A fraction like 18/24 and its simplified form 3/4 represent the exact same value — 3/4 is just easier to read, compare, and work with. Simplifying (also called “reducing”) a fraction means dividing the numerator and denominator by the largest number that goes into both evenly, until nothing bigger than 1 divides them both.
How to Simplify a Fraction (step by step)
Step One: Find the greatest common divisor (GCD)
The GCD is the largest whole number that divides evenly into both the numerator and the denominator.
gcd(18, 24) = 6
Step Two: Divide both numbers by the GCD
18 ÷ 6 = 3
24 ÷ 6 = 4
18/24 = 3/4
Step Three: Confirm nothing bigger than 1 still divides both numbers
gcd(3, 4) = 1 → 3/4 is fully simplified
With the calculator’s default values, 18/24 reduces to 3/4, and 3 ÷ 4 = 0.75, matching the original 18 ÷ 24 = 0.75 exactly.
What your results mean
The simplified numerator and denominator are your fraction in lowest terms — the version you’d write as a final answer. The GCD shows exactly what number both the original numerator and denominator were divided by; a GCD of 1 means the fraction you entered was already fully simplified.
The decimal confirms the value didn’t change — it will always match the decimal value of your original, unsimplified fraction.
Why finding the GCD directly beats guessing
You could simplify in stages — dividing 18/24 by 2 to get 9/12, then by 3 to get 3/4 — and you’d land on the same answer. But finding the GCD up front (using repeated division, known as the Euclidean algorithm) gets there in one step instead of several, which matters more as numbers get larger. For 84/126, guessing common factors one at a time takes a while; the GCD is 42, and dividing once gets straight to 2/3.
Common simplified fractions
| Fraction | GCD | Simplified |
|---|---|---|
| 4/8 | 4 | 1/2 |
| 6/9 | 3 | 2/3 |
| 10/15 | 5 | 2/3 |
| 12/18 | 6 | 2/3 |
| 15/25 | 5 | 3/5 |
| 21/28 | 7 | 3/4 |
Notice several different starting fractions in that table simplify to the same 2/3 — they’re all equivalent fractions of each other, just scaled differently.
To go the other direction and scale a simplified fraction back up, try the equivalent fractions calculator. To compare two fractions directly without simplifying either one first, use the comparing fractions calculator.