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Hello, I'm Mr. Langton, and today we're going to do a recap on fractions, decimals, and percentages.

All you're going to need is something to write with, something to write on, and try and find a quiet space where there's no distractions.

When you're ready, we'll begin.

Okay.

So we'll start with the try this activity.

When it splits into two parts, I'm going to use the number card to try and complete the number line.

And for that first part, you can use the cards more than once if you want to.

Just try and find a way that you can complete the number line.

That second part, if you're feeling really, really confident, can you find a way to complete the number line using each card once? So pause the video and have a go.

When you're ready, unpause it, and we'll have a go together.

You're going to pause it now.

Go on.

Three, two, one.

Right then.

I'm going to presume that you've had to go, and now I'm going to start off and show you what I would do as well.

So looking at the number line, it starts at zero and goes all the way along to two.

So bang in the middle, I'm going to label that.

That's one in the middle.

So that's my starting point.

I'm then going to look at its number keys, okay? So halfway between zero and one, that'll be here.

So that's going to be a half or 0.

And halfway between one and two, that would be 1 1/2, wouldn't it? Or oh, oh 1.

5, right? Okay, so that's a good one because that one there is halfway between it.

So that must be 1.

5 halfway between one and two is 1.

I'm going to cross five off.

So I know I've already used it.

Now let's have a look.

Let's look at this fraction down here.

Let's point out to it there.

So it's smaller than one.

And it's been split into thirds, which means it's either going to be 1/3, or it's going to be 2/3.

It can't be 3/3 because that'd be a whole one.

That's too big.

Now it's bigger than 1/2.

So it can't be 1/3.

So that one there must be 2/3.

So I'm now going to cross off two because I've used it there.

Let's have a look.

So this bit here, that would be a 3/4 value or a 75% value.

I've been given that both of the ones above it are percentages, I'm going to stick with our 75% of the percentage.

So the next 10 up from 75 would be 80.

And there's another one there as well, 90.

So that works.

That's going to be 80, and that's going to be 90.

So I can cross those off.

I'm starting to make some progress.

I'm quite happy with this.

And what I've got here is a percentage that ends in a five.

It's less than 1/2, which means that this one here is either going to be 15%, 25%, 35%, or 45%.

Now I know I've already used two.

And actually 25% would be there, wouldn't it? So it can't be 15% either.

So this one here is either a three or four.

I'm not quite sure yet.

So I'm just going to wait.

Let's just make a little note there.

This one is either three or four.

Now, once we get bigger than one, once we go on this side, we're looking at greater than one.

We said that's 1.

Now this, this is a percentage is greater than one.

So it must be a hundred and something.

So that bit there, must be a one.

We know bigger than 1.

So that could be 160%.

It could be 170%, and we've used the eight and nine already.

So I'm just going to wait there.

If I'm using my one, I want to cross that off.

Now let's have a look.

So that's either six or seven.

What about this fraction here? Is in quarters.

Now actually, yes, the whole number lines are split into quarters, isn't it? That's 1/4.

That's 2/4, which is 1/2.

3/4.

4/4 is a whole one.

5/4.

6/4 is 1 1/2.

So that there is 7/4.

I mean that's 7/4.

That means that that one there must be 160%.

So I've used up my six and not seven.

Now, that means that I've only gotten that percentage at the start, which you said is either 35% or 45%.

And if I'm honest, it looks closer to the half, to the half.

I think it's probably 45%, but we'll just have to see what's going to work over here at the other end.

At the reference side, we've got two whole ones, two whole ones as a fraction.

Now, normally as a fraction, that'd be two halves of one is a whole one.

Now our fraction is out of 15.

So it's converting to fifteenths and multiplying by 15.

So I'm going to multiply that by 15.

So I guess, a fraction of 30/15.

So that's a three, and that's a zero.

And that's good because I've not used those yet, three and zero, which means that that one there is 45%.

So for this one, we've got to write each value as a fraction, a decimal, and a percentage.

Let's start with 40%.

Now, the important thing about percentage is to remember what the word actually means per cent.

It means per 100 or for every 100.

So 40% as a fraction, it must be 40/100.

Now we can simplify that fraction.

Both of those numbers go into 10.

Divide the number by 10.

I'm going to get the 4/10.

And both of those also go into two.

So it's 2/5.

Now as a decimal.

Now, I've got this number line down at the bottom, to help me out just a little bit with my hundreds, my tens, my ones and after the decimal point with my tenths and my hundredths.

Now we said that 40% is 40 hundreds or 4/10.

Now 4/10 is there, which means that it's going to be 0.

Okay.

Now what about 3/8? I'm going to show you a different method for 3/8.

Do you remember that every single fraction can be represented as a division? It actually means three divided by eight.

That's quite a tricky thing to do.

So I'm going to draw a little bus stop.

How many times does eight go into three? Well eight doesn't go into three.

So I'm just going to put a zero there.

I need to carry my three.

I've got a remainder of three.

Now, three is the same as 3.

0 So now that I put that decimal point in that decimal place, I can carry that three there.

That'll make 30.

Make sure that you line up your decimal point at the top as well.

I can put as many zeros as I want here.

And that's still equivalent to three.

I don't know how many I'll need yet, but it's just worth bearing that in mind.

So let's carry on.

Eight into 30.

Anything to 30, you're going to go three times, and it's going to be six leftover.

Eight into 60.

I'm going to go seven times with four left over.

Eight into 40 are going to go exactly five times.

So as a decimal, 3/8 is 0.

375.

And if I look at my number line, I'll tell you, just let me, just move it out of the way, if I look at my number line, 0.

375.

I've got three tenths.

I've got seven hundredths.

I don't know.

It's not there.

I've also got five thousandths.

So altogether, I've got 375 thousandths.

We know that's going to cancel down to 3/8, but we now need to turn it into a percentage, don't we? We said percentages are out of 100.

So we said that are hundredths.

There are 37 of them with that 0.

Don't forget the 5 thousandths as well.

And for that, it means that 3/8 as a percentage is 37.

5%.

Finally, we've got 0.

64.

That's going to be an easy one to add to the percentage because as we've seen, let's just clear some space.

64 is going to be six tenths and four hundredths.

And percentages are out of 100.

So we've got 64%.

And a fraction as we said is out of 100, and then we need to simplify it.

We want to find the highest common factor of 64 and 100, the largest number that goes into both.

Well, they're both even.

So I can divide them both by two.

They're still both even so I should have divided by four in the first place, shouldn't I? That would've got me 16/25.

Is there anything that goes into both of them? No, no, that's good.

So lots of different methods there.

I hope you were making some notes.

If not, by all means, just rewind the video a little bit to look through those methods again.

Lots of different ways to go from percentages to fractions and decimals, right? So when you're ready, let's move on to the next part.

Okay.

So now it's your turn to have a go.

What I want you to do is pause the video and have a go with the questions on the worksheet.

When you're ready, unpause it, and we'll go through it.

Good luck.

So how did you get on? Some of the answers are on the screen now.

And I thought it might be good if we went through some of them together.

I'm going to start off down at the bottom.

Which one's largest, 87% or 7/8? Now we're going to turn them both into the same fractions or decimals or percentages.

So to do that, I'm going to start with 7/8.

It's the trickiest one.

It's going to be harder to convert, and I'm going to do that bus stop method that I showed you before.

How many times does eight go into seven? Now, stick a few zeros on the end.

And we don't know how many we'll need.

And I keep my decimal point there now, just so I don't get messed up.

Eight into seven don't go.

You need to carry that seven to make 70.

Eight into 70.

You're going to go eight times.

Eight and eight is 64.

That means I've got six leftover.

Eight into 60.

They're going to go seven times with four left over.

Eight into 40 go five times.

So 87% is being compared to 0.

875, which as a percentage is 87.

5%.

So it's very, very close, but the largest one is 7/8 by.

