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## Arithmetic (all content)

# Basic subtraction

Introduction to subtraction. Created by Sal Khan.

## Video transcript

Welcome to the video
on basic subtraction. Let's do a little bit a review
of basic addition first. If I said 4 plus 3,
what did this mean? What did that equal? Well, there were a couple of
ways we could have viewed this. We could have said I
had 4 of something. Let's say I had 4 circles
or I don't know, I had 4 lemons for breakfast. So 1, 2, 3, 4 lemons
for breakfast. And let's say, I had another
3 lemons for lunch. 1, 2, 3, and so you could
view 4 plus 3 as how many total lemons did I have? I'm adding 3 to 4. So how many total did I have? Well, it's 1, 2, 3, 4, 5, 6, 7. So I had a total of 7 lemons. Another way we could have
viewed that is we could have drawn our number line. And I'll draw it in yellow
because-- now that's not wide enough. I'll draw it in yellow because
we're talking about lemons. So let's say that's
our number line. And if I start at the number--
let me draw all of the numbers. 0, 1, 2, 3, 4, 5, 6, 7. So you could think about
this as saying, well, we're on the number line. We start at the number 4. That's this number 4. And we're adding 3 to it. So we'll increase, along
the number line by 3. So we'll go 1, 2, 3
and you end up at 7. So you could say if I have 4
and I get 3 more, I get 7. Or if I increase 4
by 3 I also get 7. So what's subtraction now? Because that's what
this video is about. I shouldn't waste all of our
time talking about addition. So let's take the
example of 4 minus 3. What is that equal to? Let me switch colors just to
keep things interesting. So what is 4 minus 3 equal to? Subtraction or minus is
the opposite of addition. So in addition you're doing
something more, you're adding. I don't want to use the word
adding to define addition, but that's what you're doing. I had 4 lemons and
then I had 3 more. In subtraction
you're taking away. So this example, if I started
with 4 lemons, let's say I had 4 lemons on a plate. If I'm subtracting 3, if I'm
saying minus 3, instead of adding these 3 and getting 7,
I'm going to take 3 away. So maybe I'm eating them
or maybe I'm giving them to you in exchange for
watching these videos. So to take away 3 from this 4,
let's say this one goes away, this one goes away, and
this one goes away. How many lemons
would we have left? Well, this is the only one
that I haven't crossed out. So we would have 1 lemon left. And this would be the
lemon that's left. Didn't have to be that
one, I could have crossed out any of the 3. Another way to view that,
let's draw the same lemon colored number line. Let's say that this is the
number line right here. And I'll draw all
the same numbers. So that's 0, 1, 2,
3, 4, 5, 6, 7. Of course, the number
line keeps going. There's no largest number. And you can imagine, any number
that you can think of, I can think of one higher than that. So there is no largest number. So that's why we draw
that arrow there. I could never draw the
entire number line. But anyway, back
to subtraction. So we're starting at
4 lemons, right? When we added 3-- plus 3-- we
went to the right 4 spaces on the number line. And that's because the
right is increasing value. So we went from 4 to 5. That was one more. 5 to 6 was two more,
and 7 was 3 more. Now we're taking away from 4. So what do we do? What would you think we do? Well, since we're taking away
we're going to decrease the total number of lemons we have. So we take away
one, we get to 3. Take away two, get to 2. Take away three, we took
away three, right? So we'll go back 1, 2, 3
along the number line and we'll end up at 1. And that's this 1 right here. So just to review, addition is
you're doing more or something. Subtraction is you
are taking away. If you think about it on the
number line, addition is increasing along the number
line by that amount. So in this case we increased
along the number line by 3. And so we went from 4 to 7. In the subtraction case
we decrease back on the number line. So we decrease by the amount
that you're subtracting. So in this case we
decreased by 3. We went back 1, 2,
3 and we had 1. And the other way to view it,
if I have 4 of something. If I give 3 away or if I ate
3 of them or I don't know what I did to 3 of them. If I lost 3 of them I
would have 1 left. Now let me show you some
interesting things about subtraction. So we know that 4 minus
3 is equal to 1. Let me show you something
else that's interesting. What is 4 minus 1? Well, we could use
either example. Let's do the lemon example. Let's do apples now; I'm
bored of the lemons. Let's say I 1, 2, 3, 4. I have a new pen, sometimes
it doesn't draw right. Let's say I had 4 apples. This is the example
we're dealing with. And I were to eat one of them. So one of them were to go away. How many apples
would I have left? Well, 3-- 1, 2, 3. So 4 minus 1 is equal to 3. And if we did it on the number
line, if we started at 4 and we subtracted 1-- we took 1 away. So we're going to
become one smaller. We go back one, we get 3. Either way works. But isn't this interesting? 4 minus 3 is equal to 1 and
4 minus 1 is equal to 3. You might say, well, did I pick
the numbers just so it worked? Well, it turns out that
it's always true. Well, I don't want to get too
technical, but we're already touching on something that
you'll learn later, maybe in algebra one day. But actually I don't want to
go into all that right now. So where does this come from? Well, this is also based on
the fact that 3 plus 1-- I didn't want to confuse you. So I apologize if I did. But I'll show you another
interesting thing. What is 3 plus 1? 3 plus 1 is equal to what? Well, that's easy. You know that from
basic addition. You can start on the number
line at 3 and add 1 do it. And where do you end up? You end up at 4. 3 plus 1 is equal to 4. Or you could have started at 1
on the number line and added 3. 1, 2, 3 and you would
have also ended up at 4. So we also know that you could
have switch this either way. Both of those are equal 4. What do you see here? Well, there's a bunch of things
I've written here and they all kind of relate to each other. 1 plus 3 is equal to 4. 3 plus 1 is equal to 4. 4 minus 1 is 3. Essentially, 4 minus 1 and
getting 3 is the exact same-- you're saying the same thing
as 3 plus 1 is equal to 4. This statement says if
I add 1 to 3 I get 4. This is saying if I take
away 1 from 4 I get 3. So if I start at 4,
move back, I get 3. This is saying if I start at
3, and I move up 1, I get 4. Hopefully that gives you a
little bit of intuition about what subtraction is. In the next video I'll just do
as many basic subtraction problems I can do
in 10 minutes. And then you'll be ready
to do the exercises. See you soon.