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

and you keep going.

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

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

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+2=4

And if I asked you what's 2-1

or let's say what's 3-2

If you start at 3 and you subtracted 2

you would end up at 1

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

And this is a joke for you.

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

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.

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

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

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

So 1-3=-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 one degree,

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

you might already know intuitively,

well then we're going to be

at a temperature of negative two degrees.

So that's all a negative number means.

And just remember when a negative number is big,

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

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

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

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

Sometimes when you start you feel like

oh, 50 is a bigger number than 20

but it's a -50 as opposed to a 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 5-12

I think you already might have an intuition

of what this equals.

But let me draw a line, 5-12

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

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

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

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

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

5-12

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...

Negative 7

That's pretty interesting.

Because it also happens to be

that 12 - 5 = +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.

In this situation we're also saying

that the difference between 5 and 12 is -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 5-12=-7

Let's do another one.

What's -3+5?

Well, let's use the same number line.

Let's go to -3 plus 5

So we're going to go to the right 5

One, two, three, four, five.

It's a two.

It equals two.

So -3 + 5 = 2

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

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

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

or -3 plus 5

A general, easy way to always do negative numbers

is it's just like regular addition and subtraction,

but now when we subtract

we can go to the left below zero

Let's do another one.

So what happens when you get

let's say, 2 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 +3

and that just equals 5

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

what is -7 minus -2?

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

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

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

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

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

That makes sense because -7 + 2

that's the same thing as 2 - 7

If it's two degrees and

it gets seven degrees colder, it's -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 -7 - 3

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

We're going to get 3 less than -7

so that's -10, right?

That makes sense, because if we had 7 + 3

we're at 7 to the right of 0

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

and we get positive 10

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

we're going to get -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 let's say 3 minus -3

well, these negatives cancel out,

so that just equals 6

What's 3-3?

Well, 3-3, that's easy.

That's just 0

What's -3 nimus 3?

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

well that's -6

What's -3 minus -3

Interesting.

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

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

we end up at 0 again.

So that makes sense, right?

Let me do that again.

-3 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 - 13

That's pretty easy.

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

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

Let's do 8 - 5

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

What's 5 - 8?

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

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