# Lesson video

In progress...

Welcome to lesson five of our fractions unit, where we'll be comparing fractions greater than one.

First of all, make sure that you have everything you'll need for this lesson, a pencil and a piece of paper, or an exercise book.

Improper fractions.

This is an improper fraction.

Its numerator is greater than its denominator, which means that its value is greater than one whole.

We can represent this fraction pictorially.

We'll need shapes that are divided into five equal parts.

Here's my first shape.

I need to shade in total eight parts.

One, two, three, four, five.

There aren't enough parts.

So I'll need another shape.

Six, seven, eight.

I shaded, in my first shape, five out of five parts.

That is equal to one whole.

In the second shape, I've shaded three up to five parts.

5/5 plus 3/5 is equal to 8/5.

We'll be looking more at calculating with fractions later on in the unit.

Now 10/6 is another improper fraction.

For this one I will need shape that are divided into six equal parts, and I will be shading 10 parts.

Here's my first shape.

One, two, three, four, five, six.

I need another shape to finish it off.

Eight, nine, 10.

On my first shape, I shaded six out of six parts, which is equal to one.

On my second shape, I shaded four out of six parts.

6/6 plus 4/6 are equal to 10/6.

Pause the video while you draw a pictorial representation of the improper fraction below.

You should have drawn to bar models, divided into four equal parts, and shaded one, two, three, four, five, six, seven.

You will notice that your fast bar was entirely shaded four out of four parts, which is equal to one whole.

And your second bar, three out of four parts, fours quarters plus three quarters is equal to seven quarters.

Now let's have a look at converting improper fractions into mixed numbers.

The fraction 8/6 is equivalent to one and 2/6.

So I have shaded in six out of six bars.

I needed another model to shade further two out of six, together is 8/6.

Remember that 6/6 is equal to one whole.

So one whole bar and 2/6 of the second bar.

Therefore 8/6 can be converted to one and 2/6.

You may be looking at this 2/6 and thinking that, from previous lessons, that that is not in its simplest form.

2/6 is equivalent to one third.

Therefore 8/6 is equivalent to one and 1/3 in its simplest form Let's have a look at 17/5.

I've already drawn my bar models.

I can see that 17/5 is made up of one, two, three groups of 5/5, which are equivalent to one whole, and that there are 2/5 leftover.

So there are one, two, three whole groups, and 2/5 left.

17/5 is equal to three wholes and 2/5.

Three and 2/5.

So I think of it as how many groups of 5/5 are in 17/5.

How many fives go into 17, or how many times does five go into 17? That's three times with two leftover, three and 2/5.

Pause the video while you represent the improper fraction pictorially, and then convert it to a mixed number.

So you will have drawn four bars divided into three equal parts in order to shade 11/3.

One, two, three four, five, six, seven, eight, nine, 10, 11.

Here we have three out of the three parts shaded, which is one whole.

Here we have three after the three, which is a whole.

Here we have three to three again.

And finally, we have two out of three.

So we can see the 11/3 is equivalent to one, two, three wholes, and 2/3.

How many times does three go into 11? That's three times, three times three is nine, with two leftover, 2/3 leftover.

Now we're going back to improper fractions, and we'll look at how we kind of compare them.

There are two strategies for comparing improper fractions.

As we know yesterday, comparing fractions is tricky when the denominators are not the same.

So the first option is to convert improper fractions to mixed numbers.

So option one would be making them from improper to mixed numbers, and see if that helps us to understand which is greater.

So how many groups of 12/12 are there in 13/12? Well, there is one group with one remaining, so that is equivalent to one and 1/12.

There is also one group of 4/4 in 6/4 with two remaining.

So that's one and 2/4.

If I think back to my equivalent fractions, I know that 2/4 is equivalent to 1/2.

So this is one and 1/2.

I also know now that they're both equivalent to one whole.

I've written 1/12, that was meant to say 1/2, one and 1/2.

So these are equivalent to one whole, and then 1/12 and 1/2.

So I have to think, which is greater, 1/12 or 1/2? Well, I can draw a bar model to support this.

It would mean expecting it down into 12 equals parts.

And then I can see 1/12 plus 1/2, 1/2 is greater.

So it looks like 6/4 is greater than 13/12.

Let's check it with our second strategy, which is to keep them improper, but we want then to convert them so that they have the same denominator.

Excuse my handwriting on here.

Okay, now, looking at these denominators, I can see that the common multiple of 12 and four is 12.

Therefore only the second fraction needs to be converted.

So 13/12 can stay the same.

I'll multiply 6/4 by three, and it will become 18/12.

Remember, that what he did to the numerator, you do the same to the denominator.

And this clears it up.

18/12 is greater than 13/12.

Pause the video and use your preferred strategy to find the smaller fraction.

So strategy one is to convert them to mixed numbers, and then compare.

Strategy two is to keep them as improper fractions, but convert them so they have the same denominators.

Pause the video now.

Have a go So using strategy one, you would have converted 7/3 into two and 1/3, because there are two lots of 3/3 in 7/3 with one remaining.

You would've converted 5/4 into one and 1/4.

You can quite clearly see that the whole number here is two, the whole number here is one, therefore this is greater than this.

Let me double check with strategy two.

I'm going to keep them as improper fractions, but convert them so that they are equivalent fractions with the same denominators.

The common multiple between three and four is 12.

7/3 becomes 28/12, and 5/4 becomes 15/12.

28/12 is greater than 15/12.

Now let's move on to comparing mixed numbers.

As we saw in the previous example, if the mix numbers have a different whole number, then it's really obvious which one is greater.

I can see that this is made of three whole parts and 2/5, but this has made a five whole parts and 7/8.

Therefore this one must be greater.

So that is nice and straightforward.

