WebyTooly

Fraction Calculator

Enter two fractions and choose the operation to get the simplified result.

Result
5/6
Decimal value
0.833333

How fractions are calculated

To add or subtract fractions, the denominators are made equal using the least common multiple. To multiply, numerators and denominators are multiplied together, and to divide, you multiply by the reciprocal fraction. The result is simplified by dividing by the greatest common factor.

a/b + c/d = (a×d + c×b) / (b×d)

These four operations are the basis for more complex fraction calculations, from adjusting a recipe (doubling or halving it) to physics problems or proportional splits.

a/b × c/d = (a×c) / (b×d)

A common mistake is adding numerators and denominators directly (e.g. 1/2 + 1/3 = 2/5), which is wrong: fractions can only be added or subtracted once they share the same denominator.

a/b ÷ c/d = (a×d) / (b×c)

Worked example

1/2 + 1/3 = (1×3 + 1×2) / (2×3) = 5/6. And 2/3 × 3/4 = (2×3) / (3×4) = 6/12, which simplifies to 1/2.

Frequently asked questions

Is the result simplified automatically?
Yes, the calculator reduces the resulting fraction to its simplest form by dividing the numerator and denominator by their greatest common factor.
What happens if the denominator is 0?
A fraction with a denominator of 0 isn't mathematically valid, and the calculator will show a warning instead of a result.
Can I use negative numbers?
Yes, both the numerator and the denominator can be negative.
Why can't I just add the numerators and denominators directly?
Because a fraction represents a proportion, not two independent numbers; adding them directly gives a mathematically wrong result. The denominators must be equalized first.
How is the result converted to a decimal number?
The numerator is divided by the denominator; the calculator shows both formats (simplified fraction and decimal value) automatically.

Related calculators