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

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what number do we add to[br]the number 5 to get to 0?

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

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

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And 0 is sitting[br]right over there.

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And we are already[br]sitting here at 5.

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

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

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that means that we[br]are adding negative 5.

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So if we add negative[br]5 right here,

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then that is going[br]to get us back to 0.

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

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And you probably[br]already knew this.

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

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

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property.

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

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I think it's kind of[br]ridiculous that it's

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given such a fancy word[br]for such a simple idea--

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additive inverse property.

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

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and you add the additive[br]inverse of the number, which

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is what most people call[br]the negative of the number--

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if you add the negative of[br]the number to your number,

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you're going to get back[br]to 0 because they have

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the same size, you[br]could view it that way.

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

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

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

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right over here-- if you[br]started at negative 3.

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

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

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and someone says, well what[br]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[br]spaces to the right now.

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And three spaces to the right[br]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[br]negative 3, I will get 0.

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

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

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

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I have to go in the[br]leftwards direction.

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So I'm going to subtract[br]the same amount.

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

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

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So this is going to be[br]the same thing as adding

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

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Similarly, if I say, what number[br]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[br]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[br]to be equal to 0.

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And this all comes[br]from the general idea

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5 plus negative 5, 5[br]plus the negative of 5,

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or 5 plus the[br]additive inverse of 5,

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

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And if you have[br]five of something,

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

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that that is just[br]going to get you to 0.