Lesson video

Hello there.

My name is Mr. Tilstone.

It's a real pleasure to be here with you today to teach you this lesson, which is all about percentages.

Percentages are a common part of everyday life, and I'll bet you already know quite a lot about them.

Well, let's take that even further.

If you are ready, I'm ready.

Let's begin.

The outcome of today's lesson is this.

I can convert a percentage to a fraction where the denominator is not 100, and you've hopefully got lots of experience of converting a percentage to a fraction where a denominator is 100.

Let's build on that.

We've got some keywords.

If I say them, will you say them back please? Ready? My turn, convert.

Your turn.

My turn, percent.

Your turn.

My turn, percentage.

Your turn.

What do those words mean? Shall we have a little recap? Convert means to change from one form to another.

So two quarters, for example, can be converted to half.

Can you think of any other conversions? Percent means the number of parts in each a hundred, and it literally translates to for every a hundred.

And a percentage is a proportion of a whole.

Our lesson today is split into two parts or two cycles.

The first will be writing a percentage as tenths and the second converting a percentage into other fractions.

So for now, let's focus on writing a percentage as tenths.

In this lesson, you will meet Aisha and Lucas, maybe you've met them before.

They're here today to give us a helping hand with the maths.

Aisha and Lucas are quite confident using percentages.

Aisha says, I know that 40% of the 100 square is shaded.

Did you know that? I bet you did.

Lucas says 40% is equal to 40 hundredths.

40% is equal to 40 hundredths.

You knew that.

I'm sure about that.

Can we write any other fractions that are equivalent? Lucas says we can divide the numerator and denominator by the same number.

40 and 100 are both multiples of 10.

Or to put it another way, 10 is a factor of 40 and 100.

So we can divide both values by 10.

We can divide the numerator and denominator by the same number.

So 40 divided by 10 and 100 divided by 10.

They're going to give us whole number answers.

What is the answer to each of those? 40 divided by 10 is equal to four, and 100 divided by 10 is equal to 10.

So we can say 40 hundredths is equal to four tenths.

Let's see that.

Here's 40 hundredths and here's four tenths.

What changed and what stayed the same? Did the amount shaded change? No.

Did the denominator change? Yes.

It's no longer split into 100 parts, it's split into 10.

And we've no longer got 40 parts shaded, we've got four.

So 40 one hundredths is equal to four tenths.

I wonder if you could think of any other examples that are similar to that.

How about this one? Aisha and Lucas converts 60 hundredths into tenths.

60 hundredths.

What do you think that could be as tenths? Well, Aisha says, I know that 60% of the 100 square is shaded.

60% is equal to 60 hundredths.

And again, I bet you knew that already.

Let's divide the numerator and the denominator by 10.

Once again, just like before, what will that give us? That will give us six tenths.

So we can say 60% is equal to 60 hundredths, which is equal to six tenths.

Let's represent this with a diagram showing tenths.

So the minute we're showing hundredths, and now we're showing tenths.

Just like before, what changed and what stayed the same? Did the amount shaded change? No, we've still got the same amount.

Did the denominator change? Yes, it did.

It's no longer split into 100 equal parts.

It's split into 10.

We no longer have 60 of them.

We have six.

So that's why 60 one hundredths is equal to six tenths.

So 60% is equal to six tenths.

Aisha counts in steps of one 10th, and you can join in too, please.

She says I'll start at zero and stop at one.

Each step of 10% is equal to a step of one 10th.

So let's start counting.

One tenth, count with me please.

Two tenths, three tenths.

Are you counting? Four tenths, five tenths, six tenths, seven tenths, eight tenths, nine tenths, and then one.

One is one whole.

100% is equal to 10 tenths.

Aisha and Lucas find equivalent amounts.

And we can use these two number lines to help us find equivalent amounts.

Which equivalent amounts can you see? Well, how about this one? 20% is equal to two tenths.

They're both in line with each other.

What other pairs of numbers are in line? What percentage and what fraction? How about this one? 80% is equal to eight tenths.

