Adding negative numbers on the number line

- [Voiceover] So we've already spent some time introducing ourselves to the idea of adding or subtracting positive and negative numbers. What I now what do in this video is do a bunch of examples using the adding negative numbers on the number line exercise on Khan Academy, so that we can think about different ways to model, or think about, or visualize adding and subtracting positive and negative numbers. So this question asks us, "Which number line model represents "the expression negative two "plus negative seven?" And a number line model seems like this really fancy thing, but they're just saying, which of these diagrams, which of these drawings are a way to think about what negative two plus negative seven is. So let's think about it. I want to start at negative two and then to that I want to add negative seven. So let's see what's going on here. This number line model I guess we could call it, it's saying this is positive two right over here. It's to the right of zero. Then it subtracts seven. This is the model that would be for positive two plus negative seven, or two, or positive two minus seven. But that's not what we have over here, we have negative two minus seven. This one right over here, let's see, this first... I guess you could say this thing, this arrow, it's going one, two, three, four, five to the left of zero. So starting at negative five, and then it goes another one, two, three, four to the left of that. So you could view this as negative five minus four. Or you could view this as negative five plus negative four, but that's not what we have up here. And then this last one, hopefully this is the answer, otherwise there would be a mistake in the exercise. Let's see, we have this first arrow that takes us two steps to the left of zero. So, one, two. So this is negative two, and then we take another seven steps to the left of that. So one, two, three, four, five, six, seven. So you can think of this arrow as representing negative two, and then we're going to that, so we're starting from this tip of this arrow. We're going to add a negative seven which makes us move seven to the left again to get to negative nine. So that's definitely the model that represents that expression. Let's keep going. All right. Which number line model represents the expression six plus negative two. So here, they've taken our number lines but they've made them go up and down, they've made them vertical. So we wanna really think about it. I want to start at six and I want to add negative two. So on a vertical number line like this, it seems like we're increasing as we go up. I want to start at six above zero. So, I want to start at six above zero, but then I want to add negative two, which should take me two steps back down. This one takes me two steps even higher, so this one right over here is positive six plus two, or positive six plus positive two. This one over here we're starting at positive four and then we're adding two, so that's not what we're talking about. This one over here, this big arrow, this tall arrow. This is going, it's pointing up. It gets us to positive six. The tip of the arrows are at positive six, But then we're going back down too. So this would be positive six plus negative two. You could think of this arrow as representing positive six, and then this arrow is representing negative two. It takes us two down. So if you take positive six plus negative two, you do the positive six. And from the tip of your arrow, from there you can start the negative two, and you go two back down and you end up at four. So it's definitely that one right over there. This is surprisingly fun. Let's keep going. Which number line model represents the expression negative 2/5 plus 4/5? So we're going to start at negative 2/5 which is going to be, it's negative, it's going to be to the left of zero. So let's see, this arrow right over here, this is negative 4/5, so that's not going to be quite right. So the second choice, what's going on here? So if I start at zero, and then I'm going 2/5 to the left of zero. So that's negative 2/5 and from that, I'm going to the right 1/5, 2/5, 3/5, 4/5. So this looks right. This looks like negative 2/5, so I'm starting at zero, I'm going to the left 2/5. So that's negative 2/5, and then I go to the right 4/5 from that tip. >From negative 2/5, I'm adding 4/5. So that looks right. Let's do one more. This is exciting. Even if you don't find it fully exciting, anything you do you should convince yourself it's exciting. You'll do a better job. Which number line model represents the expression five 1/2 plus negative three? This is positive five 1/2, so I want to go five 1/2 to the right of zero. This is five 1/2 to the left of zero, so that's negative five 1/2. That's not what I want to deal with. So this one looks interesting, and this is actually five 1/2 to the left of zero as well, so it's probably going to be this but let's just look at it. So let's see, we go five 1/2 to the right of zero. So this is five 1/2, and then from that I go three left. So that in the end gets me to two 1/2. So it's this choice, right over there. Exciting.