**Inverse property of addition**

**Inverse Property Of Addition**

- Let’s Say that we have the number 5 , and we’re asked , what number do we add to the number 5 to get to 0 ?
- And you might already know this , but I will just draw it out. Inverse Property Of Addition
- So let’s say we have a number line right over here. And 0 is sitting right over there.
- And we are already sitting here at 5.
- So to go from 5 to 0 , we have to go five spaces to the left.
- And if we are going five spaces to the left, that means that we are adding negative 5.
- So if we add negative 5 right here , 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. And you probably already knew this.
- And this is a pretty maybe common sense thing right here.
- But there,s fancy word for it called the additive inverse property.
- And all the additive i will just write it down. Inverse Property Of Addition
- I think it’s kind of ridiculous that it’s given such a fancy word for such a simple idea -additive inverse property.
- And it’s just the idea that if you have a number and you add the additive inverse of the number , which is what most people call the negative of the number. If You add the negative of the number to your number. you are going to get back to 0 because they were the same size , you could view it that way.
- They both have a magnitude of 5 , but this is going five to the right and then you are going five back to the left.

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**Similarly , if you started at let me draw another number line right over here *- if you started at negative 3.**

- If you are starting right over here at negative 3 , so you are already moved three spaces to the left, and someone says well what do i have to add to negative 3 to get back to 0 ? Inverse Property Of Addition
- Well , have to move three spaces to right now.
- And three spaces to the right is in the positive direction.
- So I have to add positive 3.
- So if i add positive 3 to negative 3 ,I will get 0.

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**1,725,314 + ( – 1, 725 , 314 ) = 0**

- So In general if i have any number – if i have 1,725,314 and I say , what do i need to add to this to get back to 0 ?
- Well , i have to essentially go in the opposite direction. I have to go in the leftward direction. So I’m going to subtract the same amount. Or I could say , I’m going to add the additive inverse, or I’m going to add the negative version of it.
- So this is going to be the same thing as adding negative 1,725,314 and that”ll just get me back to 0. Inverse Property Of Addition

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**Similarly , if i say , what number do i have to add to negative 7 to get to 0 ?.**

Well, if I’m already at negative 7 , I have to go 7 to the right so I have to add positive 7. and this is going to be equal to 0. and this all comes from the general idea 5 plus negative 5 , 5 plus the negative of 5, or 5 plus the additive inverse of 5 , you can just view this as another way of 5 minus 5. and if you have five of something , and you take away five , you have learned many , many years ago that is just going to get you to 0.

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