True or False? Four fifths is greater than three fifths.

True or False? Four fifths is greater than four sixths.

True or False? Four fifths is greater than nine tenths.

Which is greater?

Comparing Fractions

﻿Hi, welcome to today's maths lesson with me, Miss Jones. Hope you're feeling good and ready to go. Let's get started. In today's lesson we're going to be ordering fractions. We're going to start off with comparing two fractions, then move on to ordering a set of fractions, then you've got a task, and finally a quiz. You'll need today, something to write with and something to write on, such as a pencil and piece of paper. You might also want to use a ruler if you have one because we're going to be looking at number lines. If you haven't got one, don't worry too much, you can sketch one. Okay, pause the video now if you need to go and get your equipment. If you're ready, let's get started. Okay, hopefully you've got everything you need. Let's start with a brain teaser. I want you to look at each pair of fractions here and tell me for each one, which is closer to one. Now, if you're not sure, think about what representations you can use to help explore this. And think about how you might explain this in words. Pause the video now to have a go. Okay, let's go through these together. So first of all, I'm looking at 5/6 or 4/5. Now let's think about what we know by looking at our numerators and denominators. Now, we know 5/6 is split the whole's split into six parts. Here, the whole is split into five parts. That means these parts are bigger than the sixths. So this is 1/6 away from one whole, from 6/6. And this is 1/5 away. Because it's 1/5 away, this is actually further away from one. So 5/6 is closer to one than 4/5. Looking at this one, 4/5 or 3/4? Hmm, let's look at our parts. So this is a whole split into four parts, and this is a whole split into five parts. If our whole is the same size are the quarters going to be bigger, or the fifths? The quarter's will be bigger. Now this is 1/5 away from one whole. This is 1/4 away from one whole. So this is further away. 4/5 is closer to one than 3/4. Okay, let's look at these two fractions and compare them. Which is greater, 3/12 or 1/3? I'm going to let you have a think about this one. Now remember, here, our numerators and our denominators are not the same, which makes it difficult to compare. But we can use our knowledge of equivalents to help us. You might also want to use a representation to try and visualise this. Pause the video now and have a think about this one. Okay, let's have a look together. So, I've got different denominators but I know that three is a factor of twelve, so I could convert one third into a fraction with a denominator of twelve. Now I've got a representation here to help me. If I look at dividing this into thirds, I can see 1/3 would be equivalent to 4/12. If I'm only looking at 3/12 on this one, we can see that's not as much as 1/3. 1/3 is equal to 4/12 and therefore is greater than 3/12. So let's think about our symbol here. We're starting with 3/12, so we can say 3/12 is less than 1/3. Okay, this time we've got a set of fractions. Now, another representation that's useful when we're thinking about ordering is visualising where they would be on a number line. So let's think about where these numbers might be. Now, none of our fractions here exceed one whole. So I'm going to make my number line run from zero to one. Now, I'll mark halfway here and write in 1/2. So, would 3/4 be more than 1/2, or less than 1/2? Well, if we divide our number line into quarters, I know that 3/4 would be 1/4, 2/4, equivalent to 1/2, 3/4, around here. 1/8, well we would need our number lines divided into eight equal parts. So if I divide these parts in two again, and 1/8 would be just here. So I can now order these fractions. So 1/8 would be the smallest, then 1/2 and then 3/4, the greatest out of these three fractions. We could also use our knowledge of equivalents. At the moment, these all have different denominators but what I could do, is convert these so that they all have the same denominator. Now, both two and four are factors of eight. So I could convert these all into fractions with a denominator of eight. That way it will make them easy to order. Okay, so my denominator here is two, it's been multiplied by four, so I need to do the same to my numerator. I know that 1/2 is equivalent to 4/8. That makes sense because four is half of eight. 3/4, now four here has been multiplied by two to get a denominator of eight, so I need to do the same to my numerator. I need to multiply three, by two. 3/4 is equivalent to 6/8. Now I can order them, and I can see that 1/8 is the smallest. Then, so I'm going to write that in actually. Then, I'm looking at my eighths here, I can see 4/8 is the next smallest but our original fraction wasn't 4/8, it was 1/2. So I'm going to write in 1/2, because we know it's equivalent to 4/8. And finally, the greatest was 3/4, because we know it's equivalent to 6/8. Okay, you can use either method to order them. The number line might be easier in some instances but sometimes we can't just visualise where they are on the number line, without looking at our equivalents. So knowing both methods is a sure way to finding the correct order. Okay, here we've got three different fractions. How could I order these fractions? Hm, well, let's think about the number line first. Can you visualise where these fractions might be on a number line? You might want to have a quick go yourself. Okay, again, none of our fractions exceed one. So I'm going to have a number line from zero to one. Now, we've got quarters and eighths. Okay, so let's divide our number line into quarters first. Now it's quite hard for me to judge where a quarter is on my number line. So I'm going to find the halfway point round here, just by estimating. Now I'm going to mark halfway again between half and zero and between half and one to roughly put in some quarters. Okay, so I know that 1/4 would be around here. Now my other two fractions, we can see have a denominator of eight. So I need to divide my number line into eighths. Now I can just find the halfway point between my quarters to mark eighths. So, 3/8, one two, three, would be here. 7/8, 4/8 would be here around the halfway mark. 5/8, 6/8 would be here. Now, that makes sense 'cause 7/8 is near to 8/8, so near one whole. Okay, so the correct order is, 1/4, 3/8, and the greatest is 7/8. We could also have used our knowledge of equivalents to order these same three fractions. We already have a denominator of eight here and here, and we know that this denominator of four is a factor of eight. So we can easily convert this into eighths to help us. Four multiplied by two would get us eight. So let's do the same to our numerator, one multiplied by two is 2/8. 1/4 is equivalent to 2/8. Now I know that, I could order them. So, I can see here that 1/4 is the smallest because 1/4 is equivalent to 2/8. Then it would be 3/8, and the greatest would be 7/8. Okay, here's three more fractions. I'd like you to have a go at ordering these yourself now. You can use a number line or you can use your knowledge of equivalence. Or you might want to use both to convince me that you're right. Okay, pause the video to have a go. Okay, how did you get on? Let's have a look together. So, we've got our number line here, and do any of these go above one? No, so let's put in number one here and a zero. So, we've got sixths and thirds. So a bit more tricky to divide our number line but let's do roughly where a third might be, need three equal jumps, so let's put that in and we can imagine our sixths would be a half of that again, to make six equal jumps. Okay, so, 1/6 would be here. 2/3, now remember, this is 1/6 jump, 1/3 jump would be here. 1/3, 2/3. And 4/6, one two, three, four. Interesting, 4/6 is equivalent to 2/3, did you notice that one? So when we're ordering these ones we can think about 1/6 being the smallest, but these two are actually equivalent. If we're using our knowledge of equivalents we could have thought about this with a denominator of six, 'cause we know three is a factor of six. Three, to get to six we need to multiply by two so we can see it's equivalent to 4/6. So when you're ordering, 1/6 is the smallest and both of these are equally the greatest. Okay, hopefully that's enough practise of ordering fractions and you're ready to go and do your task. When you're finished, come back here and we'll finish off by going over the answers. Okay, let's go over these together. I'm going to use a number line to show you the correct order. So we've got here, A, 1/2, 3/4 and 7/8. Now here, 1/2 would be the smallest, around halfway on the number line, 3/4 is the next greatest, around here, and 7/8, which is near one whole would be more towards here on your number line. So the correct order is, 1/2, 3/4, 7/8. B, we've got 2/3, 2/6, and 6/6. Now here, 2/6 is the smallest, and you might've noticed that 2/6 is equivalent to 1/3. Then we've got 2/3, should be more up here, which is greater than halfway of the number line, and then the greatest was 6/6, because 6/6 is actually equivalent to one whole. C, 7/10, 1/5, and 3/10. Hmm, well I know that 1/5 would be the same as 2/10. So perhaps around here on my number line, and then a little bit up the number line would be 3/10, and then past half way would be 7/10. So the correct order was, 1/5, 3/10, 7/10. Let's have a look at the next set. So D, we've got, 1/9, 8/9, and 1/3. Hmm, now I know 1/3 would be the same as 3/9. So now they've all got the same denominator. And we know that 1/9 might be the smallest, around here, or is the smallest. Then it would be 3/9, or 1/3 was our original fraction, and 8/9 would be the greatest. It's not far from one whole. Okay, E, 1/10, 4/5 and 2/5. Again, you might want to use your knowledge of equivalent fractions. I know that 2/5 is the same as 4/10. 4/5 is the same as 8/10. So I can see that 1/10 is the smallest. Then the next greatest would be 2/5 because it's equivalent to 4/10. Now, that might be just before halfway, 2/5. And the greatest was 4/5 because it was equivalent to 8/10. Might be more up here, nearer to one whole. 4/5 was the greatest. And F, F was slightly less obvious. I'm looking at our denominators here, we've got quarters and sixths. Hmm, now six isn't a multiple of four, so it's a little bit more tricky to use our equivalence. There are different ways you could work this out. You could think about a multiple of four and six and convert them all into a denominator with that value. For example, convert them all into twelfths. That would help you order them. But I'm going to also use my number sense here. I know that 6/6 is equivalent to one whole. So this one is the greatest. Then I've got 1/4 and I've got 2/6, I know that 2/6 is equivalent to 1/3. Now I've got the same numerators here, and we know when our numerators are the same we can look at our denominator. 1/3 is greater than 1/4. That will be a smaller part. So my smallest is 1/4. The next greatest here would be 2/6, which is the same as around 1/3, here. So 2/6 and my greatest was 6/6. How did you get on? It's time to finish off the lesson and complete the quiz. Thanks everyone, see you soon.

