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we already know a good bit about negative numbers and we know a good bit of fraction so you can imagine we're going to start seeing negatives and fractions together a lot what I want to do in this video is just make sure we have a decent understanding how to manipulate negative signs when we see them in fractions for example if I have the fraction negative 1/2 here I have the negative out in front of the entire 1/2 this is the same thing as negative 1 over 2 and it's going to be the same thing as 1 over negative 2 now I could also think about something like negative 1 over negative 2 now it's important realize one way to think about this as a fraction is you could view this as negative 1 divided by negative 2 and we already know if you divide a negative by negative it would be a positive so this right over here is going to be the same thing as 1/2 this is going to be the same thing as positive 1/2 now with that out of the way let's think a little bit about let's do some example problems that might push our thinking on this a little bit more so this first question which of the following expressions are equivalent to negative G over H negative G over H select all that apply all right so this has all sorts of negatives here so at first it looks a little bit unusual but then we need to just realize that this part actually let me square this off in blue right over here negative G over negative H we've already figured that out we actually looked at that right over here if you have a negative divided by negative that's the same thing as the positive value divided by the positive value so negative G over negative H is the same thing as G over H and then you still have and then you still have this negative out front you still have that negative out front so this one right over here is actually equal to negative G over H one way to think about negative divided by negative is a positive and you still have this negative out here so that's the same thing and this right over here negative in front and then you have G over negative H this is going to be the same thing you could rewrite this you could put the negative on top as negative G over naked of age and then this would be equal to G over H which is different this is positive G or H this is negative G over H so we wouldn't select that and of course we wouldn't select none of the above because we found a choice that we liked all right which of the following expressions are equivalent to five over B check select all that apply all right so this one over here negative five over negative B well we could remember that this is negative we could write this this is the same thing as negative five over negative B and I just want to make it clear where that negative so this negative instead of writing it negative in front of the entire fraction I could essentially multiply the negative one times just the numerator so you could write this as negative five over negative B and negative divided by negative is going to be a positive so this actually is going to be equal to positive five over B which is what we're looking for so this is going to be right now this one negative divided by negative well that's just going to be positive so that's the same thing as 5 over B one way to think about it is that well the negatives kind of cancel each other out so five over B that looks good too and of course I won't select none of the above because I found two choices that worked all right let's do one more which of the following expressions which of the following expressions are equal to negative negative e over negative F remember we have to take this step by step here actually let's try to just simplify this directly so negative negative e over negative F well we just need to remind ourselves that this part right over here negative e over negative F let me write an equal sign negative e over N and we put this negative let me do this in a different color let me do this in purple so we have this purple so we have the purple negative right over there and negative E over negative F we've already talked about this multiple times that's the same thing as negatives divided by negative is a positive that's the same thing as e over F as positive V over F so this whole thing will simplify to negative E over F so let's see which of these choices are that well this right here is positive e over F so that's not the choice this one over here this one we could write it several ways actually we could write it negative negative e over F which of course is equal to positive e over F we could also write this we could put the negative in the denominator we could say that this thing actually let me write it over here is negative e over negative F this is also legitimate thing to do you can multi kiss negative and multiply it times the denominator right over here but either way it's going to be equal to positive e over F it's going to be these two or actually evaluate to the same expression so here I would select finally I would select I've been waiting to select none of the above alright hopefully that helps