Show your understanding on today's lesson by completing the quiz.

Fill in the gap: We can divide a line segment into a given ________ by considering the coordinates of its endpoints.

Fill in the gap: The _____________ of proportionality of ADE to ABC is 1.5.

Fill in the gap: The ratio of 𝐴𝐸: 𝐴𝐶 = 6: 9 = 2:___

Fill in the gap: The ratio of 𝐴𝐸: 𝐸𝐶 = ___: 1

A line segment ABC is split in the ratio AB to BC as 3 : 5. What fraction of the line segment is AB?

Ratio and proportion in geometry

﻿Hi, I'm Miss Kidd-Rossiter and I'm going to be taking today's lesson on dividing into a ratio. Before we get started, it'd be really helpful if you could have a pencil and a ruler, because you going to be drawing some diagrams in today's lesson. Make sure you're in a nice quiet space so that you can fully concentrate and that you've got no distractions. If you need to pause the video now to sort anything out then please do, if not let's get going. So for today's try this activity, you've got a statement here about three rectangles. I'm going to read it to you. Rectangle A's perimeter is twice the length of rectangle B's perimeter, which is three times the length of rectangle C's perimeter. Quite tricky statement there, so pause the video and reread it if you need to. You're asked to find the ratio of their perimeters. If the sum of the three perimeters is a hundred centimetres, find each individual perimeter. And then finally if rectangle A's perimeter is 75 centimetres longer than rectangle C's, find the perimeter of rectangle B. Pause the video now and have a go at this activity. When you're ready to go through some answers, resume the video. Excellent effort, well done everyone. Let's first of all look at the first part. So find the ratio of their perimeters. So the way I'm going to do this is I'm going to write it in the form A to B to C. So for me, it's easiest to start with C here. You can pick any length at all for C. So I'm going to pick the C is 30 centimetres long in perimeter. Then we're told that B is three times the length of rectangle C. So if C is 30, then B is three times that. So tell me what all that would be now? Excellent, it would be 90 centimetres, won't it? And then I'm also told that A's is twice the length of B's. So if B's is 90 centimetres, what will A's be? Tell me now. Excellent, 180 centimetres. Now you can see here, you could have come up with loads of different lengths for those perimeters. So what we need to do now is to simplify this ratio as much as possible. So can I identify a common factor of 30, 90, and 180? Tell me now. Excellent, there's loads of different ones. So whatever you said, I'm sure it was great. I'm going to divide by the highest common factor, which in this case is 30. So 30 divided by 30 is one, 90 divided by 30 is three, and 180 divided by 30 is six. So the ratio of their perimeters is six to three to one. Pause the video here and check that your ratio simplifies to this. Excellent, let's look then at, if the sum of the three perimeters is a hundred centimetres, find each individual perimeter. So I've still got the ratio on the screen there, 'cause that's going to help us. The way I'm going to do this is I'm going to draw it as a bar model. You might have been shown a different way to do it, and that's absolutely fine, but this is the way I'm going to go with today. So here is my bar model representing A, B and C. You'll notice that each part of the ratio is the same width and the same height. This is really important because each part of a ratio is equal. So we've got our one part here, our three parts here and our six parts here. And we know that the sum of these three perimeters is a hundred centimetres. So I'm dividing equally my hundred centimetres into the parts of my ratio here. How many parts do I have in total? Tell me now. Excellent, I have 10 parts, don't I? So I'm dividing a hundred centimetres by the 10 parts to get what one part would be, which is what? Excellent, 10 centimetres. So I know that each part of my ratio is 10 centimetres. If I know that to be the case, because I've worked it out, what does that mean then that the perimeter of rectangle A is? Tell me now. Excellent, what does that mean that the perimeter of rectangle B is? Tell me now. Excellent, and what does that mean that the perimeter of rectangle C is? Tell me now. Excellent, so a has A perimeter of 60 centimetres. B has a perimeter of 30 centimetres and C has a perimeter of 10 centimetres. Well done there. What fraction of A's perimeter is C's perimeter? What fraction of A's perimeter is C's perimeter? Pause the video and think about that. Excellent, so A's perimeter is 10 centimetres, isn't it that? And no, it's not sorry that's my fault. C's perimeter is 10 centimetres. A's perimeter is 60 centimetres. So as a fraction, it's 10 of 60, which we know simplifies to one sixth. So C is one sixth of A's perimeter. Or I should be more clear. C's perimeter is one sixth of A's perimeter. What fraction of B's perimeter is C? Tell me now. Excellent, it's a third, isn't it? Because it's 10 centimetres of 30 centimetres, which simplifies to a third and let's just do one more. What fraction of A's perimeter is B's perimeter? Tell me now. Excellent, it's three sixths, isn't it? Or we could be even more clever and simplify that down to a half. Really good work, well done. Final part then that you were asked to do. If rectangle A's perimeter is 75 centimetres longer than rectangle C's, find the perimeter of rectangle B. So I'm going to use the same diagram here for A, B and C. And this time I'm told that rectangle A's perimeter is 75 centimetres longer than rectangle C's. So I can see that C's perimeter is one part and A's is six. So that means that the 75 centimetres that is longer must be represented by these five parts here. So that must be my 75 centimetres. So if five parts are represented by 75 centimetres, how could I find one part? Tell me now. Excellent, I could do 75 divided by five and I shouldn't forget my unit, should I? So let's just do that again. 