Simplify Fractions Calculator
Reduce any fraction to lowest terms with the GCD, mixed-number, and decimal forms shown.
Written by Golam Rabbani, Founder & Lead Engineer
How to use this simplify fractions calculator
- Type the top number of your fraction into the Numerator field (negative values are allowed).
- Type the bottom number into the Denominator field — it must be a non-zero whole number.
- Click Simplify to instantly see the fraction in its lowest terms, the greatest common divisor (GCD) that was divided out, and the decimal equivalent.
- If the fraction is improper (numerator larger than denominator), the mixed-number form is shown automatically beneath the result.
- Use Copy to send the result to your clipboard, or Reset to clear the fields and start a fresh calculation.
About this simplify fractions calculator
A fraction is in lowest terms — also called simplest form — when the only positive integer that divides both the numerator and denominator evenly is 1. Reducing a fraction means finding that common factor and dividing it out, so the numbers become as small as possible while representing the exact same value.
The most reliable method for finding the factor to divide by is the Euclidean algorithm, which computes the greatest common divisor (GCD) of two integers through repeated remainders. For example, to simplify 18/24: first find GCD(18, 24). Divide 24 by 18 — remainder 6. Divide 18 by 6 — remainder 0. So GCD = 6. Divide both parts by 6: 18 ÷ 6 = 3 and 24 ÷ 6 = 4, giving 3/4. That fraction cannot be reduced further because GCD(3, 4) = 1.
This calculator applies that algorithm automatically. After reducing, it also converts improper fractions — where the numerator exceeds the denominator — into their mixed-number form, and shows the decimal value so you can cross-check. Negative fractions and large numbers are both supported. The tool runs entirely in your browser; no data is sent anywhere.
FAQ
- How do you simplify a fraction?
- Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by that number. The result is the fraction in its simplest form. For example, 12/18 has GCD 6, so 12 ÷ 6 = 2 and 18 ÷ 6 = 3, giving 2/3.
- What is the greatest common divisor (GCD)?
- The GCD of two integers is the largest positive integer that divides both of them without a remainder. It is computed efficiently using the Euclidean algorithm: repeatedly replace the larger number with the remainder of dividing the larger by the smaller until the remainder is zero. The last non-zero value is the GCD.
- How do I know a fraction is fully reduced?
- A fraction a/b is fully reduced when GCD(a, b) = 1, meaning the numerator and denominator share no common factor other than 1. This calculator tells you the GCD that was divided out; if it reports 1, the fraction was already in lowest terms.
- Can this tool reduce improper fractions and show the mixed number?
- Yes. Enter any improper fraction (where the numerator is greater than the denominator) and the calculator will first reduce it to lowest terms, then convert it to a mixed number automatically. For instance, 22/8 reduces to 11/4 and displays as 2 3/4.
- Does it work with negative fractions?
- Yes. You can enter a negative numerator (e.g. -9 over 12). The calculator reduces the absolute values and keeps the negative sign on the numerator in the result, so -9/12 becomes -3/4.
- Is this tool free and private?
- Completely. There are no accounts, no fees, and no data collection. All calculations happen directly in your browser — nothing is sent to a server.