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.

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

Equalize denominators

First, multiply two denominators.

$3\times{5}=15$

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

$\dfrac{2}{3}$ → $\dfrac{10}{15}$

$\dfrac{1}{5}$ → $\dfrac{3}{15}$

Add fractions

Add "NEW" fractions.

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

Summary

\[ \dfrac{2}{3}+\dfrac{1}{5}\\ =\dfrac{10}{15}+\dfrac{3}{15}\\ =\dfrac{13}{15} \]