Another method for simplifying improper fractions

Key Stage 2

Maths

Equivalent fractions

﻿Hello, year five and six. My name is Mrs. Molnar. And I'm here to teach you your math lesson today, which I'm very, very excited about. This is less than 17 within the topic of fractions. In your last lesson, in lesson 16, you were learning to simplify fractions by looking at an improper fraction. And first of all, simplifying that. Then what you had the simplified improper fraction, you converted that to a mixed number. And you were set these questions, some practise that you could do at home. So we are going have look at how you got on with those. So let's take one example at a time. The first example is 10/15 at 8/15. Now, when I look at these fractions, I can see that in both the fractions, the denominator is the same, it's 15. So I just need to add the numerators. That's easy. So 10 at eight is 18. Therefore, the sum of this fraction is 18 fifteenth. And the second step I've got to simplify this fraction. And what do we notice about this fraction? I hope like me, you have spotted that it's an improper fraction. How do we know that it's an improper fraction? Well, we know because the numerator has a greater value than the denominator. At this stage, I need to simplify this improper fraction by identifying the highest common factor of 18 and 15. Now using my times tables knowledge, I know that 18 and 15 is in a three times table and therefore three is the highest common factor. I'm going to divide 18 and 15 by three. And that is going to give me a simplified, improper fraction of six fifths. What I need to do now is to convert the simplified improper fraction into a mixed number. And I'm going to do that with the help of this representation. So I know that five fifths will make one hole, but I haven't got just five the top of of six fifths. So I can make one hole from five fifths. And then I've got one extra fifth as the fractional part. So when I convert six fifths into an next number, this is one whole and one fifth one, and one fifth. Moving on to the next example, we've got three fractions that we've got to add together here. So that might seem more difficult, but actually it's not. Because again, all of these fractions have got the same denominator. The denominator is 10. So we're just going to add the numerators. We're going to ask her the nine, eight and seven. And when we do this, we got a total of 24. So the sum of these fractions is 24 tenths. Again, can you see, that this is an improper fraction and why? Well that's because the numerator has a greater value than the denominator. And at this stage, we're going to simplify this improper fraction by identifying the highest common factor. Now looking at 24 and 10, I've identified that it is two. So I'm going to define both the numerator and the denominator by two. And that is going to simplify to 12 fifths. Now I can use that model above the picture of the fifth to help me here. I need to now convert the improper fraction into a mixed number 12 fifths. So five fifths make one hole, so I can make one hole. I can make another hole from another five fifths and that's going to be tenths altogether. And then I've got two fifths leftover. So from 12 fifths, I have made two holes and two fifths. So as a mixed number 12 fifths is equivalent to two holes and two fifths. The final example, the numbers are slightly bigger, but again, it's not actually more difficult. 32 twentieths at 12 twentieth. Notice that the denominator that the same. And therefore we just add the numerators, giving us a sum of 44 twentieths. Again, we are going to simplify this improper fraction looking at 44 and looking at 20. I know that both of these numbers are in my fall times table. And so I can use the highest common factor of four to simplify. I'm going to define both the numerator and denominator by four, which gives me a simplified, improper fraction of 11 fifths. At this stage, we want to convert the simplified improper fraction to a mixed number and helpfully with dealing with fifths again, we've got some 11 fifths. And I know for my previous question, I can use my knowledge there of 12 fifths. I know that I can make two holes. That's going to be 10 fifths, and then I'm going to have one fifth leftover. So when I convert 11 fifths into an next number, that will be two holes and one fifth. I'm sure you did absolutely brilliantly with those practise activities. Great job. So we are going to take another look at the first example from your practise activity. And the 10 fifteenths at eight fifteenths, and this was how we solved it. We, first of all, added the two fractions to get 18/15, which we've already said is an improper fraction. And at this point we simplified it by finding the highest common factor, simplifying that to six fifth and then we converted that to a mixed number. And we're going to call this method one. But there is another way that we can express this answer in its simplest form. And we're going to take a look at that now. So let's call my method, the new one method two we're going to use except for the same calculation and we're going to start in the same way. We're going to add 10 fifteenths and eight