Lesson video

Hi, welcome to your maths lessons today.

Are you feeling ready? I certainly am.

Let's get started.

In today's lesson, we'll be calculating non-unit fractions of quantities.

A non-unit fraction is a fraction where the numerator is more than one, such as 2/3 of something or 3/4 of something.

We're going to start off by looking at some problems and how we might represent those with bar models.

Then we're going to think about how we use multiplication to find non-unit fractions.

You've got a task and then a quiz.

You'll need a pencil and piece of paper or something else that you can write on and write with.

If you haven't got that, go and get it now and then come back to the video.

If you have, let's get started.

Okay, here's a problem, and I'm going to represent it with a bar model.

A school has 280 pupils, 3/4 of them get to school by car.

How many pupils get to school by car? Okay, so here's my bar, and I've labelled where the whole is.

What is our whole in this instance? Well, we know the whole is the amount of pupils in the school, which is 280, so we can label our whole here.

Now, we need to work out 3/4 of 280.

So in order to do that, the first thing we need to do is think about dividing 280 into quarters.

I'm going to sketch that, so I've got 1/2 here, and I'm going to divide those halves into 1/2 again.

So this represents four equal parts.

Now, I know that in order to find 1/4, I need to divide 280 by four.

However, we need to also find 3/4.

So the first step is to find 1/4, 280 divided by four.

Well, I know the 28 divided by four will give us seven.

So 280 divided by four will give us 70.

But we found out 1/4, in order to find 3/4, we need to then think about three lots of 70.

Three times seven is 21, so three times 70 is 210.

1/4 of 280 is 70, so 3/4 of 280 is 210.

210 pupils travel by car.

Let's think about what we did there, we divided our whole by four because we were looking into quarters, our denominator is four.

Then we multiplied by the amount of parts we need, which is three parts, 3/4, our numerator.

Let's look at the second problem.

A plane has 385 people aboard, 2/5 of those people are children.

How many children are on the plane? How many adults are on the plane? Okay, so what do we know? Well, we know the whole, what is the whole? Can you say it out loud? Okay, the whole is the amount of people on board all together, which is 385.

Now, we're working in fifths this time, 2/5 are children.

So before we find 2/5, we need to find out what 1/5 is.

So we need to divide this into five equal parts, I'm just going to show that on my bar model.

So I'll do that roughly, 1/5, I know that 2/5 is just under 1/2, 3/5 is just over 1/2, and I just need to make one more segment here.

So this is representing my five equal parts.

We can mark 2/5, which is the amount of children here, and then the rest of those I presume are adults, which is 3/5.

Okay, so let's think about what 1/5 would be.

So to do that, I need to do 385 divided by five.

Now, I'm not sure of that off the top of my head, so what I could do is a quick bus stop method to help me.

You might use a different method.

So I know that five can't go into three, 38 divided by five will get me seven with three leftover, 35 divided by five would get me seven.

So I've worked out that 1/5 would be 77.

Now, 2/5 would be 77 added to 77, or two times 77.

I think I can do that mentally.

I know that 70 times two would get me 140.

Seven times two would get me 14, so I'm going to recombine.

I know that 77 times two, or 77 add 77, is 154, okay.

So what have we worked out now? 2/5 of those are children.

So we've worked at how many are children, 154 are children.

So if we want to work out how many are adults, we need to think about how many 3/5 are.

So we could times 77 by three, or we could work from what we already know.

We know that 2/5 is 154, so we could just add on another 77.

Is there another way we could work this out? Well, we also know the whole, 385.

We know that 154 are children and 2/5, so we could do a subtraction.

We could subtract 154 to find out how many are adults, five takeaway four we know is one, eight takeaway five is three, three takeaway one is 231.

231 of these are adults.

1/5 of 385 is 77, so 2/5 of 385 is 154.

There are 154 children.

3/5 of 385 is 231, there were 231 adults.

