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let's give ourselves a little bit more practice adding and subtracting positive and negative numbers so let's say that we have the statement four is equal to negative eight minus blank like always I encourage you to pause the video and see if you can figure out what blank would be to make the statement true that negative eight minus blank is going to be equivalent to 4 that 4 is equal to negative eight minus blank so now let's work it through it together and to help us I will get a number line so there's a number line right over there and one way to think about it is I want to start at negative 8 so this is negative 5 negative 6 negative 7 negative 8 I want to start at negative 8 and I want to do something to negative 8 to end up at 4 to end up at 4 so 4 is positive 1 2 3 4 so that's 4 right over there so what I needed what do I need to do to get from negative 8 to positive 4 well let's see I have to move to the right 1 2 3 4 5 6 7 8 9 10 11 12 I have to move to the right 12 spaces another way to think about it to get from negative 8 to positive 4 I have to actually let me make sure I have some space up here I have to add 12 another way to think about it to get from negative 8 to 0 you have to add 8 and then to get 2 from 0 to 4 you have to add another 4 so you have to add 8 plus 4 or 12 but how do you do that because they're saying negative 8 minus something should be equal to 4 well whatever you have over here you want this to end up being equivalent to plus 12 so what can you do there well you could subtract a negative if you subtracted negative 12 this would be equivalent to adding 12 so notice let me rewrite it 4 is equal to let me just write it without my boxes there is equal to negative 8 minus negative 12 but what happens when you subtract a negative well that ends up being adding the positive so this is going to be the same thing as negative 8 plus positive 12 or 4 is equal to negative 8 plus 12 which we know is true you add 8 you get to 0 negative 8 plus 8 is 0 and then you add another 4 you get to positive 4 so that one was pretty interesting let's do another one we can't get enough practice this is too much fun all right so let's say we had let's say we had something blank minus negative 2 is equal to negative 7 how do we think about this well the first thing my brain wants to do is to simplify subtracting a negative so if you subtract negative 2 that's the same thing as adding positive 2 so this is an equivalent statement to saying something subtracting a negative 2 is the same thing as adding a positive 2 something plus 2 is equal to negative 7 and now we can get the number out number line out to think about it so get my number line out so my goal my goal is I want to get to negative 7 so it's negative 5 negative 6 negative 7 right there and I want to add 2 to something to get to negative 7 so if I'm adding 2 that means I'm jumping to I'm jumping to to the right that's what adding 2 looks like so what number do I need to start at that if I jump to to the right if I add 2 I end up at negative 7 well I would have to start to to the left of negative 7 if I start to to the left 1 2 if I started let me do this in a different color if I started this number right here and if I add 2 plus 1 plus 2 plus 2 I end up at negative 7 well what number is this this number that is 2 to the left of the negative 7 well that's negative 9 so this right over here is negative 9 negative 9 plus 2 so if you start at negative 9 and you move to to the right you end up at negative 7 or you could say negative 9 minus negative - because if you subtract negative - you're going to move to the right if you subtract positive - you move to the left but then if you subtract negative - you move to to the right to negative seven another fascinating one let's do one more of these and I'm having maybe a little bit too much fun all right so let's say we have negative four is equal to blank - 9 so let's get the number line out and always pause the video see if you can try it on your own but let's let's get my number line out and so let's think about it our goal we want to take some number subtract nine from it and get negative four so we want to get negative four and then there's some number that if we take nine away from it so if you take nine away from something that's moving nine to the left so another way to think about subtracting nine let me do this in a different color subtracting subtracting nine that's literally moving nine to the left one two three four five six seven eight nine so there's some number that we start with we're going to subtract nine and then we end up with negative four we're going to end up with negative four some number some number that's the blank right over here you subtract nine you move nine to the left that's going to be equivalent to negative four so another way to think about it is this number is going to be nine to the right of negative four so let's think about what that number is going to be so this number is going to be nine to the right of negative four one two three four five six seven eight nine it looks like positive five so let's let's let's see if we're right about that fight if we start at positive five and we subtract nine so let's do that one two three four five six seven eight nine yep you subtract nine you're going to end up at negative 4 so negative four is equal to five minus 9