# Lesson video

In progress...

Today's lesson is on a fraction of a quantity.

In order to achieve this, you're going to need to understand fractions of quantities.

We're going to link that to parts and division.

We're then going to look at quantities in context.

And finally, it's quiz time.

As I've mentioned, you need a pen or pencil and a piece of paper.

My star words are fraction, denominator, numerator, and vinculum.

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

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

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

The numerator is the number of parts of the whole.

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

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

An improper fraction is where the numerator is greater than the denominator.

And a mixed number fraction is when you've got a whole number and a fraction together.

Equivalent fractions represent numbers which are the same.

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

And to multiply a fraction, we multiply the numerator by the whole number.

What fractions are represented below? Are there more than one answer? Pause the video.

And when you're ready, press play to continue.

So my first one is 2 stars out of 5, so it's 2/5.

My second one is 1 part out of 6, so it's 1/6.

My third one is 3 parts out of 8.

My fourth one is 1 part out of 4.

And my fifth one, I have 2, 4, 6, 8, 10 parts out of 12 parts selected.

The only one where I can give more than one answer is this one here because I can simplify it and I can say that's equivalent to 5 parts out of 6, 5/6.

So our new learning today is all to do with quantities.

And we know that 2/5 of 5 is equal to 2.

Try saying that.

2/5 of 5 is equal to 2.

If we look at the next example, 5/6 of 12 is equal to 10.

Let's write that down and see what it looks like.

So we know 5/6 of 12 is equal to 10.

I'm taking my 12, which is the whole thing, I'm splitting it into 6 parts, and I'm selecting 5 of those parts.

So we're thinking something of 12 is equal to, well, we know the answer is 3.

I'm thinking, "What part of 12 is equal to 3?" There's two ways I can think about this.

The first way is I can count.

And I can see I've got 4 parts so each part must be 1/4.

The second way to think about it is, well, the whole thing represents 12 and 1 part equals 3.

So how many more parts must I add together to get to 12? And I can see I need a total of 4 parts.

So each part must be worth 3, so each part is 1/4.

So 1/4 of 12 is equal to 3.

So I know that 1 part is equal to 4 and I know I've got 1 part, 2 parts, 3 parts, because there's 3 parts I'm thinking about thirds.

So I know that 1/3 of 12 is equal to 4.

Hey, let's explore this idea a little bit.

What other fractions of 24 can you find? Pause the video, and when you're ready, press play to continue.

So I'm going to start logically and I'm going to split 24 into 2 parts.

So I can say 1/2 of 24 is 12.

I'm then going to go from halves to thirds.

So 1/3 of 24, I'm taking 24 and I'm splitting it into 3 parts, and I can see in each group, there are 8 counters.

I can double check this by colouring one group, two groups, three groups.

And in each group, there are eight counters.

I can carry on working logically and go to quarters.

And I can say 1/4 of 24, this means I'm splitting into 4 groups.

So 1/4 of 24 has 6 counters in each.

If I carry on working logically, I get to fifths.

Now, the problem is that I can't split this group equally into fifths, so I'm not going to do that.

I am, however, going to look at sixths, so 1/6 of 24.

Well, that means I'm splitting it into 6 parts, so 6, 12, 18.

That means that each part is going to go 4 times, cross that out and I'll write 4 times.

So 1/6 of 24 is 4.

I can carry on, but I'm running out of space a little bit, so I'll say these.

My next one is 1/7, I can't split them into groups of 7.

My next one is 1/8, I'll write it up at the top.

1/8 of 24.

That means I'm splitting it into 8 parts, 8, 16, 24.

That means each part is worth 3, it has 3 counters in.

I can't do ninths, I can't do tenths, I can't do elevenths.

And the last one I can do is twelfths.

So 1/12 of 24 is equal to 2.

So I want you to imagine for the moment we could create some sort of question on this.

We could say there are 12 cookies per tray and we have 2 trays.

I could represent these as counters.

I have 12 counters per tray, and I have 2 counters.

I want to introduce some language that you might hear and might use.

So I'm going to start by saying the part has a value of 12 and there are 2 parts.