Okay, let's have a look at a bit of a more abstract problem.

What is 2/3 of 330? Okay, I'm going to have a go at solving this, and then I'd like you to tell me the steps I took in order to solve it.

So looking at my whole, 330, now, my denominator says I need to split that into three equal parts.

I need to do 330 divided by three.

I could use the bus stop method, but I think I can do this one using my mental knowledge.

I know that 33 divided by three is 11, so 330 divided by three is 110.

Now, what we've done here is find one third.

Looking at my numerator, I need to find 2/3, so I need two lots of 110.

So I need to do 110 multiplied by two to get me 220.

2/3 of 330 is equal to 220.

Now, what steps did I take? Pause the video now and say them out loud.

Okay, let's think about this together.

So, first of all, instead of finding 2/3, I found 1/3 by dividing by three, which got me to 110.

Secondly, I then found 2/3.

I know that 1/3 is 110, so 110 multiplied by two is 220.

We first of all divided by the denominator, then multiplied by the numerator.

Okay, it's your turn to have a go at some of these.

I've left my steps from my example down below in order to support you thinking about what to do first and what to do next.

Okay, pause the video now to have a go at these, and when you're done, come back to the video.

Okay, let's look at these together.

So before I find 5/8 of 320, the first step is to find 1/8 of 320.

So 320 divided by eight, now, I know that 32 divided by eight would get me four.

So 320 divided by eight would get me 40.

Now, I need to then multiply by five because we're not thinking about 1/8, we're thinking about 5/8.

40 multiplied by five I know is 200.

Okay, next one, 3/7 of 140.

So first of all, let's think about what 1/7 of 140 is, how do we do that? We need to divide by seven.

So 14 divided by seven would get me two, so 140 divided by seven would get me 20.

Now, I'm not looking for 1/7, I'm looking for 3/7, So I need to times 20 by three, which I know is 60.

3/7 of 140 is equal to 60.

Finally, I've got 11/12 of 72.

Now, let's think about what 1/12 would be.

1/12 of 72 would be, well, I need to divide by 12, which I know would get me six.

Then I need to times by 11, so 11/12 of 72 is equal to 66.

Is there another way we could have worked out that final one? Well, instead of timesing by 11, we could have thought actually this is 1/12 away from the whole.

So we could have taken 12/12, 72, and taken away six.

Wonder if you thought of that? Okay, moving on.

We're going to look at some problem solving in different contexts, including measures.

A television costs £999 full price, in the sale, this is reduced by 2/9 of the original price.

What is the new price of the television? Okay, I think it's best we use a bar model here to make sense of the problem.

Now, we are looking at ninths here, and I know my whole, which is 999.

So I'm going to draw a bar to represent my whole, and I've divided it into nine equal parts.

The whole television originally cost £999.

I know that this is reduced by 2/9, so let's label 2/9, we can do it either end, I'm going to do it here.

And then we need to find out the new price, which should be represented by 7/9 here Now, in order to work out 2/9 or 7/9, we need to first of all think about what 1/9 of 999 is.

Now, you could use the bus stop method, or you could do this mentally, because if we use a bus stop method, you can see that each time, it will just give us 111, so you can see how you might have been able to do that mentally.

So we know that 1/9 is worth 111, and each of these has been worth 111.

So 2/9 would be two times 111, which would get us 222.

However, this is not what the answer is, it's asking us for the new price, but what we actually need to work out is 7/9 of 999.

And we could either work out 2/9 and take that away from 999, or we could just times 111 by seven.

And, again, we could use a column method here, but if we just times one by seven in the ones, the tens and the hundreds, we would get 777.

The new price of the television is £777.

Put my pound sign in there.

Let's do one more together.

Martin is cycling three kilometres to work.

After 3/10 of his journey, he stops at a traffic light.

How much further does he need to cycle? Okay, let's make sense of this by seeing if we can draw it.

We know that our whole here is three kilometres, and we are dividing three kilometres into 10ths.

