Lesson video

Welcome to lesson four of our fractions topic.

Today we'll be comparing fractions that are less than one.

First of all, make sure that you have all of the equipment needed for this lesson.

All you need is a pencil and a piece of paper or exercise book.

Pause the video now and get your equipment ready.

In today's lesson, we're going to compare fractions less than one.

We'll compare fractions where we have to change both denominators, then we'll make sure we're doing it in the most efficient way before we order fractions, and then you complete some independent learning to practise what we've learned, followed by a quiz to test your knowledge.

Here's your Do Now.

Look at the fraction below.

Which is the odd one out? Can you make a case for all of them? Pause the video while you do so.

You may have said that the first one is the odd one out because it is a unit fraction where the numerator is one.

The second one could be the odd one out because it's a non-unit fraction, where the numerator is not one.

The third one is a mixed number, which means it is greater than one.

One whole, and 2/20.

Now let's look at comparing fractions.

Would you rather have 5/6 or 6/7 of the same chocolate bar? I know you can't look at these fractions and directly compare them because they have different denominators.

The number of parts are different.

One strategy that I could use is a bar model.

I can draw two identical bars of chocolate parallel to each other, and split one into six parts and one into seven parts.

Then I can shade the parts and compare.

My top fraction is split into six parts, so I shade five out of the six on that bar model.

My bottom one is in seven parts so I shade six out of those seven parts.

Now, I know that this is perfectly accurate because I made it on the computer and I know the bars are equal.

However, if you are drawing the bars, you can only be accurate if you do careful measuring, which takes time.

So if I draw the bars freehand, then I know that they're not going to be as accurate as if I did it on the computer.

So I can see my last part is much smaller than the part next to it.

Then if I draw it for sevenths as well, my bars are not exactly the same length and they're all slightly different sizes.

So this is not the most accurate way, although it's still good to have an estimate of which one is the greater fraction.

So, we need a more efficient strategy.

We need to find a common multiple of the two denominators, six and seven.

In order to accurately compare the fractions, they need to have the same number of parts, they need to have the same denominator.

So to find a common multiple for six and seven, I can write out the timetables for each, and then find where there is a multiple that is common or a multiple that is the same.

So I'll write out my six times table first.

Six, 12, 18, 24, 30, 36, 42, 48.

I'll stop there.

Now my seven times table, seven.

Seven, 14, 28, 35, 42.

I can see that 42 is in both of those times tables, therefore, it is a common multiple.

There aren't any common ones before 42, therefore it is the lowest common multiple of six and seven.

So now, I need to convert both of the fractions into equivalent fractions with the denominator 42.

So I need to convert 5/6 into an equivalent fraction where the denomination is 42.

Remember, that whatever I do to the numerator, I must do to the denominator, and vice versa.

So, 6 X 7 = 42.

So I must do 5 X 7 = 35.

I have to do the same now to 6/7.

I need to create an equivalent fraction with denominator 42.

I know that 7 X 6 = 42, and I know 6 X 6 = 42.

It's not 42.

6 X 6 = 36.

So 6/7 is equivalent to 36/42.

Now I could directly compare these two fractions because they have got the same denominator.

I can quite clearly see that 35/42 is less than 36/42.

So if I go back to their equivalent fractions in the simplest form, I see that 5/6 is less than 6/7, and I can use an inequality sign to show that 5/6 < 6/7.

or the other way around, 6/7 > 5/6.

Let's do another one together.

Would you rather have 3/7 or 5/9 of the same bar of chocolate? Let's get an estimate by sketching a pictorial representation.

I make my first bar into seven parts, one, two, three, four, five, six.

Let me add one at the end.

This just shows how inaccurate this is.

But get a rough guide.

Now, my second one is in nine, roughly equal parts.

So if I shade 3/7, 5/9.

It looks like 5/9 is greater, but let's be accurate.

So we need to find a common multiple of seven and nine, so that we can find the common denominator.

I'll write on my seven times table.

Now you might have already thought I already know the common multiple, because I know my times tables, but I'm just going to show you the strategy for making really sure that you're using the most efficient strategy to find the lowest common multiple.

So I'm writing out my seven times table first, and I'm going to stop here because I've noticed something about 63.

Let me write up my nine times table.

Nine, 18, 27, 36, 45, 54, 63.

So I can see that 63 is a common multiple and it's the lowest common multiple.

So, I need to change these fractions so that they are equivalent fractions with the denominator of 63.

I know that I multiply 7 X 9 = 63 and I have to do the same thing to the numerator, 3 X 9 = 27.

So 3/7 is equivalent to 27/63.

And I do the same for my other fraction.

9 X 7 = 63, 5 X 7 = 35.

So, straight away I can see that 27/63 < 35/63.

3/7 < 5/9, and that's what I thought.

But now we have made sure that we've been really accurate.

Now it's your turn.

Pause the video while you work on this question.

Would you rather have 2/3 or 4/7 of the same chocolate box? Use one of the following symbols in your answer, <, > or =.

So you should have noticed that the common denominator was 21, and converted your two fractions so that they were equivalent fractions for the denominator of 21.

You would have multiplied the numerator and denominator of 2/3 both by seven, which gives you 14/21.

And in 4/7, you multiply the numerator and the denominator by three, which gives you 12/21.

So you can see that this is greater than this, 14/21 > 12/21, so 2/3 > 4/7.

Now let's make sure we are being as efficient as possible.

