Adding and subtracting fractions with unlike denominators

Adding and subtracting fractions with unlike denominators

Adding and subtracting fractions with unlike denominators

When two fractions have the same denominator, you just add or subtract the numerators. When they have different denominators, you first have to make them match — find a common denominator.

Why you can't add them straight away

A fraction tells you how many equal pieces the whole is split into. 1/2 and 1/3 are different-sized pieces, so you cannot simply add them. First you turn them into pieces of the same size.

Step by step

  1. Find a common denominator — the lowest common multiple (LCM) of the two denominators.
  2. Rewrite each fraction with that denominator (multiply the numerator and denominator by the same number).
  3. Add or subtract the numerators; the denominator stays the same.
  4. Simplify the result to its lowest terms.

Example — addition

Work out 1/2 + 1/3.

  1. The common denominator of 2 and 3 is 6.
  2. Rewrite: 1/2 = 3/6, 1/3 = 2/6.
  3. Add: 3/6 + 2/6 = 5/6.
  4. 5/6 cannot be simplified.

Result: 1/2 + 1/3 = 5/6.

Example — subtraction

Work out 3/4 − 1/6.

  1. The common denominator of 4 and 6 is 12.
  2. Rewrite: 3/4 = 9/12, 1/6 = 2/12.
  3. Subtract: 9/12 − 2/12 = 7/12.
  4. 7/12 cannot be simplified.

Result: 3/4 − 1/6 = 7/12.

Checking your answer

  • Estimate the size: 1/2 + 1/3 is a little under 1 — and 5/6 really is just below 1. ✓
  • Simplify: if the result can be reduced (e.g. 4/8), write it in lowest terms (1/2).

Common traps

  • Adding the denominators. 1/2 + 1/3 is not 2/5! The denominator does not change when you add — you make it match first.
  • Rewriting only one fraction. You must adjust both fractions to the common denominator.
  • Forgetting to simplify. Always write the result in lowest terms.

Try it yourself