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# Negative symbol as opposite

CCSS.Math:

## Video transcript

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 for if you have a if you have a number if you have a number and then we want to think about what the opposite of that number is opposite this is just a 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 it's 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 negative four negative let me write this negative negative four that literally means that literally means so you you can take this negative symbol as meaning opposite opposite opposite of four opposite of four if you were to say 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 that means the opposite opposite of opposite let me do that 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 and let's say let me put some tick marks here and I don't know how much each of these tick marks jump but let's say that a is some number that is right 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 could write opposite of a over here we could literally write opposite opposite of a is that number right over there or as a shorthand as a shorthand we can just write we can just write negative we can just write this is negative a right over here negative 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 let me do this what would be the negative of negative three encourage you to pause the video and think about it what we just said this negative means the opposite so you can think about this as meaning this means the opposite opposite of opposite of negative the opposite of negative three so what's 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 this is equal to positive three or we could just write positive three like positive three like that so hopefully this gives you a better appreciation for what opposite means and also how it relates to the actual the actual negative symbol and we could keep going you know we could we could do something like what is 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 2 which is really the opposite of the opposite of 2 well that's just going to be - every time you say opposite you flip over the you flip over the number line so this flips you over the number line 2 to the left and then this flips you back to to the right so all this is going to be 2 but then you're going to take the opposite of 2 so that's just going to be negative that's going to be negative 2 if you threw another negative in front of this would be the opposite of all of this would be the opposite of negative 2 and then no son would become positive so every time you put that negative in front there you're flipping on the other side of the number line