Fraction Calculator
Add, subtract, multiply and divide fractions and mixed numbers, simplify a fraction to lowest terms, or convert between fractions and decimals — including repeating decimals. Every answer is exact and comes with the working.
Leave the left-hand box empty for a plain fraction, or fill it in for a mixed number such as 2 ⅓. A minus sign on the whole number applies to the whole mixed number. Numbers of any length are handled exactly.
- 1Lowest common denominator of 2 and 3: 6
- 2Rewrite both fractions over 6: 3/6 + 2/6
- 3Add the numerators: 3 + 2 = 5, giving 5/6
How to use this calculator
- Pick a tab: Calculate for arithmetic, Simplify to reduce one fraction, or one of the two converters.
- Type the numerator on top and the denominator below.For a mixed number, put the whole part in the box on the left.
- Choose the operation — the answer updates as you type, in lowest terms, as a mixed number and as a decimal.
The rules
a/b + c/d = (a·d + c·b) / (b·d)
a/b − c/d = (a·d − c·b) / (b·d)
a/b × c/d = (a·c) / (b·d)
a/b ÷ c/d = (a·d) / (b·c)
w n/d = (w·d + n) / d
After each operation the result is divided top and bottom by the greatest common divisor of its numerator and denominator, which leaves it in lowest terms. In practice the calculator uses the least common multiple for addition and subtraction, so the numbers in the working stay as small as possible.
Worked examples
Adding mixed numbers
2 ⅓ + 1 ½
- Convert: 2 ⅓ = 7/3 and 1 ½ = 3/2
- Common denominator 6: 14/6 + 9/6 = 23/6
- As a mixed number: 3 ⅚
Scaling a recipe
A recipe needs ¾ cup of flour and you are making ⅔ of it.
- Multiply: ¾ × ⅔ = 6/12
- Simplify: ½ cup
A repeating decimal
What fraction is 1.2343434…?
- Type 1.2(34) in the decimal converter.
- 1000x − 10x = 1234 − 12, so x = 1222/990
- Simplified: 611/495
Frequently asked questions
Rewrite both fractions over a common denominator, add the numerators, then simplify. The smallest common denominator is the least common multiple of the two denominators.
For 1/4 + 1/6, the least common multiple of 4 and 6 is 12, so the sum is 3/12 + 2/12 = 5/12.
A whole number and a proper fraction written together, such as 2 ¾, meaning 2 + ¾. The same value as an improper fraction is 11/4: multiply the whole number by the denominator and add the numerator.
The calculator accepts either form and shows every answer both ways.
In front of the whole number, and it applies to the whole thing: −1 ½ means −(1 + ½), which is −3/2, not −1 + ½.
For a negative fraction with no whole part, put the minus sign on the numerator.
Dividing by a number is the same as multiplying by its reciprocal, and the reciprocal of a/b is b/a. Asking how many halves fit into 3 is 3 ÷ ½ = 3 × 2 = 6.
Type the repeating digits in brackets: 0.(3) for 0.333… or 0.1(6) for 0.1666…. The calculator uses the standard algebra trick of multiplying by a power of 10 so the repeating tail cancels out, and gives the exact fraction.
That is also why 0.(9) comes out as exactly 1.
Each field accepts up to 200 digits, and all arithmetic is exact — there is no rounding at any point, so it also works as a big-number fraction calculator. Only the decimal shown alongside a fraction is rounded.