Enter a numerator and denominator to reduce a fraction to lowest terms. You also get the mixed number, decimal and percentage, so you can check the answer two ways.
Enter a numerator and denominator, and the simplifier reduces the fraction to its lowest terms by dividing both by their greatest common divisor (GCD).
A fraction is in lowest terms when the numerator and denominator share no common factor other than 1. Negative fractions and improper fractions (top bigger than bottom) are supported.
How to Reduce a Fraction to Lowest Terms
Divide the numerator and denominator by their greatest common divisor (GCD), the largest number that goes into both. For 12/16 the GCD is 4, so 12 ÷ 4 = 3 and 16 ÷ 4 = 4, giving 3/4. One division by the GCD always finishes the job.
- List or work out the GCD of the two numbers: for 18 and 24 it is 6.
- Divide the top by it: 18 ÷ 6 = 3.
- Divide the bottom by it: 24 ÷ 6 = 4.
- Write the result: 18/24 simplified is 3/4.
Formula: Simplified fraction = (numerator ÷ GCD) / (denominator ÷ GCD), where GCD is the greatest common divisor of the numerator and denominator, found using the Euclidean algorithm (repeatedly replacing the larger number with the remainder of dividing it by the smaller, until the remainder reaches 0). If the reduced denominator equals 1, only the whole-number numerator is shown.
Simplified Fraction Examples
| Numerator | Denominator | Simplified |
|---|---|---|
| 12 | 16 | 3/4 |
| 18 | 24 | 3/4 |
| 100 | 40 | 5/2 |
| 9 | 27 | 1/3 |
| 15 | 50 | 3/10 |
| -8 | 12 | -2/3 |
How to Simplify Improper Fractions to Mixed Numbers
Reduce the fraction, then divide the top by the bottom and keep the remainder as the new numerator. 45/12 reduces to 15/4, and 15 ÷ 4 = 3 remainder 3, so it becomes 3 3/4. The tool shows both forms.
How to Simplify Negative Fractions
Reduce the numbers as usual and keep a single minus sign on the numerator. The tool writes -6/8 as -3/4, and if the denominator is negative it flips both signs so the bottom stays positive. A negative over a negative, like -6/-8, is simply positive 3/4.
Checking Your Answer by Hand
- Lowest terms means the top and bottom share no factor other than 1. If both numbers are still even, or both end in 0 or 5, the fraction can be reduced further.
- A denominator of zero has no meaning, so it can’t be reduced at all.
- The decimal should match before and after: 18/24 and 3/4 both equal 0.75.
Simplifying never changes the value, only how it is written, which is why comparing decimals is a quick check when a result feels off. For the idea behind lowest terms, see the Wikipedia page on irreducible fractions.
Common questions about simplifying fractions
How do you reduce a fraction to lowest terms?
Find the greatest common divisor (GCD) of the numerator and denominator and divide both by it. For 12/16 the GCD is 4, so it reduces to 3/4.What is 12/16 simplified?
12/16 simplified is 3/4, because 4 divides both 12 and 16. As a decimal it is 0.75.What is 18/24 simplified?
18/24 simplified is 3/4. The GCD of 18 and 24 is 6, and 18 ÷ 6 = 3, 24 ÷ 6 = 4.How do you simplify improper fractions to mixed numbers?
Reduce the fraction first, then divide the top by the bottom. 100/40 reduces to 5/2 (GCD 20), and 5 ÷ 2 = 2 remainder 1, so it is 2 1/2.How do you simplify negative fractions?
Reduce the numbers as usual and keep one minus sign on the numerator. -8/12 becomes -2/3, while a negative over a negative, like -6/-8, is positive 3/4.What happens if I enter 0 as the denominator?
The tool shows the error “Denominator can’t be 0,” since dividing by zero has no defined value. Enter any nonzero denominator to get a result.Related Calculators
If you need to add, subtract, multiply, or divide fractions rather than just reduce them, the fraction calculator handles the full arithmetic. When you’re comparing two quantities instead of simplifying a single fraction, the ratio calculator is a close relative, and the GCF calculator is useful if you just need the greatest common factor on its own.