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Welcome to the presentation on adding and subtracting

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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 but I think you'll

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get the picture.

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

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have 1, you have 2, you have 3, you have 4, and you keep going.

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And if I were to say what's 2 plus 2, you'd start at 2 and

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then you'd add 2 and 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 plus 2 is 4.

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And if I asked you what's 2 minus 1 or let's

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say what's 3 minus 2?

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If you start at 3 and you subtracted 2, you

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would end up at 1.

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That's 2 plus 2 is equal to 4 and 3 minus 2 is equal to 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 minus 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 -- well, now we're

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going to go below 0 -- what happens below 0?

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Well then you start going to the negative numbers.

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Negative 1, negative 2, negative 3, and so on.

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So if I start at 1 right here, so 1 minus 3, so I go 1, 2,

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3, I end up at negative 2.

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So 1 minus 3 is equal to negative 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 boy, it's very cold today, it's 1

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degree, but tomorrow it's going to be 3 degrees colder, you

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might already know intuitively, well then we're going to be

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at a temperature of negative 2 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, so like

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negative 50, that's actually colder than negative 20, right?

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So a negative 50 is actually even a smaller number than

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negative 20 because it's even further to the left

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of negative 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 oh, 50's a bigger

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number than 20, but it's a negative 50 as opposed

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to a positive 50.

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So let's do some problems, and I'm going to keep using the

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number line because I think it's useful.

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So let's do the problem 5 minus 12.

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I think you already might have an intuition of

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what this equals.

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But let me draw a line, 5 minus 12.

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So let me start with minus 10, minus 9, minus 8 --I think I'm

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going to run out of space -- minus 7, minus 6, minus 5 -- I

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should have this pre-drawn -- minus 4, minus 3, minus 2,

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

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5 minus 12.

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

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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, 4, 5, 6, 7, 8, 9, 10, 11, 12.

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Negative 7.

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That's pretty interesting.

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Because it also happens to be that 12 minus 5

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is equal to positive 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, and the difference

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

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Because in this situation we're also saying that the difference

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between 5 and 12 is negative 7, but the numbers are that far

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apart, but now we're starting with the lower number.

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I think that last sentence just completely confused you, but

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we'll keep moving forward.

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We just said 5 minus 12 is equal to minus 7.

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Let's do another one.

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What's negative 3 plus 5 equals what?

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Well, let's use the same number line.

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Let's go to negative 3 plus 5.

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So we're going to go to the right 5.

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1, 2, 3, 4, 5.

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It's a 2.

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It equals 2.

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So negative 3 plus 5 is equal to 2.

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

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Well, it turns out that 5 minus 3 is the same thing, it's just

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another way of writing 5 plus negative 3 or

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negative 3 plus 5.

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A general, easy way to always do negative numbers is it's

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just like regular subtraction and addition and subtraction,

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but now when we subtract we can go to the left below 0.

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Let's do another one.

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So what happens when you get let's say 2 minus minus 3?

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

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this will make sense.

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But it turns out that the negative number, the negative

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signs actually cancel out.

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So this is the same thing as 2 plus plus 3, and

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that just equals 5.

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

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is negative 7 minus minus 2?

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Well that's the same thing as negative 7 plus 2.

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

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going to move two to the right.

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So if we move one to the right we go to negative 6, and then

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we move two to the right we get negative 5.

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That makes sense because negative 7 plus 2, that's the

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same thing as 2 minus 7.

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If it's 2 degrees and it gets 7 degrees colder, it's minus 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, and the

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modules explain it pretty well, 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 negative 7 minus 3.

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Well, now we're going to go three to the

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left of negative 7.

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We're going to get 3 less than negative 7 so that's

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negative 10, right?

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That makes sense, because if we had positive 7 plus 3 we're at

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

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right of 0 and we get positive 10.

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So for 7 to the left of 0 and go three more to the left we're

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going to get negative 10.

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Let's do a bunch more.

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I know I'm probably confusing you, but practice is what's

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going to really help us.

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So say 3 minus minus 3, well, these negatives cancel out

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so that just equals 6.

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What's 3 minus 3?

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Well, that's easy that's just 0.

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What's minus 3 minus 3?

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Well now we're going to get three less than minus 3,

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well that's minus is 6.

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What's minus 3 minus minus 3?

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Interesting.

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Well, the minuses cancel out so you get minus 3 plus 3.

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

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the right 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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Minus 3 minus 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 those two negatives

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cancel out 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 minus 13.

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That's pretty easy.

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Well, 12 minus 12 is 0, so 12 minus 13 is negative 1

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because we're going to go one the left of 0.

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Let's do 8 minus 5.

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

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What's 5 minus 8?

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Well, we're going to go all the way to 0 and then 3 more to the

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left of zero, so it's minus 3.

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I could draw a number line here.

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If this is 0 this is 5, and now we're going to go to left 8,

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then we end up and negative 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 and I recommend

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that you just do the modules because the modules actually,

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especially if you do the hints, it has a pretty nice graphic

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that's a lot nicer than anything I could draw

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on this chalkboard.

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So try that out and I'm going to try to record some more

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modules that hopefully won't confuse you as badly.

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You could also attend the seminar on adding and

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subtracting negative numbers.

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I hope you have fun.

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Bye.