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Video transcript

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 we are already sitting here at 5 so to go from 5 to 0 we have to go 5 spaces to the left we have to go 5 spaces to the left and if we're going 5 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 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 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 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 then you're going 5 back to the left similarly if you start it at if you started 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 3 spaces to the left and someone says well what do I have to add to negative 3 what do I have to add to negative 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 so if I add positive 3 to negative 3 I will get 0 so in general if I have if I have any number if I have 1 million seven hundred and twenty-five thousand three hundred and fourteen 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 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 million seven hundred twenty-five thousand three hundred and fourteen and that'll just get me that'll get me back to zero similarly if I say what number do I have to add to negative seven to get to zero well if I'm already at negative seven have to go seven to the right so I have to add positive seven and these this is going to be equal to zero and this all comes from the general idea five plus negative five five plus the negative of 5 or 5 plus the additive inverse of five you can just view this and as another way of five minus five and if you have five of something you take away five you've learned many many years ago that that is just going to get you to zero