All language subtitles for 5. Division--- [ FreeCourseWeb.com ] ---

Hey welcome back.

Let's talk about division now and what that means in terms of blocks of numbers and also a few things

to think about with division on a computer.

So division we firstly have been thinking about numbers in terms of blocks just kids books if you like

building blocks bricks whatever you want just blocks.

OK.

So if we have the number eight and thought of in terms of blocks dividing this if you divide it by two.

The way to think about that is splitting it into two.

So you can see from the drawing up just made that if we divide eight into two we get force eight divided

by two equals four.

That's what makes these kind of graphically showing us a case of eight divided by two equals four.

Now by the way you may see this written lots of different ways.

We'll go through those in just a moment.

All right.

Now let's look at the other division of this same thing which you're saying OK well we've got eight

here but we're going to divide it by.

In this case four.

So we have eight because we got all this business here but now we're going to say eight divided by four.

I know this is sucking eggs for a lot of you but we're building some strong foundations here.

So just stay with me.

So eight divided by four means we're splitting it into four parts.

Now it's very common in computing to get doesn't equal an off by one error.

So there are three green lines required to split it into four parts I like with fences and fence posts.

You need one more fence post than you have fence panels right.

So this is just like a fence on its side.

It's the same kind of idea.

So be careful with off by one area.

Always be thinking about do I mean and I'm starting at zero.

Do I have one more or less than maybe I think I have anyway.

We're dividing this eight into four regions and that gives us to it's saying that in each region I've

got two things where we divide by two we've got four.

So what this is telling us is that division the order matters just like in subtraction the order matters

in division the order matters.

If we do division around the wrong way then we are going to get a different result.

So for example if I now do two divided by eight What do I have.

I drew I draw the two a little bit bigger just so that they're not kind of disappearing into obscurity.

But there's two here.

And if we divided that by eight.

How would that go.

Well if we wanted to do that we'd sort of have to split each of these up into four different parts so

there's one two three four.

And then this other one also would have another four like this.

Now I should actually have seven lines if I'm dividing into eight.

There you go.

So if I take two and divide it by eight I'm actually going to get a fraction of a number.

I'm going to get a part of a block.

How much of a block am I going to get one quarter because as one two three four quarters here.

OK so two divided by eight equals one over four.

So before we move on let's just make sure we understand what we mean by two divided by a equals one

over four.

It's not just a notation or thing where is this divided is the same job as this but we're also doing

something else so the numbers have changed so just take a moment to make sure when this makes sense.

Let's draw two divided by eight a different way.

So these two white boxes are going to represent the two.

And what I'm gonna do is take a green color and divide that up into eight like this by dividing through.

This way here and then along there.

So I've got one two three four five six seven eight.

OK.

It's basically exactly the same as we've just done above but just depicted a little bit differently.

So what we could say is that if we were to do that and split these things up they're going to separate

out something like this.

You're going to end up with two separate holes each one of those holes is split into four different

things right.

So the way that two splits up into eight is you end up with these little green bits here and that is

that quarter of the hole.

You can now see visually that taking two whole things as I have on the left and dividing them into eight.

Is this the same as taking one whole thing and dividing it into four in terms of the little things that

you end up with.

And it's the same in the in the diagram above here we took two whole things up here.

We divided them into eight and that was like taking one whole thing here and dividing it into four.

All right I hope that makes sense for you.

Let's look at it one other way just for people who think a little bit differently.

So if we were to take two divided by eight and divide it by one what do we get.

Well if you ever divide something by one you're kind of doing nothing.

So we get to overrate.

All right.

So another way of saying this is if two over eight divided by two divided by two because two divided

by two equals one.

Right.

So I've just taken this one and represented it a different way.

This by the way is where the creativity comes up in mass.

You decide to do things like this because it proves a point okay.

Must still equal to overwrite because this equals this one equals two over two everything else must

be the same.

That's how equations work.

