Lesson video

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Hello, I'm Mr. Langton, and today we're going to look at dividing a fraction by an integer, which is a whole number.

What are you going to need is something to write with and something to write on.

Try and make sure you're in a quiet space with no distractions, and when you're ready, we'll begin.

We'll start with the try this activity.

Which of these statements describe the same calculation? Can you put them into groups? Pause the video and have a go.

When you're ready, un-pause it and we'll go through the answers together.

Pause in three, two, one.

Okay, let's take a look.

So I've sorted them into two groups.

Some of the answers are quite so obvious.

12 divided by three is four.

How many threes make up 12? Four.

This one at the top right is a little bit trickier.

12 is three of what? And again, four.

The other the three little bit trickier, Three divided by 12 can be written fraction of 3/12, which is a quarter.

Three of 12 is a quarter.

And how much of 12 makes up three, well a quarter of 12 makes up three.

Okay, so we're going to to look at 6/7 divided by two, and there are two different methods that we can use for this.

So I want to label them method one and method two.

First, you can see from this diagram here, I've got 6/7.

If I'm going to divide it by two, I can split the 6/7 about like that, and I'm going to need that part there, which is 3/7.

I split my 6/7 into two, and I've got 3/7.

The second method, going to look at splitting up the other way.

I split it this way.

I've divided the whole shape into two equal pieces.

If I just shared the top half, then here, I've got 6/14.

So 6/7 divided by two equals 3/7, and it equals 6/14.

Both of these answers are equivalent.

So when I'm dividing by two, I've got two different methods I can use.

And now that I have half as many parts that I had before, now I can make each part half of the size that it was before.

Depending on which question I've got, depends on which method I might like to use.

In this case with 3/7 divided by two, I can make each part half the size.

In which case I've got 3/14.

Alternatively, I can do a different way.

I could take my three parts and say, I'm going to halve those three parts.

In which case now, I've got one and 1/2 parts, out of seven.

Both of these answers are correct.

But one of them looks a little bit better than the other, didn't it? I think we'd all agree.

We'd rather write that fraction than that one.

It's not, there's nothing wrong with having a decimal inside your fraction.

But it's just, it's not something that we do all the time.

It's a little bit icky.

You can tell it's making me a little bit nervous, even just talking about it, to be honest.

It's not wrong, we'd just rather not do it if we don't have to.

So we're going to pick which method we're going to use for each one.

And this time I'm going to look at some different numbers.

So 6/7 divided by three.

When I look at the numerator, we can do, I divide by three.

So we've got a third, as many parts as we have before.

Or alternatively, we can look at the seven parts it's been broken into and break each of those into three, which would give us 21 parts all together, wouldn't it? So either of those answers is correct.

And in this case, it doesn't really matter which way we do it.

Both of those give us nice, good, comfortable answers.

This one is in its simplest form, 4/7 divided by two.

So we could look at the numerator, mix it around, okay.

We'll split it into two equal parts, which is going to give me 2/7, or we could look at the denominator and say, what's currently being broken into seven pieces.

We halve the size of each piece, which were 14 pieces, okay.

Both answers are correct.

This one here is in its simplest form.

If you look at the last one, we can take our numerator and split it into three equal pieces, which is going to be 1.

3 recurring or 4/3.

Now to seven, I'm going to write now above there four out of three, out of seven.

And that is getting really messy now.

As uncomfortable as I am putting a decimal inside my fraction, it's correct, don't forget that it's correct.

I don't really like putting a fraction inside a fraction Again, it's correct.

There's nothing wrong with it.

It's just going to be rather difficult to manipulate and to work within, and I like to try and avoid it.

So a better idea would be to look at our denominator and say, well, let's make each piece three times as small, and that's going to give me 21 pieces, and I've got four of them.

Now it's your turn to have a go.

Pause the video and have a go at the task.

When you're finished, un-pause it, and we'll go through it together.

Good luck.

How did you get on? I'll put the answers on the screen for you now.

If you notice for question two, I put two different answers, because I think that both methods are equally valid.

For question three, I've done my very best to avoid having fractions inside fractions, or decimals inside fractions.

So for all the four answers I put the answer that I think is simplest.

Now for the final activity, what I'd like you to do is try and find a number that goes into each box to make those calculations correct.

The questions are quite tricky.

So take your time and have a go.

Pause the video, see how much you can do.

When you're finished, un-pause it.

We'll go through it together.

You can pause in three, two, one.

So let's have a look at the answers.

The first two were all right.

But those last two were really nasty.

Looking at the first one, we're to work out what the denominator is going to be.

Now looking at the numerator, I can see, looking at my question, asks that six divided by three is two, So that must be 6/25.

Look at the second one.

This time the numerators have stayed the same, which means that actually I'm going to be splitting my denominator, my nine parts into quarters.

Which is going to give me 36 of them altogether.

Then we go onto the freaky ones.

And our denominators are different, I don't know what my numerator is.

Now if I'm splitting something into 10 equal pieces, I get 1/16.

Then originally I've only got 10 of them.

I've only got 10/16.

So that fraction is going to be equivalent to that, we'll simplify down to 5/8.

Now 5/8 divided by 10, yep that works.

That was quite a tricky one.

Let's look at the last one.

8/15 divided by something equals 4/45.

Now, two different ways we could look at that.

I'm going to look at my denominators, and say that I know that 15 goes into 45.

I can rewrite this fraction out of 45, in which case that's going to be multiplied by three that's 24 over 45.

What do I divide 24 by to get to four? That'd be six.

So that's it for this video, you can mark your work.

And when you're done, you can have a look at the quiz online.

Thank you, I'll see you later.