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Adding integers: find the missing value

Use number lines to find missing addends in addition equations with integers. When we add a positive value, we move to the right on the number line. When we add a negative value, we move to the left. Created by Sal Khan.

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Video transcript

- [Instructor] We are asked to find the missing value, and they give us a hint. Use the number line to find the missing value. And let's see, they say, 4 plus something is equal to -6. So why don't you pause this video and see if you can work through this before we do it ourselves. All right, so let's just start at 4. So there's a couple of ways to think about it. We could just say where is 4 on the number line. 4 is here. One, two, three, four. We're going to start there, and we're going to add something to that 4 to get us to -6. To get us right there. So what are we going to add? Well, we're going to be moving to the left. So we're going to be adding a negative number right over here. And we can see what that negative number is going to be. How many units do we have to move to the left? We have to move one, two, three, four, five, six, seven, eight, nine, 10 to the left. So what do we add if we want to move 10 to the left? We have to add a -10. So this is -10 right over here. Another way to think about it, if you're four to the right of zero, well, it's going take you four just to get back to zero. That's four there. And it's going to take you another six to get you to -6. And then of course you're moving to the left, so that's going to be a -10. Let's do another a example. So let me scroll down a bit so we can see that second example. So once again, find the missing value. And pause this video again and try to work that out. All right, so there's a couple of ways we could think about it. We're saying -3 is equal to something plus 5. So let's just see where -3 is on this number line. - 3 is right over there. And something plus 5 is going to be equal to -3. So plus 5, you could view it as you're going to start someplace, and you're going to move five units to the right, something like that to get to where you end up. So where could we start to get five units to the right and be at -3? Well, if we just go five units to the left, so one, two, three, four, five. If you start from this point, and you were to add 5, you were get to -3. And so what is this point right over here? Well, this right over here, let's see, this is -5, -6, -7, -8. So we have -8 plus 5 is equal to -3. Another way to think about it is, you could have used a commutative property to say, "Hey, instead of blank plus 5, you could say this is -3 is equal to 5 plus blank. And so you could say, let's start at 5, let me do this in another color. Let's start at 5, and then what would I have to add to it to get to -3? And so, well, I would have to move to the left five and then three in order to get to -3. So you would essentially have to add -8. So that's another way that you could think about that.