WEBVTT

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Find the sum of negative 15 plus
negative 46 plus negative 29.

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To do this, let's
just first visualize

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what each of these
numbers look like.

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So I'm going to draw a
number line for each of them.

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Negative 15 might look
something like this.

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So if this is 0 and let's
say that this is negative 15,

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I could represent
negative 15 as--

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if I'd like to-- an arrow that
points from 0 to negative 15.

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The length of the arrow is
the absolute value of this.

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It's the distance from 0.

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So the length here is 15.

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And the negative says that
we are pointing to the left.

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So the absolute value is 15.

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That's the length of that arrow.

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Let's do the same
thing for negative 46.

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So once again, let me
draw my number line.

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0 is going to be
right over there.

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And negative 46 is going
to be someplace over here.

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Negative 46.

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Notice, same exact idea.

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The distance between negative
46 and 0-- or another way

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to think about that is the
absolute value of negative 46--

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this distance right over
here is going to be 46.

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And its direction
is to the left.

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That is why we get to
the number negative 46.

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The negative really tells you
whether you're to the left

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or to the right of 0,
but the absolute value

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says how far are you to
the left or the right of 0.

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And then, finally, let's do
the same thing for negative 29.

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So once again, let me
draw my number line.

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I want to use the yellow again.

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So draw my number line.

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Let's say this is 0.

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Then negative 29 is going
to be roughly over here.

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I'm estimating it.

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And once again, negative 29
is exactly 29 away from 0.

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So this length right over here
is 29, and it is to the left.

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That is why it is negative 29.

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If it was positive 29, it
would be 29 to the right of 0.

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So we've represented
all of these numbers.

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And you can see what their
absolute values are like.

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And now let's think about
what happens if you add them.

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So one way to think about
adding these numbers

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is if you added
these arrows, if you

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put this arrow on
top of this arrow

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or to the left of this
arrow, if you started where

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this arrow leaves off-- and
then you put this green arrow,

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and then you put
the orange arrow.

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So let's do that.

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Let's draw that.

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It's going to be a
longer arrow now.

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So we're going to start at 0.

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First, we have the negative 15.

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So we're going to move
15 spaces to the left

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to get us to negative 15.

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Then we're going to go
46 spaces to the left

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to get us to negative
15 plus negative 46.

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So let me draw that.

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So then we're going
to go-- and we're

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going to figure out what
that number is in a second.

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So then we're going
to go 46 to the left.

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That's about that far.

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Really just this arrow,
I'm now placing it.

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I'm starting off where
the negative 15 left off,

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and then I'm putting
that arrow after that.

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And we don't know yet what
number this gets us to.

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We're going to have to
do a little math here.

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And that's actually the
point of this problem.

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But we know what the
length of this arrow is.

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The length of this arrow is 46.

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It is 46 to the
left, and we know

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the length of this
magenta arrow is 15.

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And then, finally, we
have this orange arrow.

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The orange arrow, which we
know has a length of 29.

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Although, it's 29 to the left.

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It looks like that.

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It has a length of 29.

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So when all is said
and done, where are we?

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Where do we end up
on our number line?

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Well, the total length
that we are to the left

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is going to be 15
plus 46 plus 29.

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But it's going to
be to the left,

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so it's going to be negative.

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So what we can really view
this as, since all of these

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have the same sign,
is we could say,

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look, this is the same
thing as the absolute value

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of negative 15, which is
15, plus the absolute value

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of negative 46, which is
46, plus the absolute value

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of negative 29,
which is 29, but then

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take the negative value of it.

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So let's just add that.

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15 plus 46 plus 29 is equal
to, let's see-- 5 plus 6 is 11.

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11 plus 9 is 20.

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Carry the 2.

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2 plus 1 is 3.

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3 plus 4 is 7.

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7 plus 2 is 9.

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So you get 90.

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So this entire
length here is 90.

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The entire length, if you add
up the arrows, you get a 90.

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But it is not 90 to the right.

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So if it was 90 to the right,
these would all be positives.

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And then we would just
get a positive 90.

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But this is 90 to the left.

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So when you add these guys up,
you don't get to positive 90.

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You get to negative 90.

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So one way to think about it
is these are all the same sign.

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So this is going to be
equal to the negative

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of the absolute
value of negative 15

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plus the absolute
value of negative 46

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plus the absolute
value of negative 29.

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And the reason why we're
writing this here-- this

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might look fancy,
but this is really

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just the length of
this purple arrow.

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This absolute value
of negative 46,

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that's really just the
length of the green arrow.

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46.

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And this is just the
length of the orange arrow.

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So this is 15 plus 46
plus 29, gave us 90,

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but it is to the left.

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So that is why it
is negative 90.

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