Fraction Calculator
- 5/6
- Simplified
- 5/6
- Mixed number
- 0.83333333
- Decimal
- 83.3333%
- Percentage
The fraction calculator performs the four operations on two fractions and reports the result four ways: simplified, as a mixed number, as a decimal and as a percentage. Simplification uses the greatest common divisor, so 6/8 always comes back as 3/4 rather than being left as it was entered.
How it works
- Addition and subtraction cross-multiply to a common denominator: a/b ± c/d = (ad ± cb) / bd.
- Multiplication multiplies across: a/b × c/d = ac / bd.
- Division multiplies by the reciprocal: a/b ÷ c/d = ad / bc.
- The result is divided by the greatest common divisor of numerator and denominator, and any negative sign is moved to the numerator.
Using bd as the common denominator rather than the least common multiple produces larger intermediate numbers, but the simplification step reduces them anyway and the arithmetic stays exact for far larger inputs.
Examples
Adding halves and thirds
First
1/2
Operation
Add
Second
1/3
Result
5/6 · decimal 0.83333333 · 83.333333%
(1×3 + 1×2) / (2×3) = 5/6, which is already in lowest terms.
A result larger than one
First
7/4
Operation
Add
Second
3/4
Result
Simplified 5/2 · Mixed number 2 1/2
10/4 reduces to 5/2. The mixed number form is what you want when the fraction represents a measurement.
Dividing by a fraction
First
3/4
Operation
Divide
Second
1/2
Result
3/2 · Mixed number 1 1/2
Dividing by 1/2 is multiplying by 2/1, which is why dividing by a fraction below one makes the result larger.
Frequently asked questions
Why is the result always simplified?
Because an unsimplified fraction is the same value written less clearly. 10/4 and 5/2 are equal, but only one of them makes the size obvious at a glance. The tool divides through by the greatest common divisor every time.
What happens if I enter zero as a denominator?
The tool reports it rather than calculating. A fraction with zero on the bottom is undefined (not infinite, and not zero) so there is no sensible value to return.
Why does dividing by a fraction make the number bigger?
Because dividing by a value below one asks how many of that smaller thing fit into your number, which is more than one. 3/4 ÷ 1/2 asks how many halves fit into three quarters: one and a half.
Can I enter mixed numbers directly?
Not as input, convert them first by multiplying the whole part by the denominator and adding the numerator, so 2 1/2 becomes 5/2. The result is shown as a mixed number, since that is where the form is most useful.