# Lesson video

In progress...

Today's lesson is how to multiply a fraction by a whole number.

We're going to start by understanding multiplying.

We'll then multiply a fraction within 1.

We'll then multiply a fraction above 1.

And after that, it's quiz time.

I imagine you'll need a pencil and a piece of paper.

And our star words for today are fraction, denominator, numerator, vinculum.

We'll be talking about a proper fraction, improper fraction, mixed number fraction, and we'll be using the word multiply.

In order to access lesson, you will need to understand that a fraction is part of a whole.

The denominator is the number of parts the whole is split into.

Numerator is the number of parts of the whole.

The vinculum is the line between the numerator and the denominator.

A proper fraction is where the numerator is less than the denominator.

And an improper fraction is where the numerator is greater than the denominator.

A mixed number fraction is a whole and a fraction together.

Equivalent fractions are fractions that represent the same number.

And to simplify a fraction, you need to reduce the numerator and denominator at the same time.

Now our new learning.

Ciaran spends a quarter of an hour running.

And he runs 3 times per week.

So how long does he spend running? Pause the video.

When you're ready, press play to continue.

The question asks us to draw it.

So let's try that.

Well, I'm going to take a whole thing and I'm going to split it into quarters.

And that's once a week.

That's twice a week.

That's 3 times a week.

Now I can see that I've created 3/4.

As a fraction, I could say in the first week, on the first day he does 1/4 an hour.

On the second day, it is a 1/4 of an hour, and later it is another 1/4 of an hour, which gives me 3/4 of an hour.

If I look at multiplication, I can say I'm thinking 1/4 and I'm multiplying it by 3, which gives me 3/4.

I could also look a number line, and I could say, well I'm going 1/4, 2/4, 3/4 of the way along.

But there's lots of different ways to represent this question.

Today we're going to look at multiplication, which is 1/4 times 3, to give us 3/4.

To represent the same question a bit more formally, I can see my number line there.

I've got 1/4, 2/4, 3/4, or I've got my multiplication, which is 1/4 multiplied by 3.

So question number two.

The blink of an eye takes 3/10 of a second.

How long would it take for three blinks? Pause the video.

When you're ready, press play to continue.

If I look at my model in here, I know that 3/10 on a number line is represented here with the first green bar.

Now that's the first blink.

The second blink is another 3/10, and the third blink is another 3/10.

So in total, so I've got 9/10.

I could represent this as repeated addition and do 3/10 and 3/10 and 3/10 is 9/10.

Or I can start trying to find a quicker way to do this and look at multiplication.

3/10 times 3 is nine 9/10.

And you'll notice at that point, I'm multiplying the numerator by the whole number.

How would you solve these calculations? Think about, do you need to draw them? Do you need to represent them in a number line? Do you want to draw them out as repeated addition? You choose how you'd like to solve them, but try and be as efficient as possible.

Pause the video and when you're ready, press play to continue.

So for my first one, I'm going to represent this as repeated addition.

I am going to do 1/5 add 1/5 add 1/5 gives me 3/5.

For my second one, I'm going to represent this as multiplication.

So I'm doing 2/9, and I'm multiplying the numerator by 4.

So 2, 4, 6, 8, so 2/9 multiplied by 4 gives me 8/9.

And for my third example, I'm going to draw a number line.

So I've got seven parts and I've got 2/7, another 2/7, and another 2/7.

So in total I've got 6/7.

That brings us to our develop learning section.

What do you notice about these calculations? Pause the video, and when you're ready, press play to continue.

I'm just going to point out the things which I've notice.

1 times 3 is 3.

Three 3s are 9.

1 times 5 is 5.

1 times 8 is 8.

3 times 2 is 6.

2 times 4 is 8.

I can start to generalise and say that when I've got a fraction multiplied by a whole number, I need to multiply the numerator by the whole number.

One cup holds a quarter of a litre of liquid.

How much liquid will five cups hold? Ask yourself a question.

How is this question different to previous ones? Pause the video, have a go, and when you're ready, press play to continue on.

Now my one cup holds a quarter of a litre.

