Simplify Fractions Calculator

About the Simplify Fractions Calculator

Simplifying (or reducing) a fraction means rewriting it as an equivalent fraction with the smallest possible whole numbers in the numerator and denominator. For instance, 4/8, 3/6, and 50/100 all simplify to 1/2.

Our Simplify Fractions Calculator reduces both proper and improper fractions to their lowest terms by computing the Greatest Common Divisor (GCD), listing all factors, and displaying the equivalent mixed number, decimal, and percentage.

Fraction Simplification Formula

To reduce any fraction a/b to its simplest form, divide both the numerator and denominator by their Greatest Common Divisor:

How to Simplify a Fraction to Lowest Terms

1. List the Factors or Use the Euclidean Algorithm: Find all positive integers that divide both the numerator a and denominator b evenly.
2. Identify the Greatest Common Divisor (GCD): Pick the largest factor shared by both numbers.
3. Divide Top and Bottom by the GCD: Divide the numerator by the GCD and the denominator by the GCD.
4. Convert Improper Fractions if Needed: If the reduced numerator is larger than the denominator, divide to express it as a mixed number.

Worked Example: To simplify 18/24, the factors of 18 are 1, 2, 3, 6, 9, 18 and the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The GCD is 6. Dividing top and bottom by 6 gives (18 ÷ 6)/(24 ÷ 6) = 3/4.

Frequently Asked Questions (FAQ)

How do I know when a fraction is fully simplified?

A fraction is fully simplified (in lowest terms) when the only common factor between the numerator and denominator is 1 (meaning they are coprime).

Can improper fractions be simplified?

Yes. An improper fraction like 14/4 can be reduced by dividing top and bottom by 2 to get 7/2, and then written as the mixed number 3 1/2.

Does simplifying a fraction change its value?

No. Dividing both the numerator and denominator by the same non-zero number is equivalent to dividing by 1, so the numerical value remains identical.