Fraction Calculator

Enter fractions like 3/4, mixed numbers like 1 1/2, whole numbers or decimals. Results are exact and reduced to lowest terms.

Fraction arithmetic

Result (simplified)5/6
Decimal
0.8(3) ≈ 0.8333333333

Working

  1. Use a common denominator: 1/2 = 3/6 and 1/3 = 2/6
  2. Add the numerators: 3 + 2 = 5, giving 5/6
  3. Simplify to lowest terms: 5/6

Simplify a fraction

Improper fractions are also shown as mixed numbers.

Result (simplified)3/4
Decimal
0.75

Working

  1. Greatest common factor of 18 and 24 is 6
  2. Divide both by 6: 3/4

How fraction arithmetic works

a/b + c/d = (ad + bc) / bd

a/b − c/d = (ad − bc) / bd

a/b × c/d = ac / bd

a/b ÷ c/d = a/b × d/c = ad / bc

To add or subtract, the fractions need a common denominator. Multiplying is done straight across. Dividing means multiplying by the reciprocal (the second fraction flipped). Every result is then simplified by dividing the numerator and denominator by their greatest common factor.

Worked example

1/2 + 1/3

  1. Common denominator: 6. So 1/2 = 3/6 and 1/3 = 2/6
  2. Add numerators: 3 + 2 = 5
  3. Result: 5/6 (already in lowest terms)

1/2 + 1/3 = 5/6 ≈ 0.8333

Simplify 18/24

  1. The greatest common factor of 18 and 24 is 6
  2. 18 ÷ 6 = 3 and 24 ÷ 6 = 4

18/24 = 3/4

Input formats

  • 3/4 — a simple fraction
  • 1 1/2 — a mixed number (whole part, space, fraction)
  • -2/3 — negative fractions
  • 0.75 or 5 — decimals and whole numbers are converted exactly

Why exact results matter

This calculator works with whole-number numerators and denominators rather than floating-point decimals, so 1/3 + 1/3 + 1/3 gives exactly 1. Repeating decimals are shown with the repeating part in brackets, e.g. 0.8(3) means 0.8333…

Common questions

What does “lowest terms” mean?

A fraction is in lowest terms when the numerator and denominator share no common factor other than 1. 3/4 is in lowest terms; 6/8 is not.

Can I divide by a fraction that equals zero?

No — division by zero is undefined, so the calculator shows an error if the second fraction is 0 in a division.