We can say this 12, 2 times.

We could say it as 12 multiplied by 2, double 12, 12 add 12, 2 lots of 12, 2 groups of 12, 2 equal parts with a value of 12.

We can also represent this with a bar model.

So I've got my whole thing, which is the two trays, and one part is 12 and the other part is 12.

And then repeat this with a slightly different value.

So the part has a value of 12 and there is 1/4 of a part.

I can say I've got 12 in total, and I've split it into quarters where I've got 3 in each part.

So I could say a 12, 1/4 of the time, I could say 12 multiplied by 1/4.

I could say 1/4 of 12.

I could say 1/4 lots of 12, 1/4 of a group of 12, 1/4 of a part that has a value of 12.

And again, I can represent this as a bar model where 12 is the whole thing, I've split it into 4 parts.

We can also consider the equivalent fractions within him.

So I know that 1/4 of 12 is 3.

I can write this as an equivalent fraction.

I can say my whole thing is 12 and I used 3 of these.

When I find that as an equivalent fraction, I know both 3 and 12 are in the 3 times tables.

So if I divide by 3, I get 1/4.

So I can link these two equivalent fractions as well.

Now we've learned a little bit about the language, now let's go on to develop this learning.

So stamps are sold in sheets of 24.

Amber uses three sheets.

Michael uses 3/4 of a sheet.

How many stamps did each person use? Pause the video, have a go.

If we have a look at Amber first, she uses three sheets.

So she can say I have 24, 3 times, 24 multiplied by 3, 24 add 24 add 24, 3 lots of 24, 3 groups of 24, or 3 equal parts, each with a value of 24.

It can be represented as a diagram here.

I can also represent it as a bar model and I've got 24 and another 24 and another 24.

And in total, 24, 3 times is 72.

So Amber uses 3 sheets, which is 72 stamps.

Michael uses 3/4 of a sheet.

I can write this as 3/4 times 24.

I could say it 24, 3/4 of the time, I could say 24 multiplied by 3/4.

I could say 1/4 of 24, then multiplied by 3.

I could say 3/4 lots of 24, 3/4 of a group of 24, and 3/4 of a part that has a value of 24.

And when I'm trying to calculate how big this is, I'm looking at my diagram.

On my calculation, I've got 24 split into 4 parts, each part has 6 counters or 6 stamps in this case.

So 3 parts, 3/4 has 18 stamps.

So Michael uses 18 stamps.

You can see here, there's a big difference between the number of sheets that people use, and there's only one word which is different.

Amber uses 3 sheets, Michael uses 3/4 of a sheet.

Be very careful when you're thinking about these questions and the wording of a question.

Okay, take a moment.

Can you sort these questions into two groups based on their answers? Pause the video, and when you're ready, press play to continue.

The ones on the left hand side all have a value, an answer of 4, the ones on the right hand side, all have an answer of 3.

Next one, can you solve these questions and represent in a bar model? Pause the video, and when you're ready, press play to continue.

For the first one, 1/5 of 10.

I'm going take 10 as my whole, I'm going to split it into 5 parts.

Each part has a value of 2.

So 1/5 of 10 is equal to 2.

The next question, I'm looking at 2/3 of 9.

And 9 is my whole, I'm splitting it into 3 parts.

Each part is worth 3, and this time I've selected 2 parts of the 3, which has a value of 6.

1/4 times 16.

I've set this up exactly the same way.

16 is my whole, I'm splitting it into 4 parts.

Therefore, each part is worth 4.

I have 1/4 times 16 which equals 4.

Next question, 2/5 of 20.

I'll take my whole, I'll split it into fifths.

20 is the whole, is the total.

I have divided that by 5.

Each part is worth 4.

The question asks for 2/5 of 20, which is 8.

Finally, I've been asked for 1/3 of a group of 15.

So 15 is my total.

I'm splitting it into 3 groups, which means that each group has a value of 5.

So 1/3 of a group of 15 is equal to 5.

Match the questions to the bar model and to the fraction.

Pause the video, and when you're ready, press play for the answer.