Which of these is greater?

Which of these is the greatest?

Which of these sets of fractions are ordered from smallest to greatest?

Which of these sets of fractions are ordered greatest to smallest?

Ordering Fractions

In this lesson, we will order a set of fractions with denominators that are multiples or factors of each other. We will place them in order on a number line.

Maths

Y4 Maths

Key Stage 2

Year 4

Miss

Ordering fractions

Fractions

Number

THEME

UNIT

Recognising fractions as different representations

Calculating unit fractions of quantities

Recognising  equivalent fractions

Recognising equivalent fractions (2)

Calculating non-unit fractions of quantities

Equivalent fractions

Fractions and division

Comparing fractions

Using mixed numbers

Using improper fractions

Converting mixed numbers into improper fractions

Adding fractions (up to one whole)

Subtracting fractions

Adding fractions (with a total greater than one)

Subtracting fractions (2)

Comparing non-unit fractions of quantities

Reasoning with fractions

Which representation shows three quarters?

What does the denominator tell us?

What does the numerator tell us?

How else could I write five halves?

What is the sum of the fractions?

What mixed number is being represented?

Calculate:

What improper fraction has been represented?

A packet of paper has 261 sheets. Two thirds of the packet has been used. How much paper is left?

Lesson overview:Ordering fractions

Core Content

Fractions: