Fraction Reduction Calculator

Want to reduce a fraction to its lowest terms? Cool, try this fraction reduction calculator.




About This Calculator

This fraction reduction calculator will reduce any fraction to its lowest terms. It provides the reduced fraction answer in proper or improper form, and also as a mixed fraction if the answer is an improper fraction. In addition to providing the reduced fraction answer, this fraction reduction calculator also provides a detailed method explanation to show you how to get the answer.


Terminology

The number on top of a fraction is called the "numerator" and the number on the bottom is called the "denominator."


How to Reduce Fractions

Fractions like 8 / 16, or 6 / 9, or 55 / 66, are examples of fractions that can be reduced, which just means that it's possible to show them with smaller numbers on top and bottom without changing their overall value. For example:

  • 8 / 16 can be reduced to 1 / 2
  • 6 / 9 can be reduced to 2 / 3
  • 55 / 66 can be reduced to 5 / 6

You should always reduce a fraction so that it's got the lowest possible numbers on top and bottom, it's just considered good form.

You'll know you can reduce a fraction if you can find a number (other than 1) by which both the numerator (i.e. the number on the top) and the denominator (i.e. the number on the bottom) can be evenly divided. If you can come up with more than one number by which you can evenly divide both the numerator and the denominator then you want to use the largest number you can find, because this number will reduce your fraction the furthest (i.e. it will reduce the fraction to "lowest terms"). The largest possible number by which you can evenly divide both the numerator and the denominator of fraction is called their "greatest common divisor," or GCD. When you find a fraction's GCD it can be factored out (i.e. removed) from both the numerator and denominator of the fraction, after which it cancels itself out, becomes 1, and can disappear from the equation. Here's an example of how to reduce a fraction:

6 8 = 3 4 x 2 2 = 3 4 x 1 = 3 4

In the example above "2" is the greatest common divisor, or GCD, for the fraction 6 / 8. "2" is the GCD because it is the largest number by which both the numerator (6) and the denominator (8) can be evenly divided, and as such is the number that must be factored out of both the numerator and denominator to reduce the fraction to lowest terms.