Dividing Fractions in Mixed Contexts

Key Stage 3

Maths

Manipulating and calculating with fractions

﻿Hello, I'm Mr. Langton and today we're going to do a recap on fractions, decimals, and percentages. All you're going to need is something to write with and something to write on. Try and make sure you're in a quiet space with no distractions and when you're ready, we'll begin. Binh and Zaki are trying to calculate two thirds, divided by one sixth. Each is using a different method. Binh says that "Two thirds is a sixth of what?" Whereas Zaki says, "How many sixths, make up two thirds?" I want you to draw a diagram that matches each student's method and when you done, I want you to decide which method you want to use for each of these calculations. All right, have a go on your own. So pause it and when you're done, unpause it and we'll through it together. You can pause in three, two, one. I'm going to go through them now. We'll start with Binh's method. She says that "Two thirds is a sixth of what?" So I need to draw my sixth and two-thirds is one sixth there So that's two thirds. So it's a sixth of something. So alternate, that means each of these needs to be two thirds. So altogether I've got two, four, six, eight, 10, I've got 12 thirds, which equals four. Zaki's, method is slightly different "How many one's sixth make up two thirds?" So we need to draw diagram. And this time, we want two thirds of . How many times does one sixth go into two thirds? So that means what I'm going to need to do is pick a different colour. Let's put that there. I've now split the shape into equal sixths, haven't I? So each one of these is a sixth. Now I only need to go as far as two thirds. So altogether, how many sixth make a third? I've got one, two, three, four of them. So that's a different method. I'm getting the same answer. Now, we've asked you to draw a diagram for each of these two methods, which method will be easiest to use? So three quarters divided by a quarter. I think that Zaki's method would be easier in this case. How many times did one quarter go into three quarters? So I can draw that. There's my three quarters. And how many times is one quarter go in? To me, that one seems easier. If you look at the other, one using Zaki's method, how many times does a half going to two sevenths? That's another difficult question to do. So that's why we might be better off looking at a different method. So two seventh is a half of what? So if I draw there and label my half, if two sevenths is a half of something, then in total, I've got four sevenths. Now we're going to look at sixth divided by two thirds. Xavier and Yasmin who have drawn two different diagrams to represent the same thing. These are the two different methods that we've looked at. So Xavier has got "Six is two thirds of what?" And Yasmin has got, "How many two thirds make up six?" You should be familiar with the diagrams by now, we've used them quite a lot. But what we're going to do now, we're going to take these diagrams and turn them into function missions. What calculations are we actually doing? So in Xavier's case, starting with a six, we are drawing the diagram, we've broken it up into two thirds. That means that we have to split that six into two equal parts first. We're dividing by two, and then we're multiplying by three because we've got three of those thirds, haven't we? Altogether, the answer's going to be nine. So we've divided by two first, and then we've multiplied by three. In Yasmin's case, we're doing it differently. What we're doing first is you split each part into three equal pieces. So altogether, we've got 18 parts stretching from one end to the other. All the way along there, there are 18 parts. So she's divided the six by three. So she multiplied the six by three first to get 18. And then she's divided it by two to also get nine, because two-thirds goes in nine times. Two, three, four, five, six, seven, eight, nine. So that's two different methods, we're getting the same answer. And your task here, is to draw two function machines for each of the following questions. Pause the slide and have a go. And when you're ready unpause it, we'll go through it together. And you start in three, two, one. Okay, let's have a go. So two different methods that we can use. 15 divided by three sevenths, 15 splits into three sevens. So we're starting with 15. We can do... 15 in both of those. So we can divide the 15 by three, to get five, and we can then multiply it by seven and we get 35. We could do 15 multiplied by seven, which is not the sort of thing I can do in my head. I'm going to break that down. I'm going to do, 10 lots seven, which is 70. I'm going to do five lots of seven, which is 35. So that makes 105. And then I need to divide that by three. So multiply by seventy, divide by three, 105 divided by