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Welcome to the presentation on adding and subtracting negative numbers. So let's get started. So what is a negative number, first of all? Well, let me draw a number line. Well it's not much of a line but I think you'll get the picture. So we're used to the positive numbers, so if that's 0, you have 1, you have 2, you have 3, you have 4, and you keep going. And if I were to say what's 2 plus 2, you'd start at 2 and then you'd add 2 and you'd get to 4. I mean most of us it's second nature. But if you actually drew it on a number line you'd say 2 plus 2 is 4. And if I asked you what's 2 minus 1 or let's say what's 3 minus 2? If you start at 3 and you subtracted 2, you would end up at 1. That's 2 plus 2 is equal to 4 and 3 minus 2 is equal to 1. And this is a joke for you. Now what if I were to say what is 1 minus 3? Huh. Well, it's the same thing. You start at 1 and we're going to go 1 -- well, now we're going to go below 0 -- what happens below 0? Well then you start going to the negative numbers. Negative 1, negative 2, negative 3, and so on. So if I start at 1 right here, so 1 minus 3, so I go 1, 2, 3, I end up at negative 2. So 1 minus 3 is equal to negative 2. This is something that you're probably already doing in your everyday life. If I were to tell you that boy, it's very cold today, it's 1 degree, but tomorrow it's going to be 3 degrees colder, you might already know intuitively, well then we're going to be at a temperature of negative 2 degrees. So that's all a negative number means. And just remember when a negative number is big, so like negative 50, that's actually colder than negative 20, right? So a negative 50 is actually even a smaller number than negative 20 because it's even further to the left of negative 20. That's just something you'll get an intuitive feel for. Sometimes when you start you feel like oh, 50's a bigger number than 20, but it's a negative 50 as opposed to a positive 50. So let's do some problems, and I'm going to keep using the number line because I think it's useful. So let's do the problem 5 minus 12. I think you already might have an intuition of what this equals. But let me draw a line, 5 minus 12. So let me start with minus 10, minus 9, minus 8 --I think I'm going to run out of space -- minus 7, minus 6, minus 5 -- I should have this pre-drawn -- minus 4, minus 3, minus 2, minus 1, 0, 1, 2, 3, 4, I'll put 5 right here. 5 minus 12. So if we start at 5 -- let me use a different color -- we start at 5 right here and we're going to go to the left 12 because we're subtracting 12. So then we go 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. Negative 7. That's pretty interesting. Because it also happens to be that 12 minus 5 is equal to positive 7. So, I want you to think a little bit about why that is. Why the difference between 12 and 5 is 7, and the difference between -- well, I guess it's either way. Because in this situation we're also saying that the difference between 5 and 12 is negative 7, but the numbers are that far apart, but now we're starting with the lower number. I think that last sentence just completely confused you, but we'll keep moving forward. We just said 5 minus 12 is equal to minus 7. Let's do another one. What's negative 3 plus 5 equals what? Well, let's use the same number line. Let's go to negative 3 plus 5. So we're going to go to the right 5. 1, 2, 3, 4, 5. It's a 2. It equals 2. So negative 3 plus 5 is equal to 2. That's interesting because 5 minus 3 is also equal to 2. Well, it turns out that 5 minus 3 is the same thing, it's just another way of writing 5 plus negative 3 or negative 3 plus 5. A general, easy way to always do negative numbers is it's just like regular subtraction and addition and subtraction, but now when we subtract we can go to the left below 0. Let's do another one. So what happens when you get let's say 2 minus minus 3? Well, if you think about how it should work out I think this will make sense. But it turns out that the negative number, the negative signs actually cancel out. So this is the same thing as 2 plus plus 3, and that just equals 5. Another way you could say is -- let's do another one -- what is negative 7 minus minus 2? Well that's the same thing as negative 7 plus 2. And remember, so we're doing to start at negative 7 and we're going to move two to the right. So if we move one to the right we go to negative 6, and then we move two to the right we get negative 5. That makes sense because negative 7 plus 2, that's the same thing as 2 minus 7. If it's 2 degrees and it gets 7 degrees colder, it's minus 5. Let's do a bunch of these. I think the more you do the more practice you have, and the modules explain it pretty well, probably better than I do. So let's just do a ton of problems. So if I said negative 7 minus 3. Well, now we're going to go three to the left of negative 7. We're going to get 3 less than negative 7 so that's negative 10, right? That makes sense, because if we had positive 7 plus 3 we're at 7 to the right of 0 and we're going to go three more to the right of 0 and we get positive 10. So for 7 to the left of 0 and go three more to the left we're going to get negative 10. Let's do a bunch more. I know I'm probably confusing you, but practice is what's going to really help us. So say 3 minus minus 3, well, these negatives cancel out so that just equals 6. What's 3 minus 3? Well, that's easy that's just 0. What's minus 3 minus 3? Well now we're going to get three less than minus 3, well that's minus is 6. What's minus 3 minus minus 3? Interesting. Well, the minuses cancel out so you get minus 3 plus 3. Well, if we start three to the left of 0 and we move three to the right we end up at 0 again. So that makes sense, right? Let me do that again. Minus 3 minus minus 3. Anything minus itself should equal 0, right? That's why that equals 0. And that's why it makes sense that those two negatives cancel out and that's the same thing as this. Let's do a bunch more. Let's do 12 minus 13. That's pretty easy. Well, 12 minus 12 is 0, so 12 minus 13 is negative 1 because we're going to go one the left of 0. Let's do 8 minus 5. Well, this one is just a normal problem, that's 3. What's 5 minus 8? Well, we're going to go all the way to 0 and then 3 more to the left of zero, so it's minus 3. I could draw a number line here. If this is 0 this is 5, and now we're going to go to left 8, then we end up and negative 3. You could do that for all of these. That actually might be a good exercise. I think this will give you good introduction and I recommend that you just do the modules because the modules actually, especially if you do the hints, it has a pretty nice graphic that's a lot nicer than anything I could draw on this chalkboard. So try that out and I'm going to try to record some more modules that hopefully won't confuse you as badly. You could also attend the seminar on adding and subtracting negative numbers. I hope you have fun. Bye.