﻿Hi, my name is Mrs. Perry. And today we're going to be doing some work on equivalent fractions. Later on, you'll need a pen and paper. So it may be useful to pause the video here, go and find the pen and paper so when you need it, you can carry on. Also, don't forget that work you did at the end of last lesson, we're going to look at it first. So how did you get on? Did you manage to find the six equivalent fractions for 1/3 and for 2/3? Did you find any patterns? Did you manage to explain those patterns to the adults in your house? So let's get started. Remember, we're looking for the first six in this pattern, which starts at 1/3. Okay. If I know that the numerator is going up by one, could I just add one to the denominator as well? Oh, you're right. Can't catch you like that, can I? we have remembered already that we're working with a multiplicative relationship. So if we're scaling up by two in the numerator, we got to do the same with the denominator. That way we keep the proportional relationship the same. I need to get the next one in the series now. I've carried on, but I'm looking now at the relationship to the original fraction. This time I have to scale up by a factor of three. So I'm going to multiply by three for the numerator. Therefore, I also have to scale up the denominator by three. I'm going to multiply three by three, which is nine. That way I keep that proportional relationship the same. How did you find the next one? Did you get back to the original fraction? So what is it that I'm scaling up by this time? That's right. Scaling up both the numerator and the denominator by four. I've got to keep the numerator and the denominator in the same proportion as the third. And again, this time I'm scaling up by five. 1/3 and 5/15 these are equivalent fractions. I have to do the same to the numerator and the denominator so that they keep the same proportion, but they do have a different appearance, don't they? And finally, I scale up by six. I do the same to the numerator and the denominator to keep the fraction in the same proportion. Ooh. Oh, someone's just suggested I could have done it a different way. I'm liking what they're suggesting. How a look at this. Is that a scaling from the 1/3? Because I know 3/9 is already in the same proportion, I could have scaled from there. That would have meant that I would have had to scale by two, to go from 3/9 to 6/18. Brilliant. I like that suggestion. Now we're going to do the same activity, but we're starting at 2/3 instead of 1/3. Lets with this, through this one. Shall we? Here we go. Okay. So to go from 2/3 for the next one in the series, I'm having to scale by two for both the numerator and the denominator to keep them in the same proportion. But the next one. I'm going to get back to the first fraction. And I'm going to scale them both up by three, multiplication by the same the factor preserves the proportional relationship, between the numerator and the denominator. Did you find the relationship from the original fraction scale it up by four? Like this. Or, did you choose to go from the 4/6? Yep. Both ways you get the right answer because they keep the same proportion of the whole. So we got to the end, to get the last one, What do we have to multiply both the numerator and the denominator by? Yeah, we had to scale up by six for both parts of that fraction. So we kept the proportional relationship the same. So let's answer the second question. Can you see any patterns? If you forgot to do this before you started the video, why don't you pause it now and try and see the patterns that we're going to be identifying. So did you find anything interesting? I found two things that interested me. Firstly, I'm amazed that the denominators are the same in both of the series. Did you notice that as well? It's because we're looking at fractions that are equivalent to a third, which means that when we look at the vertical relationship, we know we do need to look at our three times table. Spot to just second thing. Did you notice the doubling of the relationship? Look at this. Can you see here? We started with one, 1/3 in this sequence, but in this one we started with two lots of 1/3. So if I was to look at the 1/3 here, it's doubled down here to 2/3. I could do the same, If I looked at some of the other ones. Let's look at the 4/12. So 4/12 here is doubled to make 8/12 down here. Interesting. Now we finish going over the work from the last lesson, we can move on to today's learning. We're going to be looking at fractions that are equivalent. That means fractions that have the same proportion of the whole. They have a different appearance to each other. Do you remember this picture? 