Lesson video

Hello there, my name is Mr. Goldie.

Welcome to today's maths lesson.

And here is the learning outcome for today's lesson.

I can compare fractions with the same numerator.

Let's take a look at those keywords, so tricky keywords today.

I'm going to say each keyword.

Can you repeat it back? The first keyword is denominator and the second keyword is numerator.

Let's take a look at what those words mean.

A denominator is the bottom number written in a fraction.

It shows how many parts a whole has been divided into.

A numerator is the top number written in a fraction.

It shows how many parts we have.

Here's our lesson outline.

So the first part of the lesson is comparing non-unit fractions, and the second part of the lesson is ordering non-unit fractions.

Let's get started.

In this lesson, you will meet Sofia and Jacob.

And Sofia and Jacob will be helping you to compare and order non-unit fractions today.

And a non-unit fraction is just any fraction where the numerator is not one.

So 2/4 is a non-unit fraction, 3/5 is a non-unit fraction, 4/9 is a non-unit fraction.

Jacob is thinking about pizza.

I think Jacob does quite a lot of thinking about pizza.

Jacob asks, "Would you rather have 2/3 or 2/4 of a pizza?" Sofia says, "Hmm, I don't know.

I suppose it depends how hungry I am." "Imagine you are really, really hungry." Says Jacob.

"Are the pizzas the same size?" Asks Sofia.

Of course, if we are comparing parts, each whole needs to be the same size.

Which do you think is bigger? 2/3 or 2/4? Sofia starts by comparing one part with another.

"First, I'm going to compare 1/3 with 1/4." So here's a pizza and Sofia cuts his pizza into three equal parts.

Each part is 1/3.

Sofia takes another pizza and Sofia cuts this pizza into four equal parts.

Each part is 1/4.

"Let's compare 1/3 with 1/4." Says Jacob.

What do you think? Which is bigger? 1/3 or 1/4? 1/3 is larger than 1/4.

"So which is larger, 2/3 or 2/4?" says Jacob.

Which is larger? 2/3 or 2/4? "1/3 is larger than 1/4," says Sofia, "so 2/3 must be larger than 2/4." Each 1/3 is greater than each 1/4.

1/3 is greater than 1/4.

Two 1/3 is greater than two 1/4.

2/3 is greater than 2/4.

"The greater the denominator, the smaller the parts." Says Jacob.

I guess that Sofia would choose 2/3 of the pizza as she is really hungry because it is larger.

Sofia thinks about comparing fractions.

"When the numerator is the same, is the fraction with the greater denominator always smaller?" "Let's compare 2/6 and 2/5." Says Jacob.

So here is a whole divided into six equal parts and a whole divided into five equal parts and the wholes are both the same size.

Each 1/6 is less than each 1/5.

Two 1/6 are less than two 1/5.

Because the hole has been divided into more parts, each part is smaller, so 1/6 is more than 1/5, 2/6 must be less than 2/5.

Sofia compares 3/7 and 3/5.

Sofia says "The numerator are the same but the denominators are different." So here is a whole divided into seven equal parts and a whole divided into five equal parts and both holes are the same size so we can compare them.

Each 1/7 is less than each 1/5 because the whole has been divided into more parts, the parts are smaller.

Three 1/7 are less than three 1/5.

3/7 is less than 3/5.

When the numerator are the same, the greater the denominator, the smaller the fraction.

3/7 and 3/5 both have the same numerator, 3/7 has a larger denominator, because it has a larger denominator, it must be a smaller fraction.

Here's one for you to try on your own.

Compare 2/10 and 2/6.

Which fraction do you think is greater? Pause the video and see if you can work out which fraction is larger.

You can use equipment to help you work out the answer.

You can draw something to help you work out the answer, but pause the video and see if you can work out which fraction is greater, 2/10 or 2/6? And welcome back.

Did you manage to work out which fraction is greater? Let's take a look and see whether you got it right.

Let's first of all, let's take 2 wholes, one divided into six equal parts, one divided into 10 equal parts.

Each 1/10 is less than each 1/6.

Two 1/10 are less than two 1/6, so 2/10 is less than 2/6.

When the numerator are the same, the greater the denominator, the smaller the fraction.

Well done if you've got the same answer.

Sofia compares each pair of fractions using less than or greater than.

The numerator are the same in each pair, but the denominators are different.

Let's take a look at that first one.

Sofia says, "1/8 is smaller than 1/6, so 4/8 are less than 4/6." And there's some images to help us understand as well.

So we've got their 4/8 and 4/6 and we can clearly see the 4/8 are smaller, are less than 4/6, so 4/8 is less than 4/6.

Let's take a look at that next one.

Sofia says "1/8 is greater than 1/12, so 7/8 are greater than 7/12." And again, just to use some images to help us work out the answer.

And you can see they're very clearly, 7/8 is quite a lot larger than 7/12, so 7/8 is greater than 7/12.

Let's look at that last one.

9/20 and 9/10.

