Adding with integer chips

0:00- [Instructor] Let's say I wanted to figure out what negative two plus negative four is equal to. There are a bunch of ways of thinking about them, but what we're gonna 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.

0:23And if I have a negative sign with a circle around it, that's a negative integer chip and that's equal to negative one. And 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 one plus negative one is of course equal to zero.

0:42So let's use that to figure out this and several other problems. So negative two, how could I represent that with integer chips? Well, that's going to be two of these negative integer chips. So negative one and then negative two. And then negative four is going to be four of these negative integer chips.

0:59So negative one, negative two, negative three, and negative four. So now how many total negative integer chips do I have? I have 1, 2, 3, 4, 5, 6. 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 seven plus negative six.

1:23How 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 1, 2, 3, 4, 5, 6, and 7. And then negative six, you can represent that as six of these negative integer chips.

1:46So we have negative one, negative two, negative three negative four, negative five, and negative six. Now we can use the fact that every positive integer, if you have a positive and a negative integer chip, well positive one plus negative one is going to be equal to zero, so they cancel out.

2:03So 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.

2:19Let'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.

2:36So that's five right there. And then positive five would be five of the positive integer chips, 1, 2, 3, 4, 5. 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.

3:00Last but not least, let's add three and negative eight. And let's represent that again with integer chips. So positive three is 1, 2, 3, positive integer chips. Negative eight is, let's see, 1, 2, 3, 4, 5, 6, 7, 8 of these negative integer chips. And these cancel.

3:30These cancel, lemme 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.

3:44And we're done.