Reduce Any Fraction to Lowest Terms
A fraction is in lowest terms when the numerator and denominator share no common factor other than 1. This fraction simplifier reduces any fraction instantly. Enter the numerator and denominator to see the simplified fraction, its decimal equivalent, its mixed number form (for improper fractions) and the greatest common divisor (GCD) used to reduce it.
How Fractions Are Simplified
Step 1: find the GCD of the numerator and denominator using the Euclidean algorithm. Step 2: divide both the numerator and denominator by the GCD.
Example: simplify 48/180. The GCD of 48 and 180 is 12. 48 ÷ 12 = 4 and 180 ÷ 12 = 15, so 48/180 = 4/15 ≈ 0.2667.
Improper fraction example: 22/8 has a GCD of 2, so it simplifies to 11/4, which is the mixed number 2 3/4, or 2.75.
The Euclidean Algorithm
To find the GCD of two numbers, divide the larger by the smaller and keep the remainder. Then repeat with the smaller number and the remainder until the remainder is 0. The last non-zero remainder is the GCD. For 180 and 48: 180 = 3 × 48 + 36, 48 = 1 × 36 + 12 and 36 = 3 × 12 + 0, so the GCD is 12.
Frequently Asked Questions
What is a mixed number?
A mixed number combines a whole number and a proper fraction, such as 2 3/4. Any improper fraction (where the numerator is larger than the denominator) can be written as a mixed number.
How do I know if a fraction is already simplified?
A fraction is fully simplified when the GCD of its numerator and denominator is 1. If the calculator shows a GCD of 1, your fraction is already in lowest terms.
Can I simplify negative fractions?
Yes. The negative sign is kept with the result. For example, −6/8 simplifies to −3/4.