Lesson video

Hello.

I'm Mr. Langton.

And today we're going to look at Distributivity and Fractions.

All you're 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.

When you're ready, we'll begin.

We'll start with the try this activity.

Look at the patterns of subtractions below.

What do you notice about the answers to the subtractions? What do you think comes next? And could you explain what you notice using a diagram? Pause the video and have a go.

When you're ready, unpause it and we'll go through it together.

You can pause in three, two, one.

Okay, how did you get on? Let's fill in some answers now.

Starts off with a 1/4, take away a 1/5, 1/4, take away 1/5.

They're both going to be written out of 20 aren't they? That's going to be 5/20 takeaway for 4/20.

So that is 1/20.

Now, if our common denominator's going to be 20, we might as well do that bottom one as well.

That's going to be 16/20, take takeaway 15/20.

And that's where we start to notice, goodness me our answers are the same.

Let's look at the next one.

I won't do the working out, but I'm sure you've already figured out that that's 1/30 and that's 1/30.

Got a little bit of a pattern going on here.

This is getting interesting, isn't it? Right.

1/6 take away 1/7 is 1/42.

And believe it or not 6/7 take away 5/6 is also 1/42.

So what's going to come next? Well, we can be pretty confident that our numerator is going to be one, in each case.

Our denominator, four times five is 20, five times six is 30, six times seven is 42.

So we're going to do seven times eight, which is 56.

That's what's going to come next.

Did you manage to draw a diagram? Because that diagram is what really makes this click and what makes you notice what's going on.

We'll have a look at that on the next slide.

So, we've got our answers and I've drawn some diagrams to represent what it is that we're looking at.

So this one over here, is 1/4 take away 1/5.

So we can see we've got our 1/4 and our 1/5.

We're looking for the difference between a 1/4 and 1/5.

If I just draw a line, continue going down there, this little bit here, that I'm going to colour in purple.

I do enjoy my colouring in.

But this little bit here, represents the difference between 1/4 and 1/5.

That little gap there is 1/20.

Now it also represents the difference between 4/5 and 3/4.

I'll just pick a different colour, let's go with orange.

We know we've got our 3/4 here, don't we? And this is our 4/5.

So this little extra bit here again, represents the difference between the two.

And that's why they're equal.

You can see that on the next one as well.

The difference between 1/5 and 1/6, and it's a really small gap.

I would've to look really closely now.

It's getting smaller.

And that the difference between the two.

And here we've got 1/30 of that figure, that's the tiniest sliver there.

That is, again the difference between them.

Okay, now it's going to get interesting.

We're going to take some really, really difficult problems and we're actually going to make them really, really simple.

All four of these questions, probably look a little bit scary at first.

We're going to look at how we can make them easier.

The first one, I know it's not a fractions question, but it should be a nice introduction for you.

Seven multiplied by 124.

5, add three multiplied by 124.

5.

And I know that your first instinct is going to be, oh my goodness, I'm going to have to do some multiplication here.

I'm going to have to write out 124.

5 and I'm going to have to multiply it by seven, dah, dah, dah, dah, dah, dah.

This is got to take me quite a while.

And I've got to do it again.

I was going to say, nah, nah, don't bother.

Let's get rid of that, he took for an easier way.

I've got seven lots of 124.

5, so seven lots, of 124.

5.

And I'm going to add on, three more lots of the same thing.

So altogether, I've got 10 lots of that, haven't I? 10 lots of 124.

5.

And that's a sum that I can do it in my head.

And I'll bet that you can do it in your head as well.

1,245.

That's much easier isn't it? Let's have a look at the second one.

2/3 multiplied by seven, plus 1/3 multiplied by seven.

If I'd have worded that slightly differently, what if I said that I had 2/3 of seven, and I'm going to add on 1/3 of seven? I'm going to get 3/3 of seven, aren't I? If I've got 2/3 of something and I have another 1/3, I've got 3/3 of it.

3/3 is a whole.

So a whole of seven, is seven.

Easy as pie.

Right, third one.

We're going to look at that same sort of technique again, 3/5 multiplied by 19, take away four multiplied by 3/5.

So, if I've got 19, lots of 3/5 and I take away, four lots of 3/5? I've got 19 lots of something and I take away four lots of something I'm left with 15 lots of that something.

Now we know how to find 15 lots of 3/5 don't we? So it's going to be 3/5 of 15 is going to be nine.

And again, 15 multiply by 3/5, or 3/5 of 15 is much easier than this horrible question we're given here.

Now for the last one.

3/4 multiplied by eight, take away eight multiplied by 3/5.

So what we could see here, is that we've got eight lots of each thing, haven't we? We've got eight lots of 3/4, and we're taking away lots of 3/5.

So if we can do 3/4 take away 3/5, we can then multiply that by eight and get our answer.

So in this case we're going to need a common denominator of 20.

That's going to give me 15/20 take away 12/20, which is 3/20.

