# What is 2/3+10/15?

Feb 13, 2017

#### Explanation:

The denominator of $\frac{2}{3}$ is $3$

and denominator of $\frac{10}{15}$ is $15$

We can add two fractions only if their denominators are same or common.

As a fraction $\frac{2}{3}$ does not change when numerator and denominator are multiplied by same number,

hence to find common denominator, we will have to multiply numerator and denominator of each fraction are by a number (albeit different numbers), so that denominators become same.

This is done by identifying Least Common Multiple (LCM) of the two denominators.

Here LCM of $3$ and $15$ is $15$ and hence we can convert both denominators tp $15$, but in second fraction, it is already so.

Hence multiplying numerator and denominator of first by $5$, we get $\frac{2 \times 5}{3 \times 5} = \frac{10}{15}$

Hence, $\frac{2}{3} + \frac{10}{15} = \frac{10}{15} + \frac{10}{15} = \frac{20}{15}$.

Feb 14, 2017

$\frac{4}{3}$ or $1 \frac{1}{3}$

#### Explanation:

$\frac{2}{3} + \frac{10}{15}$

$\therefore \frac{10 + 10}{15}$

$\therefore {\cancel{20}}^{4} / {\cancel{15}}^{3}$

$\therefore \frac{4}{3}$ or$1 \frac{1}{3}$

2nd option:

$\therefore \frac{2}{3} + {\cancel{10}}^{2} / {\cancel{15}}^{3}$

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

$\frac{4}{3}$ or $1 \frac{1}{3}$