# What is 1 1/15 + 3 3/10 - 2 4/5?

Jun 26, 2018

See a solution process below:

#### Explanation:

First, convert each mixed number to an improper fraction:

$1 \frac{1}{15} = 1 + \frac{1}{5} = \left(\frac{15}{15} \times 1\right) + \frac{1}{15} \frac{15}{15} + \frac{1}{15} = \frac{15 + 1}{15} = \frac{16}{15}$

$3 \frac{3}{10} = 3 + \frac{3}{10} = \left(\frac{10}{10} \times 3\right) + \frac{3}{10} = \frac{30}{10} + \frac{3}{10} = \frac{30 + 3}{10} = \frac{33}{10}$

$2 \frac{4}{5} = 2 + \frac{4}{5} = \left(\frac{5}{5} \times 2\right) + \frac{4}{5} = \frac{10}{5} + \frac{4}{5} = \frac{10 + 4}{5} = \frac{14}{5}$

We can rewrite the expression as:

$\frac{16}{15} + \frac{33}{10} + \frac{14}{5}$

To add fractions they must be over common denominators. We can multiply each fraction by the appropriate form of $1$ and then add the numerators:

$\left(\frac{2}{2} \times \frac{16}{15}\right) + \left(\frac{3}{3} \times \frac{33}{10}\right) + \left(\frac{6}{6} \times \frac{14}{5}\right) \implies$

$\frac{2 \times 16}{2 \times 15} + \frac{3 \times 33}{3 \times 10} + \frac{6 \times 14}{6 \times 5} \implies$

$\frac{32}{30} + \frac{99}{30} + \frac{84}{30} \implies$

$\frac{32 + 99 + 84}{30} \implies$

$\frac{131 + 84}{30} \implies$

$\frac{215}{30}$

If necessary, we can convert this to a mixed number:

$\frac{215}{30} = \frac{210 + 5}{30} = \frac{210}{30} + \frac{5}{30} = 7 + \frac{5}{30} = 7 + \frac{1}{6} = 7 \frac{1}{6}$