Let's have a look.

So I know that's one cup, two cups, three cups, four cups.

Why is four cups important? And then five cups.

Oh, five cups is important because it's four quarters, which is the same as one whole one.

So I've got one litre and one extra litres.

I could solve this by multiplication.

I could say 1/4 times 5 gives me 5/4.

1/4 and 1/4 and 1/4 and 1/4 and 1/4 is 5/4.

But actually this doesn't answer the question because the question asks how much liquid is in the cup.

do the cups hold.

Well, 5/4 is the same as one whole one and one more quarter.

If I want to convert to mixed number fractions, four quarters is one whole 1, leaves 1/4 leftover.

So the cups in total hold 1 1/4 litres of water.

I asked how this was different than previous questions.

Previous questions have worked within one.

This is the first question which goes above one.

Let's explore that a little bit more.

A ribbon is 2/3 of a metre long.

Another ribbon is five times the length.

How long is it? Pause the video.

Have a go at this question.

Press play when you're ready.

So my first ribbon is 2/3 of a metre.

I can see this represented on my number line.

Yeah.

The other one is five times the length.

I've got one times, two times, three times, four times, five times the length.

This is represented in my bar model.

I've also written this as a kind of calculation.

2/3 times 5 gives me 10/3.

If I look on my number line, that's also 10/3.

However, I need to give the answer in metres.

10/3 won't be a suitable answer.

So I need to convert this.

I can convert this because I'm thinking how many thirds are in 10/3.

Well 3/3, 6/3, 9/3.

That's 3 whole ones.

I have 1/3 leftover.

If I look on a number line, it's exactly the same.

9/3 represents 3 whole ones, and I've got the one extra 1/3.

So I've got 3 1/3 of a metre.

Now it's time for your independent task.

Solve the problems and the calculations, and then generate your own word problems. Pause the video, and when you're ready, press play to continue.

The first question asks, a small bottle holds 1/5 of a litre of liquid.

How much will seven bottles hold? My calculation should be 1/5 multiplied by 7, which gives me 7/5.

I can convert to a mixed number fraction.

That's the same as 5/5 is one whole one, and there's 2/5 leftover.

Now it asks for this as litres.

So I know I have 1 litre and 2/5 of a litre is 400 millilitres.

The next question asks, the length of a rectangle is 12 centimetres and the width is 1/10 of a centimetre.

What's its area? Let's draw this out.

So it's 12 centimetres by 1/10.

So to find the area, I'm doing 12 multiplied by 1/10, which gives me 12/10 of a centimetre.

I can convert this and I can say that's 1 whole centimetre and 2/10.

And when I measure that in centimetres, I know that's 1.

2 centimetres.

My last question is 2/7 multiplied by 5.

2 times 5 is 10.

So I've got 10/7 as a mixed number.

That's 1 3/7.

My next question asks, a hurdle is three quarters of a metre tall and a pole vaulter volts five times this height.

What height is this? So I'm thinking of 5 multiplied by 3/4 of a metre.

5 times 3 is 15, so 15/4.

I need to convert that to whole numbers.

So I've got 4/4, 8/4, 12/4, which is 3 whole ones, and there's 3/4, three quarters leftover.

Well, what is that as a metre? That's 3 metres and 75 centimetres.

My next question was 5/8 times 4.

5 times 4 is 20, so it's 20/8.

As a mixed number, I've got 8/8, 16/8, so it's 2 whole ones and 4/8.

I can simplify that to become 2 1/2.

Finally, I've got 3/10 multiplied by 7, which gives me 21/10.

As an improper fraction, that is 2 whole ones and 1/10.

If you'd like to, please ask your parent or carer to share you work on Twitter, tagging @OakNational, and also #LearnwithOak.

Now before we go, please complete the quiz.

So that brings us to the end of today's lesson on multiplying a fraction by a whole number.

A really big well done on all the fantastic learning that you've achieved.

Now, before we finish, perhaps quickly review your notes and try to identify the most important part of your learning from today.

Well, all that's left for me to say is thank you.

Take care and enjoy the rest of your learning for today.