Fraction Calculator

By Shaheer Bin Ramzan
Reviewed November 2026 · Formula sources

Enter two fractions and an operation. The calculator shows the working and reduces the answer to lowest terms.

How fraction arithmetic works

A fraction names a part of a whole: the numerator counts the parts and the denominator says how many make the whole. Each operation has one rule, and nearly every mistake comes from mixing them up.

Operation	Rule
Add or subtract	Use a common denominator, then add or subtract the numerators
Multiply	Multiply numerators together and denominators together
Divide	Multiply by the reciprocal of the second fraction

Worked examples

Adding: 1/2 + 1/3

The least common multiple of 2 and 3 is 6. Rewrite as 3/6 + 2/6, which equals 5/6.

Subtracting: 3/4 − 1/6

The common denominator is 12. That gives 9/12 − 2/12 = 7/12.

Multiplying: 2/3 × 3/5

Multiply across to get 6/15. The greatest common factor of 6 and 15 is 3, so the answer is 2/5.

Dividing: 3/4 ÷ 2/5

Flip the second fraction and multiply: 3/4 × 5/2 = 15/8, which is the mixed number 1 7/8.

Common mistakes

The most frequent error is adding denominators, so that 1/2 + 1/3 becomes 2/5. The denominator names the size of the pieces and does not change when you add. Another is forgetting to flip only the second fraction when dividing. Finally, always reduce the answer: 6/15 and 2/5 are equal, but 2/5 is the form teachers expect. To find the common factor yourself, use the GCF and LCM calculator.

Frequently asked questions

How do you add fractions with different denominators?

Find a common denominator, usually the least common multiple of the two denominators. Rewrite each fraction over it, add the numerators, then simplify.

How do you divide fractions?

Multiply the first fraction by the reciprocal of the second. Dividing by 2/5 is the same as multiplying by 5/2.

How do you simplify a fraction?

Divide the numerator and denominator by their greatest common factor. 6/15 becomes 2/5 because 3 divides both.