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Negative symbol as opposite

CCSS Math: 6.NS.C.6, 6.NS.C.6a

Video transcript

- [Voiceover] In another video we've already talked about what an opposite of a number is, but we'll review it a little bit. If we start with a positive number, say, the number four. If you have a number and then we want to think about what the opposite of that number is. Opposite. This is just the symbol for number or shorthand for number. So if the number is four, what is its opposite? Well, four is one, two, three, four to the right of zero. Positive four is four to the right of zero. So its opposite is going to be one, two, three, four to the left. So it's going to be negative four. Or another way to think about it, if you have a positive number, its opposite is going to be the negative of that number. So another way of thinking about it is, is that this negative literally means opposite. One way to think about it, this is the number that is the opposite of four. So let me write this down. So if I write negative four. Negative, let me write this, negative four. That literally means... So you can take this negative symbol as meaning opposite. Opposite. Opposite of four. Opposite of four. If you were to say negative, instead of saying a specific number let's just say a letter that could represent a number. So if I said negative A, that means the opposite of the number A. That means the opposite... Opposite of... Let me do that in blue color. Opposite of A. Of A. And if this confuses you a little bit just look, A could be any number right over here. So let me draw a number line just so this can be a little bit, make a little bit more sense hopefully. So this is a number line. Let me put some tick marks here. I don't know much each of these tick marks jump but let's say that A is some number that is right over here. Well negative A is going to be the opposite of A. So if A is three tick marks to the right negative A is going to be three tick marks to the left. One, two, three. And so the opposite of A is going to be this value right over here. And we can write that, we can write opposite of A over here. We could literally write opposite, opposite of A is that number right over there. Or as a shorthand, we can just write-- We can just write negative. We can just write this is negative A right over here. Negative A. So with that in mind, if we literally view this negative symbol as meaning the opposite of whatever this is, let's try something interesting. What would be the negative-- Let me do this in another color. What would be the negative of negative three? And I encourage you to pause the video and think about it. Well we just said, this negative means the opposite. So you can think about this as meaning this means the opposite... Opposite of negative-- The opposite of negative three. So what is the opposite of negative three? Well negative three is three to the left of zero. One, two, three. So it's opposite is going to be three to the right of zero. One, two, three. So it's going to be positive three. So this is equal to positive three. Or we could just write positive three like that. So hopefully this gives you a better appreciation for what opposite means and also how it relates to the actual negative symbol. We could keep going. We could do something like what is the negative of the negative of negative-- Let me do a different number. Of negative two. Well, this part right over here the negative, the opposite of negative two, which is really the opposite of the opposite of two, well that's just going to be two. Every time you say opposite you flip over the number line. So this flips you over the number line two to the left and this flips you back two to the right so all of this is going to be two but then you're going to take the opposite of two so that's just going to be negative two. If you threw another negative in front of this, it would be the opposite of all of this. So it would be the opposite of negative two and then all of a sudden it would become positive. So every time you put that negative in front there you're flipping on the other side of the number line.