Reducing Fractions to Lowest Terms

A fraction is said to be in lowest term if both the numerator and denominator cannot be divided by evenly by any number except one. This process is the opposite of raising the the terms of a fraction, and to reduce a fraction to its  lowest term, you simply divide both the numerator and the denominator by the same number.

Example

Reduce 18/24 to the lowest term

Solution

Divide both the numerator and the denominator by 6:

Example

Reduce 15/25 to lowest term

Solution

Divide both the numerator and the denominator by 5:

Most often than not, and also depending on the type operation that you're working on, it is desirable to a fraction to its lowest terms. This means bring the fraction down or simplify the fraction to the lowest term.This term is used also:

Simplest form. They all mean the same. The two previous examples showed only one way to do this operation. But, there is second way to do this operation. First let us review this rule.

Rule:  To reduce a fraction to lowest terms, divide both the numerator and the denominator of a fraction by the highest number  that can be divided evenly into both. To simplify a fraction the following steps must be followed:

1) Identify the greatest common factor, (GCF) of the numerator and denominator

2) Divide both the numerator and denominator by the (GCF).

Example:

Simplify, and reduce this fraction to the lowest term   48/26

Greatest common factor for 48 = 2, 4, 6, 8, 12, 24, 48…

Do the same for 26 =  2, 13, 26

What  is the highest number do they share? 2

They share or have in common 2, which means that the largest even divisor of both 48 and 26 is 2.  This only means that both the numerator and the denominator will be divided by 2

This type of fraction is known as "irreducible fraction". Because, irreducible fractions are fractions that cannot be reduced nor simplified. This type of fraction is said to be in the lowest form, or simplest form.

Example:

Reduce 3/9 in its simplest form.

Solution

Step 1) Divide both the numerator and denominator by 3

Step 2) We now have

This simple calculator is here to help you in your homework. Try to understand the concepts on how to reduce fractions to lowest terms, before using this calculator.

 /