What "simplifying a fraction" means
A fraction represents a ratio between two numbers. Many different fractions can represent the exact same value — 2/3, 4/6, and 8/12 are all the same amount, just written with different numbers. Simplifying finds the smallest possible numerator and denominator for that value by dividing both by their greatest common factor (GCF), the largest number that divides evenly into both.
Finding the greatest common factor
For 8/12: the factors of 8 are 1, 2, 4, 8, and the factors of 12 are 1, 2, 3, 4, 6, 12. The largest number common to both lists is 4, so dividing numerator and denominator by 4 gives 8 ÷ 4 = 2 and 12 ÷ 4 = 3 — the simplified fraction is 2/3.
A second example with larger numbers
The same method works regardless of size. For 36/48, the greatest common factor is 12: 36 ÷ 12 = 3 and 48 ÷ 12 = 4, so 36/48 simplifies to 3/4. Dividing by the full GCF in one step reaches the simplest form directly, rather than needing several rounds of dividing by smaller common factors like 2 or 3 first.
When a fraction can't be simplified further
Not every fraction has a common factor to divide out. For 9/16, the factors of 9 are 1, 3, 9, and the factors of 16 are 1, 2, 4, 8, 16 — the only number common to both is 1, so the fraction is already in lowest terms and stays 9/16. A fraction is "in lowest terms" exactly when its numerator and denominator share no common factor other than 1.