How to Simplify Fractions?

The term 'fraction' means a part of the whole. Here is information on the basics, as well as the method of simplifying fractions.
ScienceStruck Staff Oct 8, 2018
While math lovers would find the task of simplifying fractions to be a child's play, they can be extremely confusing for some. However, fractions are not as difficult as they may seem to be. In order to learn the process of fraction simplification, you first need to comprehend the basics.

What are fractions?

The word 'fraction' literally means a part. In Mathematics, a fraction means a part of a whole number. Fractions are composed of a numerator and a denominator.
Here is a pictorial representation of a fraction. Let us take the example of a pizza. If we cut it in to 8 equal pieces, and you take 3 pieces out of it, the portion of the pizza that you have is a fraction of pizza.

Simplifying Fractions

Let us take another example of an 8-piece pizza, of which you take 4 parts. So, from the definition, you will say that you have 4/8 part of the pizza. It is also correct to say that you have half (1/2) of the pizza. That is the simplified form of the fraction 4/8.
The image A shows 4 out of the eight parts that you have. Divide both numerator and denominator by 2 each, so that we have the image B. Thereafter, we divide the numerator and denominator by 2 to get the simplified form of 4/8, which is 1/2. So, simplifying fractions simply means reducing the fraction to its simplest form.
Moving on to improper fractions, in which the numerator is greater than the denominator. Steps to simplify improper fractions:
  • Determine a common factor between the numerator and denominator. Now, a common factor is the number that can be used to divide both numbers to get two whole numbers. For example, 2 is the common factor of 4 and 8.
  • After this, divide the numerator and denominator by the common factor.
  • Just keep repeating this process until there exists no common factors between the numerator and denominator. 
  • The fraction is simplified when no common factors exists.

Simplifying Complex Fractions

Complex fractions do not have whole numbers as numerator or denominator. Here, the numerator and the denominator is another fraction (proper or improper).
You just need to find a common factor and divide. But, first convert the complex fraction into a simple one, which may again be proper or improper. Thereafter, follow the steps discussed. Here's an example again.

Simplifying Fractions With Variables

Here's an example of a fraction with variables. Fractions with variables are more difficult when it comes to simplification. However, the method remains the same. You need to find a common factor.
Simplification of fractions and various other concepts of Mathematics will no longer seem to be difficult if you practice math on a daily basis. So, the next time you need to simply a fraction, remember the four simple steps of simplification that have been mentioned.