Simplifying fractions using highest common factor

Key Stage 2

Maths

Equivalent fractions

﻿Hello, Ms. Seton here again. Welcome back to lesson 12. Where are we going to continue to explore the simplest form in equivalent fractions. I left you with this practise activity where you had to find the equivalent fraction first and then identify which one was in its simplest form. Did you get the same pairings as me? Excellent, well done. Let's have a look at one of those together. Let's take 1/10 and 10/100. Did you say that 1/10 was in its simplest form? Fantastic, perhaps we can use that STEM sentence to explain why again did you say that 1/10 is in its simplest form because the numerator denominator have been made as small as possible whilst keeping the proportion the same. And how have the numerator and denominator been made as small as possible? The numerator and denominator, that's right. They've been divided by the same number, which is 10. Excellent. So the numerator is 1/10 of the denominator and the denominator is 10 times the numerator. Did you find that with all of the fraction pass? Excellent. What can you tell me about the fractions that we've identified as the simplest form? Do you notice one that's maybe an odd one out? Yes, super, 3/4. Why? Why did you identify that as being a bit of an odd one out? Because it's not a unit fraction. And we did say, didn't we in the previous lesson that very often the simplest form has been reflected by a unit fraction but it doesn't always have to be. I'm going to look at that more in this session. What could you find out about 2/10, I've left it in the middle there because I wasn't sure where to put it. Why did you put it? Did you say it was not in its simplest form or in its simplest form ? It's not in its simplest form, fantastic. And why not? Because the numerator and denominator can be divided by the same amount to make an equivalent fraction. And what is the amount? They can be divided by two. Fantastic. And the equivalent fraction will be 1/5 which is a unit fraction again, isn't it? And that would be in its simplest form, really well done. How did you get on with a challenge? Do you think my puppy the preferred 1/2 an hour or 30/60 of an hour for a walk? Yes, you're quite right. T decided to choose 30/60, yes because he thought that would be a longer walk. What do you think? No, you're quite right. 1/2 an hour and 30/60 of an hour are the same amount because our equivalent fractions. What else do you notice about 30/60? Every 60 minutes in an hour, fantastic. So the denominator represents the whole house being divided into 60 equal parts, which in the minutes, and 30 of those minutes is 1/2 an hour really well done. I like you to have a look at this fraction wall. And for you to tell me everything that you can about this family of equivalent fractions. So have a think back to what we did in the last session. I'd like you to pause me now and come back and tell me everything that you notice. Did you come back? How did he get on? What did you notice about this family of equivalent fractions. Excellent, so you noticed haven't you? That they're equivalent because they're all the same proportion of the whole. So for example, if we look at 9/12 here, that's the same proportion of the whole as is 3/4. Brilliant. Did you notice anything else? Excellent, yes. So for 3/4, the numerator and denominator have been kept as small as possible. But there's still the same proportion of the whole and that vertical relationship is the same proportion as well. Did you notice what that was? Brilliant, yes. So the numerator is 3/4 of the denominator, excellent. Could you tell me anything else that you noticed, I bet you've written down haven't you? That, let's say it together, 3/4 is the simplest form in this family fractions. And we met that STEM centres, didn't we, in the last session? Should we say it again together? The simplest form in this family of fractions, is 3/4. Well done. Let me look at this fraction wall in the last session. We looked at 1/4. The same and what's different between 1/4 and 3/4? When we look at them on this fraction wall. Yes, that's right. 1/4 was a unit fraction. And we did say the, on the whole a lot of the simplest farmer fractions are unit fractions. Well, in this case, three quarters is not a unit fraction. Well done. We also looked at this multiplication square didn't we? In the last session and we found an equivalent fraction family with the simplest form was 1/7 really well done. And we can see that here can't we? 1/7. Have a look at this yellow shady bar. And I wonder, could you pause me? And write the equivalent fraction family represented by these two bars pause me now and have a ago. How did you get on? Did he get the same family of equivalent fractions as me? Fantastic. Yes. So we can say count with a 5/7 is equivalent to 10/14 which is also the same proportion of the whole is 20/28. And that's the same proportion of the whole is 35/49. Why? Why are they the same proportion of the whole? What else might you have noticed? Brilliant. Excellent. So you can say can't you? That the numerator denominator multiplied by the same amount and the value of the fraction remains the same. It's some of you write as examples. So for example, here, 5/7 is the same proportion of the whole as 10/14 because they've both been multiplied by two. The numerator and denominator have been multiplied by two. 15/21, the numerator denominator has been divided or multiplied by three really well done What about 30/42 What if the numerator denominator being multiplied or divided by? They've been multiplied by six really well done. So we can see here can't we, that this generalisations correct? Let's say it again together. When the numerator and denominator are multiplied or divided by the same number the value of the fraction remains the same. Excellent. Did you notice anything else about this family of fractions? Brilliant. So yes, 5/7 is the simplest form. Now, how is that different