Simplify Fraction Calculator
The simplify fraction calculator reduces any fraction to lowest terms by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it. Enter a numerator and denominator, and the calculator instantly returns the simplified fraction, its decimal equivalent, and the equivalent mixed number. For example, 18/24 simplifies to 3/4. The calculator uses the Euclidean algorithm to find the GCD efficiently, even for large numbers.
Simplifying fractions
Find GCD(numerator, denominator)
Simplified fraction = (numerator / GCD) / (denominator / GCD)
Simplification examples
| Original | GCD | Simplified | Decimal |
|---|---|---|---|
| 6/8 | 2 | 3/4 | 0.75 |
| 12/18 | 6 | 2/3 | 0.667 |
| 15/25 | 5 | 3/5 | 0.60 |
| 20/30 | 10 | 2/3 | 0.667 |
| 7/14 | 7 | 1/2 | 0.50 |
Simplify fraction calculator: frequently asked questions
What does it mean to simplify a fraction?
Simplifying a fraction means reducing it to lowest terms by dividing both the numerator and denominator by their greatest common divisor (GCD). For example, 6/8 simplifies to 3/4 because GCD(6,8) = 2. Simplified fractions are easier to work with and represent the same value.
How do I find the GCD?
The greatest common divisor is the largest number that divides evenly into both the numerator and denominator. For 12 and 18, the GCD is 6. You can find the GCD using the Euclidean algorithm or by listing factors: factors of 12 are 1,2,3,4,6,12 and factors of 18 are 1,2,3,6,9,18, so the greatest common factor is 6.
Can every fraction be simplified?
No. If the GCD of the numerator and denominator is 1, the fraction is already in lowest terms and cannot be simplified further. Such fractions are called reduced or in lowest terms. For example, 3/4 has GCD(3,4) = 1, so it is already simplified.
Why simplify fractions?
Simplified fractions are easier to understand and work with. They also make it clear when two fractions are equivalent. For example, 6/8, 12/16, and 3/4 all represent the same value, but 3/4 in lowest terms is clearest.
What is a mixed number?
A mixed number combines a whole number and a fraction, like 1 3/4 (one and three-quarters). This calculator shows the simplified fraction, decimal value, and equivalent mixed number.
Official sources
- Standard mathematical formulas for fraction simplification and GCD.
- Euclidean algorithm for finding the greatest common divisor.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.