Adding integers: find the missing value | 7th grade | Khan Academy

We are asked to find the missing value, and they give us a hint: use the number line to find the missing value. Let's see, they say 4 plus something is equal to negative 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 four. There's a couple of ways to think about it. We could just say where is four on the number line? Four 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 negative 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. 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, ten to the left.

So what do we add? If we want to move 10 to the left, we have to add a negative 10. So this is negative 10 right over here. Another way to think about it: if you're 4 to the right of 0, well, it's going to take you 4 just to get back to zero—that's four there—and it's going to take you another 6 to get you to negative 6.

And then, of course, you're moving to the left, so that's going to be a negative 10.

Let's do another example. 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 can think about it. We're saying negative 3 is equal to something plus five. So let's just see where negative 3 is on this number line. Negative 3 is right over there, and something plus 5 is going to be equal to negative 3.

So plus five, 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 negative three?

Well, if we just go five units to the left—so 1, 2, 3, 4, 5—if you start from this point and you were to add five, you were to get to negative three. So what is this point right over here?

Well, this right over here—let's see, this is negative 5, negative 6, negative 7, negative 8. So we have negative 8 plus five is equal to negative 3.

Another way to think about it is you could have used the commutative property to say, "Hey, instead of blank plus five, you could say this is negative three is equal to five plus blank."

And so you can say, "Let's start at five." Let me just—in another color—let's start at five, and then what would I have to add to it to get to negative three?

And so, well, I would have to move to the left five and then three in order to get to negative three. So you would essentially have to add negative eight. So that's another way that you could think about that.