# Free online fraction calculator

> A fraction is one number divided by another (like 1/2 or 3/4). This calculator adds, subtracts, multiplies, or divides any two fractions and reduces the answer automatically.

Add, subtract, multiply, and divide fractions. Results are automatically simplified to lowest terms with the mixed number and decimal equivalent shown.

**Interactive version:** https://onlinecalculator.me/math/fraction/
**Category:** Math

## How to use

1. Select an operation: Add (+), Subtract (−), Multiply (×), or Divide (÷).
2. Enter the numerator and denominator of the first fraction.
3. Enter the numerator and denominator of the second fraction.
4. The result appears as a reduced fraction, mixed number, and decimal.

## The four operations

**Addition:** a/b + c/d = (a×d + c×b) / (b×d)

**Subtraction:** a/b − c/d = (a×d − c×b) / (b×d)

**Multiplication:** a/b × c/d = (a×c) / (b×d)

**Division:** a/b ÷ c/d = (a×d) / (b×c)

After computing the result, divide both numerator and denominator by their GCD to fully reduce.

## Worked examples

**1/2 + 1/3:** (1×3 + 1×2) / (2×3) = 5/6 ≈ 0.833

**3/4 − 2/5:** (3×5 − 2×4) / (4×5) = 7/20 = 0.35

**2/3 × 3/4:** 6/12 → GCD = 6 → **1/2** = 0.5

**5/6 ÷ 5/3:** (5×3) / (6×5) = 15/30 → GCD = 15 → **1/2**

## Notes

- Division by zero (denominator = 0 or dividing by a fraction with numerator = 0) shows an error message.
- Negative fractions work: enter a negative numerator.
- The GCD algorithm (Euclidean) runs in O(log n) time, so very large numerators or denominators compute instantly.

## Frequently asked questions

### How are fractions simplified (reduced)?

The calculator divides both the numerator and denominator by their Greatest Common Divisor (GCD), found with the Euclidean algorithm. For example, 6/8 → GCD(6,8) = 2 → 3/4.

### How is fraction addition calculated?

a/b + c/d = (a×d + c×b) / (b×d), then reduce by GCD. Example: 1/3 + 1/4 = (4 + 3) / 12 = 7/12.

### How is fraction subtraction calculated?

a/b − c/d = (a×d − c×b) / (b×d), then reduce. Example: 3/4 − 1/3 = (9 − 4) / 12 = 5/12.

### How is fraction multiplication calculated?

a/b × c/d = (a×c) / (b×d), then reduce. Example: 2/3 × 3/4 = 6/12 = 1/2.

### How is fraction division calculated?

a/b ÷ c/d = (a×d) / (b×c), then reduce (multiply by the reciprocal). Example: 2/3 ÷ 4/5 = (2×5) / (3×4) = 10/12 = 5/6.

## Sources

- [Fraction and arithmetic operations on fractions](https://en.wikipedia.org/wiki/Fraction) — Wikipedia

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