Fraction Calculator

Add, subtract, multiply or divide two fractions and get the answer already reduced to lowest terms — the step people usually get wrong by hand isn't the arithmetic, it's forgetting to simplify at the end.

Inputs

Numerator 1

Denominator 1

Operation

Numerator 2

Denominator 2

Result

5/6

Decimal 0.833333

How the fraction calculator works

Addition and subtraction: cross-multiply to a common denominator first — a/b ± c/d = (ad ± cb) ÷ bd.

Multiplication: multiply numerators and denominators directly — a/b × c/d = ac ÷ bd.

Division: multiply by the reciprocal — a/b ÷ c/d = a/b × d/c = ad ÷ bc.

Every result is reduced by dividing both numerator and denominator by their greatest common divisor before it's displayed.

Worked example: 1/2 + 1/3

Common denominator: 1/2 = 3/6, 1/3 = 2/6.
3/6 + 2/6 = 5/6.
5/6 is already in lowest terms (GCD of 5 and 6 is 1), so that's the final answer.

Common mistakes to avoid

Adding numerators and denominators straight across

1/2 + 1/3 is not 2/5 — that shortcut only works for multiplication, not addition. Addition and subtraction need a common denominator first.

Forgetting a fraction can simplify after the operation

Even if both original fractions were already in lowest terms, the result of adding or multiplying them often isn't — e.g. 2/4 + 1/4 = 3/4, but 1/6 + 1/6 = 2/6, which reduces to 1/3.