Adding and Subtracting Fractions (Part 1)

Key Stage 3

Maths

Manipulating and calculating with fractions

﻿Hello. I'm Mr Langton, and today we're going to start at looking at how we add fractions. 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. We'll start with the 'try this' activity. Draw a triangle and shade it in correctly for each point labelled on the number line. A complete triangle like the green one at the top is worth a whole one. B has been done for you, see how many more you can do. If you're feeling really confident could you draw and shade a shape that would lie between D and E? Pause the video and have a go. When you're ready unpause it and we'll go through it together. You can pause in three, two, one. So how did you get on? I've sketched some triangles here already, and I'm going to start shade them in. So A is 1/4 of a way along lines and if B is halfway, like that, then A would be 1/4. So, I'm going to need to shade one of these triangles. It doesn't matter which one. As long as one is shaded in. So, C is going to be 3/4. So you can shade in any three of these four like I've got here. I'm going to be careful because I'm enjoying this a little bit-- Ooh, went outside the lines. Enjoying this a little bit too much. There we go, that's good. Now, obviously anything to the right of one, is going to be larger than one, so I would have to draw more than one triangle. So, to go from one to D, I'm going to play another 1/4. So first, I need to colour in a whole one. Like so. And another 1/4. So, two ways I can describe that in saying one whole one and one quarter or I've shaded in 5/4. Part E, that's going to be 1 1/2, isn't it? Or a whole one with two more quarters. I'll show you those two quarters first. I'm going to do these two. Then, of course, I've got a whole one as well. You have no idea how much fun this is. Yeah, right, okay. I'm getting a bit carried away now. Right, okay. So, we've got it like that. Can we draw shapes that would lie somewhere between D and E? So, I'm going to need that diagram like I've got for E, but instead of the D I've shaded in a four full triangles make a whole one and then one complete triangle. For E, I've shaded in the four and then I've coloured in two triangles. Meaning shading one and a half, actually. And I'm not going to draw it this time, I'm just going to show you, it's going to look like this. Okay, should we move on? So now, we're going to write a sentence to describe the addition below. Looking at that first one, I've shaded in 1/2. A half has been shaded in and I'm adding on 3/4. And that gives me one whole one with another quarter. That's one way that I can do it. Let me look at a slightly different method now. Let's just rub that out. Instead of calling that 1/2, we could say that I've coloured in 2/4, can't we? And on this next one, I've coloured in 3/4. So all together, one, two, three, four, five. I've coloured in 5/4. Now, writing it this way, you can see a pattern, can't you? 2/4, add 3/4 makes 5/4. So, if fractions have got the same denominator, or if we say that if the fractions are denominated in the same way, we could add or subtract them just by considering the numerators. So, 2/4 plus 3/4 is 5/4. Over on the right-hand side I've put another question. I've got 11/9. I'm subtracting 4/9. So, I've got 11 of them and I take away four of them, I've got seven of them left. So, if the fractions are denominated in the same way. If they've got the same denominators, then we just have to deal with the numerators. Here are six questions that we can have a quick look at now. So, the first one: 2/10 add something makes 7/10. So how many more tenths could we need? We've got two of them, we need seven, we need to add five more tenths. If we've got 3/8 and we subtract 2/8, then we've got... Then we've got a 5/8, do we? Come on, pay attention. This is why you should always read the question. We've got 3/8 and we take away 2/8, we've got 1/8. On the third one, we've got 7/15 and we're adding 8/15 and that's going to give me a total of 15/15. Which, of course, we know is also a whole one. This next one, question D, this is very open ended. Lots of things that we could put here. We've got 24 over 25, equals something over 25 add something over 25. There are lots of different options here. As long as you pick two numbers that add up to make 24, then you did it right. So, for example, 3/25 and 21/25. That'll work. I could have 12/25 and 12/25, I could have 1/25 and 23/25. Well divided it is. And right, let's move on to E. 3/7 add some more sevenths makes 1 2/7 So a whole one is 7/7, isn't it? So all together, this here is equal to 9/7. So, if I've got 3/7 already I need to add on six more sevenths to make that work. And finally, 1 3/4 equals so many quarters take away so many quarters. And again, loads of answers that we can have. What I'm going to start off by doing is saying that one whole one would be four quarters. So, 1 3/4 is 7/4. So if I'm working quarters here, because I've got my fractions denominated in the same way, then I need a subtraction that makes seven. So, for example, I could have 10/4 take away 3/4. That makes seven. So, any two numerators that will make seven when we do the subtraction. So, now it's your turn to have a go. Pause the video, access the worksheet and see how many you can do. They're a little bit sneaky with this one cause they've thrown some decimals in there as well, but just remember to turn those decimals into fractions. Make sure you get the same denominators and have a go and see what you can do. Good luck. So how did you get on? I've put the first few answers up on the screen for you now and I'm going to go through question two with you. We're going to correct the mistakes that have been made in these calculations. 2/5 add 3/5 equals 5/10. So, what's the mistake there? The mistake is that these fractions, what they've been denominated, they've got the same denominators, this one has not. We do not add the denominators together. We've got 2/5 and I add on 3/5 and all together I've got 5/5. All right, what about the next one? I mean, 47 take away two is 45 isn't it? So, I can see why somebody would make that sort of mistake. What we've got to remember is this number here on the left is not 47. It's 0.47, which is actually, if we have to write that as a fraction, that's 47/100. And 0.2 is 2/10. Now, I'm just going to write that just up above for a moment. Because if I write 47/100 and I try to subtract 2/10, I'm going to struggle because my fractions are not denominated in the same way. So, I need to make my 2/10 into hundredths. So, 2/10 is equivalent to 20/100. Which means, if I now do that subtraction, I'm going to get 27/100, but if I wanted to write it as a decimal, then actually, it should be 0.27. We'll finish off with the 'Explore' activity. Use the number cards to complete the quality frame below. Pause the video and have a go yourself. When you're ready, unpause it and we'll do it together. You can pause in 3, 2, 1. Have you done it? I came up with a solution. I did 2/12 add 4/12 which is equal to 6/12 or 1/2. And on the other side I had 3/8 and I had 1/8 which makes 4/8 or 1/2. And 1/2 equals 1/2. There might be other ones as well, did you get anything like that? That's what we're going to finish with now. I'll see you later. Goodbye.

Adding and Subtracting Fractions (Part 1)

Adding and Subtracting Fractions (Part 1)

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UnitMaths / Manipulating and calculating with fractions

Maths