How to Add Fractions with Different Denominators

A denominator tells you what size the pieces are. Halves and thirds are different sizes, so you can't count them together yet. A common denominator cuts both fractions into pieces of the same size.

The method

Find a number both denominators divide into.
Rewrite each fraction with that denominator.
Add the numerators and keep the denominator.
Simplify if you can.

Example: $\frac{1}{2} + \frac{1}{3}$

Both 2 and 3 divide into 6.

$\frac{1}{2} = \frac{3}{6}$ and $\frac{1}{3} = \frac{2}{6}$

$\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$

Example: $\frac{2}{3} + \frac{1}{4}$

Both 3 and 4 divide into 12.

$\frac{2}{3} = \frac{8}{12}$ and $\frac{1}{4} = \frac{3}{12}$

$\frac{8}{12} + \frac{3}{12} = \frac{11}{12}$

Common mistake

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

This can't be right: $\frac{2}{5}$ is less than $\frac{1}{2}$ , yet we added something to $\frac{1}{2}$ . The correct answer is $\frac{5}{6}$ .

Asking whether an answer is bigger or smaller than expected catches many fraction errors.

Try it yourself

$\frac{1}{4} + \frac{1}{8}$
Show answer
$\frac{3}{8}$
$\frac{3}{5} + \frac{1}{10}$
Show answer
$\frac{7}{10}$
$\frac{5}{6} - \frac{1}{4}$
Show answer
$\frac{7}{12}$