Would you rather have 3/4 or 8/12 of the same bar of chocolate? Do you notice anything about these two denominators? Pause the video while you give it some thought.

Now let me write out in the multiple lists.

So I'll start with four, four, eight, 12, 16, 20, 24, 28, 32, 36, 40, 44, and 48.

I'll stop there.

12, 24, 36, and 48.

Now I can see in these two multiple lists that there are actually lots of common multiples.

And there will be more if I continued.

I'm interested in the lowest common multiple, so I can be most efficient.

And that is 12.

Now in our a second fraction, the denominator is already 12 which means that we can leave that fraction alone.

We just need to change our first fraction so that it's an equivalent fraction with a denominator of 12.

So I multiply both numerator and denominator here by three, which gives me 9/12.

I left my second fraction the same, 8/12.

I can see that 9/12 > 8/12.

So 3/4 > 8/12.

So this is to highlight that you don't always need to change both fractions.

It's your turn, pause the video while you were efficiently calculate the greatest fraction.

Would you rather have 5/8 or 11/16 of the same chocolate bar? You will have noticed that common multiple for these two denominators was 16.

Therefore, the second fraction could stay the same.

The first fraction, you multiply both numerator and denominator by two to give you 10/16.

10/16 < 11/16.

So 5/8 < 11/16.

Now let's move on to ordering fractions.

When we order fractions, we have more than two to consider.

We need to find the common denominator of all of the fractions.

So we're being asked to order three fractions from smallest to largest.

So all we have to do this time is write out three multiple lists instead of two and find the denominator.

So I'll start with three, three, six, nine, 12, 15, 18, 21, 24, I'll stop there.

Then I'll go on to two, two, four, six, eight, 10, 12, 14, 16, 18, I'm noticing that 18 is common in these two.

Let's have a look, is it in the nine times table? Nine, 18.

Yes, it is.

So, our lowest common multiple is 18.

Therefore, these three fractions need to be changed into equivalent fractions with the denominator 18.

Don't forget that whatever you do to the denominator you must do to the numerator.

This relationship needs to stay the same in order for them to be equivalent.

3 X 6 = 18.

2 X 6 = 12.

2 X 9 = 18.

1 X 9 = 9.

9 X 2 = 18.

5 X 2 = 10.

I'm going from smallest to largest or if look back at the question.

The smallest out of these three fractions is 9/18.

So that's number one.

The next one is 10/18, so that's two.

And the final one is 12/18, which is three.

I'm going to go back to the original fractions.

So I can see that 1/2 <5/9 < 2/3.

Now it's your turn.

Pause the video and order the fractions from smallest to largest.

You will have noticed that the lowest common multiple is 30.

So you would have converted these fractions to equivalent fractions with denominators of 30.

So we have 9/30, 20/30, and 15/30.

Back to the question, smallest to largest.

Smallest is this one, 3/10 or 9/30.

The next one, it's this one, 1/2 followed by this one.

So 3/10 < 1/2 < 2/3.

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.

In question one, you were asked to use the inequality symbols to compare the fractions.

For a, your common multiple four and five was 20.

So you will have converted this to 15/20 and 12/20.

15/20 > 12/20, therefore, 3/4 > 3/5.

The second one, the lowest common multiple between five and 10, is 10.

So only the first fraction needs changing.

That will become 2/10.

2/10 < 3/10.

In the third one, the lowest common multiple was 24.

16/24 and 15/24, 16/24 > 15/24.

And then the final one, the lowest common multiple was nine.

Only your second fraction needed to be changed to 3/9 by multiplying both numerator and denominator by three.

And you can see that 4/9 > 3/9.

In questions two, you were asked to order the fractions from smallest to largest That there is four fractions in part a, the lowest common multiple was 60.

So these needed to be converted into 60ths So 1/2 is 30/60, 2/3 is 40/60, 4/5 is 12/60, and, no it's not 4/5.

Let me check.

Always important to make sure you're accurate.

It's multiplied by 12, multiplied by 12, four multiplied by 12 is 48/60.

That's why the annotations are so helpful.

And the last one, I'm going to annotate this time so I don't make a mistake.

It's multiplied by 15 to give you 4 X 15 = 60, multiplied by 15 gives you 15/60.

Back to the question, largest to smallest.

The largest one is 48/60.

Then it is 40/60, then it's 30/60, and finally 15/60.

So 4/5 > 2/3 > 1/2 > 1/4.

For your second one, your lowest common multiple is 36.

So all needed converting, 27/36 by multiplying by nine, 32/36 by multiplying by four, 24/36 by multiplying by six, and 18/36 by multiplying by 18.

Now back to the question, largest to smallest.

Our largest one is 8/9 or 32/36, then 3/4, 4/6, 1/2.

Okay.

Question three was trickier.

Now you needed, first of all, to convert all of your fractions into equivalent fractions with the denomination 12 because that was your lowest common multiple.

So I did that.

And then I looked at the top left-hand corner needed to be the smallest fraction possible which was 2/12 or 1/6.

So I put the original fraction in there.

The bottom line needed to be the largest.

And then I worked systematically to go from largest to smallest.

So I surrounded 11/12 with the three next largest.

And then I worked my way down.

You may have had a slightly different answer to me.

You should pause the video now and have a look through where I've put each fraction and check your work.

Now it's time for your final knowledge quiz.

Pause the video and complete the quiz to see what you have remembered.

I'm looking forward when we will be learning to compare fractions that are greater than one.