Lesson video

Hello everybody.

My name is Mr. Kelsall and welcome to today's lesson about understanding fractions and converting between proper fractions, improper fractions, and mixed number fractions.

Before we start, you are going to need a pen and a piece of paper, and also please try and find somewhere quiet somewhere you won't be disturbed, and don't forget to remove any sort of distractions.

For example, put your mobile phone on silent, or maybe like completely.

Pause the video, and when you're ready, let's begin.

For today's lesson is about understanding fractions and converting between fractions.

We're going to start by revising, understanding what a fraction is, what makes up a fraction.

We'll then look at proper and improper fractions and also mixed number fractions.

Then we'll look at converting between these.

And finally, it's quiz time.

I've already mentioned that you'll need a pen and a piece of paper.

We're going to look at some important words for today.

We'll talk about a fraction, denominator, numerator, vinculum, a proper fraction, an improper fraction, and a mixed number fraction.

Few definitions to start with.

First of all, a fraction is part of a whole.

I mean, if I have a whole thing and I'm going to split it, I've got a whole thing and I've split it into a part.

I could say that the United Kingdom is the whole thing.

And England is one part.

Scotland is one part.

Wales is one part.

Ireland is one part.

So I'm talking about a fraction is part of a whole.

I could say my number four is the whole, and I can split that into two parts.

I can say one and three make up the whole.

So one is a part, three is a part, one and three make up the whole.

The word denominator means the number of parts that the whole is split into.

So I have a pizza and I split it into four parts and I eat three parts.

The denominator is four because I've split it into four parts.

The numerator means the number of parts of the whole.

So here I've eaten three parts.

I can say three is the numerator.

So I could say I've eaten three parts out of the four parts in total.

And the word vinculum refers to the line here between the numerator and the dominator.

And later on, you'll come to understand that that also means division.

In order to understand a little bit more about a fraction, we need to understand the fraction as a part of the whole.

Each shape here has been split into two parts.

Question is, which fraction is a half and which fraction is not a half? Pause the video, and when you're ready, press play to continue.

For my first shape, I can see that this part, and this part are equal size.

My second shape, I can see this part and this part are equal size.

However, in my third shape, these two are different sizes.

So this shape is a half.

This shape is a half.

However, this shape is not a half because it's not two equal parts.

And it's the same with our rectangle.

It is not a half because it has not been split into two equal parts.

Our triangle is a half because it's been split into two equal parts.

The facts that you need to recall.

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

So we talked about a pizza before and I started eating, three quarters of a pizza.

That is a proper fraction because three is smaller than four.

The numerator is smaller than the denominator.

Let's say I'd eat and I'd ordered two pizzas, and they were both split into quarters and I was feeling a bit hungry, so I ate one full pizza and a bit of another pizza.

I've eaten five parts of pizza.

So I've eaten five pieces.

This is an improper fraction because the numerator is greater than the denominator.

So the pizza has been split into four parts and I have eaten five of those parts.

I ate one part, two parts, three parts, four parts, five parts.

And finally I have a mixed number fraction, and this is where you've got a whole and the fraction.

So in the example of the pizza here, I could also say I've eaten one whole pizza and one part out of the remaining four.

So this is a mixed number fraction because it's one whole, and it's a fraction.

Just the word of warning for you.

Be careful when you're writing fractions, because if you've got one and five quarters, you've got a whole and an improper fraction, and they don't go very well together, and we don't write them like that.

We'll show you how to convert them later.

So we'll look briefly at a bit of information about fractions.

Have a look at the four fractions on your screen.

Can you convert these fractions? So can you convert them from a mixed number fraction to an improper fraction? Can you draw them as well, like I did? Pause the video, and when you're ready, press play to continue.

So the first one, one and a half, I'm just going to imagine I've got one whole one, and I've got another whole one.

And if I split both of these in half, that is one whole one, and one half.

So I can write this as one, and one half, or alternatively, I can say, well, how many halves do I have? I've got one half, two halves, three halves.

So I could write this as three over two.

So my first one here is a mixed number fraction because I've got a whole and a fraction.

And my second one was an improper fraction because the numerator is bigger than the denominator.

Just take a moment to think, could you do that mentally without drawing a picture? Okay, let's move on to the next one.

I'm going to draw three and two fifths.

So I've got one, two, three, and I need to split each of these into fifths.

It's not very accurate because I'm drawing on a screen, but I'm sure if you draw on paper, you used pap squared paper and made these boxes equal size.

Okay, so I've got one whole one, two whole ones, three whole ones.