Aisha and Lucas look at this 100 square.

What could you say? What can you see? Here we've got 30%.

30% is equivalent to 30 one hundredths.

30% is equal to 30 hundredths.

Next, we can divide the numerator and denominator by 10 just like we've done before.

We can convert from one hundredths into one tenths because it's a multiple of 10.

So dividing both by the same amount, dividing by 10, that common factor, and that gives us three tenths.

So we can say 30% is equal to three tenths.

30% is also equivalent to three tenths.

To convert from 100th to one tenths, both the numerator and denominator must be a multiple of 10.

So in this case, 30 is a multiple of 10, and 100 is a multiple of 10.

What about this example though? Aisha and Lucas look at this 100 square.

Can you see a multiple of 10 there that's shaded? Hmm.

No, that's 55%.

Well, 55% is equivalent to 55 hundredths.

I'm sure you knew that, but that's not a multiple of 10.

Can we convert from one hundredths to one tenths in this example? Well, 100 divided by 10 is equal to 10.

So we can convert that into tenths.

But 55 divided by 10 is equal to 5.

5.

Hmm.

We can't use a decimal number in a fraction, so that won't work.

So because 55 isn't a multiple of 10, we can't convert 55% into tenths.

Let's do a little check.

Look at this 100 square.

What can you see? What could you say? What percentage is represented? And how many hundredths are represented? Can you convert it into tenths? So can you maybe see three different things there? Pause the video.

What did you see? Well, 10% is equivalent to ten one hundredths.

So that's two things that we can see there.

But what about as tenths? Can we convert it into tenths? Well, yes, we can divide the 10 and the 100, the numerator and the denominator, they're both multiples of 10, so we can divide them by 10.

10% is also equivalent to one 10th, 'cause 10 divided by 10 is equal to one, and 100 divided by 10 is equal to 10.

Ten one hundredth is equal to one tenth, therefore 10% is equal to one-tenth.

Well then if you've got that, you are on track and ready for the next part of the learning.

And the next part of the learning is practise.

Write the missing percentages and fractions.

Number two, write the missing numerator.

Aisha says, write the percentage as one hundredths and convert into one 10th.

But Lucas has got a little word of warning for you.

He says some percentages cannot be written as one tenths.

And if that's the case, just put a little cross.

Okay, very best of luck with that.

That may not take you too long, but I'll see you quite soon for some feedback.

Pause the video.

Welcome back.

How did you get on? Would you like some answers? Let's do it.

So number 1A: 70% is equal to 70 hundreds and they're both multiples of 10 so we can divide them both by 10.

We can convert that into seven tenths.

And 50% is equal to 50 hundredths.

We can divide both of those by 10 to give us five tenths.

And number two, we've got 90% is equal to 90 hundredths, which is equal to nine tenths.

20% is equal to 20 hundredths, which is equal to two tenths.

Now 45%, we can say that as a hundredths amount.

That's 45 hundredths.

But because it's not a multiple of 10, we can't give it as a number of tenths.

And for D 8%, again, it's not a multiple of 10.

So we can give it as an amount of hundreds, that's eight one hundredths, but we cannot give it as a number of tenths.

So a cross is just fine.

E: 63% is equal to 63 one hundredths.

But again, 63 is not a multiple of 10.

So we cannot express it as tenths.

And F: 100% is equal to 100 hundredths, which is equal to 10 tenths.

That was a bit of a tricky one.

Well done if you got that.

So divide the numerator and denominator by 10 to convert from one hundredths to one tenths.

Eight one hundredths cannot be written as one tenths because it's not a multiple of 10.

You are ready for the next cycle, and that is converting a percentage into other fractions.

Percentages can also be converted into other fractions.

So we've looked at tenths.

What about other fractions? Let's start by converting the percentage into a fraction with a denominator of 100.

So what can we see here in this first one? How many hundredths? That's 20 hundredths.

So you can see 20% or 20 hundredths.

Then we need to divide the numerator and denominator by the same number.

Hmm.

