Negative Numbers

In this lesson on algebra negative numbers are covered. Get information and negative numbers practice here.

Calculating with negative numbers

Using negative numbers in arithmetic is fairly simple. There are just a few special rules to keep in mind.

Adding and subtracting negative numbers

When you're adding and subtracting negative numbers, it helps to think about a number line, at least at first. Let's take a look at this problem: 6 - 7. Even though 7 is larger than 6, you can subtract it in the exact same way as any other number, as long as you understand there are numbers smaller than 0.

6 minus 7 is - 1

6 - 7 = -1

While the number line makes it easy to picture this problem, there's also a trick you could have used to solve it.

First, ignore the negative signs for a moment. Just find the difference between the two numbers. In this case, it means solving for 7 - 6, which is 1. Next, look at your original problem. Which number has the highest absolute value? In this case, it's -7. Because -7 is a negative number, our answer will be one too: -1. Because the absolute value of -7 is greater than the distance between 6 and 0, our answer ends up being less than 0.

Adding negative numbers

How would you solve this problem?

6 + -7

Believe it or not, this is the exact same problem we just solved!

This is because the plus sign simply lets you know you're combining two numbers. When you combine a negative number with a positive one, the sum will be less than the original number—so you might as well be subtracting. So 6 + -7 is the same thing as 6 - 7, and they both equal -1.

6 + -7 = -1

Whenever you see a positive and negative sign next to each other, you should read it as a negative. Just like 6 + -7 is the same as 6 - 7:

This is true whenever you're adding a negative number. Adding a negative number is always the same as subtracting that number's absolute value.

Subtracting negative numbers

If adding a negative number is actually equal to subtracting, how do you subtract a negative number? For example, how do you solve this problem?

6 - - 3

If you guessed that you add them, you're right. Here's why: Remember how we said a negative number was the opposite of a positive one? We compared them to you and your mirror image. Your mirror image is your opposite, which means your mirror image's opposite is you. In other words, the opposite of your opposite is you.

In the same way, you can simplify these two minus signs by reading them as two negatives. The first minus sign negates—or makes negative—the second. Because the negative—or opposite—of a negative is a positive, you can replace both minus signs with a plus sign. This means you'd solve for this:

6 + 3

This is a lot easier, to solve, right? If it seems confusing, you can just remember this simple trick: When you see two minus signs back to back, replace them with a plus sign.

So 6 minus negative 3 is equal to 6 plus 3. That's equal to 9. In other words, 6 - -3 is 9.

Remembering all of the rules for adding and subtracting numbers can be overwhelming. Watch the video below for a trick to help you.