Lesson video

Hello there.

My name is Mr. Tilston.

I'm a teacher, it's great to see you today.

Today's lesson is all about percentages.

Percentages are everywhere.

They're on our phone screens and tablet screens, they're on the news.

You can't avoid percentages.

They're a big part of everyday life, and that's what today's lesson is all about.

So if you're ready to begin, let's begin.

The outcome of today's lesson is this, I can use fraction, decimal, and percentage conversions to solve problems. And we've got some keywords.

So if I say them, will you say them back please? Are you ready? My turn, convert, your turn.

My turn, percent, your turn.

And my turn, percentage, your turn.

What do those words mean? I imagine you're quite familiar, but let's have a little recap just in case.

Convert means to change from one form to another.

So for example, 2/4 can be converted to 1/2.

I wonder if you can think of a conversion from a percentage to a fraction or vice versa.

Percent means a number of parts in each hundred, and it literally means for every 100 and a percentage is a proportion of a whole.

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

The first will be solving problems with fractions and percentages and the second, problems with fractions, decimals and percentages.

Let's start by solving problems with fractions and percentages.

In this lesson, you're going to meet Aisha and Lucas.

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

Aisha is looking at the beads on her bracelet.

You might want to have a look at that yourself and see what you notice.

Can you see a little pattern perhaps? there are three different coloured beads on my bracelet says Aisha.

Lucas says, there are more blue beads than the other colours.

Did you spot that? I wonder what percentage of the beads are blue.

That's going to be a little bit tricky because there aren't 100 beads.

So we can't use 100ths.

So they start by counting the beads.

It's a good start.

Let's establish what the denominator is if we're thinking of fractions.

So there are 20 beads altogether.

That could be our denominator.

Nine of the beads are blue.

That could be our numerator.

That means that 9/20 of the beads are blue.

Here's our fraction.

Now how to turn that into a percentage.

What would you do next? We can convert this to a number of 100ths, how? What would you do? We have to multiply the denominator and numerated by the same number.

Let's start with that denominator.

Let's turn that into 100ths.

20 multiplied by five is equal to 100.

So therefore we need to multiply the numerator five as well.

And that gives us 45/100.

Now it's a bit easier to turn that into a percentage, isn't it? We've done the hard work.

45/100 is equal to 45%.

45% of the beads are blue.

So what about the purple beads? What percentage of those beads are purple? Well, we know the denominator.

There's 20 beads altogether and six of them are purple.

So that's our fraction, 6/20.

We can convert that into a number of 100ths.

We have to multiply the denominator and numerator by the same number, just like before.

And we establish what that number is.

We know what we need to do to that 20, what we need to multiply it by.

We multiply it by five to get to 100.

That's given us a number of 100ths.

And now we can multiply the numerator by the same amount.

So that gives us 30/100.

And then we can see hopefully very clearly the percentage.

Now there's not too much more thinking to do.

That's 30%.

So 30% of those beads are purple.

Let's do a little check.

What percentage of the beads are yellow? Pause the video and give it a go.

Well, Aisha says 5/20 of the beads are yellow.

That's our fraction.

And we can multiply that 20 by five just like we did before to get to 100 to give us a number of 100ths.

So then we need to multiply the numerator, the five, the number of beads by five to get to 25/100.

So that gives us 25/100 or 25%.

25% of the beads are yellow.

Well done if you said that, you're on track for the next part of the learning, 25% of the beads are yellow, Aisha and Lucas, check their answer.

Aisha says, all of the beads are either blue, purple or yellow.

100% represents the whole.

If we add the percentage of blue, purple and yellow beads together, they should equal 100%.

Well, we worked out 45% of them were blue, 30% were purple and 25% were yellow.

So we've got a little bit of addition to do.

45 plus 30 plus 25.

Hopefully that's mental maths for you.

That's equal to 100%.

It looks like our calculations are correct and it's worth taking that little bit of time just to do that final check.

Aisha and Lucas complete a litter pick.

Oh, that's very good of you.

Aisha says, we counted up the pieces.

We want to find out what type of litter is the most common.

And Lucas says, let's work out the percentage of each type of litter found.

So this is what they found.

Crisp packets, there were five of them, tin cans, there were four of them, plastic bottles, there were nine of them, and sweet wrappers, there were seven of them.

So it's not too difficult to say that plastic bottles were the most common kind of litter, but what about as a percentage? How can we work that out? Where would you start? We don't know our denominator yet.

What would you do to establish it? How could you find it out? What percentage of the litter found was crisp packets? Let's think about that.

Well, first we need to count up the total pieces of litter.

Well done if you said that, we need to add those numbers together and we found 25 pieces of litter altogether, so that can be our denominator.

So 5/25 is our fraction, let's convert.

This time we need to multiply the 25 by four to get to 100.

So therefore we multiply the numerator, the five by four as well.

So that gives us 20/100.

Now hopefully that percentage is jumping right out at you now, that's 20%.

20/100 is equal to 20%.