to what we saw in the previous lesson? Yes, we said the simplest form was 1/7. Didn't we? So the simplest form in this family of fractions is 5/7 And we're beginning to see that, that a simplest form, doesn't always have to be a unit fraction. Welcome. Can you tell me what the simplest farm is in this family, the equivalent fractions? Yes. That's right. The simplest form is 2/3. Fantastic. Why is it 2/3? And you tell me using the STEM sentence that we looked at. So 2/3 is the simplest form in this family of fractions because the numerator denominator are made as small as possible while keeping the proportion the same. And we can see can't we? The 2/3 is the same proportion of the whole. So these are equivalent fractions, well done Taken two of those equivalent fractions. And I'd like you to tell me what we said in the last session is still true. So we said in the simplest form, we have scaled. Do you remember that language? The numerator and denominator to make them a smaller so we can. Pause me, now see if that's true and see if you can tell me anything else that you notice. We come back. What did you find? Is this correct? Did you agree? Yes. You did agree so So, what have the numerator and denominator been scaled by to keep them as small as we can. So 6/9 the numerator and denominator have been divided by three. Excellent, well done. And so 2/3 is the simplest farm. Now we also said in the simplest form we made the numerator one, have a little look at those again. Is this true now? What do you think? No Not true. Is it? So in the simplest part, we don't always have to make the numerator one. So we finding out now aren't we that simply spam can look very different than a unit fraction. And we also said in the simplest form we are making the fractions as small as possible. And I hope you remember, we didn't agree with that. Did we? Have a look at those and see, do you still disagree with that statement that we're making the fractions as small as possible? And tell me why as well. What did you think? No, that's right. We're not making the fractions any smaller are we? The numerator denominator are made as small as possible while keeping the proportion the same. Shall we say that one again together? The numerator and denominator are made as small as possible while keeping the proportion the same. Well, done. What's the sequence of lessons? You've met the two generalisations at the top of this screen. I'd like us to take a moment now just to check if these are the true and also for you to prove it to me. So if we take this first generalisation let's say it together. The numerator and denominator made as small as possible while keeping the proportion the same and have a look at 4/5. I want you to pause me now, find out if this is true. And could you draw a pictorial representation to prove it see you in a moment? How did you get on? Did you say that this is true? Yes, it is. Isn't it? The numerator and denominator been kept as small as possible. And in the case of 4/5 here, the numerator and denominator, are as small as possible but they're the same proportion of the whole as these other fractions. And how did you represent that pictorially? Fantastic. Did you do ordinary and model like me? So here we can say the whole has been divided into five equal parts and four of those parts is the same proportion of the whole as if I divide the whole into 20 equal parts. And then 16 of those equal parts will be the same proportion of the whole. So well done. So that generalisation is true and you proved it You've also met this generalisation in several of the previous lessons, shall we made it together? When the numerator and denominator are multiplied or divided by the same number the value of the fraction remains the same. Do you remember that one? Super. Well, you just proved to me in the last slide that 8/10 was equivalent 4/5 because they're the same proportion of the whole when you do give me some grey area models to prove that do you think you can prove that the numerator and denominator have been divided by the same amount to keep the value in 4/5 the same? You might need you multiplication square now and have a look at those relationships as well. So pause me now. I find out what 1/2 the numerator and denominator both been divided by. How did you get on? What did you find? What did you say? The numerator and denominator have been divided by? They've been divided by two. Fantastic. So they've been divided by two. What did you notice looking at your multiplication squares? Did you notice that both eight and 10 are in the two times tables? Great. So how else can we say that? We can also say the eight and 10 are multiples of two brilliant. And that too, in that case, and two must be a factor of eight and 10. Fantastic. Were there any other ways that you could divide the numerator and denominator and keep the value of the same? No no. You had to divide by two. What I'd like you to do now, is pause me and see if you can find out what the numerator and denominator The 12/15 have been divided by to keep the value the same and then also do the same 16/20 and usual multiplication square to use that language of multiples and see which times tables you're using to help you do that. How did you get on? Let's have a look at 12/15. What did you find the numerator and dominator had been divided by? Did you say they'd been divided by three? Really well done. And what did you notice about three? Yes. It's a factor of 12 and 15. Isn't it? So 12 and 15 are in the three times tables and multiples of three. And actually we had a look at that language. Didn't we? A few lessons ago. And you said that a common factor is a factor that is shared by two or more numbers. So three is a common factor of 12 and 15. Well done. What did you find out about 16/20? What did you divide the numerator denominator by to keep the value the same? Did you divide by four? Really well done. Is four a common factor of 16 and 20. Yes, it is. Why, why is this a common factor? Because 