Adding and subtracting fractions with different denominators

Why we need the same denominator

We can only add or subtract fractions if they divide the same whole into equal parts. If the denominators are different, we must first make them the same: this is called converting to a common denominator.

Finding a common denominator

The method involves multiplying both the numerator and denominator of each fraction by the same number, so that the two denominators become equal. The simplest way is often to multiply the two denominators together, or to use their lowest common multiple (LCM).

Simple example

1/2 + 1/3

Common denominator: 2 × 3 = 6

• 1/2 = 3/6 (we multiply the numerator and denominator by 3)
• 1/3 = 2/6 (we multiply both the numerator and denominator by 2)

So 1/2 + 1/3 = 3/6 + 2/6 = 5/6

Example using the LCM

1/4 + 1/6, LCM(4, 6) = 12

• 1/4 = 3/12
• 1/6 = 2/12

So 1/4 + 1/6 = 3/12 + 2/12 = 5/12

Common pitfall

When changing the denominator, you must never forget to multiply the numerator by the same number as well. Multiplying only the denominator changes the value of the fraction, which is a common mistake.