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