Fraction Simplifier Calculator
Simplifying a fraction means writing it with the smallest possible whole numbers while keeping the same value. You do this by dividing both the numerator and the denominator by their greatest common divisor. This calculator finds the GCD with the Euclidean algorithm, reduces the fraction to lowest terms, and also reports the GCD it used and the decimal value, so you can check the result. It handles proper and improper fractions and is useful for homework, measurements, ratios and any time a fraction needs to be in its simplest form.
Fraction simplification formula
g = gcd(|numerator|, |denominator|) (Euclidean algorithm)
simplified numerator = numerator / g
simplified denominator = denominator / g
decimal value = numerator / denominator
Example: 12/18, g = 6, gives 2/3
The Euclidean algorithm computes the GCD by repeatedly taking remainders. Whole-number inputs give an exact reduced fraction.
Fraction context
- A fraction is in lowest terms when its GCD is 1.
- Improper fractions (top larger than bottom) reduce the same way and have a decimal value of 1 or more.
- The sign is carried to the numerator of the simplified fraction.
- A GCD of 1 means the fraction was already simplified.
- A zero denominator is undefined and returns n/a.
Fraction simplifier: frequently asked questions
How do you simplify a fraction?
Divide both the numerator and the denominator by their greatest common divisor (GCD). For 12 over 18, the GCD is 6, so dividing both gives 2 over 3, which is the fraction in lowest terms.
What is the greatest common divisor?
The GCD of two whole numbers is the largest number that divides both without a remainder. It is found efficiently with the Euclidean algorithm, which repeatedly replaces the larger number by its remainder when divided by the smaller until one becomes zero.
What does lowest terms mean?
A fraction is in lowest terms when the numerator and denominator share no common factor other than 1, meaning their GCD is 1. At that point the fraction cannot be reduced further.
Can this simplify improper fractions?
Yes. An improper fraction (numerator larger than denominator) is reduced the same way. For example 18 over 12 reduces to 3 over 2. The decimal value will be 1 or greater for improper fractions.
What if the denominator is zero?
A fraction with a zero denominator is undefined, so the calculator shows n/a. Division by zero has no value.
Official sources
- NIST Digital Library of Mathematical Functions: DLMF home.
- NIST: National Institute of Standards and Technology.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.