So I'm actually doing eight multiplied by 3/20.

Which is going to be 24/20.

which is also going to cancel down to 6/5.

That last one is a really tricky one to spot.

Now we've got two similar problems here.

I just want to try and represent them with a diagram, just to try and make it look a bit easy for you to see what's going on.

2/3 of seven plus 1/3 of seven.

So if this whole block here represents seven, 2/3 of seven, is going to be here.

Let's shade these in so you can see.

So if two purple sections represent 2/3 of seven.

Pick a different colour, now 1/3 of seven would be there, wouldn't it? So hopefully, that helps you see that 2/3 of seven and 1/3 of seven is the same as three lots of seven, so 3/3 of seven, or just seven.

Over on the right-hand side, eight lots of 13/12.

Well, if this blue block represents eight, then the whole one here, is 12/12.

We need an extra 12th on there.

That being there is 1/12, because 13/12 is equal to a whole one add 1/12.

So what we've actually got, if we're doing eight multiplied by 13/12, we're doing eight lots of a whole one, and we're adding on, eight lots of 1/12.

So that's eight, plus 8/12.

And I know 8/12 is 2/3.

So my final answer, is eight and 2/3.

So now it's your turn.

Question 1 is just a recap of adding fractions.

There's nothing too tricky there.

It's just to get your brain back in gear.

Question 2 is a matching set.

You've got to find the pairs that go together and that's when you're going to start to use the skills that we looked up today.

And Question 3, you're going to use those skills to answer a couple of questions.

Good luck.

How did you get done? I've put the answers for the first question up on the screen now.

I'm going to go through question two and question three with you.

So starting off with question two.

We need find a card that's going to match up to this here.

1/2 times five subtract five times 3/4.

So we've got, our common value is five.

So we've actually got five lots of 1/2 takeaway 3/4.

That's going to be this one here.

Let's use a different colour.

Let's go, let's go down this one here.

Five lots of 1/2 takeaway 1/4 times five.

So that's, I'm just going to write over on this right-hand side here.

It's similar to five lots of 1/4, sorry, five lots of 1/2, take away, five lots of 1/4.

Which means that we're going to end up with, five lots of 1/4, aren't we? If we take, if we got a 1/2 takeaway a 1/4 is a 1/2, so we're going to end up with five lots of a 1/4.

Which is here.

Let's go some card again, let's hope I've read this time.

And let's look at, let's look at this one here.

So this is, a 1/2 times five plus a 1/4, a little bit sneaky, but a 1/2 multiplied by five, it's the same as five halves, isn't it? And that's going to be, then we've just got to add on that 1/4 there, so it's going to be, this one here.

Finally, let's go for a sum block.

We can hopefully see these two are going to match up, they better do, don't they? A 1/2 of five add a 1/4 of five, that would be 3/4 of five.

That's great.

I can be happy with that.

Well done.

Now, moving on to the last question, 2/3 multiply by seven plus a 1/5 multiplied by seven.

So, I've got, we're working in seven, aren't we? So I've got seven lots of 2/3 plus 1/5.

2/3 plus a 1/5.

I'm going to need to do some working out there, but it's going to be 10/15, add 3/15.

Which is going to be seven lots of 13/15.

And on the right hand side I've got 2/7 multiplied by three, take away three multiplied by a 1/4.

So that's, my common factor is three.

And it's going to be 2/7 takeaway a 1/4.

So a common denominator in this case it's going to be 28.

So I've got three multiplied by, and over 28, we're looking at eight takeaway, this is 1/28 the answer.

Three multiplied by 1/28.

Okay, did you get that? We'll finish with the explore activity.

How many equivalent calculations can you write for six multiplied by 11/3.

I've got a couple of answers on the screen already.

They're 1/2 answers, I've not finished them but I've started them.

They might give you a little bit of guidance to help you out.

See how many you can come up with.

Pause the video and have a go.

And when you're ready unpause it and we can go through it together.

Pause in three, two, one.

I'll give you a few answers that I came up with.

I'm sure you have some more as well.

We start with this 1/2 answer that I gave you here at the top, three multiplied by 11/3.

Now the question is six lots of 11/3.

So I'm going to need three more, 11/3 actually.

And down at the bottom, if I've got six lots of three, 11/3 is equivalent to three and 2/3, isn't it? So I've got six lots of three, I'm also going to need six lots of 2/3.

Some other ideas that you could have come up with.

You could have got 6/3 of 11, instead of doing 11 divided by 3, you could have six divided by three.

Six divided by three is two, isn't it? So we could have two lots of 11.

And looking at it that way you can actually see that the answer is 22 apparently.

That's, an answer for the calculation as well.

You might come up with some more yourself.

If you have, it would be really great if you shared them with us.

So if you've got any answers from this or any other activity that you've done with us that you'd like to share, ask your parent or carer if they'll put you on Twitter tagging @OakNational and #LearnwithOak.

I'll see you later.

Goodbye.