Simplifying Fractions

Simplifying fractions is something that you must know to make your life easy while dealing with fraction algebra.

What is meant by simplifying a fraction?

Understanding the answer to this particular question can open up a number of road blocks you might be having towards learning the fraction concepts. To explain this to you I will take a very simple example. I am sure that will put things into perspective.

There is a cake kept in a plate on your dining table. You know you cannot eat the entire cake because some of your friends are joining you for small party. But then you feel hungry and are unable to resist the temptation. You pray to God to tell you what fraction of the cake is yours to eat.

You know God listens and the good child that you are; he answers your question; albeit with a twist.

“You can have 19/36th parts of the cake” he says.

With that hunger you are certainly not in a mood to divide the cake into 36 parts and then eat 19 of them. What is that you want?

A simplified answer did I hear you say.

That’s 1/4th of the cake for you. This is the power of simplifying fractions. As humans we are tuned to see simpler things in a friendly manner as against complicated presentations. 19/36 can be simplified to ¼ and your brain processed ¼ very easily.

Thus simplifying fractions is not only important for your academic success but familiarity with them will ensure you have a good and sound understanding of the application of mathematics in your day to day life.

Techniques of Simplifying Fractions

Here are two basic techniques that you can use to simplify or reduce fractions to their simplest forms. If you want to see the functions being used in examples then check this article on reducing fractions that clearly lays out the steps involved. The example mentioned will surely help you understand it better.

Technique #1 Continuous Division Till No More

Huh! Interesting name.

Well there it is. The name says it all.

In this technique the pursuit is to arrive at the simplest configuration of the fraction by continuously dividing the numerator and the denominator. It’s a good idea to be aware of the divisibility rules to use this method effectively but then to start with it’s not mandatory.

First consider dividing the numerator with small numbers like 2, 3, 5, 7 etc. If you find that the numerator is divisible then divide the denominator with the same number. Keep doing this until you arrive at a stage where the numerator and the denominator cannot be further divided by a single number. That is when the fraction arrives at its simplest form.

Technique #2 Division by Greatest Common Factor

This is a slightly different approach but the inherent logic remains same. The first step involved here is to find the greatest common factor for the numerator and the denominator.

Then in the next stage divide the numerator and denominator by the greatest common factor to get the simplest form of the fraction. That’s it! If you have the GCF ready then this is very straight forward and simple.

If you want to catch up with the steps in some more detail then please check the tutorial on reducing fractions.

Hope this article was able to give you the required information on simplifying fractions. Hope to see you around.


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