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## Arithmetic

### Course: Arithmetic > Unit 18

Lesson 5: Intro to adding negative numbers# Adding with integer chips

Let's model and evaluate sums using integer chip diagrams. When all the integer chips are negative, we can just count up our total negatives. When we have a positive integer chip and negative integer chip, those pair up to equal zero. So our sum is whatever chips are left over. Created by Sal Khan.

## Want to join the conversation?

- tihs proevs i am teh bset at splilieingssg(13 votes)
- yeths i agwethre(9 votes)

- But in school they taught us that you should keep the first number, change the sign to the opposite one(like addition is turned into subtraction and subtraction is turned into addition) and change the number to the opposite as well, negative 6 for example, would be positive 6). I never saw that in the video. Are we supposed todo that and if so how do you know when to?(5 votes)
- You can do that.

For example: 1+(-1)=1-1=0(0 votes)

- this is not that bad!!

JUST pay attention and you would know

what to do and your done before you know it(3 votes) - everyone here has been forced to do this(3 votes)
- what is pi times 87?(1 vote)
- i'm fored to do this(1 vote)
- its kinda like supraction, like 7 - -6.(1 vote)
- i want to go home(1 vote)
- DYK That if you pause then unpause the video, it gives you more energy points? Pretty cool! EDIT: You can stop commenting telling me im wrong now. I have learned my lesson. Blessings!(0 votes)
- I don't think so...it just seems like it, you still end up with the same amount as u usually would(1 vote)

## Video transcript

- [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. And 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. So 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. So 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. 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 1, 2, 3, 4, 5, 6, and 7. And then negative six,
you can represent that as six of these negative integer chips. So 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. 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 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. Last 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. These 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. And we're done.