What factors can you think of that are common factors of 20 and 100? How about this one? 20 and 100 can both be divided by five? Well, let's try that.

So what would the result be of dividing both that numerator and that denominator by five? What would we get? Well, that would give us four twentieths.

So we can say that 20% is equal to four twentieths.

20 and 100 can both be divided by 20.

20 divided by 20 and 100 divided by 20, that will give us one fifth.

So we can say that 20% is equal to one fifth, and that's a good one to memorise if you can.

That's a very common equivalence.

20% is equal to one fifth.

Aisha and Lucas convert 25% into different fractions.

So here you can see 25% or 25 one hundredths.

Let's start by converting the percentage into a fraction with a denominator of 100.

Let's do that.

So that's 25 hundredths.

Now, let's think about some common factors of 25 and 100.

We need to divide the numerator and the denominator by the same number.

What number could work here? How about five? Both of them divide by five.

So let's try that.

So 25 one hundredths is equal to five twentieths.

There's a more common way of expressing an equivalence though for 25%.

Let's look at a different one.

How about this one? It can be both divided by 25.

So let's do that.

25 divided by 25 is equal to one and 100 divided by 25 is equal to four.

So 25% is equal to one quarter.

And once again, that's very common equivalence.

So that's one worth writing down or memorising.

Aisha and Lucas convert 45% into a fraction.

That's not as common as the other ones.

Let's start by converting 45% into a fraction with a denominator of 100.

Well, that's the easy part, I think.

45% is equal to 45 one hundredths.

Now let's look at the factor pairs of 45 and 100.

So 1 and 45, 3 and 15 and 5 and 9 are all factor pairs of 45.

So any of those numbers is a factor of 45.

Then the factor pairs of 100 are 1, 100, 4, 25, 5, 20, 10, and 10.

So any of those is a factor of 100.

Now, can you spot a common factor that appears in both lists because we could use that as our divisor.

It is this one, five.

Five is a common factor of 45 and 100.

So we can divide both the numerator and denominator by five.

So let's do that.

45 divided by five and 100 divided by five.

What would that give us? That would give us nine twentieths.

So we can say 45% is equal to nine twentieths.

That's not really a common equivalence.

I wouldn't say that one's worth memorising, but we can say they're equivalent.

Aisha and Lucas converts 75% into a fraction.

75% is a common percentage.

You hear that one a lot.

Let's see, you might even be able to see what it is even before we convert.

Let's start says Aisha, by converting 75% into a fraction with a denominator of 100.

Well, that's the easy part I think.

Here we go.

75% is equal to 75 one hundredths.

And then let's look at the factor pairs of 75 and 100.

Well, here they are.

Can you spot a common factor? Anything that appears in both lists.

I can see a couple.

This is one of them.

Let's look at the factor pairs of 75 and 100, 25 is the largest common factor.

So let's try that one.

Let's divide by 25 so we get the smallest possible denominator.

Good idea.

So 75 divided by 25 and 100 divided by 25.

That gives us three quarters.

You may have even seen three quarters right from the start, but that's what 75% is equivalent to.

It's a very common equivalence.

It's worth writing down and it's worth memorising.

75% is equal to three quarters.

Let's do a little check.

Convert 80% into a fraction.

So start by converting into a number of hundredths and then go from there.

Pause the video.

How did you get on? Did you start by converting? And then did you find the answer with the smallest denominator? Well, let's see.

We've got 80% is equal to 80 one hundredths.

Now a common factor, and in fact, the highest common factor of both of those numbers is 20.

So we can divide both of them, the numerator and the denominator by 20.

So let's do that.

And when we do that, we get four fifths.

If you've got four fifths, well done, you are on track and you are ready for the next part of the learning.

80% is equal to four fifths.

It's a fairly common conversion.

Aisha and Lucas find the missing number.

So we've got 16% is equal to something, 20 fifths.

Hmm, a little more challenging.

What could we do here? Well, let's start, says Aisha, by converting 16% into a fraction with a denominator of 100 because at the moment it's got a denominator of 25.

