Comparing non-unit fractions of quantities

Key Stage 2

Maths

Fractions

A packet of paper has 261 sheets. Two thirds of the packet has been used. How much paper is left?

Natalie goes on holiday for two weeks and two days. She spends three eighths of her holiday in Devon, and the rest of the holiday in Cornwall. How much time did she spend in Cornwall?

﻿Hi, welcome to today's maths lesson with me, Miss Jones. How are you today? Hope you're feeling good and ready to start. Let's have a look at what we're going to be doing today. In today's lesson, we're going to be comparing non-unit fractions of quantities. We're going to start by comparing fractions of quantity problems. Then we're going to play the game would you rather? You've got some questions and a task based around that. Finally, you've got the quiz. You'll need today pencil and piece of paper or something else to write with and write on. If you haven't got that already, go and get what you need and pause the video. If you've got everything, let's get going. Okay, here's a problem we're going to go through together. Tamal and Harry are buying some football cards. They can either buy a packet of 24 between them or buy a bumper pack of 55, along with Sam, Lisa and Andy. Either option would share the cost and the cards between each person equally. So should they go for option A, you can see I've drawn them out here, or option B, 24 shared between two or 55 shared between five or in fifths? Which option should they go for and why? See if you can have a go answering this one. Okay, let's have a look together, shall we? Okay, so if they would pick option A, they have 24 cards and we need to halve them or split them into two equal parts. If they pick option A with a whole of 24, each part would be worth half of 24, which is 24 divided by two, which is 12. One part would be worth 12. If they were to pick option B, which is 55 cards but split into five equals parts or fifths. Let's think. The whole would be 55. That would be my whole. One part would be 1/5 or 55 divided by five, which would be 11. So actually, option A would mean that they get more cards. Tamal and Harry should choose option A, because they would get 12 cards each, which is one more than they would receive if they chose option B. Okay, let's look at this next problem. Rita wants to buy a laptop. She finds two that she likes. And these are the prices. She could have laptop A, which has an original price of 640 pounds but has 1/4 off. Or laptop B, which has an original price of 750 pounds but has 2/5 off. Which one would be the cheaper laptop? Which one should she buy? Pause the video now to have a go at this one. Okay, let's have a look together. So we've got 640 and we need to think about what the price would be if there was 1/4 off. So if the original price was 640, we need to think about what 1/4 would be, we need to divide by four. Now, 64 divided by four, we possibly could do in our head. I'm just going to use the bus stop method here to check my answer. And I know that four into six goes once. Then four into 24 goes 16. So I know that 1/4 would be 160. Now, the laptop doesn't cost 160 because it was 1/4 off. So this would be the new price of the laptop. So we can either think about 640 subtract 160 or you could work out what 3/4 is, three lots of 160. I'm going to subtract. So 640 take away 160, again you could try this mentally. I'm just going to use a method just to double check. So here I know that that's going to be zero ones. I'm going to regroup here. I've got 14 take away six will get me eight. Five take away one will get me four. So I know that this part needs to be 480. Laptop A would cost 480 pounds. Now, let's look at laptop B. Maybe you can help me out with this one a little bit. So I've got a bar that's divided into five equal parts 'cause we're working in fifths. I know that the original price was 750. I know that it's 2/5 off. So let's have a think about what 1/5 would be. What would 750 divided by five? We could do this mentally again. Let's use this to double check. We've got 150. So 2/5 would be 300. Now again, it's not asking us what 2/5 are. It's 2/5 off. So actually, this amount, which is 3/5 would be our answer, which is 450, three lots of 150. So this laptop costs 480, this one costs 450. So if she wants the cheaper laptop, she should pick option B. Laptop A costs 480. Laptop B costs 450. Rita should buy laptop B because it's 30 pounds cheaper. Did you get the same answer as I did? Would you rather? So this is going to be our main game today. You need to say which option you would rather have or rather do and tell me why. So would you rather have 2/5 of 120 pounds or 3/4 of 60 pounds? Now, I'm going to answer this one but first, I need to do a bit of maths to help me. I would certainly rather the one with the most money. So let's work that out. So first of all, in our first option, 2/5 of 120, dealing with fifths. So I've got my whole and I've divided it into five equal parts. My whole is 120. So we need to work out what 2/5 of 120 is. Well, 1/5 of 120 is 120 divided by 5, which I know is 24. How do I know that? Well, I knew that 120 divided by 10 was 12 and I multiplied it by two but you might have done it in a different way. So 1/5 is 24, which means that 2/5, which is what we're dealing with here would be double 24 or 24 times two, which would be 48. So the first option is 48 pounds. Sounds good to me. But let's see what the second is. 3/4 of 60. So my whole is 60 and I'm working in quarters. So I need four equal parts. 60 is our whole. Let's think about what 1/4 would be if we divide 60 by four. Do you know what 60 divided by four is? Well, I know that 60 divided by two would be 30, so 60 divided by four would be 15. I need to work out what 3/4 is. So counting in 15s. 15, 30, 45. 