Reduce any fraction to its simplest form. This free fraction simplifier divides by the greatest common divisor to give lowest terms, plus the mixed number, decimal and percentage.
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 the Fraction Simplifier Works
Simplifying a fraction means reducing it to the smallest numerator and denominator that still represent the same value. This tool takes any numerator and denominator and reduces the fraction to lowest terms, then converts it to a mixed number, decimal, and percentage.
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.
- Numerator — the top number of the fraction
- Denominator — the bottom number of the fraction
Example Scenarios
| 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 |
Fraction Simplifier FAQ
How do I simplify a fraction to its lowest terms?
Enter the numerator and denominator into their fields. The simplifier finds the greatest common divisor of both numbers and divides each by it, leaving a fraction that can’t be reduced any further — for example 12/16 becomes 3/4.What is the greatest common divisor and why does it matter here?
The greatest common divisor (GCD) is the largest number that divides evenly into both the numerator and denominator. Dividing both parts of a fraction by their GCD in one step guarantees the result is fully reduced, rather than needing several rounds of smaller simplifications.How does the calculator handle negative fractions?
If the denominator is negative, the calculator flips the sign of both numerator and denominator so the negative sign always appears on the numerator, keeping the denominator positive. The fraction’s value is unchanged — only its displayed form is normalized.Can I simplify an improper fraction like 100/40?
Yes. An improper fraction (where the numerator is larger than the denominator) simplifies the same way — 100/40 reduces to 5/2 — and the calculator also shows it as a mixed number, 2 1/2, alongside the decimal and percentage forms.What happens if I enter 0 as the denominator?
The calculator shows an error message, “Denominator can’t be 0,” since dividing by zero has no defined value. Enter any nonzero denominator to get a valid simplified fraction.How do I convert a simplified fraction to a percentage?
You don’t need to do it manually — once you enter a numerator and denominator, the calculator automatically divides the reduced numerator by the reduced denominator and multiplies by 100 to display the percentage alongside the decimal value.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.