Lesson video

Hi, everyone.

Welcome to today's Math lesson with me, Ms. Jones.

Let's find out what we're doing today.

In this lesson, we're going to be comparing fractions.

Going to start off by comparing fractions with the same denominator.

For example, one quarter and two quarters.

Then we're going to be comparing fractions with different denominators, e.

g.

one quarter and one eighth.

Then you've got a true or false task.

And the quiz to finish off.

You'll need today a pencil and piece of paper or a pen and piece of paper.

And if you've got one, it might be a good idea to use a ruler, as we're using number lines today.

Pause the video and go and get what you need.

If you've got everything, let's get started.

Before we start our main learning today, here's a fun starter.

What fractions can you identify in the flags? Now a quick tip.

Remember, in order for our fractions to be correct, the whole needs to be divided into equal parts.

Okay, pause the video now to have a quick explore.

What fractions did you find? Well, I'm going to start with Mauritius here, as that one I can see has clearly been divided into four equal parts or quarters.

I could say one quarter is red, one quarter is blue, one quarter is yellow, and one quarter is green.

Some of these are less straightforward though.

We can see Cameroon here has been divided into three equal parts.

But this part in red has actually got a star in it.

So I could say, one third of this flag is green.

But I couldn't say one third is red, because actually, we can see that less than a third's red because part of that third is actually yellow.

So there are some tricky things here.

For Egypt, I could say one third is red.

But I couldn't say one third is white.

'Cause some of that white part has an image on it.

Interesting.

What other fractions did you find? Okay, so let's start comparing fractions.

Now when we're comparing, we're going to be thinking about which is greater, and how we know.

So look at these two fractions.

Which one do you think is greatest? How would we be able to prove our answer? Hmm, pause the video now, to have an explore.

What did you think? Well, I've used a representation to help me.

I can see that three eighths here is represented by my bar.

And this bar represents seven eighths.

I can clearly see this seven eighths is greater than three eighths.

Now, looking at our fractions, I can see that seven eighths has a bigger numerator than three eighths.

When the denominators are the same, so we've got the same amount of parts, the fraction with the greatest numerator, is the greatest.

So I want you to think about, is this always true? If the denominator is the same, the fraction with the greater numerator will have the greatest value.

See if you can think of any other examples.

Did you have a think about it? Yes, it is always true.

For example, if we had three quarters, and, two quarters our denominators are the same.

So this would look like, I'm going to use circles here.

Imagine my circles are exactly the same size, divided into quarters, equal parts.

Clearly see that two quarters is not as big as three quarters.

Three quarters is greater than two quarters.

So, when our denominators are the same, we need to look at our numerator.

The greatest numerator is the greater fraction.

Okay, let's look at two different fractions with different denominators.

How could we compare the size of these fractions? Which fraction is greater? How do you know? And what can we say about fractions with the same numerator? Convince me! Use a representation to prove you're right.

Okay, so I have used some representations here.

We've got three quarters I've tried representing of a circle, and three fifths.

We can see that, three quarters is taking up more of a portion of this circle than three fifths.

Let's look at the bars.

It might be a little bit more clearer here.

We can see three quarters is taking up more than three fifths.

Three quarters here, with this rectangle, is greater than three fifths.

So when our numerators are the same, we need to look at our denominator.

The denominator with the greater value, fifths, is actually the smaller fraction.

This is because, if you think about it here, it's, let's look at this one.

It's split into more parts.

So three out of five parts.

It's not as much as three out of four parts.

These parts will be smaller than these parts.

When the numerators are the same, the fraction with the lower denominator is greater.

Okay, so, how could we compare the size of these fractions which is greater, and how do you know? This time, we've got two different fractions with different denominators, and different numerators.

This person says the numerator is greater.

So the fraction must be greater.

So they think four ninths is greater.

Do you agree? Hmm, what could we think about to help us? Well, something that I'd like you guys to think about this time is, is the fraction greater or less than a half? That's a really good starting point to think of.

Now we know when we look at a half, the numerator is half of the denominator.

In this fraction, the numerator is more than half of three.

In this fraction, the numerator is less than half of nine.

