Fraction Simplifier
Reduce any fraction to its lowest terms instantly by finding the greatest common divisor. Use it when adding fractions, checking equivalence, or simplifying homework answers.
About this calculator
A fraction is in its simplest form when the numerator and denominator share no common factors other than 1. To reduce a fraction, divide both the numerator and denominator by their Greatest Common Divisor (GCD). The GCD is found using the Euclidean algorithm: repeatedly replace the larger number with the remainder of dividing the two numbers until the remainder is zero. The formula is: simplified fraction = (numerator ÷ GCD) / (denominator ÷ GCD). For example, GCD(8, 12) = 4, so 8/12 simplifies to 2/3. This process always produces a unique, fully reduced fraction.
How to use
Suppose you want to simplify 18/24. Enter 18 as the numerator and 24 as the denominator. The calculator finds GCD(18, 24) = 6. It then divides both parts: 18 ÷ 6 = 3 and 24 ÷ 6 = 4. The result is 3/4. You can verify: 3 and 4 share no common factors other than 1, confirming the fraction is fully reduced.
Frequently asked questions
How do you simplify a fraction to its lowest terms?
To simplify a fraction, divide both the numerator and denominator by their Greatest Common Divisor (GCD). The GCD is the largest integer that divides both numbers evenly. Once both parts are divided by the GCD, the resulting fraction cannot be reduced further. For example, 12/18 simplifies to 2/3 because GCD(12, 18) = 6.
What happens when you simplify an improper fraction?
An improper fraction — where the numerator is larger than the denominator — is simplified the same way as a proper fraction: divide both parts by their GCD. For example, 14/6 simplifies to 7/3, which is still an improper fraction. You can optionally convert it to a mixed number (2 and 1/3), but the simplification step itself does not change the process.
Why is simplifying fractions important in math?
Simplified fractions are easier to compare, add, and work with in further calculations. Two fractions that look different, like 4/6 and 2/3, are actually equivalent — simplifying reveals this immediately. In fields like engineering, cooking, and finance, working with reduced fractions avoids arithmetic errors and makes results more readable. Most math teachers and standardized tests also require answers in simplest form.