 \cdot 3} + \frac{2 \cdot 2}{3 \cdot 2} = \frac{3}{6} + \frac{4}{6} = \frac{7}{6}$

So, now you have the following:

$\frac{2}{9} \cdot \frac{3}{5} \div \frac{7}{6}$

To divide by a fraction you need to multiply by its reciprocal, so basically, you "turn" the fraction $\frac{7}{6}$ and replace the division ("$/$ or $\div$) by multiplication ($\cdot$):

$\frac{2}{9} \cdot \frac{3}{5} \div \frac{7}{6} = \frac{2}{9} \cdot \frac{3}{5} \cdot \frac{6}{7} = \frac{2 \cdot 3 \cdot 6}{9 \cdot 5 \cdot 7} = \frac{2 \cdot \cancel{\textcolor{b l u e}{3}} \cdot 6}{\cancel{\textcolor{b l u e}{9}} \textcolor{b l u e}{3} \cdot 5 \cdot 7}$

$= \frac{2 \cdot \cancel{\textcolor{g r e e n}{6}} \textcolor{g r e e n}{2}}{\cancel{\textcolor{g r e e n}{3}} \cdot 5 \cdot 7} = \frac{4}{35}$