So we can say that 20% of the litter is crisp packets.

Let's think about the tin cans.

What can we do now? Well, here's our fraction, 4/25.

And we know we need to multiply the 25 by four to give us an amount of hundreds.

So let's do the same for the numerator as well.

So that's 16/100.

So 16% of the litter is tin cans.

What about the plastic bottles? Well, here's our fraction.

9/25, let's convert, multiply them both by four, the numerator and the denominator.

And that gives us 36/100.

So therefore, 36% of the litter is plastic bottles.

And the sweet wrappers, you're going to tell us, pause the video.

So let's start by thinking about a fraction.

And the fraction is 7/25.

Seven outta those 25 pieces of litter were sweet wrappers.

So if we multiply that 25 by four, that will give us an amount in 100ths and we do the same to the numerator.

The seven multiply both by four 28/100.

And that's hopefully quite easy to turn into a percentage, that's 28%.

So 28% of the litter were sweet wrappers.

If you said that brilliant, you're on track and you're ready for the next part of the learning.

Let's have another quick check though.

How could you check the answers? Pause the video.

Well, Aisha says, remember 100% represents all of the litter found.

So you could add those percentages of each type of litter found together.

Does the total equal 100? Is that what you did? And did it equal 100? Yes it does.

Well done if you said add them all together to check, it looks like the answers could be correct.

They should be, shouldn't they if we check them, let's do some practise.

What percentage of beads are yellow, purple or blue? Start off by counting the total number of beads that will establish the denominator.

Number two, Aisha and Lucas complete another litter pick.

You've got to say what the percentage of the litter found was for each type of litter.

Use the table says Lucas, to work out the percentage of each type of litter found.

If your teacher is happy for you to do so, I would recommend working in partners.

It's always good to do that.

Then you can share ideas, bounce ideas off each other and check each other's thinking.

Pause the video.

Welcome back, how did you get on? Let's have a look.

Here are the answers.

Number one, so 9/20 multiplied by five gives us 45/100.

So that's 45%, that's the yellow beads.

The blue beads, that's 7/20.

Multiply them both by five.

That gives us 35/100, so 35%.

And for the purple beads, multiply them both by five.

So 4/20 multiplied by five gives us 20/100.

So that's 20%.

And when you add those up, they should equal 100%.

And indeed they do.

And number two, 18% of the litter found was crisp packets 'cause there were 50 pieces of litter altogether.

So if we multiply 9/50 by two, we get 18/100.

So that's 18% and 10% of the litter found was tin cans 'cause that was 5/50.

Multiply both of those by two and we get 10/100.

That's 10%.

There were 50 pieces of litter altogether.

So you needed to double each number to work out each percentage in this case.

And C, 44% of the litter found was plastic bottles.

22 out of those 50 pieces of litter was plastic bottles, multiply both by two or double them if you like.

And that gives us 44/100 or 44% and 28% of the litter farm was sweet wrappers because 14 of those 50 pieces of litter was sweet wrappers.

And then if you double 14/50, we've got 28/100, so 28% 18, 10, 44 and 28, add together those percentages and you get 100%.

you're doing really well and it's time to look at problems with fractions, decimals and percentages.

Aisha wants to convert this percentage to a fraction, so we've got 68%.

Now, I don't know about you, but a fraction has jumped straight out at me there.

It's 100ths, but she says I want to write the percentage as a fraction in its simplest form.

And it may not be in its simplest form the one I'm thinking of.

Lucas says that means we need to make the denominator as small as possible.

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

That's what I was thinking of.

So 68% is equal to 68/100.

Then let's write the factor pairs of 68 and 100.

Here they are, one and 68 are a factor pair of 68, as are two and 34 and four and 17.

And for the factor pairs of 100, we've got one and 100, four and 25, five and 20 and 10 and 10.

Can you spot any common factors there? Yes, four, four is a common factor and in fact it's the highest common factor as well.

So we can divide both 68 and 100 by four to find the fraction written in its simplest form.

And to divide by four, you could halve and halve again.

So that gives us 17/25.

Asia matches the percentages and fractions.

So we've got 70%, 75% and 80% and we've got 4/5, 7/10 and 3/4.

And one of those in particular is especially common.

75% is quite a common percentage.

Aisha says I need to match each percentage to a fraction that is equal to it.

How could she go about that? I'll start by converting each percentage into a fraction with a denominator of 100.

Good idea, fairly easy to do, I think.

So 70% is 71/100, 75% is 75/100 and 80% is 80/100.

70 and 100th can both be divided by 10.

10 is a factor of both of them and in fact it's the highest common factor of both of them.

So let's do that.

So 70% is equal to 7/10 and that's one of our options.

75%, well 75 and 100 both have 25 as their highest common factor.

So they can both be divided by 25.

So let's do that.

When you do that, that gives you 3/4 and that's another option.

Now that's a very common equivalence.

That one's worth memorising I think, that comes up a lot.

And 80%, well it should be 4/5, but let's have a check.

