Adding Fractions

When adding fractions, the first thing to check is if the denominators are the same.

Adding Fractions with Like Denominators

Fractions with the same denominators are called like fractions.

To add fractions with like denominators, add the numerators , and write the sum over the denominator.

$\frac{3}{8} + \frac{2}{8} = \frac{5}{8}$

Example :

Find $\frac{4}{9} + \frac{3}{9}$ .

Since the denominators are the same, add the numerators.

$= \frac{4 + 3}{9}$

$= \frac{7}{9}$

You may get an answer which is not in lowest terms , even if the fractions you were adding and subtracting both were. In this case, you have to reduce the fraction .

$\frac{7}{12} + \frac{1}{12} = \frac{8}{12} = \frac{8 \div 4}{12 \div 4} = \frac{2}{3}$

Adding Fractions with Unlike Denominators

If the denominators are not the same, then you have to use equivalent fractions which do have a common denominator . To do this, you need to find the least common multiple (LCM) of the two denominators.

For example, suppose you want to add:

$\frac{1}{11} + \frac{2}{3}$

1/11 + 2/3

The LCM of $3$ and $11$ is $33$ . So, we need to find fractions equivalent to $\frac{1}{11}$ and $\frac{2}{3}$ which have $33$ in the denominator. Multiply the numerator and denominator of $\frac{1}{11}$ by $3$ , and multiply the numerator and denominator of $\frac{2}{3}$ by $11$ .

$(\frac{1 \times 3}{11 \times 3}) + (\frac{2 \times 11}{3 \times 11}) = \frac{3}{33} + \frac{22}{33}$

Now we have like denominators, and we can add as described above.

$= \frac{25}{33}$

3/33 + 22/33 = 25/33