How to Simplify Negative Fractions

Instructor: Sarah Palacios

Sarah has completed her master’s degree in Education from the University of Texas and has received her bachelors in Interdisciplinary Studies specializing in Mathematics. She graduated with honors, Magna cum Laude, from Texas A&M University. She currently holds a principal certificate, a teaching certificate for Mathematics grades 4-8, a teaching certificate for EC – 6 as a generalist, as well as an ESL certificate. She has been an elementary school teacher for the past 4 years and is passionate about educating students to the highest degree.

We all like it when things are easy and simple. Simplifying fractions makes them easier to work with. And the best news is, simplifying fractions, both positive and negative, is, well...simple! This lesson will show you how to simplify fractions and will provide many examples.

Fraction Action

Have you ever noticed that many times when a math concept deals with fractions, pizza becomes involved? That is because not only does pizza make a great meal, but it also makes a great fraction example. Take a look at our pizza image - this pizza has 8 slices. As you know, a fraction represents a part of a whole. Since no one has yet eaten any of this pizza, we still have all the parts of the whole, and can write the pizza slices fraction as 8/8.

But, you got hungry and have just eaten 4 of the slices! Now our fraction is going to be 4/8 - we now only have 4 pieces out of the 8 original pieces. I don't know about you, but I like it when things are easy or simple. Although we could work with our 4/8 fraction like it is, we could also simplify, or reduce, it and make it easier to work with. Let's see how.

8 slices in a pizza

Make It Simple

Keeping things simple, there are only two steps that you need to take to simplify a fraction:

Step 1: Find the Greatest Common Factor, also known as GCF, of the numerator and denominator

Factors are numbers that are multiplied together to get another number (known as the product). For example, if we multiply 3 x 5 to get 15, the 3 and the 5 are factors of 15. The GCF would then be the largest factor that is common to both the numerator and denominator, and can be found by listing all the factors of both the numerator and denominator and finding the greatest of these.

Finding GCF

Step 2: Divide both the numerator and denominator by the GCF

OK. Now that we have our simple two-step process, let's look at the fraction we discussed above: 4/8. How can this be simplified?

Step1: Find the GCF of the numerator and denominator:

The factors of 4: 1, 2, 4

The factors of 8: 1, 2, 4, 8

The common factors are 1, 2 and 4. However, the greatest of these common factors is 4.

Step 2: Divide both the numerator and denominator by the GCF:

In this case, the GCF was 4.

Simplify Fraction

Therefore, the simplified, or reduced, fraction is 1/2.

Simplifying Negative Fractions

We are going to continue with our 'keep it simple' theme. We use the same easy process to simplify negative fractions, but add one final step.

Let's look at the following negative fraction: -2/8

We simply ignore the negative sign and continue with our original two steps:

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