Reduce proper fractions, improper fractions, and mixed numbers to their simplest irreducible form. Displays greatest common divisor (GCD) proofs, prime factorization trees, and mixed number equivalents.
A fraction is in simplest form when its numerator and denominator are coprime integers, meaning their Greatest Common Divisor (GCD) is exactly 1. Follow these simple steps to reduce any fraction:
Enter the numerator and denominator, along with any optional whole number.
Find the Greatest Common Divisor of both numbers using Euclidean division.
Divide both the numerator and denominator by the GCD in a single step.
Verify that the new fraction cannot be reduced further (its new GCD is 1).
The fastest mathematical method. Divide top and bottom by their GCD:
Example: 24/36 → GCD(24, 36) = 12 → (24÷12) / (36÷12) = 2/3.
Break both numbers into prime factor trees and cancel shared prime factors:
Cancelling 2 × 2 × 3 (which equals 12) leaves 2 in the numerator and 3 in the denominator.
The Euclidean algorithm reveals GCD(120, 150) = 30. Divide numerator and denominator by 30:
GCD of 42 and 16 is 2. Reduce to 21/8, then express as mixed number:
Unreduced fractions like 120/150 or 84/144 obscure the underlying magnitude. Reducing to 4/5 or 7/12 reveals clear, intuitive proportions.
Bypasses tedious trial-and-error division by identifying the exact GCD in a single algorithmic sequence with prime factor cancellation proofs.
Math curricula and exams mandate final answers in lowest terms. This tool verifies irreducibility and provides mixed number forms for improper fractions.
Architectural and machine measurements like 28/32 in simplify immediately into standard fractional tooling sizes (7/8 in).
Calculates the exact Greatest Common Divisor instantly, dividing top and bottom in a single optimal step.
Visualizes the complete prime factorization of numerator and denominator with cancelled shared factors.
Automatically converts improper reduced fractions into mixed numbers and provides 4-decimal precision values.
| Original Fraction | GCD Divisor | Simplest Form | Decimal Equivalent |
|---|---|---|---|
| 12 / 16 | 4 | 3 / 4 | 0.75 |
| 18 / 24 | 6 | 3 / 4 | 0.75 |
| 25 / 100 | 25 | 1 / 4 | 0.25 |
| 45 / 60 | 15 | 3 / 4 | 0.75 |
| 50 / 200 | 50 | 1 / 4 | 0.25 |
Reduce fractions to simplest form using Euclidean GCD.
Find and generate lists of equal proportional fractions.
Convert fractions to exact terminating or repeating decimals.
Convert improper fractions into mixed numbers with quotient remainders.
Find the least common denominator across multiple fractions.
Order multiple fractions ascending or descending.
