Simplify Fractions Calculator

About Simplify Fractions Calculator

To simplify a fraction, find the GCD of the numerator and denominator and divide both by it.

How to use this calculator

1. Enter the numerator and denominator of your fraction.
2. Click calculate to find the GCD of the two numbers.
3. The calculator divides both parts by that GCD.
4. Read the simplified fraction and the step-by-step reduction.

The formula explained

The formula \(\frac{a}{b} = \frac{a/\gcd(a,b)}{b/\gcd(a,b)}\) shows how a fraction is reduced to simplest form. It computes an equivalent fraction with the same value but smaller whole-number terms.

• a = the numerator, or top number, of the fraction
• b = the denominator, or bottom number, of the fraction
• gcd(a,b) = the greatest common divisor of a and b, the largest number that divides both exactly

Step by step method

1. Find the greatest common divisor of the numerator and denominator.
2. Divide both the numerator and denominator by that number.
3. Write the result as the simplified fraction.

Worked example

Problem. Simplify the fraction \(24/36\).

1. The greatest common divisor of 24 and 36 is 12.
2. Divide both numbers by 12: \(24 \div 12 = 2\) and \(36 \div 12 = 3\).
3. So the fraction in simplest form is \(2/3\).

Tips and common mistakes

• Only divide by a common factor, then check that no number greater than 1 still divides both parts exactly.
• If the fraction is improper or negative, simplify it the same way, because the reduction process does not change the value.

Frequently asked questions