Lesson video

Hello, I'm Mr. Langton.

In this lesson, we're going to review multiplying and dividing fractions.

You're going to need something to write with and something to write on, and try and find a quiet spot where you won't be interrupted, and when you're ready, we'll begin.

We'll start with the Try This activity.

The diagrams show different lengths marked on the unit square, and the area of the bottom left rectangle is 0.

075 square units.

Work out the areas of the remaining shaded triangles.

And if you're confident, you can pause it and have a go straight away.

If you want a hit, just leave it going a little bit longer and I'll give you a little bit of a starting point.

So if you ready, pause in three, two, one.

Okay, let's go for a hint.

So if we're going to look for the area of this, we've got this area here, 0.

075 units, let's try and find this length.

We know that 1/4 times something is going to be equal to 0.

075.

I'm going to write that decimal as a fraction, because that would be 75/1000.

And at the moment, it's not very easy to see what the numerator and the denominator of this fraction must be.

But I know that a quarter is 25%, or 25/100.

And we're still trying to make 75/1000 but I can now see what fraction I'm going to need.

Can you see it? How I'm going to get from 25 to 75? I could multiply by three and from 100 to 1,000, I'll multiply by 10.

So this length here must be 3/10, or if you multiply to the decimal, 0.

3.

Okay, that's the first hint, now, pause it and carry on and let's see how many of those green areas you can work out.

Pause in three, two, one.

So what I'm going to do now is see if we can find the other two missing lengths.

This one here, and this one here.

Let's starts off with the one on the right hand side.

So we know the whole length from top to bottom is one, which means 4/10 plus 1/4 plus that third one is going to make a whole one.

Now the fact that there are different denominators I could work with, but actually I know that 4/10 is the same as 40%.

And I know that 1/4 is 25%.

What do I need to add to that to get 100%? So 40 and 25 is 60 that means that that'd be there it must be 35%.

Now 35% is equivalent to 0.

35 or 35/100.

Now actually we've got that as a decimal, and let's do the same there, 0.

35.

Now I can work out the area of this square.

I'm going to be doing 0.

35, multiply by 0.

35.

And 0.

35 is 35/100, and that's going to cancel down they both went to five, so it's going to be 7/20.

So I need to do 7/20 multiplied by 7/20.

That's going to give me 49/400.

Now this length in the bottom right, if these two here add up to 0.

65, then once again, this is going to be 0.

35.

So this time, let's do 0.

35 multiplied by 1/4.

We've said not 0.

35 is 7/20, so 7/20 multiplied by 1/4 is going to be 7/80.

And now I just need the green rectangle in the top left, which we know that one side is 4/10 and the other side is 0.

3, which is 3/10, which means that I've got 12/100.

And if I want to show off a little bit, I can cancel it out to 3/25.

How many of those did you get first time? Let's go through these four examples together.

For the first two, we need to calculate the area of the rectangles.

So the area of this first one will be 3/4 multiplied by 7/8.

Which is going to be 21/32.

And it won't simplify, now don't forget your units, let's put it on there, 21/32 metres squared.

Okay, now to the one on the right.

I'm going to multiply length by the width again.

So we're doing 1.

2 multiplied by 0.

6.

There're few different ways that we can do this.

But given that they're decimals, and they're only one decimal place, it doesn't hurt to turn them into fractions into tenths.

We've got 12/10 multiplied by 6/10, 12-sixes are 72/100.

And we can simplify that fraction, but if we're going to give our answer through the decimal, we're better off leaving it like that because we've got 72/100, 0.

72 metres squared.

Now for the next two, we need to calculate one of the missing lengths for each rectangle.

And that means that this time we need to do a division.

So for the first one, we're doing 2/3 divide by 8/9.

So what I like to do, I like get a common denominator.

The common denominator of three and nine would be nine.

So an equivalent fraction will be 6/9, which I'll divide by 8/9.

Which is going to give me 6/8 or 3/4.

So this length here is 3/4 of a metre.

And then finally, we've got 0.

063, we're going to have to divide by 0.

9, 0.

063 divided by 0.

9.

Now there's lots of ways that we can do this.

We'll start off, let's have a look at the numerator of these fractions.

So 0.

063 is 63/1000.

And 0.

9 is 9/10.

So a common denominator would be 1,000 63/1000 divide by 900/1000, that's going to give us 63/900.

Let's cancel that down, they both come into nine, which is going to give me 7/100.

And since we're working in decimals, that is 0.

07.

So this means the length here is 0.

07 centimetres.

So now we're going to move on to the independent task.

This is where you get to show what you can really do.

Pause the video, and have a go at the questions.

When you're finished, unpause it and we'll go through it together, good luck.

So how did you get on? I've simplified some of the fractions here so perhaps you might have slightly different answers to me.

Just double check them to see if you've made any mistakes.

This is the last activity.

The areas of the shaded rectangles in the unit square have been marked.

What could the marked lengths be? Can you find more than one set of lengths? It's a really difficult problem.

I'm not going to give you any answers, I'm going to leave it with you.

And the reason for that is if you can work this out, I want you to share this with us so that we can see just how good you really are.

Ask your parents or caregivers if you'll share your work on Twitter, tagging @OakNational and #LearnwithOak.

Good luck.