Fraction Calculator
Add, subtract, multiply and divide fractions and mixed numbers exactly, simplify a fraction, or turn a decimal into one.
Your fractions
Filled in with example values. Replace them with your own.
Results update as you type.
Result
1/2 + 1/3 = 5/6 ≈ 0.8(3)
Result
5/6
- DecimalDigits in brackets repeat
- 0.8(3)
How it’s calculated
Common denominator
lowest common multiple of 2 and 3 = 6
Add the numerators
3/6 + 2/6 = 5/6
How the fraction calculator works
Type fractions the way you would write them: 3/4, a mixed number such as 1 1/2, or a negative such as −5/6. The calculator adds, subtracts, multiplies or divides them exactly and gives the answer in lowest terms, as a mixed number and as a decimal, with the working shown.
It can also simplify a single fraction or turn a decimal such as 0.375 into a fraction.
The rules
a/b + c/d = (a·d + c·b) / (b·d)
a/b × c/d = (a·c) / (b·d)
a/b ÷ c/d = a/b × d/c
Results are simplified by dividing the numerator and denominator by their greatest common divisor.
Worked examples
- 1/2 + 1/3 = 3/6 + 2/6 = 5/6 (0.8(3)).
- 3/4 − 5/6 = 9/12 − 10/12 = −1/12.
- 2/3 × 9/4 = 18/12 = 3/2 = 1 1/2.
- 12/18 simplifies to 2/3 (dividing both by 6), and 0.375 = 375/1000 = 3/8.
Frequently asked questions
How do I add fractions with different denominators?
Rewrite both fractions over a common denominator, usually the lowest common multiple of the two denominators, then add the numerators. For 1/4 + 1/6, the common denominator is 12: 3/12 + 2/12 = 5/12.
How do I divide fractions?
Multiply by the reciprocal of the second fraction, that is, turn it upside down. 1 1/2 ÷ 3/4 = 3/2 × 4/3 = 12/6 = 2.
What do the brackets in the decimal mean?
The digits in brackets repeat forever. 1/3 = 0.(3) means 0.333…, and 1/6 = 0.1(6) means 0.1666…
Why is 0.1 + 0.2 exactly 3/10 here?
The calculator works with whole-number numerators and denominators of any size, so it never rounds. Many calculators store decimals in binary and show 0.30000000000000004.