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### Course: 7th grade (Eureka Math/EngageNY) > Unit 2

Lesson 1: Topic A: Addition and subtraction of integers and rational numbers- Zero pairs worked example
- Zero pairs
- Adding with integer chips
- Add with integer chips
- Adding negative numbers on the number line
- Adding negative numbers on the number line
- Adding negative numbers example
- Signs of sums on a number line
- Signs of sums
- Adding negative numbers
- Subtracting with integer chips
- Subtract with integer chips
- Adding the opposite with integer chips
- Adding the opposite with number lines
- Adding & subtracting negative numbers
- Subtracting a negative = adding a positive
- Understand subtraction as adding the opposite
- Subtracting negative numbers
- Adding & subtracting negative numbers
- Adding negative numbers review
- Equivalent expressions with negative numbers
- Subtracting negative numbers review
- Number equations & number lines
- Number equations & number lines
- Graphing negative number addition and subtraction expressions
- Interpret negative number addition and subtraction expressions
- Interpreting numeric expressions example
- Absolute value to find distance
- Absolute value as distance between numbers
- Interpreting absolute value as distance
- Absolute value to find distance challenge
- Associative and commutative properties of addition with negatives
- Commutative and associative properties of addition with integers
- Equivalent expressions with negative numbers
- Adding fractions with different signs
- Adding and subtracting fractions with negatives
- Comparing rational numbers
- Adding & subtracting negative fractions
- Adding & subtracting rational numbers: 79% - 79.1 - 58 1/10
- Order rational numbers
- Adding & subtracting rational numbers: 0.79 - 4/3 - 1/2 + 150%
- Adding & subtracting rational numbers
- One-step equations with negatives (add & subtract)

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# Adding the opposite with integer chips

Use integer chips to explore the conjecture that subtracting a number gives the same result as adding the opposite of the number. Created by Sal Khan.

## Want to join the conversation?

- never in your life jk(3 votes)

- CHICKENUGGET is da best(10 votes)
- Mhmm chimken nuggies wid da barbabue swauce is awdome(5 votes)

- my teacher is making me watch these even though i know how to do it(5 votes)
- what flavor are the integer chips?(3 votes)
- Flame-n hot confusion that's the flavor of the integer chips .(5 votes)

- Im not great at math yet i am acing this with 100% on everything. Um please explain. :p(4 votes)
- I think that the problems are always easy in the beginning of the unit. It gets more complicated at the end. Maybe this is a really-easy-to-understand-unit.(2 votes)

- Why did you add two positive chips when the question was both negative? I mean it would be much easier to just subtract 3 from 5 to find the answers.(3 votes)
- Im in 5th grade and I'm going this whhaaqaaaaaaat! this is 7th grade MATH!(2 votes)
- how do you subtract(2 votes)
- why is it so hard(2 votes)
- Because some math is hard(2 votes)

- Fried chicken from KFC(2 votes)

## Video transcript

- [Instructor] So let's
use integer chips again to start exploring a little bit more when we deal with negative numbers. So let's say we wanted to compute what negative one minus seven is. See if you can pause this video and figure that out using integer chips. Well, let's do this together. So we're starting with negative one. We could represent negative
one as just one integer, one negative integer chip, but we need to subtract seven,
positive seven from that. We have no positive integer chips here, so, and we need to have at least seven positive integer chips in
order to subtract seven. So how could we get some
positive integer chips? Well, we can just add pairs of negative and positive integer chips. So if I add one negative integer chip and I add one positive
integer chip, just like that, this is still negative one over here because these two integer chips are going to cancel each other out. So let me just do that seven times. So let me just do this. So that's two, three, four, five, six and seven. And then I just have to
add the corresponding positive integer chips three, four, five, six and seven. So notice, what I just wrote, this is just another way
of writing negative one. But I wrote it this way
because I can actually subtract out positive seven now from this. So now let's subtract out positive seven. So subtract out one, two, three, four, five, six, seven. And then what are we left with? Well, we're left with all of
this business right over here. And what is that? That's one, two, three, four, five, six, seven, eight. This is equal to negative eight. Now that's interesting by itself, but you might notice something. What I have left over
when I take a negative one and I subtract positive seven from that, I'm left with essentially the equivalent of negative one and negative seven. So another way of
writing what we just have left over here is I have negative one is that one negative integer
chip right over there. And then I have negative seven, these seven negative integer
chips right over there. So you could also view
this as the same thing as negative one plus negative seven. And so this makes us
think about something. Is it true that if I subtract a positive, that's the same thing
as adding the inverse of that positive, adding, in
the case of a positive seven, in the case of subtracting
a positive seven, that's gonna be the same thing
as adding a negative seven? Interesting. And let's see actually if it works the other way around. So let's see what happens
when we subtract a negative. So if we have negative
three minus negative five, maybe, maybe this is the
same thing as negative three plus the opposite of negative five, which would be positive five. Let's see if these two things actually amount to be the same thing. So let's just start with
this first one up here. We're gonna start with negative three, so that gives us three
negative integer chips. So negative one, negative
two, negative three. Now if we wanna subtract
out negative five, if we wanna take away five
negative integer chips, well we need more negative
integer chips here. We need at least two more
negative integer chips. So if we have two more
negative integer chips, we're not changing the value of that if we have two more
positive integer chips. What I have depicted here
is still negative three because that and that cancel out. And so this is still the
number negative three being represented, but
I added these two pairs because now I can subtract out
five negative integer chips. That's what negative five represents. These top four negative integer
chips, there's five of 'em, I can take 'em all away. That's subtracting out a negative five. And what am I left with? What I'm left with is just these
two positive integer chips. So this is going to be
equal to positive two. Well, that's interesting
because that's kind of feeling very similar to what we have here. If we start with negative
three, so negative one, negative two, negative three,
and I add a positive five, so five positive integer chips, one, two, three, four and five. Well, we already know that
that cancels with that, that cancels with that,
that cancels with that. This is the equivalent of positive two. And what I just did here on both sides, this isn't a proof that
this will always work, but hopefully this gives you an intuition that it does seem to work. And I will tell you that without
giving you the full proof that it actually does always work, that it is actually the case
that if you subtract a number, it's the same thing as adding
the opposite of that number. If you subtract a number
it's the same thing as adding the opposite of that number.