16 and 20 are in the four times tables. They're both multiples of four. Excellent. Really well done. So have proven this generalisation? Yes. So when the numerator and denominator are multiplied or divided in this case, by the same number the value of the fraction remains the same. And we've used that language. Haven't we? Have common factors. So perhaps we could sharpen up our realisation and saying, instead Say it with me when the numerator and denominator are multiplied or divided by the same common factor, the value of the fraction remains the same. Well done. What about these equivalent fractions? I'd like you to pause me now and have a think about everything you notice about them. What did you find? Yes. You found that there's the same proportion of the whole because 4/12 and 1/3 are equivalent. What else did you notice? Fantastic So the numerator and denominator have been divided by the same amount. Can you tell me what that was? They'd be divided by four, really well done. And what else can you tell me about four? So the numerator and denominator can both be divided by it because it is a common factor. So it's a factor of the numerator four and it's also a factor of the denominator 12th. And we've said, haven't we? That when the numerator and denominator are multiplied or divided in this case, by the same common factor, the value of the fraction remains the same. Brilliant Are there any other common factors? So, four is a common factor of four and 12. And you can probably see that on your multiplication square again, can't you? So four and 12 were in the four times tables four and 12, the multiples of four. That's why four is a common factor of both the numerator and denominator. Are there any other common factors? I'm just going to pause you for a moment. I'd like you to find all the other common factors. Did you find any? What did you find? Yes. Fantastic. There are other common factors and what are they? So four and 12 have a common factor of one. Excellent. And they also have a common factor of two. Fantastic. Let's have a look at what happens if we divide by the different common factors. So let's divide by the common factor one and have a little think what happens when we divide any number by one. So pause me and divide the numerator and denominator by one and tell me which equivalent fraction you get. How did you get on, what did you get? Did you find that this was equivalent to 4/12? It's in the same form, isn't it? So we can say that the fraction stays in the same form when we divide it by one. How about if we divide it by the other common factor two? Would you like to have a go with that? So pause me again and divide the numerator and denominator by two and tell me which equivalent fraction that you get What did you get? Okay. So if we divide the numerator and denominator by two did you find that you got 2/6? So this is an equivalent fraction, is it in its simplest form? No, it's not in its simplest form. How could I get you to be in its simplest form? I could divide it by two again, really well done. If I divided by two again, what will my fraction be? It will be 1/3, well done. Because, why is that? Because they are the same proportion of the whole, and actually, we can see again, can't we? The numerator denominator have been divided by the same common factor and the value of the fraction remains the same. Do you notice anything about what's different between... We divided 4/12 by four didn't we? In the previous slide and we found the equivalent fraction of 1/3. We divided it by two. And then by two again, do you notice anything about that? Excellent. So divided by two and then divided by two again is the same as divided by four. Isn't it? Well, done. You quite rightly told me that the common factors of four and 12 are one, two and four. Excellent. And we could divide the numerator denominator by any of these common factors and equivalent fraction, actually which common factor expressed 4/12 in its simplest form which common factor? Brilliant, screaming at me now, aren't you? You screaming at me. You saying it was fours Ms. Seton, it was four, you're quite right. So when we divided by four, we expressed 4/12 in its simplest form. Can you tell me anything about the common factor four? So have a look at one, two and four which are the only common factors of four and 12. And what can you tell me about four? You remember the language? It's the highest common factor. Isn't it? Let's say that together. The highest common factor the numerator and denominator is four really well done. One more time. The highest common factor of the numerator and denominator is four. We've made a lot of connections in this session. We now know how to identify a fraction in its simplest form, because we know that the numerator and denominator have been kept as small as possible whilst keeping the value the same. And we now know that we can find the highest common factor of both the numerator and denominator and divide the numerator and denominator by the highest common factor to find the simplest form. So I find you to do that for your independent activity. I put 6/15, and find all the common factors for the numerator and denominator. And then I'd like you to just approve if you can that when you divide by the highest common factor it expresses it and its simply form and you might want to have a look at those STEM sentences because you'll be using them in the next session. And see if you agree with what they say and a little challenge there. Thinking back to my poppy do you think you would have wanted to go out for 45/60 of an hour? And how could we express that In it's simplest form? Those using the highest common factor help us. I hope you really enjoyed our session today. I have, I really look forward to seeing you again. Bye. Bye.

Simplifying fractions using highest common factor

Simplifying fractions using highest common factor

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UnitMaths / Equivalent fractions

Maths