The highest common factor of 80 and 100 is 20.

So if we divide them both by 20, we've got 4/5.

So 80% is equivalent to 4/5, over to you.

A little check, match the percentages and the fraction.

So we've got 30%, 25%, and 24%, 3/10, 6/25 and 1/4.

And one of those is especially common.

Pause the video.

How did you get on, how did you find that? Let's have a look.

Well, let's start by converting each percentage into a fraction with a denominator of 100.

So 30% is equal to 30/100, 25% is equal to 25/100 and 24% is equal to 24/100.

Not too taxing I don't think that part.

This is a slightly harder part finding the common factor, the highest common factor of both of them.

Well in this case we can divide them both by 10.

So 30/100 can be converted into 3/10.

And for 25%, 25 and 100 both have 25 as their highest common factor.

So divide them both by 25 and we get 1/4.

and then 24% is equal to 24/100.

The highest common factor of those two numbers, that numerator and denominator is four.

So we need to divide both by four and that gives us 6/25.

Well done if you match them like that.

Lucas is trying to complete the table.

So he's got a fraction, that's 1/2, but he hasn't got the decimal or the percentage yet.

He's got the decimal.

That's 0.

2 or 2/10 you could read that, but he hasn't got the fraction or the percentage and he's got 9%, but he hasn't got the fraction or the decimal, let's help him to work it out.

He says, I'm looking for the missing fractions, decimal numbers and percentages.

I know that 1/2 is equal to 0.

5 and I bet you knew that too.

I bet that's committed to your memory.

And it's also equal to 50%.

0.

2 can be converted to 20%.

20% is equal to 20/100.

20 and 100 can both be divided by 20.

That makes 1/5.

So that's that in its simplest form, we can say 2/10, that is true.

But 1/5 is the simplest form that we can express that in.

And then 9% is equal to 9/100.

It cannot be simplified any further because nine and 100 have no common factors except one.

So therefore the decimal is 0.

09, which we can read as 9/100.

The fractions 9/100 and the percentage is 9%.

Zero is used in the 10s because there are nine 100s, but zero 10s.

So that's really important to use that placeholder zero.

It is time for a check.

Complete the table.

We've got a decimal 0.

61.

What is that as a fraction and what is that as a percentage? Pause the video.

Did you get it? What's the missing fraction and percentage? 0.

61 can be converted to 61% and 61% is equal to 61/100.

It can't be simplified any further because 61 and 100 have no common factors except one.

You're ready for some final practise I think.

So number one, write each percentage as a fraction in its simplest form.

So we've got 90%, 18% and 96%.

Make the denominator as small as you can.

Number two, match the percentages and the fractions, start by converting each percentage into a fraction with a denominator of 100.

The fractions here are not all written with the smallest possible denominator.

So watch out for that.

Number three, complete the table.

Work out the missing fractions, decimal numbers and percentages and write each missing fraction with the smallest denominator that you can.

So simplify as much as possible.

Rightio, pause the video and away you go.

Welcome back, how did you get on? How are you feeling? Are you feeling good, are you feeling confident? Let's give you some answers.

So A, 90% is equal to 90/100, which is equal to 9/10.

And a common factor of 90 and 100 is 10.

So we can divide both by 10.

And for B, 18% is equal to 18/100, a common factor of 18 and 100 is two, the highest common factor in fact.

So we can divide both by two and that gives us 9/50.

And for C, 96%, 96/100, the highest common factor of both of those is four.

So it can divide both by four.

And that gives us 24/25.

For B, the highest common factor of 18 and 100 is two.

Number two, 75% is equal to 3/4 and that's a very common percentage fraction equivalent.

It's worth memorising.

3/4 is also equal to 6/8.

And that's the one we've got here.

80% is equal to 4/5.

The highest common factor of 84 and 100 is four.

So therefore 84% is equal to 2/25.

85% is equal to 17/20, 90% is equal to 45/50, well done if you got those.

And number three, here are the answers.

1/10 is equivalent to 0.

1, which we can read as 1/10 and 10%.

The highest common factor of 34 and 100 is two.

So we can use that to work out that 34% is equal to 17/50.

So 17/50, 0.

34 and 34% are all equivalent.

0.

65 is equal to 65% and 13/20 in its simplest form.

11/100, 0.

11 and 11% are all equivalent.

And 5/25 is equivalent to 0.

2 or 2/10 and 20%.

We've come to the end of the lesson.

You've been amazing.

Today we've been using knowledge of fraction, decimal and percentage conversions to solve problems in a range of contexts.

To convert from percent to a fraction, start by converting each percentage into a fraction with a denominator of 100.

I think that's the easy part.

Use factor pairs to help you identify the highest common factor.

That's a bit trickier.

The percentage parts add together to equal 100%.

Well done on your accomplishments and your achievements today, give yourself a gentle pat on the back and say, well done me.

I hope to see you again for another math lesson at some point in the near future.

But until then, have a fabulous day whatever you've got in store, be the best version of you.

Take care and goodbye.