What is the Simplify Fraction Calculator?
This calculator reduces any fraction to its lowest terms. A fraction is in lowest terms when the numerator and denominator share no common factor other than 1. To get there, we divide both the top and bottom of the fraction by their greatest common factor (GCF), also called the greatest common divisor (GCD).
How to use it
Enter the numerator (top number) and the denominator (bottom number), then read the simplified result. The tool also shows the GCF used, the decimal value of the fraction, and an equivalent mixed number. Negative numbers are allowed — the sign is shown on the numerator.
The formula explained
The key step is finding \(g = \gcd(a, b)\). The calculator uses the Euclidean algorithm: repeatedly replace the larger number by the remainder of dividing the two numbers until the remainder is zero; the last nonzero value is the GCF. The reduced fraction is then $$\frac{a}{b} = \frac{a \div g}{b \div g}, \quad g = \gcd\!\left(a,\ b\right)$$ Because \(g\) is the largest factor common to both, dividing by it guarantees the result cannot be reduced further.
Worked example
Take \(\frac{24}{36}\). The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24 and of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The greatest one they share is 12, so \(g = 12\). Dividing both gives $$24 \div 12 = 2 \quad\text{and}\quad 36 \div 12 = 3$$ so \(\frac{24}{36}\) simplifies to \(\frac{2}{3}\), which equals \(0.6667\) as a decimal.
FAQ
What if the fraction is already in lowest terms? The GCF will be 1 and the fraction is returned unchanged.
Can I enter an improper fraction? Yes. For example \(\frac{9}{6}\) reduces to \(\frac{3}{2}\), shown as the mixed number \(1\tfrac{1}{2}\).
What about negative fractions? The calculator simplifies the magnitudes and places the overall sign on the numerator.