fifteenths. And that's going to give us a sum of 18 fifteenths. Now at this stage, we know that this is an improper fraction and we're not going to simplify it. We are going to convert this to a mixed number and we're going to use this representation to help us. We can see 18 fifteenths here, and we know that one hole will be made up of 15 fifteenths, and we can identify that here. So we've got one hole and then we've got three remaining fifteenths, three fifteenths. So when I convert 18 fifteenths as an improper fraction into a mixed number, this is one and three fifteenths. Now this fraction is not in its simplest form and that's what we need to do now. We know that we don't simplify whole numbers. So we just need to ignore the one for the moment and focus in on that fractional part of three fifteenths. In the same way as we did before, I'm going to ask myself, what is the highest common factor of the three and 15? And I think that we can see that it's three. Three and 15 or both in the three times table. And the numerator of three is a factor of 15. So I'm going to divide the three and the 15 by three. And that is going to give us remember that, one is coming back in and one fifth. So we've simplified at a different stage there that's called method two. So let's take a look at another example, using method two to simplify. This time, it's a subtraction, but the steps are the same. Notice the denominators are exactly the same. So what do we need to do? That's it. We just need to focus in on those numerators. And we're going to subtract four from 22. 22 subtract four is equal to 18. So the answer to this once you've thought it is 18 twelves, and we have an improper fraction. Now, can you remember what the difference was now with method two? What do we do at this stage? Do we simplify it or do we convert it to a mix number? That's right, we're going to converse it to a mixed number and we are going to use this representation to help us. So we've got 18 twelves. How many twelves will make one hole? That's right. It's 12, twelfths. We'll make one hole and we can see that here. So we've got one hole and we've got six remaining parts or six twelfths leftover as the fractional part. So I've now converted 18 twelves into one hole and a fractional parts, which is one and six 12th. Is this all fraction in its simplest form? Can you remember? Have we simplified yet? No, we haven't. And that's what we do at this stage. So how do we simplify? We have to identify being highest common factor. Do we need to simplify the one? Now we don't simplify whole numbers. So we're going to focus in on that fractional part of six 12th and identify the highest common factor. We can see that six and 12, both in the six times table and six. The numerator is a factor of 12. So the highest common factor is six. So we are going to define both of them by six and to remembering that one hole, which we didn't need to simplify that. Now we have one and one half that is all fraction in its simplest form. And we've done that using method two. Okay, so I think you are now ready to have a go at solving and simplifying on your own, and you're going to use my method, method to, to do it. So here is the calculation that I'd like to work with. I want you to pause the video, have a go at that using method two, and then we'll see how you get home. So how did you do? You will have noticed on shore that the first step is easy, the denominator is the same tenths. So we're going to add 13 and nine giving us a total of 22 tenths. Now, what did you do at this point? Did we simplify it or did we change the improper fraction into a mixed number? That's right with math two, we're going to change it into a mixed number from the improper fraction. And you may have drawn something like this to help you, but if not, it's here now. Now we're dealing with tens. So we know that 10, tenths are going to make one hole. So how many holes can we make from 22 tenths? How many groups of 10, tenths? Hopefully you've spotted that we can make two holes, two groups of 10, tenths to make those two holes. And then we have two tenths remaining or leftovers the fractional part. So we have two and two tenths. Now I'm sure at this point, this is where you said, Oh, I've now got to simplify. I've got to find the highest common factor. Of course, I think you will have remembered that we don't simplify whole numbers. So we just leave that for the moment. And we focus in on the two tenths, the fractional part. Looking at two, I can see the that it's a factor of 10 and therefore the highest common factor will be two. If I'm going to divide two and 10 by two, and that is going to simplifying to two and one fifth. So two and two tenths simplified in its simplest form then is two and one fifth. So we are going to look at both methods side by side. We've got method one and method two. And we're going to use a very familiar calculation, 10, fifteenths at eight fifteenths. Kind of moment, I'm going to ask you to pause the video. And I want you to think about what's the same and what's different about both methods. So pause the video now and have a good think about that or discuss it with somebody who's next year. So what did you identify with the