Fraction Calculator
Add, subtract, multiply and divide fractions, simplified.
Good to know. To divide by a fraction, flip it and multiply. It works every time, even if nobody remembers why.
How it works
In plain words
To add or subtract, give both fractions the same denominator by cross-multiplying. To multiply, multiply tops and bottoms. To divide, flip the second fraction and multiply. Then simplify by dividing top and bottom by their greatest common divisor.
The formula
a/b + c/d = (ad + bc) / bd a/b − c/d = (ad − bc) / bd a/b × c/d = ac / bd a/b ÷ c/d = ad / bc
Worked example
1/2 + 1/3 = (1 × 3 + 1 × 2) / (2 × 3) = 5/6, which is about 0.833.
Sources
No outside data or rates: this is plain arithmetic.
13 automated tests check its answers on every change.
About the fraction calculator
Fractions turn up in recipes, measurements, woodwork and homework, and they are easy to get muddled with. This calculator handles the four basic operations and always gives the answer in lowest terms.
You can type fractions in the natural way: 3/4, a mixed number with a space like 1 1/2, a whole number like 3, or a decimal like 0.25. Negative numbers work too: -1/2 or -1 1/2.
Adding and subtracting need a common denominator. The simplest way is to multiply the two denominators together, then adjust the tops to match. 1/2 + 1/3 becomes 3/6 + 2/6 = 5/6. Multiplying is easier: multiply straight across, so 2/3 × 3/4 = 6/12 = 1/2. To divide, flip the second fraction upside down and multiply: 1/2 ÷ 1/4 = 1/2 × 4/1 = 2. That’s why dividing by a fraction smaller than one makes a number bigger.
Simplifying means dividing the top and bottom by the largest number that goes into both, their greatest common divisor. 6/12 becomes 1/2 because 6 goes into both.
An improper fraction, where the top is bigger than the bottom, is also shown as a mixed number, like 7/4 = 1 3/4, which is usually easier to picture.
Questions people ask
How do I add fractions with different denominators?
Rewrite them over a common denominator, then add the tops. 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
How do I divide fractions?
Flip the second fraction and multiply. 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 1 1/2.
How do I simplify a fraction?
Divide the top and bottom by their greatest common divisor. 18/24: both divide by 6, giving 3/4.
Can I enter mixed numbers?
Yes. Type the whole number, a space, then the fraction, like 2 3/8.