5%.

Okay.

Let's pick a different colour.

That's work in red this time.

Write down a decimal, which is between 1/3 and 1/2.

There are loads of answers you could give here, literally infinite number of answers.

But any number that is larger, 1/3 is 0.

333333333, 0.

3 recurring and 1/2 is 0.

So if you've got a decimal, so we need something that's going to go between those, don't we? You need a decimal that either begins with 0.

4, and you could have some more numbers after it, and that would work.

If it begins with 0.

3, then your next number, ideally, needs to be a four or a three and a four or a three and a three and a three and a three and then a four or something a little bit higher than that.

So it needs to be a little bit bigger than 0.

3 recurring.

For example, 0.

34, 0.

35.

Anything up to 0.

49999999999999999999 And I'll stop there 'cause it's just going to be silly now.

Okay.

So let's have a different colour so we can do the last problem.

Let's just draw a little wavy line there so I don't get confused.

This is the question that I'm going to finish with.

So complete the number line below.

We've got a value of 0.

7 here.

I'm about 90% there.

We've been given those.

Now 90% is the same as 0.

So that's going to be useful.

That's going to help me work out what it is that I'm trying to get to.

So 0.

All those gaps that are there must be 0.

8 'cause that's evenly spaced between them.

And 0.

8 is 80%.

And I need a fraction that's halfway between 0.

7 and 0.

As a decimal, that would be 0.

75, which is 3/4.

And I'm going to need, if we know what's going on by 0.

5 each time, that's going to be 0.

95 or 95%, which means as a fraction that's 95/100.

Is that okay? Well, it's almost okay.

What you should be saying is the number line there, Mr. Langton.

You've not simplified that fraction, and you'd be right.

So the highest common factor of 95 and 100 is five.

So I'm going to divide each of those numbers by five.

So you get 19/20, and that's what this fraction here is.

Okay, one last activity.

How many ways can you complete the fraction cards to form numbers that lie between those shown on the number line? Pause the video and have a go.

See what you can work out.

And when you're done, unpause it, and we'll go through it together.

So you can start in three, two, one.

Okay.

So how did you get on? Let's see what we can do.

I'm going to start off with this fraction's card on the right hand side, working with something over 1,000.

And the reason I'm going to do that is that I can write both of these decimals as fractions out of 1,000.

332 is the same as 332/1000 0.

334 is the same as 334/1000.

And we need to find a fraction over 1,000 that will sit somewhere between 332/1000 and 334/1000.

So it must be 333/1000.

I want to look at now is the card on the left hand side, the fraction out of 10,000.

They've already said that 0.

332 can be written as 332/1000.

Now I actually want to find a fraction that's out of 10,000.

So to do that, I need to multiply my denominator by 10, which means I need to multiply my numerator by 10.

So 0.

332 is also equivalent to 3,320/10,000.

I can do the same thing over here.

And you might be able to see where I'm going with that.

I'm going to get 3,340/10,000.

So I need a fraction after 10,000, that lies between 3,320 and 3,340.

That's what my numerator needs to be.

So anything as low as 3,321, all the way through to 3,339.

Now to get an equivalent fraction for the five thousandths is quite trickier.

We said it earlier, but 0.

332 is equivalent to 332/1000.

Now, I want to try and make that out of 5,000.

So to do that, I'm going to need to multiply my denominator by five, which means having to multiply my numerator by five.

And 332 times five is 1,660.

Don't worry.

I don't expect you to do the bit of working out for that.

Over on the other side, 0.

334 is the same as 334/1000.

And if we want it out to 5,000, once again, we have to multiply the numerator and the denominator by five.

And in this case, it's 1,670.

So any number between 1,660 and 1,670 can be our numerator.

So the lowest it could be is 1,661 all the way through to 1,669.

And finally, I'll put the rest of the answers up there for you.

So you can check your working out.

Now you've got the method.

You should be able to do all of those yourself.

I hope you got on well with this.

I'll see next lecture.

I've finished the video