Is 9/20 less than 9/10 or is it greater than 9/10? 1/20 is smaller than 1/10.

As the denominator gets bigger, the parts get smaller.

9/20 are less than 9/10.

And again, we can show that with an image where there a whole divided into 20 equal parts, nine of them are coloured.

And a whole divided into ten equal parts, nine of them are coloured.

9/20 are less than 9/10, so the correct symbol there will be less than.

Compare each pair of fractions using less than or greater than the numerator are the same in each pair, but the denominators are different.

Pause the video and see if you can work out whether you should use a symbol less than or greater than to compare each pair of fractions.

And welcome back.

How did you get on? Let's take a look to see whether you got the right answers.

So Sofia says "1/10 is larger than 1/12, so 5/10 are greater than 5/12." Here's a couple of images to help us understand.

You can see there 5/10 is greater than 5/12.

Let's look at that next one.

1/7 is smaller than 1/6.

6/7 are less than 6/6.

And again, we've got a couple of images there to help us understand.

6/7 is less than 6/6.

6/6 is actually equal to one whole.

Remember, when the numerator and the denominator are both the same number, the fraction is equal to one whole.

Very well done if you've got both of those correct.

And let's move on to task A.

So in the first part of task A, you're going to shade the fractions and then compare them.

So in that example A, we've got 2/8 and 2/9.

The numerator are the same, the denominators are different.

Is 2/8 greater than 2/9 or it's 2/9 greater than 2/8? And then C and D.

C and D are similar problems. You've got to compare 3/10 and 3/11, but this time it says is less than.

So we're not saying one fraction is greater than the other, we're saying one fraction is less than the other, so make sure you get it in the right order.

So there's part one of task A, let's take a look at part 2 of task A.

So this time you've got to compare the fractions using greater than or less than.

So A, 3/4 is it greater than 3/7 or is it less than 3/7? So in each example, the numerator is the same, the denominators are different.

And remember, when the denominator gets larger, the parts get smaller.

So pause the video and have a go at task A.

And welcome back.

How did you get on? Did you get onto to part 2 at task A? Let's take a look at those answers.

So here are the answers for part one of task A.

So we've got 2/8 and 2/9.

2/8 is greater than 2/9.

5/6 is greater than 5/9.

The numerator is the same in both fractions, but nine is a greater denominator.

As the denominator gets larger, the parts get smaller.

So C, 3/11 is less than 3/10.

3/11 has a larger denominator than 3/10.

So it must be a smaller fraction because the numerator are the same.

And then D, 9/10 is less than 9/9.

And you may have spotted something about 9/9? 9/9 is equal to one.

Let's take a look at part 2 of task A.

So A, 3/4 is greater than 3/7.

B, 8/12 is less than 8/11.

And C, 11/20 is less than 11/12.

Very well done for having a go at task A and excellent work if you manage to get onto part 2 and complete some of those comparison questions as well.

And let's move on to part 2 of the lesson.

So part 2 of the lesson is ordering non-unit fractions.

So we've done also work comparing them, now we're gonna have a go trying to order them.

Sofia orders these fractions.

She's got 3/4, 3/3 and 3/5.

Sofia says "The numerator are all the same.

When the numerator are the same, the greater the denominator, the smaller the fraction." Let's take a look at what 3/3 looks like.

3/3 is actually equal to one whole, the numerator and the denominator of the same number so the fraction is equal to one whole.

3/3 is the largest fraction.

It is equal to one whole.

3/3 is greater than 3/4.

3/4 is greater than 3/5.

So all the fractions have the same numerator.

As that denominator gets larger, the fraction gets smaller.

So 3/3 is greater than 3/4, 3/4 is greater than 3/5.

Let's take a look at another one.

So Sofia orders these fractions, 5/9, 5/5, and 5/7.

"The numerator are all the same." Says Sofia.

"When the numerator are the same, the greater the denominator, the smaller the fraction." So again, let's start with 5/5.

The 5/5 must be the largest fraction because the denominator is the smallest.

5/5 is the largest fraction.

It is equal to one whole.

5/5 is greater than 5/7, 5/7 is greater than 5/9, so 5/5 is greater than 5/7, 5/7 is greater than 5/9.

So the numerator are all the same, as that denominator gets larger, the fraction gets smaller.

Now it's your turn to have a go.

Order these fractions, 2/5, 2/7, 2/3.

Can you put 'em in order starting with the largest fraction? Sofia has noticed that the numerator are all the same, so you can certainly compare the fractions 'cause remember when the numerators are the same, the greater the denominator, the smaller the fraction.

So if you want to use any equipment to help you or draw pictures to help you work out the answer you can do.

Pause the video and see if you can order those three fractions.

And welcome back.

How did you get on? Do you think you definitely got them in the right order? Let's take a look to see whether you got it right.

So let's start off with 2/3.

2/3 is the largest fraction.

The numerator are all the same, it's got the smallest denominator, therefore it must be the largest fraction.

So let's start off with 2/3.

2/3 is greater than 2/5.

2/5 is greater than 2/7.

