Inverse Property of Addition

The simple idea that a number plus its negative is 0

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

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

and you might already know this but let's draw it out

so let's say we have a number line over here and 0 is sitting right over there

we are already sitting here at 5

so to go from 5 to 0 we have to go 5 spaces to the left

and if we are going 5 space to the left that means we are adding negative 5 (-5)

so if we add negative 5 right here than that is going to bring us back to 0

and you probably already knew this

and this is a pretty... maybe common sense thing here

but there is a fancy word for it called the additive inverse property

and i'll just right it down, i think it's ridiculous that this is given such a fancy word for such a simple idea

additive inverse property, and it is just the idea that if you have a number and if you add the additive

inverse of the number, which most people call the negative of the number

you add the negative of your number you will 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 5 to the right and this is going 5 to the left

Similarly, if you started at negative 3 (-3) if your starting over here at -3

so you already moved 3 spaces to the left.

and someone says... "What do i have to add to -3 to get back to 0?"

well i have to move 3 spaces to the right now.

and 3 spaces to the right is in the positive direction

so i have to add positive 3 (+3)

so if i add positive 3 to negative 3 i will get 0

so in general, if i have any number...

1 million seven hundred twenty five thousand three hundred and fourteen (1,725,314)

and i say... what do i need to add to this to get back to zero

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 can say i can add the additive inverse or add the negative version of it.

so this is going to be the same thing as adding -1,725,314

and that will get me back to zero (0)

similarly, what number do i need to add to -7 to get to 0.

well if i'm already at -7 i need to add positive 7 ( 7 to the right)

so this is going to be equal to 0

and this all comes form the general idea.

5+-5 : 5+ the - of 5: or 5 + the additive inverse of 5

you can just view this, and as another way as 5 - 5

and if you have 5 of something then you take you take away 5

then you learned many many years ago that, that is going to get you 0