Now we can just divide each of the things so we can say that two divided by two equals one.

And on the bottom you're allowed to join these things.

Eight divided by two equals four which must equal the two over eight because what was on the left must

be the same as on the right.

So this is kind of a mathematical way of showing that to overrate it was one over for.

And there's kind of a visual way of showing that they divide up to give the same little bit.

So hope that's helpful to you.

Let's scrub it out and carry on there's actually a relationship.

If we swap these round and get them round the wrong way we end up with one over the thing we were looking

for.

So that's the consequence of doing division by the wrong way.

The result ends up the wrong size with subtraction it ends up the wrong sign.

For example two minus three equals minus one whereas three minus two equals plus one.

So with subtraction you get the wrong sign with division.

If you get them run the wrong way you get the wrong size.

All right.

So that is what happens with division now.

This no space that we talked about before this still applies.

By the way this tool that we had where we said OK we've got two different numbers we're going to call

them A and B and we're going to talk about plus A plus B and minus a and minus B and we're going to

talk about the general case of going a divided by B equal C or just a divided by B.

What's going on there.

Well if a and b a positive what is an a a positive divided by positive equal.

Well you guessed it it equals a positive.

Okay.

If we take a positive number along here and divide by a negative number what do we get.

So let's draw in an example for example four divided by minus two where the B is minus two.

What do we end up with.

We end up with a negative number and it's going to be negative two minus four divided by minus two.

What does that equal.

Well that is gonna equal plus two.

It's the same quadrant that we used in the multiplication video and the same goes for the exercise to

the reader to generate yourself an example of a negative number.

Times are divided by positive number.

Okay so this quadrant holds and works in this case as well.

So that's pretty good news and it's gonna be super handy when we get to angles and the like.

So let's over to the computer for a minute and just look at a few other notes on division for you with

plus and times the order doesn't matter doesn't matter which order you do them in.

But with subtraction the order matters.

It affects the sign of the answer.

You're going to get the opposite side again you get a negative if you do it the wrong way.

And we division and that's another way of doing Division on a computer we tend to use a forward slash

order matters again and it'll affect the size of the answer.

So the next rule is Thou shalt not divide by zero.

We'll talk about that a little bit more later because it's a bit subtler.

We have to understand how how functions work and stuff in order to think about what happens if you're

trying to buy by zero but it will blow your brain up and it blows mathematicians brains up.

So we just generally don't do it and know that on some computer systems a divide might be slower than

a multiply but it actually depends on your hardware.

So it's worth looking that up and knowing where you are whether you should be dividing or multiplying.

So for example if you want a half something you could multiply by point five or you could divide by

two.

And if speed matters to you just look up and find out which your system is fast tracked and couple of

other points with plus and multiply you tending to make things bigger so you may run out of range on

your number you may not be to represent the size of the number with minuses and divide you tend to end

up running out of precision with minuses actually you could run out of range as well because you could

be going so negative that the number gets too big and negative.

So just be aware all the normal pitfalls with the same as addition and subtraction computers don't support

every single number that's out there.

So here's a quick pop quiz for you for the end of the election.

Don't spend too long agonizing over this because it's designed to be annoying.

The actual question is almost invalid because it's not got enough information.

We'll see more of that later when we look at brackets and things.

But if you take this expression here nine minus three divided by a third plus one.

What does that equal.

Have a little chat in the discussions about what it might equal and why it might equal that.

But let's not get into much of a right and wrong argument really.

I'm telling you from the start that the question is kind of wrong in that it doesn't really give you

enough information it's ambiguous.

If it creates discussion it's ambiguous and there are ways of making it less ambiguous at which we will

see later.

So anyway brief primer on division of whole numbers and we'll come to the pub fractions and decimals

and things like that later on but hopefully that gives you some insight hopefully we learn something

if you're familiar with mass just pop in the comments.

One thing you've learned that you didn't think about the division before and I shall see you in a bit.