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

Jul 7, 2018

$\frac{37}{5}$

#### Explanation:

Given: $\left(2 \frac{1}{3} + 1 \frac{2}{5}\right) + 3 \frac{2}{3}$

First switch each mixed number to an improper fraction:

$\left(2 \frac{1}{3} + 1 \frac{2}{5}\right) + 3 \frac{2}{3} = \left(\frac{7}{3} + \frac{7}{5}\right) + \frac{11}{3}$

Find a common denominator for $33$ and $5 : \text{ } 15$

Multiply each fraction by $1$ to get our common denominator so we can add the fractions:

$\left(\frac{5}{5} \cdot \frac{7}{3} + \frac{3}{3} \cdot \frac{7}{5}\right) + \frac{5}{5} \cdot \frac{11}{3}$

$\left(\frac{35}{15} + \frac{21}{15}\right) + \frac{55}{15} = \frac{111}{15}$

Now reduce, since $1 + 1 + 1 = 3$ which means $111$ is divisable by $3$:

$\frac{111}{15} \div \frac{3}{3} = \frac{37}{5}$