Graphing negative number addition and subtraction expressions | 7th grade | Khan Academy

In this video, we're going to add and subtract negative numbers on a number line. 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 it wherever you're starting, and then you move that many units to the left, whatever the absolute value of that negative number is.

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 6. So we're going to start at negative 10 right over here. So let's look at that on the number line. That's a negative 10 right over there. We're going to start over there, and then we are adding positive 6.

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 6. So 1, 2, 3, 4, 5, 6. So we're going to go right over there. We started at negative 10, and since we're adding positive 6, we go 6 units to the right and we end up right over here at negative 4. So this is equal to negative 4.

Now let's do this one: where are we starting? We are starting at negative 8, so that's negative 10, negative 9, negative 8 is right over there. Now we're going to subtract negative 2. So let's be very careful here. If we were adding negative 2, we would go two units to the left like that. But we're subtracting negative 2, so we're going to do the opposite. We're going to, instead of going two units to the left, we're going to go 2 units to the right.

So we're going to go one, two units to the right, and we are going to end up right over there. So that's negative 7, negative 6. So this is equal to negative 6. Remember, if we were adding negative 2, we would have gone two units to the left, but when you subtract, you do the opposite of what you would have otherwise done.

So now we're going two units to the right, even though it's a negative 2, because we're subtracting negative 2. All right, we're starting at 4 in the third example. So we're starting right over here at 4, and we are adding negative 7. So negative 7, you're just going to move the absolute value of that to the left. The absolute value of negative 7 is just 7.

So you're going to move seven units to the left, and we're not subtracting that, so we're just going to move seven units to the left. We're not going to 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 4 minus 7. 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 5 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.