A common denominator occurs when two or more fractions have the same denominator.

In order to add or subtract fractions, we need them to have a common denominator. All is not lost, however. We can put fractions over a common denominator.

To do this, we multiply both the top and bottom of each fraction by an equal amount.

For example, to add \(\dfrac{1}{5}\) and \(\dfrac{2}{3}\):

• Multiply \(\dfrac{1}{5}\) by \(\dfrac{3}{3}\) and multiply \(\dfrac{2}{3}\) by \(\dfrac{5}{5}\).
• Then \(\dfrac{1}{5}\) becomes the equivalent fraction \(\dfrac{3}{15}\), and \(dfrac{2}{3}\) becomes the equivalent fraction \(\dfrac{10}{15}\).
• These two fractions have the common denominator of \(15\), so we can add them!
• Calculate: \(\dfrac{3}{15} + \dfrac{10}{15} = \dfrac{13}{15}\ ).