Modelling fractions by division (Part 1)

Key Stage 3

Maths

Manipulating and calculating with fractions

Calculate the answer in it's simplest form:

﻿Hello, I'm Mr Langton and today we're going to look at how we can model dividing by a fraction. All you are going to need is something to write with, and something to write on. Try and make sure you are in quite place with no distractions. When you are ready, we'll begin. We'll start off with the try this activity. Antoni made a statement about the first bar model so 30 is a third of 90. So lets have quick look, so 30 is a third of 90, so 30 covers a third of the bar, and each bit is worth 30. Then all together, it is a third of 90. What I would like you to do is have a look at these other four statements and have a go. See if you can write a statement similar to Antonis. Pause the video, when you are done, unpause it, we'll go through it together. You can pause in three, two, one. OK, let's make a start. Looking at the next one, we said that it's worth 30 and we shaded in two fifths. Now, if there are two fifths are worth 30 each of those individually must be 15 mustn't it? and that means each of these is also 15 giving us 15, 30, 75. So 30 is two fifths of 75. Now let us look at the next one. The other part is still 30 this time we have three parts of this so each of those must be worth ten. So we can say that 30 is three quarters shaded three quarters of 40. On the next one. We've shaded five ninths seven of 30. This five ninths of what? What is 30 split in to these five parts? each of these parts is six, 12, 18, 24, 30, 36, 42, 48, 54. And finally, we've got one, two, three, four, six sevenths so 30 is six sevenths of what? So, if we split 30 into six equal pieces each of them is worth five, 10, 15, 20, 25, 30, good. So 30 is six sevenths of 35. Antoni's statement can also be written like this: 30 divide by a third equals 90. We can use this idea to rewrite fraction statements and solve them. In the case of this example on the left we've got to do four elevenths divided by two fifths. Now we can write that as statement as if four elevenths is two fifths of something. Try and work out what that could be. We can draw a bar model to show two fifths. This bit here represents two fifths and those two fifths make up four elevenths. Which means each individual fifth must be two elevenths. So all together, before we put all these elevenths, we've got two elevenths, four, six, eight, ten elevenths. So we've solved it. Four fifths is two fifths of ten elevenths and that means that four elevenths divided by two fifths is ten elevenths. So I'm going to go through the first one now. Eight elevenths divided by two thirds we can rewrite that as a statement. I'll write it here, eight elevenths is two thirds of something. So let's draw a bar model to represent two thirds. And we know that these two thirds here represent eight elevenths. So that means that one third will be half of that wouldn't it be four elevenths? So if each third is worth four elevenths then in total I've got three of them. I've got twelve elevenths. So if we think about what we did there we took out two thirds we split them up in to two pieces and we needed three of them didn't we? Just bare that in mind as we move on. Second one. Three fifths divided by three quarters. So that means that three fifths is three quarters of something. I'll draw a bar model. It's going to represent three quarters because there are three quarters, represent three fifths. Then split those three fifths in to three equal parts. Is that OK? So I've divided by three and all together I've got four fifths. So if each one is one fifth and I've got four of them got four fifths. Right, next one. Two thirds divided by three quarters. So two thirds is three quarters of something. Start of drawing the bar model for three quarters. That bit there represents two thirds. We've got a problem here because our first step is that we need to divide that two thirds by three and we can't do that very easily with the bar model. What you should remember, hopefully, from last lesson if you look back is that we could do two thirds divided by three to get two ninths. And if you're not sure on that just have a look back on the last lesson just to make sure you've got your head round it. All together, we've got four lots of that so we've got, eight ninths. So have a think about what we've done for each of these that we've, when we were trying to find two thirds we divided it by two, we divided by that numerator we multiplied by the denominator. Divide it by two, multiply by three. When we're trying to find three quarters of something we split it in to three equal pieces we divided by three first and then each time we need four of them. We divided by the denominator, we multiplied by the numerator. You can use that for the next part. OK, so now its your turn. You're going to pause the video and have a go at the activity. When you're ready, unpause it and we'll go through the answers. Good luck. So here are the answers, you can mark your work now. Now it's time for the last activity. We've got a question up there 12 divided by three tenths. What I want you to consider is what would happen to the answer if we were to swap one of those three cards for a six? Pause the video and have a go. See how you get on and we'll go through it together. You can pause in three, two, one. All right, so the first thing that I did would work out what twelve divided by three tenths actually is. So if twelve represents three tenths, I can draw a bar model, but it's going to get quite long. I'm going to be a little careful with how I draw it I'm just going to split it up here with that bit being by three tenths. 12 is three tenths of the whole thing. So one tenth would be four wouldn't it? So if one tenth if four, then all together I've got 40. So if I'm going to replace the 12 with six then I might do six divide by three tenths. Now I can see straight away my number is half as big because I had 12 before, now I've only got 6. I've got half as much as I had before. If I'm sharing at half as much as I had before that's going to have to be 20. So if I half this number here, if I have the number that I started with then my answer is halved. All right, have we looked at the three? Let's have a different colour. So if we look at 12 divided by six tenths now it might help to draw a diagram here. Once again, bar models going to get quite messy when we're doing things such as tenths. So we have to be a little bit careful. That there is six tenths so I split my 12 in to six equal pieces, each piece is going to be two and I'm going to want 10 of them. So once again, the answer is 20. So if I halved the numerator sorry, if I double the numerator, then I half my answer. Finally, let's look at that 10. Let's have a different colour again. So this time I'm going to be doing 12 divided by 3 sixths. Well three sixths is a half so it'll be a bit easier for me to do 12 divided by a half. How many halves go in to 12? That would be 24. Now my answer, it's not very easy to see what the fraction is is the answer there, but if I originally had 40 and now I've got 24, then my answer is going to be six tenths of what it was originally. That's it from me, if you'd like to try replacing the number in the boxes with different numbers and have go from scratch and see if you can come up with anything interesting. See if there are anymore patterns you can see. See you later. Goodbye.

Modelling fractions by division (Part 1)

Modelling fractions by division (Part 1)

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UnitMaths / Manipulating and calculating with fractions

Maths