Oh, I need another whole one, don't I, as my fourth whole one.

So I've got all of these shaded all these shaded, all of these shaded.

So, that's three whole ones, and I've got one fifth, two fifths.

So, I've got my three and two fifths, but what would it be as an improper fraction? Well, here, I've got five fifths.

Here, I've got another five fifths, another five fifths.

So I've got five fifths, 10 fifths, 15 fifths, and two more fifths, which means I've got a total of 17 fifths.

So I know that three and two fifths is the same as 17 fifths.

Can you make a link between one whole one being five fifths? And I've got three whole ones.

So I could say one whole one is five, two whole ones is 10, three whole is 15 fifths, and then up two more is 16, 17 fifths.

See if you can do the same with the next one.

So after eight thirds.

Oh, this is different this time.

This time, I've been given an improper fraction, not a mixed number fraction.

Okay, I still think I can draw it.

I'm going to draw a whole one.

I split it into three parts.

How many thirds have I got? One, two, three.

So I need some more.

I'll draw another whole one, split it into three parts, four, five, six.

So I've got six thirds so far.

Another whole one split into thirds, seven, eight.

So I've got eight thirds, but how many whole ones have I got? Well, I've got three thirds here.

Got another three thirds here, so that's two whole ones.

And I've got one, two, two thirds.

Can you spot a pattern? So eight thirds is equivalent to two and two thirds.

Can you make a link between the two, the three and the two and somehow make this equal eight.

Let's do it with the next one.

We've got seven halves.

Okay, there's two halves, four halves, six halves, eight halves.

So I want one, two, three, four, five, six, seven halves.

And that's the same as one whole one, which is two halves, two whole ones, four halves, three whole ones, six halves.

Cut the extra one seven halves.

So it's three whole ones and one half.

Pause the video, just review those and see if you can do them mentally and when you're ready, press play to continue.

Keep that word in your mind, we'll come back to it later.

A quick reminder for you, revision.

Fractions.

A fraction is a part of a whole.

Denominator.

Say this with me, so you can understand it.

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

The numerator, is the number of parts of the whole.

Vinculum is the line between the numerator and the 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 a whole and a fraction.

Hey, let's develop this learning.

We're looking at two parts here.

Understanding fractions and converting between fractions.

So which of these shapes have been divided into four equal parts.

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

Okay, I've split these now.

Just want to talk through a couple.

This one is an interesting one.

Imagine you fold the shape equally.

I've got two halves.

And then imagine I just look at the top shape, if I fold that again, that gives me half of a half, which is a quarter.

And then if I look at the bottom shape, I've got a half and if I fold it equally, I've got two shapes which are equal size.

Therefore, this is a quarter and this is a quarter.

So actually, each of these shapes is of an equal size.

Compare this with something like this shape.

I folded it once, so I know each of these shapes is a half.

As I folded it again, I haven't followed it accurately, so I haven't made an equal part.

So this shape can not be equal parts What I would like to point out is this one.

If I draw a line there.

And I draw a line there.

I can see that, actually I've split this into eight equal parts, and the question was that's one part, that's one part, that's one part, and that's one part, and I can see that each of those parts has two of the eight equal parts.

So actually, I'm quite happy this has been split into equal parts.

So now we're going to come back to converting between fractions.

If I start with an improper fraction, how do I convert this to a mixed number fraction mentally? Well, if I've got, let's say an improper fraction, five thirds.

I want to convert this to a mixed number fraction.

Well, my first question is, how many thirds have I used already? I've used three thirds and three thirds is one whole one.

How many thirds are left? Two thirds are left.

So I've started with five thirds.

Three thirds is one whole one, which means I've got two thirds remaining.

Let's try number a little bit bigger.

If I start with nine quarters.

Well, four quarters is one whole one.

So eight quarters is two whole ones.

And that means I've got one quarter leftover.

See if you can convert the two fractions on the screen.

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

So, three halves, well, two halves is a whole one, and I've got one half remaining.

When I'm looking at eight thirds, three thirds is a whole one, six thirds is two whole ones.

And I've got two thirds remaining.

Now I need to think about not the other way around, but I need to convert mixed number fractions to improper fractions.

If I start with the example I've just used, one and one half.

Well, how many whole ones have I got? One.

If I split that into halves, that would be two halves.

So I've got two halves and one more half, gives me three halves.

If I use another example, this time I've got two and one third, over two whole ones, is how many thirds? Well, one whole one is three thirds.

So two whole ones is six thirds.

And I've got my extra third, which means that that's seven thirds.