1/5 of the pizza is the same proportion of the pizza, its 2/10. They're not different, but they're the same proportion. So our activity today is to complete families of equivalent fractions. That means what we're looking for is fractions that have the same proportional value, but they look different. So I'm going to start by looking over here at what the proportional relationship is in my fraction. So this fraction here tells me that proportional relationship is seven. That denominator is seven times as big as the numerator. So when I'm looking at my next one in the sequence, I still have to keep that proportional relationship the same. In order to do that, I've got to divide 14 by seven, and that's going to give me an answer as two. So that means that 2/14. Is the same proportion as 1/7, but they would look different those fractions wouldn't they? Okay. We're moving on to another one where the denominator is 21. I get to tell you that the answer for this is going to be 3/21 is equivalent to 1/7. Can you explain how I got that? That's right. What I did was I took the 21, as the denominator and I divided it by seven , and that gave me the new fraction of 3/21. Now this one is going to be slightly different. Isn't it? Because I've been given the numerator. I still have to keep the proportional relationship the same. The proportional relationship is seven. So what I've got to do now is I've got to multiply four by seven, and that's going to give me my new denominator. My new denominator is 28. So my new fraction is 4/28. Having done that one, I'm going to be able to do this one on time, because I've still got the numerator, five sevens are you got it, 35. Now I'm going to have to change track just for a moment because I've gone back to having the denominator. My proportional relationship is same. So I need to divide 42 by seven and that's going to give me my new fraction is 6/42. And finally, I've got the numerator. Do you remember what we do with the numerator? That's right. We multiply by it seven to keep the same proportional relationship. So my final fraction is going to be 7/49. Oh 7/49, that's the same value, but a different appearance to 1/7. Amazing. So where would we put the seventh on the number line? Can you see I've made an area model just here, and the area model shows me my whole is 7, sevenths. And my part is 1/7. So I've got my 1/7 lined up on the number line. I feel happy with that. Okay. What I want you to do now is I want you to imagine, where would I put this number? Our new number it's 2/14. Can you imagine? Hmm. So can you see the 2/14. I show you with my laser. Can you see the two parts? And can you see the, yep. That's 14 parts and that group, can you see them? But why do they belong on the number line? That's right. It's the same value, but a different appearance 2/14 has the same value, but a different appearance to 1/7. When would I put this number? 6/42, I would think about it. And then look at the next slide. So where you, right? Can you see the six parts, and the 42 parts that this whole is now made up of, can you see them? Look, it is the equivalent fraction to 1/7. It's the same proportion, but it has a different appearance. So what have we shown? We've shown that 1/7, 2/14 and 6/42, all have the same proportional value, but they have a different appearance. So we can say that 1/7 equals there's an equivalent fraction to 2/14, and to 6/42. We're going to look at this in a slightly different way now, can you say that this is a times tables grid. Can you spell the 10 times table? That's right, just down here. Oh, up there as well. Can you see that five times table? That's right along there. Now, on this one, I've made the grid the one times in the seven times table, stand up by making them blue. Can you see that? The one, and the seven times table. Okay. So let's have a look at 1/7. Would we look at that together? Here is our one, and here is a seven. 1/7. Interesting. That works. Doesn't it? Lets have a look a couple more, and see if we look at them using our times tables, if it also works. How about 6/42? Lets have a look. 6/42, we've got the same proportional relationship. And if we did one more, 7/49, can you see that relationship? It is the same proportional relationship. Right, final bit from me for this lesson. I want you to have a go at doing these three sequences before we come back to our next lesson. And in order to do this, you are going to need to remember to keep the proportional relationships the same. So I'm going to start by looking at our first sequence. And we're going to start by looking at this relationship. We've got 9/81 at the beginning, and we've got 1/9 at the end of the sequence. Can you tell me what the sequence, proportional relationship is and these fractions? That's right. It's a proportional relationship of nine. Nine, is nine times the size of one, one is 1/9 the size of nine, or we can see it the same up here. Nine, is 1/9 of the size of 81. Okay. You're going to have a go at doing that one. And your proportional relationship is nine. And then you can have a go at the 2/7 sequence and at the 2/5 sequence. See you at the next lesson.

In this lesson, we will explore the relationship between numerators and denominators including non-unit fractions.

In this lesson, we will explore the relationship between numerators and denominators including non-unit fractions. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

Lesson overview:Numerators and denominators in non-unit fractions

Core Content

Equivalent fractions: