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.


Equalize denominators

First, multiply two denominators.


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.



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