Fraction Operations
Addition/Subtraction:
a/b ± c/d = (a×d ± c×b) / (b×d) → then simplify by GCD
Multiplication:
a/b × c/d = (a×c) / (b×d) → then simplify by GCD
Division:
a/b ÷ c/d = a/b × d/c = (a×d) / (b×c)
Simplify: Divide numerator and denominator by GCD(num, den)
How to Simplify Fractions
A fraction is in its simplest form when the numerator and denominator share no common factors other than 1. To simplify, find the Greatest Common Divisor (GCD) of the numerator and denominator using the Euclidean algorithm, then divide both by the GCD.
For example: 12/18 → GCD(12,18) = 6 → 12÷6 / 18÷6 = 2/3.
Common Fraction Equivalents
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333… | 33.33% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 2/3 | 0.667 | 66.67% |
| 1/8 | 0.125 | 12.5% |