La Fonction

Fraction adding calculator

The calculator on this page handles the two multiplications and the addition that adding fractions needs. The three steps below turn any pair of fractions into a single answer, with a worked example and the mistake to avoid.

12 × 12 = 144

Adding 12 to itself 12 times gives the same answer.

Add two fractions in three steps

Take 2/3 + 1/4. The bottom numbers are different, so they have to be made the same before anything is added.

  1. Multiply the two bottom numbers: 3 × 4 = 12. That is the new bottom number.
  2. Cross-multiply the tops: 2 × 4 = 8, and 1 × 3 = 3.
  3. Add those two results: 8 + 3 = 11. The answer is 11/12.

That order works for every pair of fractions.

When the bottom numbers already match

Add the tops and leave the bottom alone. 3/8 + 2/8 = 5/8. Do not add the bottom numbers as well: 1/2 + 1/2 is 1, not 2/4. That slip is behind most wrong answers here.

Reducing the answer

Cross-multiplying always gives a correct answer, but not always the tidiest one. Divide top and bottom by the biggest number that goes into both.

  • 1/4 + 1/4 gives 8/16, which reduces to 1/2.
  • 1/6 + 1/3 gives 9/18, which reduces to 1/2.
  • 1/2 + 1/3 gives 5/6, already as small as it goes.

Mixed numbers

Deal with the whole numbers on their own. For 2 1/2 + 1 3/4: 2 + 1 = 3, and 1/2 + 3/4 = 10/8, which is 1 1/4. Put them together for 4 1/4.

If the answer looks wrong

  • A top number bigger than the bottom is not an error. 5/4 is a real answer; it means 1 1/4.
  • Check that you multiplied across the diagonal, not straight down.
  • A very large bottom number usually means the two denominators shared a factor. The result is still right, it just needs reducing.
  • Want it as a decimal? Divide the top by the bottom. Going the other way, turn a decimal back into a fraction.

For a fraction plus an ordinary number, use the whole number fraction calculator. To find a missing value inside a fraction, try solve for x in a fraction. The rest of the tools sit on the calculators page.