Lesson video

Hiya, my name's Ms. Lambe.

Really pleased that you've decided to join me today to do some maths.

Come on, let's get started.

Welcome to today's lesson.

The title of today's lesson is Ordering Fractions by Converting.

And this is within our unit, comparing and ordering fractions and decimals, including positives and negatives.

By the end of this lesson, you'll be able to compare and order fractions by converting them into decimals.

We're just going to be concentrating today on decimals.

Here are some keywords that we're going to be using throughout today's lesson, and these will be familiar to you, but it's always worth a recap, isn't it? So we're going to be looking at decimal form.

So a number is in decimal form when the decimal point is shown and there are digits to the right of the decimal point.

We're going to be using a lot of decimals today and we're also going to be looking at fractions.

So just a reminder that the numerator is the expression in a fraction that is written above the fraction line, and that's the dividend.

And the denominator is the expression in a fraction that is written below the fraction line, and that's our divisor.

Today's lesson, we are going to split into two separate learning cycles.

We're going to look firstly at reviewing our knowledge of converting fractions into decimals.

So we need to make sure that we've recapped that so that we can move our learning on.

And once we've done that, we'll look at the second learning cycle at ordering fractions by converting into decimals.

Let's get started on that first learning cycle.

Jun and Laura are converting 2/5 to a decimal.

We'll take a look at what they've done.

Here's Jun's method.

I'd like you to pause for a moment.

Have a look through Jun's method.

Do you understand his method and do you understand every step of what he's done? And here's Laura's method.

So again, just take a moment to have a look through Laura's method and see if you understand why she's done what she's done.

Jun says, "I needed to make the denominator 10, 100 or 1,000 to use the place value chart." Jun is really confident with using the place value chart and has decided that actually, he's going to use that as a way to convert this fraction into a decimal.

Laura says, "Why did you multiply by two over two?" Do you know why she didn't multiply by two over two? Well, from previous learning remember, we know that two over two is actually equivalent to one.

So if we've done 2/5 multiplied by one, the value is still 2/5.

What we've done is we've created an equivalent fraction with a different numerator and denominator, in this case, 10, so that Jun could use his place value chart.

And Jun knows that 4/10 is 0.

4 because after decimal point, the first column is a tenths column.

What method has Laura used to convert 2/5 into a decimal? Has remembered that two over five is this equivalent to two divided by five, fraction is another way of writing a division.

So she's decided to use the short division method.

Notice, both of them get the same answer because both methods are correct and relevant in this situation.

But Laura's decided that actually, she's going to try Jun's method next time.

17/20 to a decimal.

This is a question they're now considering.

What do we do here? I can't make the denominator 10 as that would give a decimal numerator.

So Laura's remembered that in the previous example, Jun made the denominator 10.

Laura's noticed if she does that, that will give her a decimal numerator, which she knows she can't have in a proper fraction.

Jun, however says, "Remember, I said that you can make the denominator either 10, 100 or 1,000." So it wasn't just 10 because remember that place value chart, the headings are tenths, hundreds, thousands, et cetera.

"Ah, yes," says Laura, "I can make the denominator 100 or 1,000." Jun says, "I recommend 100 but only because I think it's easier." So either would give you the right answer, but Jun's just looking at that efficient method.

Sometimes, we think of that as the easier method, but let's call it at most efficient from now on.

17 over 20, we're going to make the denominator 100.

20 multiplied by five makes 100, doesn't it? Remember, we cannot change the value of the 17 over 20, otherwise, we can't have those equals symbols there.

So the first part of our numerator is going to be 17.

We need to multiply that by five 'cause remember then, we're not changing the value of 17 over 20 because we're just multiplying it by five over five, which is equivalent to one.

17 multiplied by five is 85.

85 over 100 is 0.

85.

Maybe take a moment to just check back through that you understand each of those steps.

Super.

What about this one? Convert 3/8 to a decimal.

Jun's posed the question, "What denominator will we use here?" I think Jun thinks he's the teacher right now.

Eight is not a factor of 10 or 100, so it will have to be 1,000.

So Laura's very good on factors and she knows that 10 and 100 are not divisible by eight.

So therefore eight is not a factor of those.

She's going to use a factor.

She's going to use, sorry, the denominator of 1,000.

Same process then.

So we start with 3/8.

We want to make our denominator 1,000.

What do we pair with eight to make a 1,000? What's eight multiplied by 125? Remember, the three stays the same.

