## Inverse property of addition | Arithmetic properties | Pre-Algebra | Khan Academy

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’ll just draw it out. 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’re 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. 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 a fancy word for

it called the additive inverse property. And all the additive–

I’ll just write it down. 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’re going to get back

to 0 because they have 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’re

going five back to the left. Similarly, if you started at–

let me draw another number line right over here– if you

started at negative 3. If you’re starting right

over here at negative 3, so you’ve 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? Well, I have to move three

spaces to the 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. 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

leftwards 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. 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’ve

learned many, many years ago that that is just

going to get you to 0.

## superdau

Sep 9, 2011, 9:26 pm@Twinsfan36

The result is the same. And you'd maybe think: what's the difference?

But this is actually used. Some CPUs/micro controllers don't have a separate "subtract" function (because every additional function needs space on the chip). So to subtract you have to add the inverse.

## bolshevik

Oct 10, 2011, 1:26 pmshit im a 4th grader and already learning pre algerbra 0_0

## jonjonjon1370

Oct 10, 2011, 10:58 pm@mikestertech101 i learned it when i was in 3rd. Trust me, it pays off in middle school because if you werent paying attention in class you probably already know it.

## bolshevik

Oct 10, 2011, 11:32 pm@jonjonjon1370 Thanks for the tip 😀

## jonjonjon1370

Oct 10, 2011, 10:47 pm@mikestertech101 no problem, btw- i checked out ur minecraft videos and theyre great. Im subscribing to you!

## bolshevik

Oct 10, 2011, 10:54 pm@jonjonjon1370 Hey thanks a bunch 🙂

Nice to hear something like that from someone i dont even know !

## Mountainvictory

Feb 2, 2013, 1:28 pmI love this. It was tickling my brain.

## AngryBurrito569

Feb 2, 2013, 12:34 amthe things the teacher says are gibberish, but you say it kid freindly 😀

## Braxianna Otto

Aug 8, 2015, 10:26 pmI'm in seventh grade and I'm learning this now?!

## Caleb Godwin

Oct 10, 2015, 12:19 pmDope stuff breh, fire bars on this one ???

## Leanne Syron

Aug 8, 2017, 9:33 amextremely helpful. teaching algebra for the first time. DOING algebra for the first time. learning curve has G forces!

## KSL Success

Sep 9, 2017, 3:24 amI kinda get this video

## Tougher Than Leather

Nov 11, 2017, 2:54 pmProof math can be simple!

## Makayla Russell

Aug 8, 2018, 1:58 amI'm in 5th grade and I'm learning it now and i get thr video

## Poison Darkk

Oct 10, 2018, 9:53 pmSub plz

## HEy loOk iTs NobOoDy!

Apr 4, 2019, 2:34 amour teacher gave us a worksheet where we had to work with this.None of us students knew what i was and when we asked the teacher, turns out he didn't know either and told us to search it up

AND HERE I AM