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 |
Frequently Asked Questions
Yes, our fraction calculator performs all four basic arithmetic operations on standard fractions, mixed numbers, and whole numbers.
Absolutely. The output is automatically simplified to its lowest terms and displayed as both an improper fraction and a mixed number.
Convert your mixed number to an improper fraction (e.g., 1 1/2 becomes 3/2) to input it into the numerator and denominator fields.
½ Calculate fractions instantly — result in simplified form + decimal
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