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what I hope to do in this video is go through a bunch of examples that will hopefully give us some even better understanding of what it means to add or subtract a positive or a negative number and as I go through these I encourage you to keep pausing the video and trying to solve it on your own and then see how we can solve it together so let's start if I were to say that negative 1 is equal to 7 minus blank what should be in that blank what number either positive or negative I guess it could be 0 what would that number be all right let's work through it together so let me throw a number line here so let me put a number line right over here and let's just think about what's going on so we are trying to get to negative 1 we're trying to get to negative 1 and we are starting at 7 so 7 this is 5 6 7 so we're starting at 7 so what do we have to subtract from 7 to get 2 to get to this negative 1 here well we have to move we have to move 1 2 3 4 5 6 7 8 8 to the left so what we just did is we just subtracted we just subtracted 8 from 7 to get to negative 1 so what do we need to subtract we just subtract we need to subtract 8 let's do another one of these this is kind of fun let's say we need to figure out let's say we have negative 10 plus blank is equal to negative 5 what would the blank be in this case let's give ourselves a number line again so let's give ourselves a number line again and let's see we are going to start at negative 10 so let's see this is negative 10 right over here so we're going to start at negative 10 and we're going to add something to it to get to negative 5 remember negative 5 is right over here so for adding that means we're going to be going to the right on the number line that is if we're adding a positive number and we see here we're going to the right we're going from negative 10 to negative 5 so we are going to be adding a positive number if we add as a negative number we would move to the left so how much are we adding well let's just count we're going to add one two three four five so we just added we just added positive five so that would be a five right there negative ten plus five is equal to negative five we just became five less negative is one way to think about it let's do another one all right so let's say we had four is equal to negative two plus blank four is equal to negative two plus blank well we can do this the same way we've been doing others let's get our number line out here let's get our number line out here and let's see we're going to one way to think about our goal is to get to four our goal is 4 right over here so this is 1 2 3 4 get to positive 4 that's positive 4 right there we're starting at negative 2 we're starting it I'm just in a different color we're starting at negative 2 we're saying 4 is the same thing as negative 2 negative 2 is right over here negative 2 plus some amount and it's clear we're going to be moving to the right by let's see we're going to move to the right by 1 2 3 4 5 6 so we moved to the right by 6 so we added 6 so negative 2 plus 6 plus 6 is equal to 4 this is fascinating let's do that's just let's just do several more of these I can't stop all right so let's say we wanted to figure out let's say we wanted to figure out I have 6 plus blank 6 plus blank is equal to negative 8 like always try to pause the video and figure out what this blank is going to be let me throw my number line back here so my number line and one way to think about it one way to think about it is I am starting at 6 I'm starting at 6 so that's 5 this is 6 right over here and I'm going to add something to get to negative 8 to get to negative 8 this is negative 5 negative 6 negative 7 negative 8 I want to get right over here I want to get to negative 8 so what do I have to do to get from 6 to negative 8 to go from 6 to negative 8 well it's clear I have to go to the left on the number line and how much do I have to go to the left well let's count it I have to go 1 2 3 4 5 6 7 8 9 10 11 12 13 14 so going 14 to the left you could say that I just subtracted 14 and if we phrase it as 6 plus what is equal to negative 8 well 6 plus negative 14 6 if this said 6 minus something I could have just said 6 minus 14 but I'm saying 6 plus 1 is going to be 6 plus negative 14