In order to make sure we don't change the value 3/8, we need to make sure we're multiplying by one, which is 125 over 125, which is 375 over 1,000, and then we can write that as a decimal.

And we've done that in previous lessons, so you'll be super good at that.

Now, let's have a look at this one.

Convert 5/16 to a decimal.

And remember, we are not using a calculator.

It's really important we can do these things without a calculator.

Jun says, "We can't make the denominator 10, 100 or 1,000.

So what do we do now?" Laura says, "Ah, now we need to use my original method." We're going to do five divided by 16.

Now, it's really common to get these two numbers the wrong way round, the dividend and the divisor.

So remember the dividend, the numerator goes underneath the bus stop, and 16, the divisor, is what we're dividing by.

It goes outside of the bus stop.

Now, I don't know about you, I'm not super good at my 16 times table, so I certainly don't want to be going through one multiplied by 16, two multiplied by 16 and so on.

So what I'm going to do, to save myself some time, is I'm going to list a few of the 16 times table.

But before I do that, I know that 16 doesn't divide into five.

So I end up with zero and I haven't used the five.

So now, 16s into 50.

Let's look down my list.

We can see it goes in three times.

We've got a remainder.

Ah, what do I do now? I've got a remainder, but I've got no digit to go with it.

Yep, that's right, you remembered, we add that zero, don't we? Now, I've got my remainder of two.

16s into 20, so let's look down the list.

We can see that it just goes in once.

I've got a remainder, so add that extra zero and then the four.

And then 16s into 40.

Oh my goodness, is this going to stop? 16s into 40 we can see is two, remainder eight.

Phew, I say, I say it is going to stop because 16 into 80 is five.

We've converted 15 over 16 into 0.

3125.

Now, I'd like you to have a look and decide which of these fractions would you need to use the short division method for, a, seven over 20, b, 17 over 32, c, four over five, or d, seven over eight.

Pause the video, and when you're ready, come back and we'll check your answer.

Brilliant.

Hopefully, you identified b because 20 is a factor of 100, five is a factor of any three of those that we are going to use.

And eight is a factor of 1,000.

32 is not a factor of 10, 100, 1,000, et cetera, so we would need to use that short division method.

It's always useful to be able to spot when to use which method.

We'll do this one together and then you can have a go at the one on the right-hand side.

Convert 17/25 into a decimal.

So I know that 25 is a factor of 100, so that's what I've decided.

I always go to the smallest denominator I possibly could.

25 multiplied by four is 100.

Remember, the numerator needs to stay 17 multiplied by four because the four over four is equivalent to one.

17 multiplied by four is 68, so this is 0.

68.

You are now ready to have a go at this one by yourself.

Off you go, pause the video, when you're ready, come back.

Well done.

Now, let's check that answer.

Hopefully, you decided to convert 20 into a new denominator of 100.

You may have done 1,000.

That's not a problem, you'll have ended up with the same answer.

You may just have a zero after the five.

So 20 multiplied by five is 100.

So therefore, in order to make sure we've multiplied by one, so as not to change the value, we need the numerator to also have a multiply five.

That's 45 over 100, which is 0.

45.

Well done if you've got that right.

If you didn't, maybe now's the time to just rewind the video and just go back the last few slides.

Let's take a look at this one now.

So hopefully, already, you've spotted that actually, we're going to need to use the short division method to do this one.

I think maybe it was the same fractions I gave you in the check for understanding.

Pretty certain it had a denominator of 32 anyway.

So seven divided by 32.

Remember, the divisor, the denominator goes outside.

Again, I'm not super good at my 32 times table, so I'm going to write them down.

There they are.

So the zero had already appeared.

So 32 into seven we know doesn't go.

Now, 32 into 70.

So look down my list.

We can see it goes twice.

Remember, we can add as many trailing zeros as we need to.

And then we've got a remainder of six, 32s into six, goes one, remainder 28.

32s into 280 is eight remainder 24.

32s into 22, sorry, 240 is seven.

Goodness me.

Is this one gonna finish? And our remainder is 16.

And then we breathe a sigh of relief because 32 into 160 is five.

So 30, sorry, seven over 32 is equivalent to a decimal of 0.

21875.

Now, you are ready to have a go at one of these by yourself.

And I've been super kind, I know you know I'm super kind, and I've listed out the 16 time tables for you.

Make sure you get your divisor and your dividend the right way round in your bus stop.

Think about it.

Your answer is less than one because 16 over 16 is one.

