Quick guide
How to simplify a fraction
- Choose a positive or negative sign, then enter the numerator and denominator.
- Select Simplify fraction.
- Read the fraction in lowest terms along with its greatest common factor, mixed number, and decimal value.
- Open the steps to see exactly how the numerator and denominator were divided.
The denominator must be greater than zero. The numerator may be zero or larger than the denominator, so the calculator works with proper fractions, improper fractions, and zero.
What is the simplest form of a fraction?
A fraction is in simplest form—also called lowest terms—when its numerator and denominator share no whole-number factor other than 1. Reducing a fraction changes how it is written, not its value.
For example, 6/8 and 3/4 represent the same amount. Because both 6 and 8 can be divided by 2, 6/8 is not in lowest terms. The fraction 3/4 cannot be reduced further.
Reduce fractions with the greatest common factor
The fastest exact method is to find the greatest common factor (GCF), sometimes called the greatest common divisor (GCD). Divide both terms by that one number:
Using the GCF avoids repeated trial division. When the GCF is 1, the original fraction is already in simplest form.
Worked example: simplify 42/56
The common factors of 42 and 56 include 1, 2, 7, and 14. The greatest common factor is 14.
42 ÷ 14 = 3
56 ÷ 14 = 4
Therefore, 42/56 = 3/4. The result is in lowest terms because 3 and 4 share no common factor greater than 1.
Improper, negative, and zero fractions
Improper fractions
Reduce them in the same way. The result section also converts the simplified fraction to a mixed number.
Negative fractions
Simplify the absolute numerator and denominator, then keep one negative sign with the result.
Zero numerator
A zero numerator over any nonzero denominator reduces to 0.