Adding and subtracting fractions

If you were to add \frac{1}{2} and \frac{1}{3}, it is hard to picture what the answer would be. Rewriting the fractions with a common bottom number, or denominator (in this case, {6}), makes it easier.

curriculum-key-fact
Remember, you can only add and subtract fractions when the bottom numbers, or denominators, are the same.

So, to add or subtract fractions:

  1. Change the fractions so they have the same denominator.
  2. Add or subtract the top numbers, or numerators.

Example

\frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}

\frac{7}{10} - \frac{2}{5} = \frac{7}{10} - \frac{4}{10} = \frac{3}{10}

Question

What is \frac{1}{4} + \frac{1}{3} = ?

Diagram showing 1/4 + 1/3 = ?

\frac{1}{4} + \frac{1}{3}= \frac{3}{12} + \frac{4}{12} = \frac{7}{12}

Diagram showing 3/12 + 4/12 = 7/12

Mixed numbers

To add or subtract mixed numbers, it is usually easiest to change them to improper fractions first and then change the answer back into a mixed number (if needed).

Question

3 \frac{1}{3} + 4 \frac{1}{2} = ?

3 \frac{1}{3} + 4 \frac{1}{2} = \frac{10}{3} + \frac{9}{2} = \frac{20}{6} + \frac{27}{6} = \frac{47}{6} = 7 \frac{5}{6}