Adding & Subtracting Negative Fractions

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  • 0:00 Working with Negative Numbers
  • 0:55 Adding Negative Fractions
  • 2:43 Subtracting a Negative…
  • 4:31 Lesson Summary
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Lesson Transcript
Instructor: Mia Primas

Mia has taught math and science and has a Master's Degree in Secondary Teaching.

Negative numbers often cause a bit of confusion for students. Combined with fractions, it can be a perfect storm of frustrating math problems! But have no fear. Follow the steps in this lesson and you will feel comfortable with negative fractions in no time. After the lesson, take a short quiz to show those negative fractions who's boss!

Working with Negative Numbers

So, you know how to add, you know how to subtract, you know what fractions are and how to add them. So, what's the next step? Well you may remember that not all numbers are positive numbers. If you think of a number line, the line of numbers goes out from zero in both directions. To the right, we have all the positive numbers, and to the left of zero, are all of our negative numbers. In between the whole numbers, there are even negative parts of numbers, which may be written as fractions.

In this lesson, we'll look at how to add and how to subtract negative fractions. When working with negative numbers, or numbers that are less than zero, it's often helpful to think of them in terms of money or time. Having negative values for money or time means that we owe that amount.

First let's look at an example that will show you how to subtract fractions as they apply to time.

Adding Negative Fractions

My son gets a behavior report every day from school. Based on how well he did in school, he gets rewarded with free time to play with his friends or to watch TV. If his report is poor, he owes me time by doing extra chores around the house.

Last week was an especially challenging week for him. On Monday, he had 3 negative comments from his teacher, so he owed me 30 minutes of chores. Tuesday was a little better, but he still owed 15 more minutes of chores. Mathematically, we would represent his total time owed as:

Total time owed in minutes
example 1a

We would add the total minutes and the result would be -45 minutes, meaning that he owes me a total of 45 minutes of chores. But this lesson is about fractions, so let's re-write our equation using hours as our units. Our equation now becomes:

Total time owed in fractions of an hour
example 1b

Notice that I placed the negative sign in the numerator. With negative fractions, the negative sign can be placed in the front of the fraction, in the numerator, or in the denominator. I find it most helpful to keep it in the numerator when doing calculations.

Let's continue with our calculation. It is important to remember that when adding or subtracting fractions, they must have a common denominator, which means that the number on the bottom of both of the fractions have to be the same. We can change the first fraction to -2/4 so that both fractions have a denominator of 4.

Fractions written with common denominators
example 1c

Next, we add the numerators and keep the denominator the same.

Example 1 completed
example 1d

Our total is -3/4 hours. So, for Monday and Tuesday, my son owed me 3/4 of an hour of chores. This is equal to the -45 minutes that we calculated earlier.

Now let's take a look at how to subtract negative fractions.

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