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Fraction Calculator

Add, subtract, multiply, and divide fractions — results are simplified automatically and shown as improper fractions and mixed numbers.

Result (simplified)
5/12
= 5/12
Decimal: 0.416667

Addition/subtraction use the least common denominator; division multiplies by the reciprocal. Results are simplified by GCD.

Denominators Must Match — But Not by Multiplying Everything

Adding fractions needs a common denominator, but the efficient one is the least common denominator, not the product of the two: 1/6 + 1/4 works with denominator 12, not 24 — smaller numbers stay manageable and the final simplification is lighter. Multiplication, unlike addition, never needs matching denominators: multiply straight across, then simplify. Division flips the second fraction; the most common error is flipping the first one instead.

The Formula Behind the Result

  1. Enter two fractions as numerator/denominator (mixed numbers like 2 1/2 are accepted).
  2. Choose the operation: +, −, ×, or ÷.
  3. Addition and subtraction show the least common denominator used; division shows the reciprocal flip.
  4. The result is simplified by GCD and also displayed as a mixed number and a decimal.
Formula & Technical Standard
a/b ± c/d = (ad ± cb)/bd · a/b × c/d = ac/bd · a/b ÷ c/d = a/b × d/c · simplified by GCD.

Worked Example

Sum with different denominators
Input: 1/4 + 1/6
Output: 5/12 (LCD 12: 3/12 + 2/12)
The LCD step is shown explicitly, which is the part students most often get wrong by hand.
Division as reciprocal
Input: 3/4 ÷ 2/5
Output: 15/8 = 1 7/8
Dividing by a fraction multiplies by its inverse — the tool shows both representations.

Common Questions

Are negative and zero denominators handled?

Yes — a zero denominator is rejected with a clear message, and negative fractions are carried through the operations correctly.

What is a mixed number?

A whole number plus a proper fraction, e.g. 1 7/8 instead of the improper 15/8. The tool shows both.

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