Subtracting integers find the missing value | 7th grade | Khan Academy

So if I were to ask you if I were to tell you that negative 3 minus blank is equal to negative 4, can you pause this video and figure out what this blank is?

All right, now let's do this together, and I'm going to do this by drawing out a number line because that's what my head tries to do with things like this. Let me draw a straighter line than that.

All right, that's a pretty good number line. Let's see, I'm going to be dealing with negative 3, and I'm going to subtract something from it to get to negative 4. So let me focus on the negative end here. So let's say this is zero; that could be positive one. Then I have negative 1, negative 2, negative 3, negative 4, negative 5. Let's go negative 6; that's the other end of it.

So this is negative 1, negative 2, negative 3, negative 4, and negative 5. So let's start at negative 3. So negative 3 is that point on the number line, and I want to end up at negative 4. That is that point on the number line.

So to go from negative 3 to negative 4, I have to go one step in the leftward direction. So one step in the leftward direction, you could either view that as subtracting one, or you could view that as adding a negative one. Now we're already subtracting here, so the simplest thing to do is just say, okay, this is the same thing as subtracting one, and we're done.

Negative 3 minus 1 is indeed equal to negative 4.

Let's do another example. Let's say we had negative 1 is equal to negative 7 minus what. Pause the video and try to work through that and try to do a number line; I always find that useful.

All right, let's work through this together again. So let me draw a number line here. Let's see, I have negative 1; I have negative 7, so I'm going to deal with the negative end of things. So let me make this zero; I'll make that positive 1, negative 1, negative 2, negative 3, negative 4, negative 5, negative 6, negative 7. Let me write this; this is negative 7 right over here, negative 8, negative 9, negative 10. I think that's probably enough.

So let's see, we're saying negative 1 is equal to negative 7 minus something. So essentially, we're starting at negative 7 here. We're starting at negative 7, and we're subtracting something from that to end up over here at negative 1. This is negative 1 right over there.

So let's just think about what the arrow needs to do to get from negative 7 to negative 1. Well, to do that, you're going to have to go, it looks like, six units to the right. One, two, three, four, five, six. We go six units to the right.

Now there's two ways to describe going six units to the right. You could say that is just plus six, or you could view that as the same thing as minus negative six. And we've seen that subtracting a number is the same thing as adding its inverse. And since we already have a minus sign here, we might as well say, well, this is the same thing as subtracting a negative six. Uh, negative six, I'll put in parentheses to make it a little bit cleaner, and we're done.

Let's do another example. Another example here, so let's say we give ourselves a clean slate.

Let's say we wanted to figure out, so I have blank minus negative 5 is equal to 13. How would you tackle that? Well, let me just draw my number line again. I have my whole real estate to use this time, so let me just go all the way there.

Let's see, I'm dealing with something; it's going to be roughly five away, it feels like, from 13. So let me just make my number line. I'm just going to say this is zero; I have to get to 13.

So actually, let me give myself a little bit more space. So this is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18. I think that is sufficient.

So we don't know where we're starting; we know we want to end up at 13. So 13, let me put that on our number line here. So it's one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen. So thirteen is right over here.

And now how did we get to 13? Well, we are subtracting a negative 5. Now, as I just mentioned, subtracting a number is the same thing as adding the inverse of the number, so this is the same thing as adding positive 5. It's another way of thinking about that.

So, another way of depicting either of these subtracting negative 5 or adding positive 5 would essentially be you're starting someplace and you're going five units to the right. So you started someplace, and you're going five units to the right to end up at 13.

So that means you started five units to the left. One, two, three, four, five. You started right over here; you go five units to the right, and you ended up at 13.

Well, this right over here, five units to the left of 13, this is going to be 8, and it is indeed the case that eight minus negative 5 is equal to 13.

Now, there are other ways that you might be able to think about this. If something minus negative 5 is equal to 13, then another way you could think about it is if I were to tell you that 3 minus 2 is equal to 1, you could also say that an equivalent statement is that 3 is equal to 1 plus 2.

You could turn that subtraction equation into an addition equation. So over here, if I say this minus this is equal to that, then that means that 13 plus negative 5 must be equal to blank, our mystery number.

And if I add 13 and negative 5, you might recognize that as being equal to 8. So either way, there's a lot of ways that you could approach this, but they all get you to either kind of the same conceptual place.