What does it mean to simplify a fraction?
Simplifying means rewriting the fraction with the smallest possible whole-number numerator and denominator that keep the same value.
Fraction Simplifier Calculator
Reduce a fraction to its simplest form and see the GCD used to get there.
Enter a fraction to simplify
Type the numerator and denominator, then calculate to reduce to lowest terms.
About this calculator
How to use Fraction Simplifier Calculator, plus the formulas and logic behind the results.
Tool description
The Fraction Simplifier divides the numerator and denominator by their greatest common divisor so the fraction is in lowest terms.
How to use
- Enter the numerator.
- Enter a non-zero denominator.
- Select Calculate to view the simplified fraction.
- Compare the original and simplified forms in the results.
Formulas & reference
g = gcd(|numerator|, |denominator|)Simplified = (numerator ÷ g) / (denominator ÷ g)
Simplifying reminders
- Divide top and bottom by the same GCD
- 8/12 simplifies to 2/3
- A denominator of 1 means a whole number
- Zero over any non-zero denominator is 0
Calculation logic
Integer inputs are reduced with Euclid’s algorithm for the GCD. The sign is normalized so the denominator is positive.
If the fraction is already in lowest terms, the simplified result matches the original (aside from sign normalization).
Fraction Simplifier Calculator FAQ
Common questions about this calculator and how to use the results.
What is the greatest common divisor?
The GCD is the largest positive integer that divides both the numerator and the denominator with no remainder.
Is 4/6 the same as 2/3?
Yes. Both represent the same value; 2/3 is the simplified form.
Can improper fractions be simplified?
Yes. Improper fractions simplify the same way as proper fractions.
What if the numerator is zero?
Zero over a non-zero denominator simplifies to 0/1 (or just 0).
Why is the denominator always shown positive?
By convention the negative sign belongs with the numerator (or the whole value), not the denominator.