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Welcome to the presentation

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on adding and subtracting negative numbers.

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So let's get started.

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So what is a negative number, first of all?

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Well, let me draw a number line.

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Well it's not much of a line,

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but I think you'll get the picture.

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So we're used to the positive numbers, so if that's 0

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you have one, you have 2, you have 3, you have 4

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and you keep going.

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And if I were to say what's 2+2

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you'd start at 2, and then you'd add 2

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you'd get to 4.

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I mean most of us it's second nature.

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But if you actually drew it on a number line,

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you'd say 2+2=4

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And if I asked you what's 2-1

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or let's say what's 3-2

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If you start at 3 and you subtracted 2

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you would end up at 1

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That's 2+2=4, and 3-2=1

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And this is a joke for you.

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Now what if I were to say what is 1-3?

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Huh.

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Well, it's the same thing.

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You start at 1 and we're going to go 1--

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well, now we're going to go below 0

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what happens below 0?

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Well then you start going to the negative numbers.

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-1, -2, -3, and so on.

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So if I start at 1 right here, so 1-3

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so I go 1,2,3, I end up at -2

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So 1-3=-2

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This is something that you're probably already doing

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in your everyday life

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If I were to tell you that

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boy, it's very cold today, it's one degree,

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but tomorrow it's going to be three degrees colder,

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you might already know intuitively,

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well then we're going to be

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at a temperature of negative two degrees.

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So that's all a negative number means.

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And just remember when a negative number is big,

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so like -50, that's actually colder than -20, right?

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So a -50 is actually even a smaller number than -20

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because it's even further to the left of -20

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That's just something you'll get an intuitive feel for.

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Sometimes when you start you feel like

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oh, 50 is a bigger number than 20

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but it's a -50 as opposed to a 50

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So let's do some problems,

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and I'm going to keep using the number line

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because I think it's useful

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So let's do the problem 5-12

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I think you already might have an intuition

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of what this equals.

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But let me draw a line, 5-12

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So let me start with -10, -9, -8--

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I think I'm going to run out of space-- -7, -6, -5

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I should have this pre-drawn -- -4, -3, -2, -1

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0,1,2,3,4, and I'll put 5 right here.

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I'm gonna push this arrow out a little bit. Okay.

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5-12

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So if we start at 5-- let me use a different color--

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we start at 5 right here and we're going to go to the left 12

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because we're subtracting 12

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So then we go 1,2,3...

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Negative 7

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That's pretty interesting.

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Because it also happens to be

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that 12 - 5 = +7

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So, I want you to think a little bit about why that is.

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Why the difference between 12 and 5 is 7,

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and the difference between

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-- well, I guess it's either way.

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In this situation we're also saying

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that the difference between 5 and 12 is -7,

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but the numbers are that far apart,

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but now we're starting with the lower number.

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I think that last sentence just completely confused you,

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but we'll keep moving forward.

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We just said 5-12=-7

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Let's do another one.

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What's -3+5?

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Well, let's use the same number line.

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Let's go to -3 plus 5

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So we're going to go to the right 5

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One, two, three, four, five.

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It's a two.

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It equals two.

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So -3 + 5 = 2

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That's interesting because 5 - 3 is also equal to 2

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Well, it turns out that 5 - 3 is the same thing,

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it's just another way of writing 5 plus -3

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or -3 plus 5

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A general, easy way to always do negative numbers

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is it's just like regular addition and subtraction,

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but now when we subtract

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we can go to the left below zero

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Let's do another one.

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So what happens when you get

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let's say, 2 minus -3?

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Well, if you think about how it should work out,

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I think this will make sense.

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But it turns out that the negative number,

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the negative signs actually cancel out.

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So this is the same thing as 2 plus +3

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and that just equals 5

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Another way you could say is-- let's do another one--

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what is -7 minus -2?

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Well that's the same thing as -7 + 2

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And remember, so we're doing to start at -7

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and we're going to move 2 to the right.

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So if we move 1 to the right we go to -6

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and then we move 2 to the right we get -5

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That makes sense because -7 + 2

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that's the same thing as 2 - 7

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If it's two degrees and

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it gets seven degrees colder, it's -5

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Let's do a bunch of these.

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I think the more you do, the more practice you have,

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and the modules explain it pretty well.

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Probably better than I do.

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So let's just do a ton of problems.

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So if I said -7 - 3

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Well, now we're going to go 3 to the left of -7

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We're going to get 3 less than -7

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so that's -10, right?

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That makes sense, because if we had 7 + 3

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we're at 7 to the right of 0

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and we're going to go 3 more to the right of 0

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and we get positive 10

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So for 7 to the left of 0 and go 3 more to the left,

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we're going to get -10

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Let's do a bunch more.

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I know I'm probably confusing you,

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but practice is what's going to really help us.

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So let's say 3 minus -3

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well, these negatives cancel out,

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so that just equals 6

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What's 3-3?

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Well, 3-3, that's easy.

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That's just 0

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What's -3 nimus 3?

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Well now we're going to get 3 less than -3

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well that's -6

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What's -3 minus -3

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Interesting.

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Well, the minuses cancel out, so you get -3 plus 3

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Well, if we start 3 to the left of 0 and we move 3 to the right,

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we end up at 0 again.

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So that makes sense, right?

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Let me do that again.

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-3 minus -3

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Anything minus itself should equal 0, right?

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That's why that equals 0

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And that's why it makes sense that

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those two negatives cancel out

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and that's the same thing as this.

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Let's do a bunch more.

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Let's do 12 - 13

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That's pretty easy.

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Well, 12 - 12 = 0, so12 - 13 = -1

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because we're going to go 1 the left of 0

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Let's do 8 - 5

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Well, this one is just a normal problem, that's 3

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What's 5 - 8?

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Well, we're going to go all the way to 0

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and then 3 more to the left of 0, so it's -3

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I could draw a number line here.

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If this is 0, this is 5

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and now we're going to go to left 8,

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then we end up at -3

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You could do that for all of these.

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That actually might be a good exercise.

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I think this will give you good introduction

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and I recommend that you just do the modules,

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because the modules actually

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especially if you do the hints

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it has a pretty nice graphic

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that's a lot nicer than

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anything I could draw on this chalkboard.

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So, try that out

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and I'm going to try to record some more modules

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that hopefully won't confuse you as badly.

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You could also attend the seminar

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on adding and subtracting negative numbers.

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I hope you have fun!

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Bye.