Fraction Simplifier Calculator

Simplify any fraction to its lowest terms instantly. Enter the numerator and denominator and get the reduced fraction with step-by-step GCF factoring and a visual diagram.

📐 Fraction Simplifier Calculator
Result
Visual Diagram
Definition

What is Fraction Simplifier Calculator?

A Fraction Simplifier Calculator reduces a fraction to its simplest form by dividing both the numerator and denominator by their Greatest Common Factor (GCF). A fraction is in simplest form when the numerator and denominator share no common factors other than 1.

Simplifying fractions is a fundamental math skill used in algebra, geometry, cooking, engineering, and everyday measurements. For example, 12/16 simplifies to 3/4 because GCF(12, 16) = 4.

The Fraction Simplifier Calculator finds the GCF using the Euclidean algorithm, divides both parts of the fraction, and shows every step of the process. The calculator also displays a visual pie chart comparing the original and simplified fractions to confirm the fractions represent equal portions.

Interactive Visualization
Formula

Fraction Simplifier Calculator Formula

To simplify a fraction, divide both numerator and denominator by their GCF:

Simplified = (Numerator ÷ GCF) / (Denominator ÷ GCF)

Step-by-step process:

  1. Find GCF of numerator and denominator using the Euclidean algorithm
  2. Divide numerator by GCF
  3. Divide denominator by GCF
  4. The resulting fraction is in lowest terms

Example: Simplify 24/36

GCF(24, 36) = 12 → 24 ÷ 12 = 2, 36 ÷ 12 = 3 → Result: 2/3

Examples

Worked Examples

Simplify 18/24

GCF(18, 24) = 6. Dividing both by 6: 18÷6 = 3, 24÷6 = 4. Result: 3/4.

Simplify 45/60

GCF(45, 60) = 15. Dividing both by 15: 45÷15 = 3, 60÷15 = 4. Result: 3/4.

Simplify 7/21

GCF(7, 21) = 7. Dividing both by 7: 7÷7 = 1, 21÷7 = 3. Result: 1/3.

Already Simplified: 5/8

GCF(5, 8) = 1. The fraction 5/8 is already in simplest form because 5 and 8 share no common factors.

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FAQ

Frequently Asked Questions

Common questions about the fraction simplifier calculator.

Find the Greatest Common Factor (GCF) of the numerator and denominator, then divide both by the GCF. Example: 12/18 → GCF(12,18) = 6 → 12÷6 / 18÷6 = 2/3.

Simplifying a fraction means reducing the fraction to its lowest terms — the smallest possible numerator and denominator that represent the same value. The fraction 6/8 and 3/4 have the same value, but 3/4 is simplified.

A fraction is fully simplified when the GCF of the numerator and denominator is 1. This means the numerator and denominator share no common factors other than 1.

Yes. Simplify the absolute values normally, then keep the negative sign in the numerator. Example: -15/25 → GCF(15,25) = 5 → -3/5.

The Greatest Common Factor (GCF) is the largest number that divides both numbers evenly. The Euclidean algorithm finds the GCF by repeatedly dividing: GCF(48,18) → 48÷18 = 2 remainder 12 → 18÷12 = 1 remainder 6 → 12÷6 = 2 remainder 0 → GCF = 6.