With a common denominator of 6 it is 3/6 + 2/6 = 5/6.

How do I divide by a fraction?

Multiply by its reciprocal. Dividing by 2/3 is the same as multiplying by 3/2.

How do I turn a fraction into a decimal?

Divide the numerator by the denominator. 3/8 = 0.375.

How to Add, Subtract, Multiply and Divide Fractions

The four fraction operations, each with one clear rule and one worked example, plus how to simplify and convert mixed numbers.

By Editorial Team · Updated September 19, 2026 · 1 min read

Fractions follow four rules. Add and subtract need matching denominators. Multiply and divide do not.

Adding fractions

Convert both fractions to a common denominator, then add the numerators.

a/b + c/d = (a×d + c×b) ÷ (b×d)

3/4 + 2/3: a common denominator is 12. 3/4 = 9/12 and 2/3 = 8/12. Adding gives 17/12, which is the mixed number 1 5/12.

Subtracting fractions

The same method, with the numerators subtracted.

5/6 − 1/4: use 12. 5/6 = 10/12 and 1/4 = 3/12. The difference is 7/12.

Multiplying fractions

Multiply the tops together and the bottoms together. No common denominator is needed.

2/3 × 3/5 = 6/15, which simplifies to 2/5 by dividing both parts by 3.

Dividing fractions

Flip the second fraction and multiply. This is called multiplying by the reciprocal.

3/4 ÷ 2/3 = 3/4 × 3/2 = 9/8, or 1 1/8.

Simplifying

Divide the numerator and denominator by their greatest common divisor. For 6/15 the greatest common divisor is 3, so 6/15 = 2/5. A fraction is in simplest form when the only shared factor is 1.

Mixed numbers

To turn a mixed number into an improper fraction, multiply the whole number by the denominator and add the numerator. 1 5/12 is (1 × 12 + 5) ÷ 12 = 17/12. To go back, divide the top by the bottom: 17 ÷ 12 is 1 remainder 5.

Common mistakes

Adding the denominators as well as the numerators. 1/2 + 1/3 is not 2/5.
Forgetting to flip the second fraction when dividing.
Leaving an answer unsimplified when a course asks for simplest form.

The fraction calculator shows the simplified result, the mixed number and the decimal.

Try it yourself

2/5 + 1/3
7/8 − 1/2
3/4 ÷ 3/8

Answers: (1) 11/15; (2) 3/8; (3) 2.

Frequently asked questions

What is 1/2 + 1/3?: With a common denominator of 6 it is 3/6 + 2/6 = 5/6.
How do I divide by a fraction?: Multiply by its reciprocal. Dividing by 2/3 is the same as multiplying by 3/2.
How do I turn a fraction into a decimal?: Divide the numerator by the denominator. 3/8 = 0.375.

About the author

Editorial Team. The Editorial Team writes, checks and maintains every tool and guide on this site. The calculation logic behind the calculators is covered by automated tests, examples are worked out and re-checked before publishing, and pages are updated when we find a mistake or a rule changes. Corrections are welcome through the contact page.

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