Simplifying a fraction means rewriting it with the smallest possible whole numbers on top and bottom, without changing its value. 8/12 and 2/3 represent exactly the same quantity — 2/3 is just 8/12 written with smaller numbers. The method is to find the greatest common factor (GCF) of the numerator and denominator, then divide both by it. For 8/12, the GCF of 8 and 12 is 4, so dividing both by 4 gives 2/3, which can't be reduced any further because 2 and 3 share no common factor besides 1.
Worked example one: simplify 18/24. The GCF of 18 and 24 is 6 (18 = 2 × 3², 24 = 2³ × 3, and the shared prime factors at their lowest shared power are 2¹ × 3¹ = 6). Dividing both by 6 gives 3/4. Worked example two: simplify 45/60. The GCF of 45 and 60 is 15, so 45 ÷ 15 = 3 and 60 ÷ 15 = 4, giving 3/4 as well — a reminder that different-looking fractions can simplify to the identical reduced form.
Simplifying in Smaller Steps
If you don't immediately spot the full GCF, simplifying in smaller steps works just as well and reaches the same final answer: 18/24 could first be divided by 2 (giving 9/12), then by 3 (giving 3/4) — two smaller steps landing on the same result as one big one. The only requirement is dividing the numerator and denominator by the exact same number each time, and stopping only once no common factor besides 1 remains.
When a Fraction Is Truly Done
A fraction is "simplified" or "in lowest terms" specifically when its numerator and denominator are coprime — meaning their GCF is 1. This is a definite stopping point, not a judgment call: 3/4 is fully simplified because GCF(3,4) = 1, while 6/8 is not, because GCF(6,8) = 2. The most common mistake is stopping one step early — reducing 24/36 to 4/6 (dividing by 6) and treating that as final, when 4 and 6 still share a common factor of 2 and the fraction can go one step further to 2/3.
Simplifying works the same way for improper fractions (numerator larger than denominator) as for proper ones — 42/28 simplifies via GCF(42,28) = 14, giving 3/2, which can also be expressed as the mixed number 1 1/2, though the improper fraction and mixed-number forms represent the identical value and neither is more "simplified" than the other in the GCF sense; that's a separate stylistic choice depending on context. A fraction with a numerator of 0, like 0/7, simplifies to 0/1 (or just 0), since the GCF of 0 and any number n is n itself, and 0 ÷ n = 0.
Spotting Common Factors at a Glance
Simplifying relies on exactly the same factoring skill used throughout this site's Factors pages — the GCF calculation here is identical to the GCF Calculator's, just applied specifically to a fraction's two parts. Simplifying also applies naturally to fractions that already contain a common factor visible at a glance, without needing the full prime-factorization machinery — 100/1000 reduces immediately to 1/10 by recognizing both numbers share a factor of 100, and 6/9 reduces to 2/3 by spotting the shared factor of 3 without computing a full GCF table. Building this kind of pattern recognition for small, common factors (2, 3, 5, 10) speeds up everyday simplifying considerably, while the formal GCF method remains the reliable fallback for fractions where the shared factor isn't obvious on sight.
If you want the fraction as a decimal instead of a reduced fraction, use the Fraction to Decimal Converter; for the underlying method taught step by step with more examples, see How to Simplify a Fraction.