Adding integers on the number line

0:00- [Instructor] So we've already spent some time introducing ourselves to the idea of adding or subtracting positive and negative numbers, and what I now want to 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.

0:25So 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, well, which of these diagrams, which of these drawings, are a way to think about what negative two plus negative seven is?

0:45So let's think about it. I wanna start at negative two, and then to that, I wanna add negative seven. So let's see what's going on here. So this number line model, I guess we could call it, it's starting, this is positive two right over here, it is to the right of zero, and then it subtracts seven.

1:06So this is the model that would be for positive two plus negative seven, 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 line, this arrow, it's going one, two, three, four five, to the left of zero.

1:30so 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'd be a mistake in the exercise.

1:51Let'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 add to that, so we're starting from this tip of this arrow, we're gonna 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.

2:22Let'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 one way to think about it. I wanna start at six and then I wanna add negative two, so on a vertical number line like this, and it seems like we're increasing as we go up, I wanna start at six above zero.

2:48So I wanna 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.

3:08This 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 arrow is right at positive six, but then we go back down two, 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.

3:27It takes us two down. So if you take positive six plus negative two, you do the positive six, and then for the tip of your arrow, from there, you could 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.