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

Jul 29, 2016

$= \frac{31}{30}$

#### Explanation:

$\frac{1}{3} + \frac{1}{2} + \frac{1}{5}$
$= \frac{10 + 15 + 6}{30}$
$= \frac{31}{30}$

Jul 29, 2016

To add fractions, you must have common denominators. So, you need to get the bottom numbers to be the same.

The least common multiple of $3$, $2$, and $5$ is $30$, since $3 \times 2 \times 5 = 30$, and $3$, $2$, and $5$ are all prime numbers.

Therefore, you just need to get $30$ in the denominators by multiplying by unit fractions. i.e. $\frac{x}{x} = \frac{y}{y} = \frac{z}{z} = 1$.

$\frac{1}{3} \cdot \stackrel{= 1}{\overbrace{\frac{10}{10}}} + \frac{1}{2} \cdot \stackrel{= 1}{\overbrace{\frac{15}{15}}} + \frac{1}{5} \cdot \stackrel{= 1}{\overbrace{\frac{6}{6}}}$

$= \frac{10}{30} + \frac{15}{30} + \frac{6}{30}$

$= \textcolor{b l u e}{\frac{31}{30}}$

Or, if you know your decimals...

$\frac{1}{3} + \frac{1}{2} + \frac{1}{5}$

$= 0. \overline{33} + 0.5 + 0.2$

$= 1.0 \overline{33}$.

Since $0.0 \overline{33} = \frac{0. \overline{33}}{10} = \frac{1}{3} \cdot \frac{1}{10} = \frac{1}{30}$,

$1.0 \overline{33} = \frac{1}{30} + \frac{30}{30} = \textcolor{b l u e}{\frac{31}{30}}$.