How to Reduce Fractions: Terms & Overview

Instructor: Jennifer Beddoe

Jennifer has an MS in Chemistry and a BS in Biological Sciences.

Not only is it mathematically more accurate, but it just makes common sense that when you write a fraction it should be written in its simplest form. This lesson will show you two ways to reduce fractions. At the end, there is a quiz to test your understanding.

What is a Fraction?

'I ate half a pizza for dinner, and I'm stuffed!'

'I can't believe the government takes $220 from my $1000 paycheck.'

Each of these are statements that you have heard - or maybe even said before - and both of them represent fractions. Fractions are ratios of numbers that represent a part of a whole. When you want to talk about something that is only a portion of the entire thing, you use fractions, like the ½ of a pizza statement above. It is a portion of the pizza.

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In the other statement, 220/1000 is a fraction that represents the portion of money that is taken out in taxes from this fictional worker.

Simple Fractions

A simple fraction is one that is in its simplest form. This means that the Greatest Common Factor between the numerator (number on top) and denominator (number on bottom) of the fraction is 1. There are no other numbers that will divide into both the numerator and denominator evenly.

Why Simplify Fractions?

The next question you may be asking is, why bother? Why not just leave them the way they are? Well, there are a few reasons that you might want your fraction in its simplest form.

  • It's common mathematical practice. In mathematics, it is just a given that a person will always reduce their answer to its simplest form. This makes it easier for other mathematicians who come along later to understand and use the information without a lot of confusion.
  • It makes it easier to work with. Which problem seems easier to handle?

215/645 + 96/144 or 1/3 + 2/3

You probably said the second one, because the fractions used are in their simplest form.

  • It makes sense. If there were a dozen cookies on the table, and after a few minutes, only six of them were left, you wouldn't say, 'Oh, 6/12 of the cookies were eaten.' No, you would say that half of the cookies were eaten.

How to Simplify Fractions

There are two ways to simplify fractions, and it's really just a matter of personal preference which method you choose to use.

1. Divide both the numerator and denominator by the same number until there are no more numbers they have in common.

Example: Simplify the fraction 24/108.

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The first step is to divide both numbers by 2, then divide them by 2 again, and then finally divide both numbers by 3. At this point, the fraction is 2/9, and there are no numbers that will divide evenly into both 2 and 9, so the fraction is in its simplest form. There is no rule as to the order by which you divide. If you wanted to divide by 3 first, then by 2 and then 2 again, that would work as well. The only rule is that you have to do the same thing to both the numerator and denominator. For example, you can't divide the numerator by 6 and the denominator by 4.

2. Find the Greatest Common Factor of the two numbers and divide both by that number.

You can find the greatest common factor of both numbers by following these steps:

  • List all the factors of each number (let's use the numbers 36 and 54 as examples)

36 - 1, 2, 3, 4, 6, 9, 12, 18, and 36

54 - 1, 2, 3, 6, 9, 18, 27, and 54

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