Fraction calculator with steps
Type two fractions, pick an operation and get the answer in its simplest form, as a mixed number and as a decimal, with the working laid out line by line.
How the fraction calculator works
Fractions only add or subtract cleanly when the bottom numbers match, so the calculator first finds a common denominator: the lowest common multiple of the two bottoms. It rewrites both fractions over that number, combines the tops and then simplifies by dividing top and bottom by their greatest common factor.
Multiplying is simpler. Tops go with tops and bottoms with bottoms. Dividing turns into multiplying once you flip the second fraction upside down.
The formula behind it
- Add or subtract: a/b ± c/d = (a×d ± c×b) / (b×d), then simplify.
- Multiply: a/b × c/d = (a×c) / (b×d).
- Divide: a/b ÷ c/d = a/b × d/c.
A worked example
Add 3/4 and 2/3. The lowest common multiple of 4 and 3 is 12, so 3/4 becomes 9/12 and 2/3 becomes 8/12. Add the tops: 9 + 8 = 17, giving 17/12. That cannot be simplified, and as a mixed number it is 1 5/12.
Questions people ask
Why do I need a common denominator?
Because you can only add things that are measured in the same-sized pieces. Quarters and thirds are different sizes, so we convert both into twelfths first.
What is a mixed number?
A whole number with a fraction beside it, like 1 5/12. It is the same value as the improper fraction 17/12, just easier to picture.
Can I use negative numbers?
Yes. Put a minus sign in the top box, for example -3 for the numerator. The calculator keeps the sign on the top of the answer.
Does it work with whole numbers?
Write a whole number as a fraction over 1. For example, 5 becomes 5/1.