Graphing negative number addition and subtraction expressions

- [Instructor] In this video, we're going to add and subtract negative numbers on a number line, and the important thing to realize is, if you are adding a positive number, you start at some point on the number line and you move that many units to the right. If you are adding a negative number, you start at wherever you're starting and then you move that many units to the left, whatever the absolute value of that negative number is, and if you're subtracting either of them, you do the opposite, so we're going to see a few examples of that. So let's start with this first example, negative 10 plus negative six. So we're going to start at negative 10 right over here, so let's look at that on the number line. That's negative 10 right over there. We're gonna start over there, and then we are adding positive six. So what do we do? Well we start here, and as I mentioned, we're going to go six units to the right because it's a positive six, so one, two, three, four, five, six. So we're going to go right over there. We started at the negative 10, and since we're adding positive six, we go six units to the right, and we end up right over here at negative four, so this is equal to negative four. Now let's do this one. Where are we starting? We are starting at negative eight, so that's negative 10, negative nine, negative eight is right over there. Now, we're going to subtract negative two, so let's be very careful here. If we were adding negative two, we would go two units to the left, like that, but we're subtracting negative two, so we're going to do the opposite. We're going to instead, instead of going two units to the left, we're going to go two units to the right. So we're gonna go one, two units to the right, and we are going to end up right over there, so that's negative seven, negative six. So this is equal to negative six. Remember, if we were adding negative two, we would've gone two units to the left, but when you subtract, you do the opposite of what you would've otherwise done, so now we're going two units to the right, even though it's a negative two, 'cause we're subtracting negative two. All right. We're starting at four in the third example. So, we're starting right over here at four, and we're adding negative seven. So, negative seven, you're just going to move the absolute value of that to the left. So the absolute value of negative seven is just seven, so you're gonna move seven units to the left, and we're not subtracting that so we're just going to just move seven units to the left. We're not gonna do the opposite of that or anything like that, so we just go seven units to the left. We're adding negative seven so one, two, three, four, five, six, seven. We end up right over here. So we have positive four minus seven. We've gone seven units to the left and now we're at, let's see, this is zero, negative one, negative two, negative three, so that is equal to negative three. Now this last one, try to do it on your own before we do it together. All right. Now some of you might be tempted to say oh, five and negative five, aren't those additive inverses? Don't those just cancel out? Well they would if you were adding. Five plus negative five is equal to zero, but here we're doing five minus negative five. So let's just do it step by step. We're starting at five. Now if we were adding negative five to that, we would go five units to the left and we would end up at zero, but we are not adding negative five. We are subtracting negative five, so instead of going five units to the left, we're going to go five units to the right, so one, two, three, four, five. We end up right over there, and so we end up at 10, and we are done.