What Is the Simplify Fraction Calculator?
This calculator reduces any fraction to its lowest terms — the simplest equivalent fraction where the numerator and denominator share no common factor other than 1. For example, \(12/18\) simplifies to \(2/3\). It works for proper fractions, improper fractions, and negative values, and also shows the greatest common divisor (GCD) used and the decimal equivalent.
How to Use It
Enter the numerator (top number) and denominator (bottom number) of your fraction, then read the result. The tool returns the fully reduced fraction, the GCD it divided by, and the decimal value. Any negative sign is moved to the numerator so the answer stays in standard form.
The Formula Explained
To simplify a fraction a/b, find the greatest common divisor of a and b, then divide both parts by it:
$$\frac{a}{b} = \frac{a \div \gcd(a,b)}{b \div \gcd(a,b)}$$
The GCD is computed with the Euclidean algorithm: repeatedly replace the pair \((a, b)\) with \((b, a \bmod b)\) until the remainder is zero. The last non-zero value is the GCD. Dividing by the largest shared factor guarantees the result is already in lowest terms.
Worked Example
Take \(12/18\). The factors of 12 are 1, 2, 3, 4, 6, 12; the factors of 18 are 1, 2, 3, 6, 9, 18. The greatest shared factor is 6, so \(\gcd(12, 18) = 6\). Dividing both parts: \(12 \div 6 = 2\) and \(18 \div 6 = 3\), giving the simplified fraction 2/3, with a decimal value of about 0.6667.
$$\frac{12}{18} = \frac{12 \div 6}{18 \div 6} = \frac{2}{3} \approx 0.6667$$
FAQ
What if the fraction is already simplified? If the GCD is 1, the fraction cannot be reduced further, so the calculator returns it unchanged.
Can I enter negative numbers? Yes. The calculator places the sign on the numerator and simplifies the absolute values, so \(-4/-8\) becomes \(1/2\) and \(4/-8\) becomes \(-1/2\).
What about a zero denominator? Division by zero is undefined, so a denominator of 0 is not a valid fraction and cannot be simplified.
