Add and Subtract Fractions

It can often be difficult to add and subtract fractions since you must always make sure they have the same denominators.

Adding and Subtracting Fractions with the Same Denominator

If fractions have the same denominator, simply add or subtract the numerators and keep the denominator the same:

\[\frac{3}{8} + \frac{2}{8} = \frac{3+2}{8} = \frac{5}{8}\]

\[\frac{5}{7} + \frac{3}{7} = \frac{5-3}{7} = \frac{2}{7}\]

Adding and Subtracting Fractions with Different Denominators

To add or subtract fractions with different denominators, first find a common denominator (usually the least common multiple of the denominators), then adjust the numerators accordingly.

\[\frac{1}{4} + \frac{1}{6}\]

Find the common denominator.

4 times table = 4, 8, 12, 16, ...

6 times table = 6, 12, 18, 24, ...

Common denominator = 12

Rewrite each fraction with the common denominator.

\[\frac{1}{4} = \frac{3}{12}, \quad \frac{1}{6} = \frac{2}{12}\]

Add or subtract the numerators.

\[\frac{3}{12} + \frac{2}{12} = \frac{5}{12}\]