So your answer has to start with zero point something.

If yours doesn't, it probably means you've got your divisor and dividend around the wrong way.

Good luck.

Pause the video now and come back when you're ready.

Great work.

Now, let's check that answer.

So you should have got an answer of 0.

5625.

And well done, I know you did.

You are now ready to have a go at your first independent task.

This task, you need to identify the mistakes in this puzzle and correct them.

Each fraction should meet up with its decimal equivalent.

So for example, 4/5, is that equal to 0.

6? If it isn't, identify that as a mistake and write the correct decimal equivalent.

You need to do any that are paired up, so with the fraction above or below or to the side of it.

Good luck with this, remember, no calculators.

And then when you are ready, come back, you can pause the video now.

Great work.

Let's see whether you identified all of the mistakes and there were six of them.

Oh, and actually, that one I gave you as an example, 4/5, I suspect you were all shouting at me, is not 0.

6, it should have been 0.

8.

3/25, for some reason, there was an extra zero in there.

The answer should have been 0.

12.

17 over 25 was not 0.

34, it should have been 0.

68.

5/8 is not 0.

635, it should be 0.

625.

And then 11/20 is not 0.

5.

I think that was quite an easy spot 'cause we know that 10/20 is, but then yet I wanted you to write it correctly, which was 0.

55.

11/20 is 0.

55.

Good work on that.

Now, we can move on to our second learning cycle, ordering fractions by converting them.

So we've just done some fantastic work on making sure we can remember how to convert fractions into decimals.

And now, we are going to use that so that we can order fractions.

Jun and Laura have decided to stick with us for this second learning cycle, thank you, guys.

And they are going to be looking at this question, write these fractions and decimals in ascending order.

Jun says, "I can do this.

I'm going to change the fractions into decimals to make it easier." So we've just done that in the first learning cycle.

So Jun is like, "Oh yeah, yeah, I know how to do this.

I'll change into decimals.

That will make them easier to compare." But Laura says, "I don't think you need to." Hmm, interesting.

Do you agree with Laura? She says, "We know that 3/4 is bigger than 1/2," yep, 'cause I'd definitely rather have 3/4 of a pizza than 1/2 a pizza.

And we know that 4.

8 is smaller than 1/2, right? So 3/4 is bigger than 1/2, so 1/2 must go that side of it, and 0.

48 is less than 1/2 because we know that 1/2 is 0.

5.

Now, we just need to look at 0.

125.

Well, that's clearly less than 0.

48 'cause it only has 1/10 and 0.

48 has 4/10.

So we've ordered them.

So it's not always necessary to change them all into the same format if actually those fractions and decimals possibly very different to each other, or we've got some knowledge that we might be able to use to help us to order them like we did in this case because we had some very familiar fractions there.

1/2 we know is 0.

5 and 3/4 we know is 0.

75.

Let's have a look at this one then.

Again, we're going to write these fractions in ascending order.

Or sorry, I should have said fractions and decimals, there is a combination of them, in ascending order.

Have a think about what order you think they go in.

Well, we know that 2.

4 is less than 2 1/2 'cause 2 1/2 is 2.

5.

So we know that 2.

4 is less than 2 1/2, so we know the order of those two.

2.

9 is greater than 2 3/4 because we know that 2 3/4 is 2.

75 and 2.

9 is greater than that.

Now, we just need to just quickly double check that the 2 1/2 and the 2 3/4 are the right way round.

And yes they are because we know that 3/4 is greater than 1/2.

So again, we didn't actually do any formal conversions of the fractions into the decimals.

We just used our number knowledge and what we knew about those fractions and those decimals.

So don't always jump in to finding equivalent decimals.

Sometimes, you won't need to.

I'm gonna challenge you now to make sure that you can do that with this check for understanding.

Pause the video, put them in order, smallest to largest, ascending order, and then when you're ready, come back.

Good luck.

Great work.

So hopefully, you had them in this order and this was the way that I did it.

I knew that 5.

2 was less than five, and (groans) excuse me, 5.

2 was less than 5 1/4, so I knew those two.

I knew that 5 1/2 was greater than 5 1/4, and that 5.

55 was greater than 5 1/2, and so I got 'em in that order.

I'm sure you did too.

Well done.

However, it's not always gonna be obvious, is it? And you might need to convert them into decimals.

But what I don't want you to do is I don't want you to just quickly think, oh, I'm gonna change 'em all into decimals.

