Fraction Arithmetic Rules
Addition & Subtraction(a/b) ± (c/d) = (a×d ± c×b) ÷ (b×d)
Example: 1/2 + 1/3 = (1×3 + 1×2) ÷ (2×3) = 5/6
Example: 1/2 + 1/3 = (1×3 + 1×2) ÷ (2×3) = 5/6
Multiplication & Division(a/b) × (c/d) = (a×c) ÷ (b×d)
(a/b) ÷ (c/d) = (a/b) × (d/c) = (a×d) ÷ (b×c)
Example: 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2/1 = 2
(a/b) ÷ (c/d) = (a/b) × (d/c) = (a×d) ÷ (b×c)
Example: 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2/1 = 2
Simplifying Fractions — GCD Method
Results are automatically simplified using the Greatest Common Divisor (GCD), also called HCF (Highest Common Factor). The GCD is the largest number that divides both numerator and denominator without a remainder.
Example: 12/8 → GCD(12,8) = 4 → 12÷4 / 8÷4 = 3/2
💡 Our calculator uses the Euclidean algorithm for GCD calculation, which is efficient for any size numbers: gcd(a,b) = gcd(b, a mod b), repeating until b=0.
Common Fraction Examples
| Operation | Result | Decimal |
|---|---|---|
| 1/2 + 1/4 | 3/4 | 0.75 |
| 3/4 − 1/4 | 1/2 | 0.5 |
| 2/3 × 3/4 | 1/2 | 0.5 |
| 5/6 ÷ 5/3 | 1/2 | 0.5 |
| 7/8 + 3/8 | 5/4 | 1.25 |
½ Calculate fractions instantly — result in simplified form + decimal
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