same and what did you identify with different? Well, the same in both methods is the sum that we have a sum of one and one fifth. What's also the same is that when we simplify, we use the highest common factor of three and that four, we divide by three to simplify or fractions. So what different, well, hopefully you thought about when we simplify and the order in which we do things. So in method one with 18, fifteenths, which is an improper fraction, we simplified that point to get a simplified, improper fraction before converting to mix number. Whereas in method two with 18, fifteenths, at that point, we converted to a mixed number and then we focused in on that fractional parts and we simplified at that point to get one and one fifth. So well-done for identifying those similarities and differences. And I guess the next thing to consider is, when should we use each method? When is it best to use method one and when's it best to use method two? And that's a tricky thing. It's not an easy answer. And I think sometimes it depends on the numbers. And so we're going to have a look at another couple of examples to try and reason that through, to decide when it would be easiest, most efficient, most accurate to use one method or the other. So we are going to look at a calculation and we are going to think about and consider which method would be easiest, most efficient, help us to simplify. So 58, thirtieth and 13, thirtieth is 72 thirtieth. And the first thing I think, obviously that those numbers are quite large. And at the moment I'm struggling to think off the top of my head of the common factor of 72 and 30, the highest common factor. It's a bit tricky. If you can do that, that's fantastic. But my gut feel is that, I think I'd like to convert 72 thirtieth into a mixed number at this point. So I'm going to use method two. So all hole will be made up of 30 thirtieth. So I'm going to ask how many groups of 30 thirtieth, how many holes could I make from 72 parts, 72 thirtieth. and I can make one group 30 thirtieth and another group that would be using 60 thirtieth. And there would be 12 thirtieth remaining as the fractional part. So I've made two holes and I've got 12 thirtieth remaining as a fractional part. Now these numbers feel a bit friendlier. We know, but we don't simplify whole numbers. So we can just ignore the two for the moment and focus in on that fractional parts. And they do feel friendly at 12 and 30. When I look at those, I know that they are both in my six times table. So I'm going to divide the numerator and the denominator of that fractional part by six in order to simplifying and remembering my two holes, that means that my fraction simplifies it to two and to two fifths. Well done if you use method one, I felt that method two would be easier for me. And so that is the way that I simplified it. So again, we've been to look at a particular calculation and decide which we feel would be the most efficient or the easiest method to use in order to solve and simplify this calculation. So we've got 83/14 subtract six 14th, and that gives us an answer of 77, fourteenth. Now straight away. I think that I can identify the highest common factor of 77 and 14. Those numbers feel a bit friendlier. And have you spotted it? It's seven. So I'm good to use a method one. I'm going to simplify it this point. So thinking about the highest common factor being seven, I am going to divide both the numerator and the denominator by seven. And that is going to give me a simplified improper fraction of 11 halves. At this point, what have we got to do? Yeah, we've got to convert into a mixed number. So I've got to ask myself how many parts, how many equal parts is my whole major path it's made up of two equal parts. So how many holes, how many groups, if those two equal parts, can I make from 11 halves? So I can make five holes out of 11 halves, and that's going to be 10 half with one remaining half leftover. And therefore when I convert 11 halves into in mixed number is fine and one half. So in this case method one proved to be quite efficient. So here are the practise activities that I'd like you to have it go up before next time. So what I want you to do, is to look at these calculations and use method one or method two to express the answer to these calculations in the simplest form. But what's really important here is that you consider why you've picked those methods. And you were able to explain your choice. If you're not sure, perhaps you could use both and consider which one felt easy, which one felt more comfortable. But remember the really important part is being able to justify why you picked method one or method two as the most efficiently easiest. And which one did you choose again? And if you have time on a medic for a challenge, then there's a challenge at the bottom there of the slide. So I just want to say thank you so much for working so hard in today's maths lesson. I've really enjoyed teaching you. And I hope that I see you again very soon. Bye for now.

Another method for simplifying improper fractions

Another method for simplifying improper fractions

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UnitMaths / Equivalent fractions

Maths