So I've got my whole divided into 10 equal parts.

We know that 3/10 of this journey he cycles first, then he stops.

How much further does he need to cycle? So what do we need to work out? Our whole is something we know is three kilometres, or 3000 metres.

Let's just write that here because we might find it easier to divide using our amount in metres.

We know that he's already been 3/10, so actually what we need to work out is 7/10 of 3000 metres or three kilometres.

So what's 1/10? Now, we could divide this by 1/10, which would get a 0.

3, or we could divide this by 1/10.

I'm going to work in metres this time.

I know that 3000 divided by 10 would get me 300 metres, 1/10 is equivalent to 300 metres.

We could mark that in one of our parts just so we know, we know that our parts are equal.

So 7/10 would be seven lots of 300 metres.

What's seven times 300? Well, seven times three is 21, so seven times 300, let's right that down, seven times three is 21, seven times 300, see if you can tell me, would be 100 times greater, so it would be 2100 metres.

Okay, he's got 2100 metres left to travel.

What if we wanted to write that back in kilometres? Well, our answer would be two kilometres and 100 metres or 2.

1 kilometres.

Okay, it's time for you to have a go at some of these problems. Pause the video now to have a go, and then we'll go over them together.

Okay, question one.

Omar is 186 centimetres tall, his grandma is 5/6 of his height, how tall is grandma? So our whole here is 186 centimetres.

I've divided my bar into six equal parts because we're working in sixths.

I know that 1/6 of 186 would get me 31.

His grandmother was 5/6, so I need to do 31 multiplied by five.

You might've used a written calculation here, that would have gotten you 155 centimetres, or one metre, 55 centimetres.

Question two, a bag of sugar weighs one kilogramme.

Tim uses 3/10 of the sugar when cooking, how much sugar does he have left? So I know my whole here is 1000 grammes, I'm using 1000 as I'd prefer you to divide using whole numbers.

I could use one kilogramme and go into decimals.

3/10 of the sugar was used, so let's work out what 1/10 is, 1000 divided by 10 is 100.

So 1/10 is 100 grammes.

3/10 is how much he's used, which would be 300, but that's not what the question's asking us.

Let's read carefully, how much sugar does he have left? So what we actually need to work out is 7/10, which would be 700, seven lots of 100.

Our answer is 700 grammes.

Question three, a TV programme is scheduled from six o'clock or 18 o'clock to 19 o'clock, which is seven o'clock in the evening.

So it's one hour long.

1/12 of this time is used to show adverts, how much of the time was spent showing the programme? Okay, so my whole here would be one hour, or it might be easier, because we're using division, to write this in minutes.

My whole would be 60 minutes.

1/12 is used to show adverts, so let's work out what 1/12 is.

60 divided by 12 would give us five.

Now, we know the rest is the length of the programme.

So we could either do five times by our 11, or we could just take five from 60, which might be easier.

This amount is equal to 55 minutes.

I'll put mins for short.

Question four, a bicycle costs £145, but the price was reduced by 2/5 in the sale.

How much does the bicycle now cost? Okay, so our whole here was £145.

We're working in fifths, so I've divided into five equal parts.

Now, 145 divided by five would get us 29.

A way you might think of that is 150 divided by five would get us 30, or you could've used the bus stop method, of course.

Now we need to work out what the bicycle costs now.

It was reduced by 2/5, so we could work out 2/5 and take that away, or we could just simply work out the new cost by calculating 3/5.

Two lots of 29 would have got you 58, but that's how much was discounted.

So you could take that away from 145, or you might have done 3/5 straightaway, 29 multiplied by three would have got you nine times three is 27, two times three is six, add that on, it would have got you £87, the new price.

Okay, how did you get on? If you made any mistakes, hopefully you can use this chance to correct any of your answers and have a look at it.

Once you're finished looking at your answers, it's time to complete the quiz.

Thanks very much, take care.