3/4 is equal to 45 pound. Now, let's see which one is more. Let's compare. So 48 is the larger amount. So I would rather 2/5 of 120 because that is equal to 48, which is three more pound than the second option. Next one, would you rather walk 2/7 of two kilometres 100 metres to the park or walk 1/2 of one kilometre 500 metres to the parks? Have a think about this one and see if you can do the maths and write your explanation. Pause the video now to have a go. Okay, let's look at these together. So would you rather walk 2/7 of two kilometres 100 metres to the park or 1/2 of one kilometre 500 metres? Let's do the maths first and then we'll think about our answer. So here I've got my bar model divided into seven equal parts. So I'm going to work out 2/7 of two kilometres 100 metres. Now, to make my division slightly less complicated for myself, I'm going to convert these into metres. So I know that two kilometres is the same as 2,000 metres. So 2,100 metres would be the amount in metres. 1/7 of 2,100, well, I know 1/7 of 21 would be three. 21 divided by seven would be three. So 1/7 of 2,100 would be 300. But I don't need to work out 1/7, I need to work out 2/7. So we need 300 times by two, which would get us 600 metres. So would I rather walk 600 metres to the park or would I rather the second option? Let's work this one out. So one kilometre 500 metres, I know is the same as 1,500 metres. Marking my whole and working in halves this time. Now I just need to find out what 1/2 is. I know that 1/2 of 1,500 is 750. So would I rather walk 600 metres to the park or 750 metres to the park? Now, the nice thing about this one is that there's not a right answer. It depends how you're feeling. If I feel like walking a lot, if I want to exercise, I might choose 750 metres. But today I say I'm feeling a little bit tired. Today I would rather pick 600 metres. What about you? Which option would you prefer in this scenario? Okay, I think it's time for you to complete your would you rather activity. For each one, make sure you work out each option, using your knowledge of fractions of amounts and then you can write an explanation, explaining which one you would prefer. Pause the video now to complete your task and then we'll look at the amounts for each option when you get back. Okay, let's have a look at these together. Would you rather have 3/4 of a chocolate bar with 28 pieces or 2/7 of a chocolate bar with 56 pieces? Why? Okay? So the first option was 3/4 of a chocolate bar with 28 pieces. Our whole is 28. I know that 1/4 would be 28 divided by four, which is seven. So 3/4 would be 21 pieces. So would I rather 21 pieces or the second option. Here we started with 56 pieces of chocolate. And we're looking at 2/7. Now, I know that 1/7 of 56 is 56 divided by seven, which is eight. 2/7 therefore is 16. Which would you rather? 21 pieces of chocolate or 16 pieces of chocolate? I'm a chocolate lover, so I would definitely prefer 21. But I suppose it depends if you like chocolate or how full you're feeling. Question two. Would you rather have 1/4 of 80 pounds or 2/3 of 57 pounds? Okay? So let's think about 1/4 of 80. Well, let's divide 80 into four equal parts. 1/4 would be 20. 80 divided by four is equal to 20 pounds. Let's look at the second option. 2/3 of 57 pounds. Well, this time, our whole is 57. We need to do 57 divided by three. It might be able to do that in your head. I know that 57 is the same as 30 and 27, which might help, or you might want to do a bus stop method. We know that here's one three here in this five remainder two and we can see that 57 has 19 threes. So 1/3 would be 19, which means that 2/3 would be 38 pounds. I can definitely see that the second option is more money. I would certainly prefer more money, so I would pick the second option because I get more money than option one. Next one, would you rather walk 2/5 of two kilometres to the supermarket or walk 3/10 of one kilometre to the corner shop? Why? Okay? So let's have a look at this. So it's 2/5 of two kilometres to the supermarket. So let's put our whole as two kilometres or I'm going to put it in metres. Two kilometres is the same as 2,000 metres. Now, 1/5 of 2,000. Well, 1/5 of 20 would be four, so 1/5 of 2,000 would be 400. So 2/5 would be 800. So would I rather walk 800 metres to the supermarket or next one, 3/10 of one kilometre. So one kilometre is 1,000 metres. So I know that 1/10 would be 100. So 3/10 would be 300 metres. Okay? So would I rather walk 800 metres to the supermarket or 300 metres to the corner shop? Why? Now, this depends on your own opinion, how you're feeling and the quality of your corner ship or supermarket. I might want to walk a bit further, get some exercise and choose 800 metres. I might just not have as much time and want to just do the 300 metres. Which would you rather? Okay, and last one. Would you rather have 1/6 of a box of 360 marbles or 5/7 of a bag of 84 marbles, okay? So if our whole here is 360, 1/6 of 360 would be 360 divided by six. Now, I know 36 divided by six is six. So 360 divided by six would be 60. So 60 marbles. Here I've got 5/7 of 84. Okay, so my whole is 84. Now, I know that 1/7 of 84 would be 84 divided by seven, which is 12. Then I need to times by five. 5/6 or five lots of 12 would get me 60. Oh, interesting. We've got the same amount. So actually, it doesn't matter which one I choose. I would get the same amount. How did you do? It's time to complete your quiz. Thanks very much. Bye bye.

Comparing non-unit fractions of quantities

Comparing non-unit fractions of quantities

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