   # Reducing Fractions to Lowest Terms

 Our Pre-Algebra tutorial software program contains over 60 topic areas. One of them is Reducing Fractions to Lowest Terms, and this page summarizes the main ideas of this topic. This page is intended for review, and is not a substitute for the interactive, self-paced tutorials of the MathTutor pre-algebra software program.

General Explanation

In this lesson we will learn to reduce fractions to LOWEST TERMS.

A fraction in lowest terms is equivalent to the original fraction. To reduce a fraction to lowest terms, divide the numerator by the greatest common factor larger than 1. If there is no common factor greater than 1, the fraction is already in lowest terms.

Sample Problem 1

Reduce 70/231 to lowest terms.

Solution

First, we must find the greatest common factor of the numerator and denominator. To do this we will factor the numerator and denominator:
```70 = 2 x 5 x 7
231 = 3 x 7 x 11
```
The greatest common factor (GCF) is the product of the factors both the numerator and denominator have in common. From the factorization above we see that the only factor the numerator and denominator share is 7. So 7 is the GCF and we divide the top and bottom of the fraction by 7:
```70 / 7 = 10
231 / 7 = 33
```
Therefore, 70/231 in lowest terms is 10/33.

Sample Problem 2

Reduce 22/165 to lowest terms.

Solution

First we must find the GCF of 22 and 165. To do this we factor:
```22 = 2 x 11
165 = 3 x 5 x 11
```
The GCF is 11, so we divide the top and bottom by 11:
```22 / 11 = 2
165 / 11 = 15
```
So the final answer is 2/15. Therefore, 22/165 in lowest terms is 2/15.