2.Topic 2-Video 1

Hello. So, in this video, I'm going to be comparing fractions with different denominators and trying to put them in order of size. I'm going to go through 3 sets of examples of fractions. The first set is where all the denominators are the same actually. But, the numerators are different. I think that's probably a good place to start if you're not sure about what we're doing. Then I'm going to go on to looking at fractions where all the numerators are the same, but, the denominators are different. And, then I'm going to look at fractions that have numerators and denominators that are different. Okay now, if you click on the green bubble, it will take to straight to that part of the video. And, if you already feel comfortable with that, then you can click straight on to the yellow bubble. And, that will take you to that part of the video. And, if you're already okay with that, then you can go straight on to the orange part of the video. And, any one time, you can click on the return to menu button on the top. And, that will take you back to this page. Okay. You can get your notebooks and pencils ready. We will begin. Put these fractions in order of size, from smallest to biggest. Four sixth, five sixth, and three sixth. Okay. That's probably very straight forward. But, if it seems like a bit of a mystery, then let me try and use a diagram to help you understand what's happening. four sixth, five sixth, and three sixth. Okay. Here, I have a bar. Another bar, and another bar. And, then I cut them all up into sixths. First one done. Second one done. And, third one done. Now, I was asked to compare three sixths with five sixths with four sixths. There we go. You see how I've coloured them in. 3 out of 6, 5 out of 6, and 4 out of 6. We can see that the smallest one is three sixths. The largest one is five sixths and the one in between is four sixths. So, in which case, I need to put them in this order. Three sixths. Okay, three sixths. Four sixths. And, five sixths. Done. Okay. Next one. Put these fractions in order of size from smallest to biggest. Now, this is where all the numerators are the same. But, the denominators are different. And, you might be thinking from the previous example. Well, I'll just choose the smaller number, now will be my smallest, and the bigger number will be my biggest. You really need to understand what's going on. I don't want to just say what the rule...if there's a rule or not. Let me help you try to understand by way of another diagram. So, here is... this represents one whole. That's a green bar that represents one whole. If I start cutting it up into fractions I want to show what happens. Here, I've cut it into 2. So, the size of one half looks like that half of the whole. Okay. Now, I've cut into three. And, I choose one third. Then it looks like that. And, if I cut the whole into quarters, and then choose one of them, it looks like that. Can you see what's happening every time I increase the denominator, every time I cut it up into more pieces? If you can't, let me do it this way. So, the bottom one is cut into 5 pieces. This one is cut to 4 pieces. The next one I'll cut into 3 pieces. And, choose one of them. And, the top one, I'm going to cut into 2 pieces, and, choose one of them. Look, what's happening. Every time the denominator gets bigger by 1, the piece... one of those pieces will get smaller. That's got to make sense, right! The more pieces you cut a whole into the smaller each piece is going to be. Okay. Well, in that case, that's going to help us with this. One fifth is being cut into 5 pieces, and, we've got one of them selected. So, it's going to be the smallest, because, it's been cut into more pieces than these 2 fractions. This was going to be the middle fraction, in order of size, this one is been cut into 4 pieces. And, this one is going to be the biggest out of the 3, because, it's only been cut into 3 pieces. And therefore, each individual piece, each and all individual third would be bigger. If you're certain to see a pattern, the pattern also applies when you change the numerator, let's say from 1 to 2, but, keep the numerator all the same across these different fractions. So, a two fifth is smaller than two quarters which is smaller than two thirds. Quick demo of that. Here's also that two fifths. Here's also that two quarters. Here's also that two thirds. I'll select two halves. As long as the numerators are the same, you can see that the bigger the denominator is, the smaller the fraction would be, because, you're cutting them into more and more pieces. It sounds intuitive to start with having a bigger number somewhere, meaning an actual smaller amount. But, with fractions, remember the... remember what was going on. Think of that little picture inside your mind. Okay. We're onto the third and final set of fractions which is to put these fractions which have different numerators and different denominators into order of size, starting with the smallest. Four sixths, three fifths, and seven tenths. If you aren't sure with fractions, and this is your first time trying to put things in order, you may have come up with a rule by yourself that says right or left there, there's a bigger number on top, then that probably means it's bigger. But, if there's a smaller number on the bottom, then that means it's bigger. I'm trying to mish-mash different rules together. That doesn't work. Rules do not help you understand what is going on. But, pictures do. So, we've got four sixths, three fifths, and seven tenths. What I really need to do is to put each of these fractions into an equivalent fraction which all share the same bottom number, which all share the same denominator, because, then, it becomes an example like this where all the numerators are different, but, the denominators are the same. That's because, with same denominators, it becomes really easy. So, let's try and do that. Let's turn these into fractions that all have the same denominator. What do I need to do to achieve that? I need to look at the current denominators. 6, 5 and 10. And, think of a common multiple that is a number where the 6 times table meets the 5 times table, and also meets the 10 times table. It doesn't take me long to figure out that the common denominator or a common denominator that they all share is 30. They also share 60, by the way. But, 30 is smaller, and that would mean that multiplication is going to be as big, then it wouldn't be prone to fewer errors. So, we'll turn these all into something out of 30. There are other videos that you can watch to turn one fraction into another equivalent fraction. And, you can link to that by clicking the bubble that's just stand out. But, before I go ahead and show you how to do that, again, I want to turn to a diagram. So, I'm going to turn four sixths into something out of 30. Here's I've got a bar that's cut into 30 pieces. And, here I've got a bar that's cut into 6. So, we said four sixths. What is that is the same as in thirtieths? All of you are counting with me. The answer is 20. Four sixths is the same as 20 out of 30. Okay, how did we get that? Four sixths. Well, to turn 6 into 30, one way to do that will be to multiply by 5. Okay, to turn 6 into 30 using multiplication, I've needed to times by 5. And, whatever you do to the bottom, you need to do to the top. That's one way of looking at it. The diagram is the other way. Okay. So, we've got three fifths. So, we want to turn that into thirtieths. So, here's a fifths, and about three of them. I don't need quite as many thirtieths for that. I need only 18. There are 18 thirtieths there. And, that's the same as or equivalent to three fifths. How does that work? So, what can I times by 5 to make 30? 6. Whatever I do to the bottom, I do to the top. So, times the top by 6, then, you get 18. Now, we've got seven tenths to play with. And, I'm going to turn that into thirtieths. So, the bottom bar is now changed into tenths. And, I need 7 of them. 1, 2, 3, 4, 5, 6, 7. 1, 2. And, that means I need 21 thirtieths to match the seven tenths. 21 thirtieths is equivalent to 7 tenths. You could do this way on your paper by figuring out what you need to multiply 10 by to make 30, which is 3. And, you do the same to the top times that by 3. And, you get 21. And, now look. I've got 3 fractions, all out of 30. And, it makes it very easy to compare the fractions, because, you just look at the numerators. There we go. So, which one's the smallest? It's this one, because, it's equivalent to eighteen thirtieths. Three fifths is the smallest. And, which one's the net smallest. This one, four sixths. There you go. And, the biggest is the seven tenths. Seven tenths is the biggest. Okay. So, that's the end of this video. Go back to the menu if you want to watch the parts that you need to revisit. But, please remember. Think of diagrams, not just rules. You really need to understand what's going on behind all this. And, not just trying to remember a series of oh, well, is the top number is bigger or the bottom number is bigger, then you have that kind of fraction. It just... it's not a helpful way to learn things. Draw a picture if you need to. And, then, the rules will start to make sense. This has got to make sense to you before you can learn basic sets like this. Okay. That's the end. Bye bye!