Simplify Fractions Calculator — Reduce to Lowest Terms
Enter a numerator and denominator to get the fraction in its simplest (lowest-terms) form — the calculator finds the Greatest Common Divisor and divides both parts by it.
- 1
GCD via Euclidean algorithm
GCD(12, 18) = 6The greatest common divisor — dividing by it reaches lowest terms in one step. - 2
Simplified numerator = |num| ÷ GCD
12 ÷ 6 = 2 - 3
Simplified denominator = |den| ÷ GCD
18 ÷ 6 = 3 - 4
Decimal value = simplified num ÷ den
2 ÷ 3 = 0.66666667
How does this calculator work?
Divide both numerator and denominator by GCD(a, b) — found via the Euclidean algorithm (repeatedly replace with the remainder until 0). For example 12/18 → GCD = 6 → 2/3. One step reaches the lowest-terms form because the GCD is the largest common factor.
Formula
How this is calculated
A fraction a/b is in lowest terms when GCD(a, b) = 1 — the numerator and denominator share no common factor other than 1. To reduce it, divide both parts by their GCD. The GCD is computed with the Euclidean algorithm: repeatedly replace the larger number with the remainder when dividing by the smaller, until the remainder is zero; the last non-zero remainder is the GCD. Dividing by the GCD is the single most efficient step because it reaches the lowest-terms form immediately.
For example, 12/18 → GCD(12, 18) = 6 → 2/3. Both represent the same value (≈ 0.6̄) but 2/3 uses the smallest whole numbers. Improper fractions (numerator larger than denominator) are simplified the same way: GCD(8, 6) = 2 → 4/3.
By convention, the negative sign is placed in the numerator: −12/18 simplifies to −2/3, and 12/−18 also simplifies to −2/3. Division by zero is undefined and produces no result.
Frequently asked questions
The GCD is the largest common factor of numerator and denominator. Dividing by the largest common factor in one step removes all shared factors at once. Any smaller common factor would still leave shared factors, requiring additional reduction steps.
Yes. An improper fraction like 8/6 simplifies to 4/3 using the same method (GCD = 2). The result stays as an improper fraction — converting to a mixed number (1⅓) is a separate operation.
Yes. If exactly one of numerator or denominator is negative, the result is negative. By convention the negative sign is placed in the numerator: −12/18 and 12/−18 both simplify to −2/3.
Also known as
TG we-Calculate Editorial Team. (2026). Simplify Fractions Calculator — Reduce to Lowest Terms [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/simplify-fractions-calculator
TG we-Calculate Editorial Team. "Simplify Fractions Calculator — Reduce to Lowest Terms." TG we-Calculate. 2026. https://we-calculate.com/calculator/simplify-fractions-calculator.
TG we-Calculate Editorial Team, "Simplify Fractions Calculator — Reduce to Lowest Terms," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/simplify-fractions-calculator
@misc{wecalculate_simplify_fractions_calculator, title = {Simplify Fractions Calculator — Reduce to Lowest Terms}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/simplify-fractions-calculator}}, year = {2026}, note = {TG we-Calculate} }
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