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Let's say that we have the
number 5, and we're asked,

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what number do we add to
the number 5 to get to 0?

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And you might already know
this, but I'll just draw it out.

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So let's say we have a
number line right over here.

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And 0 is sitting
right over there.

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And we are already
sitting here at 5.

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So to go from 5 to 0, we have
to go five spaces to the left.

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And if we're going five
spaces to the left,

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that means that we
are adding negative 5.

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So if we add negative
5 right here,

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then that is going
to get us back to 0.

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That is going to get us
back right over here to 0.

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And you probably
already knew this.

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And this is a pretty maybe
common sense thing right here.

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But there's a fancy word for
it called the additive inverse

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property.

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And all the additive--
I'll just write it down.

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I think it's kind of
ridiculous that it's

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given such a fancy word
for such a simple idea--

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additive inverse property.

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And it's just the idea
that if you have a number

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and you add the additive
inverse of the number, which

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is what most people call
the negative of the number--

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if you add the negative of
the number to your number,

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you're going to get back
to 0 because they have

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the same size, you
could view it that way.

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They both have a magnitude
of 5, but this is going five

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to the right and then you're
going five back to the left.

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Similarly, if you started at--
let me draw another number line

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right over here-- if you
started at negative 3.

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If you're starting right
over here at negative 3,

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so you've already moved
three spaces to the left,

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and someone says, well what
do I have to add to negative 3

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to get back to 0?

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Well, I have to move three
spaces to the right now.

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And three spaces to the right
is in the positive direction.

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So I have to add positive 3.

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So if I add positive 3 to
negative 3, I will get 0.

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So in general, if I have any
number-- if I have 1,725,314

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and I say, what do I need to
add to this to get back to 0?

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Well, I have to essentially
go in the opposite direction.

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I have to go in the
leftwards direction.

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So I'm going to subtract
the same amount.

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Or I could say, I'm going
to add the additive inverse,

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or I'm going to add the
negative version of it.

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So this is going to be
the same thing as adding

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negative 1,725,314 and
that'll just get me back to 0.

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Similarly, if I say, what number
do I have to add to negative 7

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to get to 0?

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Well, if I'm already at negative
7, I have to go 7 to the right

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so I have to add positive 7.

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And this is going
to be equal to 0.

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And this all comes
from the general idea

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5 plus negative 5, 5
plus the negative of 5,

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or 5 plus the
additive inverse of 5,

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you can just view this as
another way of 5 minus 5.

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And if you have
five of something,

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and you take away five, you've
learned many, many years ago

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that that is just
going to get you to 0.