Fraction calculator

Formula

How it works

To add or subtract, use a common denominator; to multiply, multiply numerators and denominators; to divide, multiply by the reciprocal. Results are reduced with the greatest common divisor.

Worked example

The same calculation with the default values:

• First fraction: numerator 1
• First fraction: denominator 2
• Second fraction: numerator 1
• Second fraction: denominator 3

1. 1/2 + 1/3 = (1×3 + 1×2) ÷ (2×3) = 5/6 → 5/6
2. 1/2 − 1/3 = (1×3 − 1×2) ÷ (2×3) = 1/6 → 1/6
3. 1/2 × 1/3 = (1×1) ÷ (2×3) = 1/6 → 1/6
4. 1/2 ÷ 1/3 = (1×3) ÷ (2×1) = 3/2 → 3/2

Result: Sum: 5/6 ≈ 0.833333 · Difference: 1/6 ≈ 0.166667 · Product: 1/6 ≈ 0.166667

Common mistakes

• Adding or subtracting numerators directly without a common denominator first - 1/2 + 1/3 is not 2/5; the denominators must be made the same before adding the numerators.
• Dividing fractions without flipping the second one - dividing by a fraction means multiplying by its reciprocal; skipping the flip gives the wrong operation entirely.
• Entering zero as a denominator - a fraction with a zero denominator is undefined, not a very large or very small number.