three, it's three times, there's one leftover. That's good, it's still 35. So both methods work. Let's look at the next one, four ninths, divided by two fifths. So I can divide by two, to get two ninths and then multiply by five. So if I've got two ninths multiply by five, I've now got 10 ninths. Alternatively, I can multiply by five first, to give me 20 ninths. And we're going to divide that by two, 20 ninths divided by two is 10 ninths. So again, two different methods for the same answer. Finally, we've got a little bit Algebra thrown in there, but your method is exactly the same, just because we don't know the values of A and B doesn't mean we can't see how we do it. We starting with 10 in each case, and we could divide by A, and multiply by B or we could start with 10 and we could multiply by B and then divide by A, I don't really mind if you don't know how to write the answer at the moment, because it's the method that we're focused on. It would look something like this, one possible answer is 10B over A, or you might just write 10 times B, sorry, B divided by A, it's little small for it to fit in the box. But like I said, I'm not too fast, if you can't do the algebra part yet. This method here. That's what you should be looking at. That's the bit you want to be working on. Okay. Now it's time for the independent task. Pause the video on the next screen, access the worksheet and have a go at the questions. When you're ready, unpause it and we'll go through it together. Good luck. How did you get on? I put the first few answers on the screen for you. I'd like to go through question three with you to see what we go through in a bit more detail. So part A, it takes Tom, a quarter of an hour to ice a cake. How many can he ice in two and three quarter hours. So the first off, the calculation that we need to do, is two and three quarters, divided by one quarter. How many times does one quarter go into two and three quarters? It might help to make two and three quarters into a top heavy fraction, an improper fraction, which would be 11 over four, divided by one over four. So how many times does one quarter go into 11 quarters? Well, that's going to go 11 times in say. Okay, that's a good start, right. Siobhan has mown two thirds of the lawn in her garden. She's mown 20 metres squared so far. We've got to find the area, the total area of the lawn. So the calculation we're doing is 20 divided by two thirds. So let's think back to our function machines now. We could do 20 divided by two and multiply by three over 20 multiplied by three and divide by two. It doesn't matter which way we do it. I would like to make my 20 smaller first. I'm going to do 20 divided by two then multiply it by three. So 20 divided by two is 10 ,and 10 times three is 30. So the total area of the lawn should be 30 metres squared. So let's think about that. If the total lawn is 30 metres squared and she's mown two thirds of it, then two thirds would be 20. So yes, I'm happy I got that right. Never hurts to check. Finally, one litre of paint covers three quarters of a wall. How many litres do we need all together? So we're doing one divided by three quarters. Right, one divided by three quarters. So I can either divide by four and multiply it by three. It's the other way round, sorry. I can either divide by three and multiply by four, or I can multiply by four and divide by three. I like that last idea best. If I start with my one, and I'm multiply it by four, I'm going to get four whole ones. And I divide that by three. Then I'm going to get four whole ones split into three equal pieces or four thirds. And that's how many litres, how much I need. We'll finish off with the explore activity. Using each of the number cards, how many ways can you complete the following three diagrams? Pause the video and have a go. When you're ready unpause it, and we'll look at some options together. You can pause in three, two, one. So here's one possible answer. There are quite a few more that you could try as well. In particular, we're looking at what's equal. Well I've got two thirds divided by four, sixth in the middle, that's four sixth would cancel down two thirds, won't it? So its two thirds divided by two thirds, which is one. You could also have two quarters, which is equivalent to a half divided by three sixth, which is also equivalent to a half and a half divided by a half is going to be one. So there are other options as well, but here's something that you can work with, but that's the end for this lesson now. I'll see you later. Goodbye.

Dividing Fractions in Mixed Contexts

Dividing Fractions in Mixed Contexts

Slide deck

Lesson details

Key learning points

Licence

Video

Worksheet

Starter quiz

5 Questions

Exit quiz

5 Questions

Lesson appears in

UnitMaths / Manipulating and calculating with fractions

Maths