Simplifying Fractions
Simplifying (or reducing) a fraction means expressing it in its lowest terms by dividing both the numerator and denominator by their greatest common divisor (GCD).
Process
- Find the GCD of numerator and denominator
- Divide both by the GCD
- The result is the simplified fraction
What is GCD?
The Greatest Common Divisor (also called Greatest Common Factor) is the largest number that divides both the numerator and denominator evenly.
Examples
Example 1: Simplify 12/16
GCD(12, 16) = 4
12/4 / 16/4 = 3/4
Example 2: Simplify 18/24
GCD(18, 24) = 6
18/6 / 24/6 = 3/4
Why Simplify?
- Easier to understand and compare
- Standard mathematical form
- Simpler for further calculations
- Required in many academic settings
Already Simplified?
A fraction is already in simplest form when the GCD of numerator and denominator is 1. These numbers are called relatively prime or coprime.
Quick Tips
- Double-check your inputs for accurate results
- Use parentheses to clarify order of operations
- Results are rounded — consider significant figures
Frequently Asked Questions
Divide both numerator and denominator by their GCD.
The Greatest Common Divisor - the largest number that divides both numbers evenly.
Not all - some are already in lowest terms.
12/16 = 3/4
When the numerator and denominator have no common factors except 1.