All language subtitles for 4. Multiplication & Number Blocks--- [ FreeCourseWeb.com ] ---

Pagel had many hours of fun with this despite the fact it's nearly entirely a luck based game there's

enough skill to make it fun.

And what we're seeing on the screen is multiplication.

Every time you destroy some pegs it's being multiplied by a number to give you a total.

So very simple concept but let's dive in and see multiplication in math.

Hi welcome back.

We have briefly talked about addition and subtraction.

Let's go into the natural thing next which is multiplication you're going gonna use this a lot of the

time in game development things like just time speed factors working up speed distance time all sorts

of things to do with lives count all over the place you're gonna be using multiplication.

And of course division.

Let's focus on a multiplication here just to make sure we've got some idea of how that works.

So firstly let's just talk about it from a number line perspective right briefly.

So here is a number line.

We've used that before but I'll just explain that we're looking at the whole numbers here.

So each of these taxes is 1.

So 1 2 3 4 5 6 7.

Okay.

And if we were to take the question of something like what is two times three then there's a few different

ways we can look at this.

But for simplicity I'm just going to say it's a jump of three.

Twice.

So one two three here one two three here.

And of course we get to the answer everybody would expect which would be six.

Okay so that's two times three.

Very simple.

Now let's talk about what happens if we have negative numbers so let's just start to talk about that

then I'm going to introduce you to a powerful way of thinking about this which is going to really set

you up for the future.

So here we have another number line this is zero in this case again as zero.

We had up here but now we're going backwards along the number line.

So I'm just going to label one or two of those that would be minus one two three four.

And that would be minus five for example.

Now if we were to ask a very similar question what we would say what is maybe two times minus three.

What does that equal.

Well we know that it's minus six if we know anything about mass.

But let's just see on the number line what we're doing there.

We are taking two hops of minus three.

So there's one.

And the second takes you there two minus six so I could draw that under the axes as not to disturb my

writing.

There you go.

Boom.

Okay so two times three equals minus six.

Now that will start to beg the question as to what would happen if we started to do two negatives or

if we started to talk about minus two times three.

For example we'd know we get the same answer.

If you've done any math before but let's look at a much more interesting way of looking at this number

line.

One thing will be visiting the number line by the way lots of times in the course we're starting right

now we're just the integers the whole numbers the things you can count on your fingers.

Then as an overview we're going to look into the things in between those called the rationals the things

that can be expressed as fractions a half third quarter and then we'll go on eventually to look at the

irrational things that can't be expressed as fractions anyway.

Let's take a look at a different space.

This is not the number line.

So because it's not the number line I think it's use a slightly different color.

I'm going to use a blue here.

So what we've got on this line is two different dimensions for the two different numbers that we are

multiplying.

So imagine we are in general multiplying A times B to give C where A B and C it's algebra the unknown

will be doing more algebra unknown later but these are just numbers that we can fill in later.

So what we're saying is if we if this is plus a going this way and these are negative A's going this

way and these are negative B's going this way and these are positive B's going up this way then what

happens in various circumstances.

Let's look at the results.

So if you have a positive number times a positive number so it's positive because it's over here on

a Times of positive B so it's up here.

So now you're in the quadrant that I have just marked I guess rub out that mess but you get the idea

then what you end up with is a positive number in this quadrant OK.

What happens then if you have a positive a times a negative B.

So for instance three times minus two.

Or as in the example on the previous page two times minus three what happens there was positive.

So it's down here somewhere and it's negative.

B what you actually end up with is a negative answer.

Okay now if we do a negative times a negative you probably heard that like the idea of saying not not

you know it's not not not not the way you do things or it wasn't wasn't me guv then that is too negative

balancing out and you have a positive and if you do it the other way a negative times a positive run

the other way.

Again you get a negative.

So you've got this this quadrant here which goes from clockwise round it goes positive negative positive

negative okay.

Worth remembering that because we're gonna be using that type of Quadrant not exactly the same thing

but that type of Quadrant loads of times in the future.

So given that it allows you to predict things like the idea that minus two times three would also equal

minus six.

We know that it's gonna be six and we know it's going to be minus because it is minus two so the aim

is negative in here.

And then the three is positive here.

So you've got a minus sign.

OK.

That's what we're doing there.

And if we were to do minus two times minus three you would get plus six.

OK so let's look at this in terms of rectangles rectangles can be really useful when thinking about

multiplying numbers because they set us up to understand prime numbers properly which are going to be

underlying things like encryption on your computer all sorts of stuff like that.

So let's remove these quadrant labels just for a moment because I want you to be remembering them as

we go.

And just quickly pop through some of these examples so I'm going to stop.

Start with our top example this guy here.

Two times three equals six.

So one way to depict that the aim is to you multiply by three which means coming up here and you get

six cubes if you like if you want to talk about this in terms of stacking actual blocks of things like

you may have done as a kid.

So two plus three two time three rather it's six.

And it is in the positive quadrant remember the quadrants positive over here negative positive negative.

Okay cause that's the first example now.

Next one down so we can take that off gives a big tick.

There you go.

Next on down to Times minus three.

So it is two and B is minus three.

Then we end up something like this.

We end up down here and we have got ourselves again six things but they're in the negative quadrant.

You see there.

Therefore you've got minus six minus two times three.

I think you get the idea now minus two would be here.

But if it's times three three high and you end up with something like that.

So that is again minus six and minus two times minus three.

You're in this bottom left quadrant.

OK.

All pretty simple stuff but starting to look at things in terms of rectangles can be super handy because

it helps you to start thinking about the sign of the number about what happens when you multiply positives

and negatives and how they balance out.

And also we're going to say it sets us up to understand prime numbers very nicely.

Now looking back at the computer just for a moment got a couple of things for you.

One of those things is a challenge I want you to ask your first question so visit one of the linked

resources against this video like the Wikipedia article.

Ask your first question or just introduce yourself in the conversation below this video.

And I'd like to know things like where you are what you experience with mathematics et cetera that will

really help you to help other students so please go ahead and do that get yourself engaged and I look

forward to seeing you in the next video.