WEBVTT

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Find the sum 15 plus
negative 46 plus 29.

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Let's just think about
this first part over here

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where we have 15
plus negative 46.

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And we'll worry about
the plus 29 later on.

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So let's just do
15-- let me do that

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in a different color--
plus negative 46.

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I'll do it in that orange.

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Let me draw a number line
here, just so we can properly

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visualize what is going on.

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That's my number line.

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And we're starting at 15.

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So let's draw a 0 over here.

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And so we're starting at 15.

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15 could be right over here.

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So this is 15.

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Let me draw a big fat arrow
to signify this is 15.

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15 has an absolute value of
15, so the length of this arrow

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would be 15.

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Now we're adding
negative 46 to that 15.

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This is equivalent
to 15 minus 46,

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which means we are going to
move 46 spots to the left of 15.

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A negative sign or
a minus means we're

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moving to the left
on the number line.

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So we're going to
move 46 to the left.

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We're starting at 15, and we are
going to move 46 to the left.

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So the length of this arrow
right here is going to be 46,

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and we're moving to the left.

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This is the negative 46
that we're adding to the 15.

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We're going to end up
at some point over here.

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That point is clearly 0.

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Because we were 15 to the right.

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Now we're going to
move 46 to the left.

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So we're definitely going
to be to the left of 0.

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It's definitely going
to be a negative number.

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And we can even think
about the absolute value

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of that negative number.

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We can just visualize it.

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This yellow arrow
has a length of 15.

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This orange arrow
has a length of 46.

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The blue arrow that
I'm about to draw,

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which is the sum
of these two, is

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going to have this
length right over here.

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And just visually,
how can we figure out

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the length of this
blue part if we

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know the length of
this orange part

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and we know the length
of this yellow part?

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Well, it's just going
to be the difference.

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It's just going to be the
difference of these two.

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So the absolute
value of the sum is

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going to be the difference
between this length, 46,

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and 15.

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Let me just figure
that out, 46 minus 15.

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6 minus 5 is 1.

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4 minus 1 is 3.

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So the length of this
is going to be 31,

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and it's going to be
31 to the left of 0.

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So this is going to be
negative 31 right over here.

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We know that this first part
over here is negative 31,

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and then to that we
are going to add 29.

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So we're going to add 29.

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Let me do that in another color.

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What does that mean?

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That means that we're going
to start at negative 31,

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and we're going to
move 29 to the right.

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We're adding 29, so we're
going to move 29 to the right.

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So maybe that gets
us right about there.

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I'm trying to draw an
arrow of length 29.

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I can draw a cleaner
looking arrow than that.

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I'll do it right
over here, actually.

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So then we're going to
move 29 over to the right.

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That's the 29 part.

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Now this is a positive
29, and so how

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do we figure out what this is?

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This is 29 right here
that we're adding.

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This is going to land us right
over here on the number line.

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So how do we figure out
what number that is?

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Well, once again, we
can just visualize it.

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And eventually you won't have
to draw number lines and stuff,

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but I think it'll
be useful here.

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We're starting at negative 31.

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We're adding 29 to it, so it's
going to make it less negative.

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But we're still
adding less than 31,

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so we're not going to get
all the way back to 0.

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We're still going to
have a negative number.

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But how could we figure
out the absolute value

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of that negative
number, its distance?

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Well, once again, that little
white part right there,

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that white part plus
this 29, is going

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to equal 31, if you just
think of absolute value,

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if we don't think
about the signs,

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if we just think
about the length.

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Or another way to think
about it, 31 minus 29

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will give us the length
of that white part.

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And of course, it's
going to be negative,

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because the negative
number here is

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larger than the positive number.

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And we're adding the 2.

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If we do 31 minus 29, you
could borrow and all of that,

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but that's clearly just
going to be equal to 2.

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You could say that's 11.

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This is a 2.

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You subtract, this
is equal to 2.

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But since it's
negative 31 plus 29,

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it's going to be a negative 2.

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We're still going
to stay negative.

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We haven't moved far to
the right enough to pass 0.

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So this right here is
going to be negative 2.

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Or another way to
think about it,

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the length of this white
bar, the absolute value,

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is going to be 2.

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2 plus 29 is 31.

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But we're operating to the
left of 0, so it's negative 31.

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This is negative 2.

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Anyway, hopefully you
found that useful.

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And let me make it clear.

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Our final answer is negative 2.