Number opposites

- [Voiceover] What I want to do in this video is think about what it means to have an opposite of a number. Let me draw a number line here. Let's draw a number line. And let's put some numbers on this number line. We can start at zero, and if we go to the right we have positive numbers. One, two, three, four, five. As we go to the left we get more and more negative. So negative one, negative two, negative three, negative four, and I can keep going on and on and on. Let's pick one of these numbers. Let's say that we pick the number three. What is going to be the opposite of the number three? Well the opposite of the number is a number that's the same distance from zero but on the other side. So three is three to the right of zero. One, two, three. So its opposite is going to be three to the left of zero. One, two, three. So the opposite of three is negative three. Let me make a little table here. If we have the number, the number. And then we have its opposite. We have its opposite. So we just figured out that if you have the number three, its opposite is going to be negative three. Now what if your number is negative? What if your number, let's say the number negative four. What's the opposite of that? And I encourage you to pause the video and try to think about it on your own. Well, you say, okay, negative four is right over here. That's negative four. It is four to the left of zero. One, two, three, four to the left of zero. So its opposite is going to be four to the right of it. So one, two, three, four. It's going to be positive. It's going to be positive four. So you're probably starting to see a pattern here. The opposite of a number is going to be the opposite sign of that number. If you have a positive three here, its opposite is going to be negative three. If you start with negative four, its opposite is going to be positive four. One way to think about it, it's going to have the same absolute value but have a different sign. Or another way to think about it is, however if this is three to the right of zero, its opposite is going to be three to the left of zero. Or if the number is four to the left of zero, its opposite is going to be four to the right of zero. So we'll do one last one. What is the opposite of... What's going to be the opposite of one? Well one is one to the right of zero, so its opposite is going to be one to the left of zero, or negative one. Or another way to think about it, one is positive so its opposite is where you're going to change the sign. Instead of being positive it's going to be negative. It's going to be negative one. Either way that you can think about it.