What is the Fraction Calculator?
Fractions represent parts of a whole, and operating on them follows precise rules that are easy to mix up: addition and subtraction need a common denominator, multiplication works straight across, and division means multiplying by the reciprocal.
This calculator performs all four operations on any two fractions and always reduces the answer to lowest terms using the greatest common divisor (GCD). It also shows the result as a mixed number and a decimal, so it doubles as a fraction-to-decimal converter.
Fraction Calculator Formula & How It Works
- Add/subtract: cross-multiply over the common denominator bd
- Multiply: multiply numerators and denominators straight across
- Divide: flip the second fraction and multiply
- Simplify: divide both parts by GCD
After any operation, the result is simplified by dividing the numerator and denominator by their greatest common divisor. For instance 6/8 reduces to 3/4 because GCD(6,8) = 2. An improper result like 7/2 is also shown as the mixed number 3 1/2.
Worked Examples
Add: 2/3 + 3/4
(2×4 + 3×3) / (3×4) = 17/12 = 1 5/12 ≈ 1.4167.
Divide: 5/6 ÷ 2/3
5/6 × 3/2 = 15/12, simplified to 5/4 = 1 1/4 = 1.25.