So 16% is 16 one hundredths.

The denominator has been divided by four to get 25.

So what should we do with that numerator? The denominator's been divided by four, and the numerator needs to be divided by four as well.

16 divided by four is equal to four.

So we can say 16% is equal to four twenty fifths.

That's by no means a common equivalence.

Aisha and Lucas find the missing denominator.

78% is equal to 39 something.

Again, we can work this one out.

It's not a common one.

It's not worth memorising, but we can work it out.

So 78% is equal to 39 something.

Let's start by converting 78% into a fraction with a denominator of 100, just like we did before.

That's a fairly easy part I think.

I hope you agree.

That's 78 one hundredths.

The numerator has been divided by two to get 39.

So what do we do with the denominator.

We divide that by two as well.

100 divided by two, nice easy one is equal to 50.

So we can say that 78% is equal to 39 fiftieths.

Let's do another check.

Find the missing numerator.

65% is equal to something twentieths.

And Aisha says, start by converting 65% into a fraction with a denominator of 100.

And Lucas says, divide the denominator and numerator by a common factor.

Pause the video.

65% is equal to 65 100th.

So that's converted it into hundredths.

Now, what did we do to go from 100 to 20? What did we divide 100 by to get to 20? Five.

So what do we do to the 65? We divide it by five as well.

And that's 13.

So we can work out that 65% is equal to 13 twentieths.

Very, very well done if you've got that.

You are ready for the next step.

And the next step is some practise.

So number one, convert these percentages into fractions.

So we've got 60%, 35% and 46%, and we've got some little scaffolds there to help you out.

Aisha says start by converting each percentage into a fraction with a denominator of 100.

And then Lucas says, can you find the answer with the smallest denominator? So look for the largest common factor, the highest common factor.

Number two, find the missing numerator and denominators.

Aisha says, start by converting each percentage into a fraction with a denominator of 100, and Lucas says then divide the denominator and numerator by common factor.

And again, look for that highest common factor.

Right here, pause the video and away you go.

Welcome back.

How did you get on with that? Well, here's some answers.

Let's see.

So a: 60% is equal to 60 one hundredths and we can divide 60 and 100 by 20.

That's the highest common factor giving us three fifths.

35% is 35 one hundredths.

The highest common factor of 35 and 100 is five.

Divide them both by five and it gives us seven twentieths.

And 46% is equal to 46 one hundredths.

The highest common factor of 46 and 100 is two.

So 46 one hundredths is equal to 23 fiftieths.

And number two, 70% is equal to seven tenths.

70 hundredths both can be divided by 10 to give us seven tenths.

85%, well, 85 and 100 both have five as the highest common factor.

So if we divide both by five, it gives us 17 twentieths.

and C: a common factor, although not the highest common factor of 50 and 100 is 25.

So we could divide both of them by 25 to give us two quarters.

However, there is a more common of saying that, it's half.

In B, 100 has been divided by five.

So 85 also needs to be divided by five.

And 2D, 36% is equal to nine twenty-fifths.

E, 40% is equal to two fifths, and F 12% is equal to three twenty fifths.

In D 36 has been divided by four so 100 also needs to be divided by four.

We've gotta divide them by the same amount.

We've come to the end of the lesson.

I've thoroughly enjoyed exploring this concept with you and hope you have too.

Explain how to convert a percentage to a fraction without a denominator of 100.

Start by converting each percentage into a fraction with a denominator of 100.

Divide the denominator and numerator by a common factor.

And you might like to consider the highest common factor.

25% is equal to one quarter, for example, and 75% is equal to three quarters.

And we've looked at lots of examples today, a very common percentage in fraction equivalences, and I would say they're two of them.

They're worth memorising.

You've been amazing today.

Give yourself a pat on the back.

It's very well deserved and say, well done me.

I hope to see you again soon for another maths lesson.

But until then, have a fantastic day.

Whatever you've got in store, be the best version of you that you can possibly be.

Take care and goodbye.