So that's giving us, a little bit of an indication.

Also, we're going to think about equivalent fractions to help us.

If two thirds was written as a fraction with a denominator of nine, what would that look like? Okay, have a little think and see if you can work out which one is greater.

Okay, I've got a representation here.

We've got two thirds.

I've got a number line and a fraction bar here.

Two thirds, we can see, is actually equivalent to six ninths.

I know that because if I look at the relationship between my numerators and denominators, two has been multiplied by three.

Three has been multiplied by three.

Now, if these are equivalent, two thirds must be greater than four ninths.

And you can see that on our representation here using our number line.

Did you pick any other representations to compare these fractions? You might've picked a representation that shows the equivalents between two thirds and six ninths.

Here, we've got two representations, both split into nine parts.

Now I know that two-thirds is the same as six ninths.

So this is representing two thirds as six ninths here.

And I can clearly see that this time six ninths is greater than four ninths.

When our denominators are the same, it makes it far easier to compare them because we know fractions with the same denominators are comparable by looking at the numerator and just selecting the one with the greatest numerator.

So therefore, what you could do is convert your fraction into an equivalent with the same denominator and then compare them.

So let's look at this pair of fractions and do just that.

Which fraction is greater? How do you know? So here I've got four fifths and seven tenths.

My numerators are different, and my denominators are different.

But what could I do to four fifths, in order to make this easier to compare to seven tenths? Hmm, well, I could find an equivalent fraction.

I know that 10 is a multiple of five.

So it should be easy enough to convert this into a fraction of a denominator of 10.

Five multiplied by two gets me to 10.

Four multiplied by two gets me to eight.

Eight tenths is equivalent to four fifths.

Now, if we know that four-fifths is the same as eight tenths, we can say that four fifths is greater than seven tenths.

Now you could prove this by using representations such as those rectangles divided into parts.

Let's look at another example.

Which fraction is greater, and how do you know? Something I want you to think about with this one in particular, and in many other problems. We've already talked about which one is greater than one half.

But how far from one whole are these fractions? That's a useful thing to think about.

Is 11 twelfths closer to one whole than five sixths? Hmm, what we could also do here is think of our equivalent fractions to make sure we're right.

I know that's actually, 12 is a multiple of six.

I could convert this fraction into twelfths.

What would my numerator be here? Well, I can see that six has been multiplied by two to get to 12.

So I need to do the same with five.

10 twelfths is equivalent to five sixths.

Now if five sixths is equal to 10 twelfths, I know that it is less than 11 twelfths.

For today's task, I want you to look at each of these inequalities and tell me, is it true or false? You'll need to convince me.

So make sure you explain each answer and use a representation to prove you're right.

Okay, pause the video now to go and have a go at your task.

When you're done, come back and we'll go through the answers together.

Okay, hopefully you've had a chance to have a go at your true or false task.

Let's see how you got on.

So this first one.

Two thirds is less than one half.

Is that true or false? Now for this one, I'd think about what I know about two thirds.

Is that greater than a half or less than a half? I know that two is more than half of three, so that should help me.

This one is actually false.

Two thirds is actually greater than.

So this is the wrong symbol.

Okay, let's look at the next one.

Two quarters is less than five eighths.

Is that true, or is that false? That's true.

Two quarters, which I know is equivalent to a half, is less than five eighths, which I know is more than a half.

Seven ninths and two-thirds.

This one is true.

Seven ninths is greater than two thirds.

If you think about it, two thirds would be equivalent to six ninths.

So seven ninths has to be greater.

Next one, fourth fifths and seven tenths.

Four fifths is greater than seven tenths, that's true.

If we think about it, four fifths would be equal to eight tenths.

So it has to be greater.

Next one, one third is less than three sixths.

That's true.

One third would actually be equivalent to two sixths.

So it's less than three sixths.

And finally, five sixths is greater than 11 twelfths.

That's false.

Five sixths would actually be equivalent to 10 twelfths which is less than 11 twelfths.

How did you get on? That's the end of the lesson.

So it's time to go and complete the quiz.

Thanks very much, bye-bye.