So 2/3 is greater than 2/5, and 2/5 is greater than 2 sevens.

Very well done.

If you've got those three fractions in the correct order.

Alex, Andeep, Laura and Izzy are running a race.

And you can see the race there with the start being represented by the number zero and the finish being represented by the number one.

And those four runners are somewhere on that number line.

And in fact, you can see four marks representing where each of them are.

Alex has run 4/9 of the race.

Laura has run 4/15 of the race.

Andeep has run 4/7 of the race.

Izzy has run 4/5 of the race.

Work out the positions of each runner, so where are they in that race? Let's start with the greatest fraction first of all.

So here are the fractions.

Sofia makes the observation that the numerator are all the same, so we can compare the fractions easily.

When the numerator are the same, the greater the denominator, the smaller the fraction.

The greater the denominator, the smaller the parts.

So Sofia says "4/5 is the greatest fraction." So outta those four fractions, they've all got the numerator four, the smallest denominator is five, so 4/5 must be the greatest traction.

There's the whole divided into five equal parts and four of them are shaded, that represents 4/5.

Izzy has run 4/5 of the race, so she must be in the lead.

So this is where Izzy is placed in the race.

Who's in second place? "4/7 is the next greatest fraction." Said Sofia.

Here's the whole race divided into seven equal parts.

Four of them have been shaded.

You can see that one of those marks, it's exactly where 4/7 should be.

Andeep has run 4/7 of the race, so he's in second place, so Andeep must be here.

Work out who is in third and fourth place.

So Alex has run 4/9 of the race, Laura has run 4/15 of the race.

Can you work out where Alex and Laura are in that race? Pause the video and see if you can work out where those final 2 runners are.

And welcome back.

Did you manage to find out where Alex and Laura both are in the race? Let's take a look and see if you've got them in the right places.

So 4/9 is greater than 4/15.

Alex must be in third place.

And you can see that representation of 4/9 been exactly where that mark is, so Alex must be here.

4/15 is the smallest fraction, so Laura is currently last.

And again, there's a representation there showing exactly where 4/15 would be.

That's where Laura is, so Laura is quite far behind.

I wonder if she could still win.

I don't know.

I'm not so sure.

So very well done if you managed to work out where Alex and Laura were in that race.

And let's move on to task B.

In part one of task B, you're going to order each set of fractions starting with the smallest list.

So for A, you've got the fractions, 6/10, 6/7, 6/13.

They have all got the same numerator, which of those is the smallest fraction 'cause that's the fraction you're gonna start with.

And remember, as the denominator gets larger, the parts get smaller.

And here's part 2 of task B.

Six children are taking part in an obstacle race.

Alex has run 7/9 of the race, Laura has run 7/13 of the race, Andeep has run 7/15 of the race, Izzy has run 7/20 of the race, Jacob has run 7/11 of the race and Sofia has run 7/8 of the race.

Can you work out the positions of each runner? So you've gotta look to see which fractions are larger or smaller and see what position those children would be in the race.

And you've go where the start and finish line with those six runners somewhere on that number line.

So you might have noticed that all the fractions have the same numerator, but all the denominators are different.

Can you order those fractions? So good luck.

Pause the video and have a go at task B.

And welcome back.

Did you manage to have a go at both parts of task B? Did you get onto the race as well? Very well done if you did.

I wonder if you got the runs in the right order.

Let's take a look and see whether you did get it right.

Here are the answers for part one of task B.

So you had to order each set a fraction started with the smallest.

So the smallest fraction in question A was 6/13.

6/13 is less than 6/10 which is less than 6/7.

And then B, there were four fractions you had to put into order.

So 5/11 is small less than 5/9, which is less than 5/8, which is less than 5/6.

So very well, if you managed to order those fractions correctly.

And let's move on to part 2.

Here are the answers.

So Jacob says "Izzy was in last place." Izzy who is in that first place in that running race, she's in last place in the obstacle race.

7/20 is the smallest fraction because it has the greatest denominator, so Izzy puts in last place in the race.

Sofia says, very proudly, "I was in the lead.

I had run 7/8 of the race which is the greatest fraction.

So Sofia was in that lead and you can see there the positions of the other runners.

So Sofia was in the lead, Alex was second, Jacob is third, Laura was fourth, Andeep with fifth, and poor Izzy was in last place currently.

But of course, she might still be able to win, but I dunno if she could beat Sofia.

Sofia's nearly finished the race, hasn't she? She's only got 1/8 still to run.

So very well done if you managed to get onto part 2 and managed to put those six runners in order.

An excellent work today.

And hopefully you are feeling much more confident about comparing an ordering numbers where the numerator is the same.

And looking very carefully at denominator and working out which fraction is less or greater than the other.

Excellent work today.

Very well done.

And finally, let's move on to our lesson summary.

To compare fractions with the same numerator, the whole must be the same.

When the numerators are the same, the greater the denominator, the smaller the fraction.

When the numerators are the same, the smaller the denominator, the greater or larger the fraction.