MATH · FRACTION
Fraction Calculator
Simplify a fraction to its lowest terms, or add two fractions and get the result in simplified form. Uses GCD reduction.
About This Calculator
Fractions simplified to lowest terms are easier to read and compare. This calculator reduces a single fraction using the greatest common divisor (GCD), or adds two fractions and gives the result in simplified form — all in integer arithmetic with no rounding.
How It Works
In Simplify mode, enter the numerator and denominator of one fraction. In Add mode, enter both fractions. The result is always reduced to lowest terms using the Euclidean GCD algorithm. Negative denominators are automatically normalised so the sign appears in the numerator.
The Formula
Simplify: n/d → (n/gcd)/(d/gcd) Add: a/b + c/d = (a·d + b·c) / (b·d) → simplify
- gcd
- greatest common divisor of numerator and denominator
Frequently Asked Questions
- What does "lowest terms" mean?
- A fraction is in lowest terms when the only common factor of numerator and denominator is 1. For example, 6/8 simplifies to 3/4 because gcd(6,8)=2.
- Can I simplify a negative fraction?
- Yes. A negative denominator is normalised to a positive denominator with a negative numerator — so 4/−8 simplifies to −1/2.
- Why is adding fractions done in integers?
- Cross-multiplying and then simplifying avoids floating-point rounding errors that would occur if you converted to decimals first.