Sometimes though we compare numbers, where the whole number is the same.

So we've got some work to do.

We need to convert the fraction so that they have the same denominators, and then they can be compared.

So we can, at the moment, ignore the whole number, and just work on the fractions.

The common multiple of five and four is 20.

So we're going to multiply this by four.

Five times four is 20.

Do the same to the numerator.

Two times four is eight.

So we can bring the whole number back into it.

This is three and 8/20.

Let's do the same for the 3/4, took that up to 20ths.

We multiply by five.

Four times five is 20.

Do the same to the three.

Three times five is 15.

Don't forget to bring back in our whole number.

Now we're comparing three and 8/20 or 3 and 15/20.

And we can clearly see that 15/20 is greater than 8/20, therefore 3 8/20 is less than three and 15/20.

You could also use a second strategy, where you convert the mixed numbers into improper fractions, and then you convert the denominators, so that they are same, and then compare that way.

So let's just do one of these.

Three and 2/5.

We have to think about how many lots of 5/5 are there in three.

That's 15, and then two more.

So that is equal to 17/5.

So the maths behind it is thinking how many groups of 5/5, how many wholes are there three? That's 15.

Three times five is 15, and add the two, is 17/5.

Then the other one is three and 3/4.

How many lots of 4/4 are there in three? Well, there are 12.

Add to the three, is 15/5.

15/4.

My mistake.

You have to be very careful when you're transferring denominators.

Then you would convert these into fractions over the same denominator, and then compare.

Let's do another one together.

So again, we've got the same whole number.

So we just need to look at the fraction.

We need to convert the fraction, so that it's an equivalent fraction with the same denominator.

The common denominator is 12.

So we're converting this by multiplying by four.

Three times four is 12, two times four is eight.

Bring the whole number back down.

Then we convert it into 12ths.

Four times three is 12.

Three times three is nine.

Bring it back the whole number.

Two and 8/12 can now be compared with two and 2/9.

And 8/12 is less than 9/12.

Two and 8/12 is less than two and 9/12.

Now that you're done, pause the video, and find which is the greatest mixed number.

So you will have noticed that the common denominator for two and a seven is 14, And we do two multiplied by seven, and then one multiplied by seven, 7/14, bring back the whole number, four and 7/14.

Four 3/7 we multiply by two.

Three times two is six.

Bring back the whole number.

And we can see clearly that four and 7/14 is greater than four and 6/14.

Now it's time for some independent learning.

Pause the video and complete the independent task.

Come back here when you've finished, so that we can go through the answers together.

For question one, you were asked to draw a pictorial representations of the improper fractions.

For 19/5, you will have drawn four bars divided into five equal parts, and you will have shaded 19 of those parts.

So that's 5/5.

One whole.

There's another 5/5, and we're on 10.

That's another 5/5, so we're on 15.

16, 17, 18, 19.

That's 4/5.

So how many lots of 5/5 are there? There are three lots of fifths with four remaining.

You weren't asked to do this but you may have converted it to a mixed number.

Three and 4/5.

For 12/6, you will have drawn two bar models, split into six parts.

And you were shading 12 parts.

One, two, three, four, five, six.

That's one whole Sorry, seven, eight, nine, 10, 11.

That's also one whole.

Therefore 12/6 is equal to two wholes, because there are two lots of 6/6 in 12/6.

For question two, you were asked to convert the improper fractions to mixed numbers.

So you need to ask yourself how many groups of 3/3 are there in 10/3.

Well, there are three groups with 1/3 remaining.

In this one, there are also three groups with 1/2 remaining.

Then we have one group with 2/5 remaining.

How many groups of 10/10 are there in 38/10? There are three and 8/10.

You may have simplified 8/10, because you would have read 10 plus four.

Two is a factor of both eight and 10, so it could be simplified to three and 4/5.

And finally, 20/12 is equivalent to one and 8/12.

Again, that could be simplified, because four is a factor both of these numbers.

So that's one and 2/3.

Now it's the reverse, converting the mixed numbers into improper fractions.

Okay? So we're thinking, how many groups of 10, how many 10/10 are there in three wholes.

Well, it's 30, plus the four is 34/10.

This one, it's 10/3.

There is a way of looking at it, where you multiply the denominator by the whole number.

And then you add the numerator.

Then we have 29/8.

Then we have 10/4.

And finally, 23/6.

Question three, you have to put these fractions in order from smallest to largest.

And you were given hint, convert them all to improper fractions.

So two and 1/3 is equivalent to 7/3.

This is an improper fraction, as is this.

This one will be converted to 25/6.

So now I need to have them all with the same denominator because I can't compare them.

Looking at three, four, 12, six, and three, the common denominator is 12.

So I convert them all to equivalent fractions with a denominator of 12, 28/12, 39/12, 36/12, 50/12, and 112/12.

Smallest to largest, always go back to the question.

So the smallest of these is this one, 28/12, followed by this 36/12, then this one, 39/12, then 50/12, and finally, 112/12.

Question.

This one required a bit more thought.

So you had to fill in the two missing numerators to the incomplete fractions.

The way I looked at this was to think about what is the common denominator between all of these fractions, because this will make it easier for me.

So I saw that the common denominator was 20.

I changed this fraction into a fraction over 20, which is four and 2/20.

And this one would be three and something 20ths.

This half as a fraction is 10/20, and 3/4 as a fraction is 15/20.

So I start this way.

Then if I go the other way, I'm subtracting 10/20.

So four and 2/20, I'm subtracting 10.

Well, if I subtract 2/20, that gets me to four, and then I have a further 8/20 to subtract.

And that gets me to 12/20, three and 12/20.

But we were asked for our answer in fifths, so I need to convert 12/20 to fifths.