I'd like you to stop and think about whether that's actually necessary.

Because remember, I want to make you the most efficient mathematician that you can possibly be.

We are gonna order the following.

Hmm, now, yes, if I look at those, I certainly have no idea which is the smallest and which is the biggest just by looking at them like I could do previously.

So we do need to involve that extra strategy now of converting them all into decimals.

But we know how to do that.

We did that in the first learning cycle and we did it fantastically and we are brilliant at it.

So this is just going to be exactly the same, but we're just gonna take it a step further by then ordering those when we get to the end.

So 9/20, we know that 20 is a factor of 100, so that's gonna be our new denominator.

So we end up with 45 over 100, which is 0.

45.

11 over 25, again, 25 is a factor of 100, so I'm going to make my new denominator 100.

So there are my calculations.

Remember, if you're not sure about how I'm getting these, just rewind that video.

Go back to that part of the first learning cycle.

Now, 16 is not a factor of 10, 100 or 1,000, et cetera, so we need to do our short division.

So there's my 16 times table again, and then I can go through each part of that and I can get my final answer of 0.

4375.

And then finally, the last one, 125 is clearly not a factor of 10 or 100, so we must be using 1,000.

My multiplier is eight, remembering to multiply the numerator and the denominator, sorry, to make the numerator and the denominator the same.

And that will give us 480 over 1,000, which is 0.

48.

Now, we can write those in order.

So we're gonna write them in order first in their decimal form.

So in order as decimals, we've got 0.

4375, 0.

44, 0.

45 and 0.

48.

And then, in order as fractions, we can just look at what those were equivalent to.

So it was seven over 16, 11 over 25, nine over 20 and 60 over 125.

You should be familiar with writing decimals in order, you've done that previously.

Now, you are ready to have a go at a couple of questions independently.

Now, in this first question, I'd like you to rewrite these fractions and decimals in order from smallest to largest.

So remember, ascending, smallest to largest.

Now, for question number one, you shouldn't need to convert them all into the same format.

I've tried to make sure that it's obvious which are the biggest and which are the smallest and so on.

So try to use that method that we used previously rather than converting them all into decimals.

Good luck with that and when you're ready, you can come back.

Pause the video now.

And question number two.

Here, yes you will.

You'll need to convert all of the fractions into decimals first.

So you're gonna write them all as decimals, remembering if the denominator is a factor of 10, 100 or 1,000, you can use that place value equivalent fraction method.

If, sorry, if the denominator is not a factor of 10, 100 or 1,000, you'll need to use short division.

Remember, it's okay to use short division for the other ones as well if you prefer.

Good luck with these.

You can pause the video now and come back when you're ready to check in with your answers.

Well done.

Here are our answers then.

So a, which are 2/5, 0.

404, 0.

483 and 1/2, b, 2.

065, 2 2/3, 2 3/4, 2.

753, c, seven point, sorry, 3.

7, 3 3/4, 3 4/5, 3.

9, d, 7 1/5, 7 1/4, 7.

256 and 7.

28.

And then moving on to question number two, and I've given you the decimal equivalence there just in case you've done that as your answers, that would be okay.

B, 5/16, 7/20, 9/25, 3/8, c, 76 over 125, 5/8, 27/40, 11/16, and d, 17/20, 7/8, 23/25 and 15 over 16.

Obviously ,if I went too quick for you, you could pause the video, mark those, and then when you're ready, come back because we're gonna do a summary of our learning from today's lesson.

In summary that what have we done during today's lesson more? We've done a lot of fantastic maths learning, that's for certain.

But the main things we focused on are that fractions with the denominator, which is a factor of 10, 100 and 1,000, can be converted to decimals using equivalent fractions.

And there's an example there of one that we did in the lesson.

So remember, if the denominator is a factor of 10, 100 or 1,000, then we can use that method.

We could use the short division method if we wanted to, but other fractions, so if their denominator is not a factor, we have to use that short division method, and there's an example there.

Really important, and this is something I want you to really concentrate on from this lesson, is that it is not always necessary to convert fractions to decimals in order to order them.

In order to order them? To be able to order them, maybe that's better way of saying it.

Writing a fraction as a decimal can help with ordering fractions.

So it can help, but it's not always necessary.

So first, have a look and think do you know enough about those numbers? Do you know some already common equivalents that would mean that you are able to order those fractions? You've done fantastically well with today's learning, I'm so glad that you decided to join me.

Look forward to seeing you again.

Bye.