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## Arithmetic

### Course: Arithmetic>Unit 18

Lesson 5: Intro to adding negative numbers

# Zero pairs worked example

When we have a positive unit and a negative unit, they add up to zero. We call that a zero pair. Let's use integer chips to represent the number -2, but not just with 2 negative chips. This will open the door for us to add and subtract with negative numbers. Created by Sal Khan.

## Video transcript

- [Instructor] We're told, "This is the key for the integer chips." So this yellow circle with a plus is equal to one. This, I guess, pinkish circle, peach circle, with a minus, that is equal to negative one. "Consider the following image." And so, there we have a bunch of the positive yellow circles, and then we have even more of the pink, or peach-looking negative circles. "Complete the description of the image. There are blank zero pairs and blank units left over." If you're actually doing this exercise, this is a screenshot from the exercise, you would fill in something here, and there's a dropdown over here. So the first question you might ask is, "What is a zero pair?" So a zero pair is when you take two opposite numbers, and they essentially, when you add them, they cancel out to get to zero. An example of that would be one plus negative one. These two numbers are opposites, so they are a zero pair, because when you add them together, you get zero. Why does that make sense? Well, imagine if positive values were walking forward, and negative values were walking backwards. So you could view this as one step forward plus one step backward. That's just going to get you back to where you were before. You could have other zero pairs. You could have things like positive two plus negative two. That's also a zero pair. You walk two steps forward and then two steps backward. That's just going to get you back to where you were before. You will not have moved after all, or you'd be back to where you were before. So let's think about how many zero pairs there are over here. Well, we know that each of the ones forms a zero pair with each of the negative ones. So that's one zero pair, two, three, four, five zero pairs. So I'll just write a five right over here. You would type that in if you were doing this. And then how many units are left over? Well, you could see right over here, we see that we have two of the negative one units left over.