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Add fractions

Enter two fractions, such as 2/3 and 1 3/4, and see the sum simplified, as a mixed number and as a decimal. The steps show how to find the common denominator.

For example 3/4, 1 1/2, −2 or 0.25.

Fill in the fields; the answer appears here straight away.

How it works

  1. Enter the values

    Type the numbers or the formula. Decimals may use a point or a comma. No idea? Click Fill in an example.

  2. Instant answer

    The answer appears as you type, with the most important intermediate values.

  3. See the working

    Under "How it's worked out" you see the steps, handy for checking your own calculation.

How to add fractions

  1. Make the denominators equal. For 2/3 + 1/4 the least common multiple of 3 and 4 is 12, so 2/3 = 8/12 and 1/4 = 3/12.
  2. Add the numerators. 8/12 + 3/12 = 11/12.
  3. Simplify if possible, by dividing the numerator and denominator by their greatest common divisor.

What can you enter?

Ordinary fractions (3/4), mixed numbers (1 1/2), whole numbers (−2) and decimals (0.25). Negative fractions work too. The calculation is exact, so there are no rounding errors. Also see subtract fractions and multiply fractions.

Worked example

Add 2/3 and 1 3/4. The mixed number is 7/4. The least common multiple of 3 and 4 is 12, so 2/3 = 8/12 and 7/4 = 21/12. The sum is 29/12, which is 2 5/12 as a mixed number and about 2.4167 as a decimal. That is exactly the example the calculator starts with.

Mistakes to avoid

  • Adding the denominators: 1/2 + 1/3 is 5/6, not 2/5. The denominator describes the size of the pieces, and you can only add pieces of the same size.
  • Forgetting to simplify: 1/6 + 1/3 = 3/6, which is 1/2.
  • Dropping the carry: 3/4 + 3/4 = 6/4 = 1 1/2, so the sum is larger than 1.

When both denominators are equal, simply add the numerators: 3/8 + 2/8 = 5/8. To find the common denominator yourself, use the LCM calculator.

Frequently asked questions

How do I add fractions with different denominators?

Rewrite both with a common denominator, usually the least common multiple, then add the numerators. For 2/3 + 1/4 the common denominator is 12: 8/12 + 3/12 = 11/12.

How do I add mixed numbers?

Turn them into improper fractions, add, and convert back. 1 3/4 + 2 3/4 is 7/4 + 11/4 = 18/4 = 4 1/2. The calculator accepts mixed numbers as you would write them, such as 1 3/4.

Can I add a fraction and a decimal?

Yes. The decimal is converted to an exact fraction first, so 0.25 + 1/3 gives 7/12 without rounding errors.

Is the answer always simplified?

Yes. If the sum can be reduced, the last step shows the division by the greatest common divisor, for example 3/6 becoming 1/2.