Adding & subtracting integers
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- [Voiceover] What I hope to do in this video is go through a bunch of examples that will hopefully give us an 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 try 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 one is equal to seven minus blank, what should be in that blank? What number, either positive or negative, I guess it could be zero, what would that number be? Alright, let's work through it together. So let me throw a number line here. So let me put a number line right over here. Now let's just think about what's going on. So we are trying to get to negative one. We're trying to get to negative one and we are starting at seven. So seven; this is five, six, seven. So we're starting at seven. So what do we have to subtract from seven to get to this negative one here. Well, we have to move one, two, three, four, five, six, seven, eight. Eight to the left. So what we just did is we just subtracted eight from seven to get to negative one. So what are we going to subtract? We need to subtract eight. 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 five. What would the blank be in this case? Let's give ourselves a number line again. 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 gonna start at negative 10 and we're gonna add something to it to get to negative five. Remember, negative five is right over here. So if we're 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 five, so we are going to be adding a positive number. If we added a negative number we would move to the left. So how much are we adding? Well, let's just count. We're gonna add one, two, three, four, five. So we just added positive five. So that would be a five right there. Negative 10 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! Alright. So let's say we had four is equal to negative two plus blank. Four is equal to negative two plus blank. We could 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. One way to think about it, our goal, is to get four. Our goal is four right over here. So this is one, two, three, four, get to positive four. That's positive four right there. We're starting at negative two... Let me do this in a different color. We're starting at negative two. We're saying four is the same thing as negative two, negative two is right over here, negative two plus some amount. And it's clear we're gonna be moving to the right by, let's see, we're gonna move to the right by one, two, three, four, five, six. So we moved to the right by six. So we added six. So negative two plus six is equal to four. This is fascinating. Actually, let's just do several more of these, I can't stop. (laughs) Alright. So let's say we wanted to figure out, I have six plus blank. Six plus blank is equal to negative eight. 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 is I am starting at six. So it's five, this is six right over here. And I'm gonna add something to get to negative eight. To get to negative eight this is negative five, negative six, negative seven, negative eight. I want to get right over here, I want to get to negative eight. So what do I have to do to get from six to negative eight? To go from six to negative eight. We're 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 one, two, three, four, five, six, seven, eight, nine, 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 six plus what is equal to negative eight? Well, six plus negative 14. If this said six minus something I could have just said six minus 14, but if it's saying six plus what it's going to be six plus negative 14.