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Adding Fractions Calculator

Enter two fractions and this fraction addition calculator shows the sum, the least common denominator it used, and every step in between.

Adding fractions is the operation where the denominators actually matter. You cannot add thirds to fifths any more than you can add centimetres to inches: the pieces are different sizes, so the numerators are not comparable yet. The fix is to rewrite both fractions so they are cut into pieces of the same size, which means finding a common denominator, and then the addition itself is trivial because you are just counting pieces. That is the entire concept, and it is why the single most common wrong answer in fraction addition comes from adding the denominators together as well as the numerators.

This calculator walks the whole route. It finds the least common denominator of the two fractions you enter, shows what each fraction becomes when rewritten over that denominator, adds the numerators, reduces the result to lowest terms, and converts it to a mixed number if the sum passes 1. When the denominators already match it says so and skips the rewriting, which is worth seeing: it makes clear that the extra work exists only to line the pieces up. Every answer also comes with a reverse check, subtracting one fraction back off the sum to land on the other, so you can confirm the result rather than trusting it. Mixed numbers work fine here, just convert them to improper fractions before you type them in.

Worked example: 2/3 + 1/5

  1. Compare the denominators. 3 and 5 are different, so the fractions have to be rewritten before they can be added.
  2. Find the least common denominator. 3 and 5 share no factors, so the least common denominator is 3 × 5 = 15.
  3. Rewrite the first fraction. Multiply top and bottom by 5: 2/3 = 10/15.
  4. Rewrite the second fraction. Multiply top and bottom by 3: 1/5 = 3/15.
  5. Add the numerators. 10 + 3 = 13, and the denominator stays 15, giving 13/15.
  6. Simplify. 13 is prime and does not divide 15, so 13/15 is already in simplest form.
  7. Check. 13/15 − 3/15 = 10/15 = 2/3, the fraction you started with.
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Two more cases worth seeing

Matching denominators: 3/8 + 5/8

  • The denominators are both 8, so nothing needs rewriting.
  • Add the numerators: 3 + 5 = 8.
  • Keep the denominator: the sum is 8/8.
  • Simplify: 8/8 = 1.

Three eighths plus five eighths is eight eighths, one whole. If you had added the denominators too you would have got 8/16, which is a half, and clearly wrong.

A sum bigger than 1: 5/6 + 3/4

  • The least common denominator of 6 and 4 is 12, not 24.
  • Rewrite: 5/6 = 10/12, and 3/4 = 9/12.
  • Add the numerators: 10 + 9 = 19, giving 19/12.
  • 19/12 is already in simplest form, and as a mixed number it is 1 7/12.

Both fractions sit a little under 1, so the sum should land between 1 and 2. An answer under 1 would mean something went wrong in the rewriting.

Subtracting Fractions Calculator

The same method in reverse, with the rewriting step shown.

Multiplying Fractions Calculator

Multiply across the top and bottom, with cancelling explained.

Dividing Fractions Calculator

Divide fractions with keep, change, flip shown step by step.

Fraction Calculator

All four operations in one place, with steps and a shareable link.

For students

Compare your working line by line against the steps to find the exact point where your answer diverged.

For teaching the LCD

Run a pair with matching denominators, then a pair without, to show a class what the extra step is actually for.

For everyday sums

Doubling recipes and combining measurements both come down to adding fractions with awkward denominators.

Frequently Asked Questions

Common questions about adding fractions

Find the least common denominator of the two fractions, rewrite each fraction over that denominator, then add the numerators and keep the denominator. For 2/3 + 1/5 the least common denominator is 15, so the sum becomes 10/15 + 3/15 = 13/15.

Then you skip straight to adding the numerators and leave the denominator alone. 3/8 + 5/8 = 8/8, which simplifies to 1. Never add the denominators together: 3/8 + 5/8 is not 8/16.

The least common denominator is the least common multiple of the two denominators. List the multiples of the larger denominator and stop at the first one the smaller denominator divides into. For 4 and 6, the multiples of 6 are 6, 12, and 12 is divisible by 4, so the least common denominator is 12. Multiplying the denominators together also works, it just gives bigger numbers to simplify later.

Convert each mixed number to an improper fraction first, then enter it. 1 1/2 becomes 3/2 and 2 1/4 becomes 9/4. The answer is shown as an improper fraction and as a mixed number, so you can read whichever form your work needs.