Let's use a little bit of a bigger number.

Let's try five and two quarters.

Okay.

One whole one is four quarters.

Two whole ones is eight quarters, three whole ones, 12 quarters, four whole ones, 16 quarters, five whole ones, 20 quarters.

I've got another two quarters left, so that's 22 quarters.

There's two more questions on the screen.

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

Okay.

So I know the one whole one is equivalent to three thirds and I added on my two thirds, which gives me five thirds.

For the second question, I know that one whole one is equal to four quarters.

So one whole one is four quarters, two holes is eight quarters, three whole ones is 12 quarters.

Add on my extra one quarter gives me 13 quarters On your screen, there are a range of mixed numbers and improper fractions and equivalent fractions.

Try and match these.

When you're ready, pause the video and press play to continue.

I am hoping that this task really got you thinking.

I just want to talk for a couple.

One more quarter is equal to five quarters, and you'll probably notice that 10 eighths appear there as well.

10 eighths is an equivalent fraction, it's a same size fraction.

Two and three eighths is equivalent to 19 eighths because one eighth, one whole one is eight eighths Two whole ones is 16 eighths, add my three eighths, 17, 18, 19 eighths.

I've put this number here for a reason.

Think about why later.

My next one, three and seven tenths is a nice, easy one because I can do three multiplied by 10, gives me 30, add on my seven.

Did you see how it started to move to a mental process there? Again, I've put this number over here.

It's an equivalent fraction, but I don't like them.

I'll talk why in a moment.

My final one, one and three eighths.

Well I can do one times eight, is eight, add on three, is 11, so I've got 11 eighths.

And 11 eighths is equivalent to 22 sixteenths.

Okay, going back to these two fractions.

One and 11 eighths.

Well, I've got a whole number and an improper fraction together.

And we don't like writing fractions like that.

So 11 eighths.

Let me just write this number here.

One and 11 eighths.

Well, 11 eights is the same as eight eighths, which is a whole one and three eighths.

So let me just say that's the same as one whole one, and add eight eights, and my three eighths.

Well, eight eighths is one whole one.

So, I've got one whole one, and one whole one, and my three eighths.

So actually, this is the same as two, and three eighths.

It's much better to write a fraction like that, rather than having a whole number with an improper fraction.

And if you'd like to do the second one together.

Well, 17 tenths is the same as 10 tenths, and seven tenths left over.

So 10 tenths is a whole one.

So two whole ones, and my other whole one, gives me three whole ones, and I've still got my seven tenths leftover.

Now for your independent task.

What fraction is shaded? Explain your reasoning.

So for this question, I simply added a few more lines.

Soon as I added these lines, I realised I've got one, two, three, four, five, six, seven, eight, nine parts, shaded out of four, eight, 12, 16.

So my fraction was nine sixteenths.

For my next question, I did a similar thing.

I started off by drawing line here, and I thought, well, this shape actually fits here.

So I've got one part out of eight shaded.

This bit here, fits here.

So that's my one part.

That's another part I've now got shaded.

And this bit fits here.

That's another bit I've got shaded.

So actually I've got three full parts out of eight parts shaded.

So my fraction is three eighths.

Last question, I realised that actually is quite a lot of small triangles, so I'm going to try to draw some extra lines to show the small triangles, and then I can count those.

Now, once I've added my extra lines, I've got within each square, I've got two triangles.

So I've got, two, four, six, eight, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32 parts to the shape, and I've got one part, two parts, three parts, four parts shaded.

So my final fraction is four thirty-twoths.

My second independent task is all to do with converting fractions.

Can you draw these conversions as a mixed number fractions and improper fractions.

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

The answers are on the screen, and there's two I wanted to draw your attention to.

The first one is 20 sixths.

Well, I'm counting in sixths now.

Six sixths is one whole one, 12 sixths is two whole ones, 18 sixths is three whole ones, 19, 20.

So I've got two sixths left, and two sixths is this the same as one-third.

The other one I wanted to draw your attention to was one and four thirds.

Well, one is a whole one and four thirds is an improper fraction.

So we got that problem again.

So I've converted my four thirds to one whole one.

Come one third.

I've added it to my other one, which was there, which gives me a total of two and one third.

Congratulations on completing your task.

If you'd like to, please ask your parent or carer to share you work on Twitter, tagging at Oak National, and also hashtag, learn with oak.

Now before we go, please complete the quiz.

So that brings us to the end of today's lesson on understanding fractions and converting fractions.

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

Now, before you finish, perhaps take a moment to quickly review your notes and try to identify the most important thing 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.