How to add fractions with different denominators (ex. 2/3 + 1/5)

Adding fractions with same denominators is OK. All we have to do is adding numerators. But if the denominators are different, that is difficult. Let’s calculate the below.

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

Equalize denominators

First, multiply two denominators.

$3\times 5=15$

Next, convert these fractions to “NEW” fractions with the same denominator.

$\frac{2}{3}$ → $\frac{10}{15}$

$\frac{1}{5}$ → $\frac{3}{15}$

Add fractions

Add “NEW” fractions.

$\frac{10}{15}+\frac{3}{15}=\frac{13}{15}$

Summary

$$\begin{gathered} \frac{2}{3}+\frac{1}{5} \\ =\frac{10}{15}+\frac{3}{15} \\ =\frac{13}{15} \end{gathered}$$