Adding and Subtracting Fractions (Part 2)

Key Stage 3

Maths

Manipulating and calculating with fractions

﻿Hello, I'm Mr. Langton, and today we are going to look a little bit more at adding and subtracting fractions. All you're going to need is something to write with and something to write on. Try and make sure that you're in a quiet space with no distractions, and when you're ready, we'll begin. We'll start with a "try this" activity. Using the number cards below, how many ways can you complete the inequality frame? The first time I tried, I found six different ways. See if you can beat me. Pause the video, and when you've finished, un-pause it and we'll go through it together. Pause in three, two, one, go. So in total, there are ten different ways that you could do it. Did you beat me? Now we're going to use the fraction wall, or any other representations that we can think of, to see if these statements below are true or false. When it starts up with the first one, a half and a third is less than one, I'm going to label it "1", because I'm a bit of a traditionalist, and it's the first one I'm doing. Let's have a look at the diagram. Is a half and a third less than one? Now, it's going to help if I can look at some equivalent fractions here. I can see that a third is equivalent to two sixths. I'll just make a little note of that, two sixths. And a half is equivalent to three sixths. So, three sixths and two sixths will be five sixths. We'll check. I'll show you this in blue. Two sixths plus my three sixths... if I add on three sixths, I've got five sixths. And I can see that I've clearly less than one. So that means that my first answer is true. A half and a third is less than one. Now my second one, which I'm going to label question "2", a half and a third is less than a quarter and a half. Now I've just worked out a half and a third, I found it was five sixths. So I'm going to leave that on now, I'm not going to work that out. I've got that on there in blue. Can you see that there? I'm just going to put a little reminder in purple. That's five sixths, that is a half and a third. I compare that to a half and a quarter. Now, a half is made up of two quarters, isn't it? Which means that a half and a quarter is going to be three quarters. So let's shade three quarters. So, we can see that this is going to be slightly small. This purple bit that I've shaded, these three purple boxes I shaded, three quarters, is slightly smaller than five sixths. Now, the question says it is five sixths, and so we said that that was five sixths, didn't we? Let's make a little note. And we said that that's three quarters, and we can see actually that that's bigger, which means that that must be false. Right, we're doing pretty well, but what I'm going to need to do is I'm going to rub out this working out now, because I've only got one grid to work on. And I'm going to need this grid again. When you do your work, and I'm sure your teacher will tell you, I'm going to tell you now, don't you ever rub out your working out. There is marks for it. There are always marks available for it. This is a video, I've only got one screen, and I've only got so much space. So that's why I can do it. Right, next up after question two, let's call this one question "3". So, a half is smaller than two thirds take away one eighth. Right, two thirds, let's shade that in first. And I'm going to shade that in this orange-y colour here, we've already got that there, I'm shading another one. That there is two thirds-- oops, yep there we go. Made a little mistake, but that's okay, I fixed it. So, two thirds, now two thirds is definitely bigger than a half. Let's get a red line up, a big red line, all the way down the middle, so we can see where a half is-- oops, mm... Oh, it's all gone. Oh, I've got to do that again. That line is so important to me. I'm going to make sure that it's there. So we can see, two thirds is currently larger than a half. So a half is smaller than two thirds. What happens if we take off an eighth? Now, we can also see that two thirds, if I draw a dotted line down here, two thirds is equal to four sixths. Make a little note, now my four sixths is there. And as you can see, it's still larger than a half. If I take off an eighth, an eighth is equivalent to this block that I'm shading in here, isn't it? If I take that away, and watch just above it, that goes, let's shade in blue everything that's going to be left. I'm going to have that bit there. And I've still got this bit here, and I've got this bit here. And we can see, that with this extra bit here, it's still larger than a half. So a half is smaller than two thirds take away an eighth. So I can label that one as true. And now we move on to the last question, which I'm going to label with a "4". Seven tenths is equal to one take away two fifths. I'm going to give you a little bit of time to think about that, just while I rub out all this colouring in. Is seven tenths equal to one take away two fifths? So, where to begin? Where to begin? Where to begin? Let's start off by shading in seven tenths. This is where I really wish I had a pink, and I don't, unfortunately, but I can colour it in red. So that's two tenths, three tenths, four tenths, five tenths, six tenths, seven tenths. And I'm going to do a whole one take away two fifths. So, two fifths is going to be, let's go for green, so oh, it really should be that orange-y yellow colour. That's a fifth there, so that's a second fifth. Two fifths. And if I follow that line down, two fifths is equivalent to four tenths. Let's make a little note of that, so I don't forget those, four tenths. So what I'm now doing, is I'm doing a whole one, take away-- oops, take away four tenths. And a whole one take away four tenths is going to be six tenths, isn't it? Is six tenths equal to seven tenths? Nope. That one's going to be false. Oof, that was a lot, wasn't it? It's time for the independent task. It's your turn to have a go. You can use the fractions wall from the previous slide, or you can have a go on your own. See what you can get from these. Which ones are true, and which ones are false? And can you put a fraction on that second part to make the statements true? Good luck. How did you get on? Let's get through some of the answers together. In the first case, a third plus a quarter is smaller than one. Now I know that a third is smaller than a half, and a quarter is smaller than a half, so I'm adding up two numbers that are both smaller than a half, which means it's impossible for me to get an answer that's greater than one. So that first one is true. Second one: fifth sixths and two thirds is greater than one and a quarter. Right, so let me think. So if I've five sixths, now two thirds is the same thing as four sixths, that's giving me nine sixths, which is one and a half. One and three sixths, one and a half. Now one and a half is larger than one and a quarter. So that one is also true. Third one, starting to get a little bit trickier. But let's look at how we can rewrite it. So we've got five over four, five quarters, that's one and one quarter, and we're taking away a fifth. We want to know if the answer is going to be smaller than one. So really, what we're saying, is if this part of the question is negative, then the answer is more than one. So what's larger, a quarter or a fifth? Well a quarter is larger than a fifth, which means that one and a quarter, if we take away a fifth, our answer is going to still be larger than one. So that means that this one must be false. So now we've gotten to the last one. Four fifths take away a quarter, and I spent quite a lot of time thinking about this one, I know that the fractions , but I can kind of do the same sort of thing. I can look at some equivalent fractions. Four fifths is equal to eight tenths. Now I can't turn quarters into tenths. What about if I turn eight tenths into sixteen twentieths? So I can turn quarters into twentieths, can't I? So I've got one quarter. That would be, if we're making it into twentieths, it's going to be multiplied by five, so we'll multiple by five, that's going to be five twentieths. So, is sixteen twentieths, subtract five twentieths, greater than a half? Well the answer to that is eleven twentieths, and eleven twentieths is greater than a half, we're looking for smaller than a half, so that means that that statement must be false. Now for question two, I've put the answers there already because there are lots of potential answers. I'm giving you one thing that you could have used. You may have come up with some others, as well. So finally, one last problem for you. The first part: use the digits one, two, four, and eight, just once each, to make a fraction sum that is equal to one. Once you've done that, see if you can find any other fraction sums made from four different digits, that will be equal to one. Pause the video and have a go. When you're ready, un-pause it, and we'll share some answers. You can pause in three, two, one... So these are the answers that I got. There might be some more, as well. Have a look through mine, compare them with yours, and see if there's anything that you need to work on. That's it for today. I'll see you later. Goodbye.

Adding and Subtracting Fractions (Part 2)

Adding and Subtracting Fractions (Part 2)

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UnitMaths / Manipulating and calculating with fractions

Maths