Adding with integer chips | Integers: Addition and subtraction | 7th grade | Khan Academy

Let's say I wanted to figure out what negative 2 plus negative 4 is equal to. There are a bunch of ways of thinking about them, but what we're going to do in this video is think about it using something called integer chips.

So, with integer chips, if I have a chip that looks like this, a positive sign with a circle around it, that is equal to a positive one. If I have a negative sign with a circle around it, that's a negative integer chip, and that's equal to negative one. Of course, if I have exactly one positive integer chip and one negative integer chip, well then they're going to cancel out, because positive 1 plus negative 1 is of course equal to zero.

So, let's use that to figure out this and several other problems.

So, negative two—how can I represent that with integer chips? Well, that's going to be two of these negative integer chips: so negative 1, and then negative 2. And then negative 4 is going to be four of these negative integer chips: so negative 1, negative 2, negative 3, and negative 4.

So now, how many total negative integer chips do I have? I have one, two, three, four, five, six. So that's going to be six negative integer chips, or negative six.

Let's do another example. Let's say I now have positive 7 plus negative 6. How can I represent this with integer chips? Pause this video and think about it.

Well, positive seven, you could view that as seven of these positive integer chips: so one, two, three, four, five, six, and seven. And then negative six, you can represent that as six of these negative integer chips: so we have negative 1, negative 2, negative 3, negative 4, negative 5, and negative 6.

Now we can use the fact that every positive integer, if you have a positive and a negative integer chip, well positive 1 plus negative 1 is going to be equal to zero, so they cancel out.

So those cancel; those also add up to zero; those also add up to zero; those also add up to zero; those add up to zero; those add up to zero. So you have a bunch of zeros and then a positive one. So all you're left with is a positive one here, so that's going to be equal to one.

Let's do another example. It's really helpful to see these different scenarios: negative five plus five. You might already suspect what that is, and pause that video—actually try to represent it with integer chips.

Well, negative five—that's five of these negative integer chips, so that's five right there. And then positive 5 would be 5 of the positive integer chips: one, two, three, four, five. And what's going to happen here? Well, those add up to zero; those add up to zero; those add up to zero; those add up to zero; those add up to zero. So you're just adding a bunch of zeros, which is of course going to give you a big zero.

Last but not least, let's add three and negative eight, and let's represent that again with integer chips. So, positive three is one, two, three positive integer chips. Negative eight is, let's see, one, two, three, four, five, six, seven, eight of these negative integer chips.

And these cancel; these cancel. Let me scratch that out a little bit better. Those cancel; those cancel; and those cancel. So you have zero plus zero plus zero plus what do you have left over? Five of these negative integer chips, five negative integer chips. That's going to be equal to negative five, and we're done.