75 centimetres divided into five parts gives me 15 centimetres. So this time each part of my ratio is 15 centimetres. And if I know that these parts are all 15 centimetres, then that means that every part of my ratio must also be 15 centimetres. I've then asked you to work out B's perimeter. So B's worth three parts of this ratio. So B's perimeter so I'm just going to say P for perimeter. So perimeter of being is 15 centimetres multiplied by three, or you could have done 15 add 15 add 15, absolutely fine. So 15 centimetres multiplied by three, which gives me 45 centimetres. Pause the video here and navigate to the independent task when you're ready to go through some answers, resume the video, good luck. So here's the first question of the independent task then. So the first thing I want to redo is I would draw my bar model. Then I think what do I know about angles in a trapezium? Interior angles in a trapezium. Well I know that interior angles in a trapezium add up to 360 degrees. So I know that this full ratio here must represent 360 degrees. I've got how many parts to my ratio? Tell me now. Excellent, I've got 18, haven't I?. So I'm doing 360 degrees divided into my 18 parts this tells me that one part must be worth 20 degrees. Now I'm not going to write them all in here because it will take me a while. But you know that every part of this ratio is worth 20 degrees. So that means then that the first angle here is how many degrees? Tell me now. Excellent, 60 degrees. This angle here represented by the four parts is how big? Tell me now. Excellent, 80 degrees. The angle here represented by the five parts is how big? Tell me now. Excellent, a hundred degrees. And then the final one represented by the six parts is worth how many degrees? Tell me now. Excellent, 120 degrees. Don't forget your units here. Then we were asked to sketch the trapezium. So here's a trapezium that you could have sketched and we're going to label on the angles. So we've got two acute angles, haven't we? So we know that this angle here could either be 60 degrees or 80 degrees 'cause it's only a sketch. So it's not super accurate. So let's call this one 60 degrees and other acute angle here would be 80 degrees. How do I know which angle this will be here? Pause the screen and think about that. Excellent, this one will be 120 degrees it, which means that this one will be a hundred degrees because these two angles here are co-interior, aren't they? Which means that they sum to 180 degrees. And we have the same here at pair of co-interior angles. Next question then. So the first thing you would identify is that these five parts here are 10 centimetres, which means that one part has to be two centimetres. And if each of those parts is two centimetres, then that means that every part of my ratio must be two centimetres. So to calculate the length of each side, I would just look at my ratio here. So I know that each side, the first one is 8 centimetres, the second one is 12 centimetres, and the third one is 18 centimetres. And you're asked to calculate the perimeter. So to do that, you would just add up your eight centimetres, your 12 centimetres and your 18 centimetres, and get 38 centimetres. And then finally, what fraction of the perimeter is the longest side? Well, the longest side we know is 18 centimetres, and we know that the perimeter is 38 centimetres. So we know that 18 over 38 simplifies to 9 over 19. We didn't actually need to work all that out though, did we? There's another way that we could have worked that fraction out, can you tell me? Excellent, we could have used the ratio at the top, couldn't we? So we can see that we've got our nine parts of our ratio out of the total 19 parts, excellent work. Right, we moving finally then onto the explore task. Pause the video here and have a go at this activity. If you're struggling a little bit with this activity, think about what you could use to represent that one. So I'm going to give you an example. I could say that this is 30 degrees, then N would be, let's say 60 degrees, and M would be 90 degrees. So I've got what type of triangle here, tell me now. Excellent, it's a right angled triangle, isn't it? Because I've got a 90 degree angle. Think about what other value I could use. So I could use this time, I could use one to N to M. This time I could say that this is 45 degrees. This is 55 degrees and M is 80 degrees. What type of triangle would it be this time, tell me now. Excellent, it would be scalene, wouldn't it? Because all the angles are not equal. So we've got three different types of angle there. Pause the video now and have a go at this activity. Excellent work everyone. I hope you've had a really good go at that explore task. There's a couple of answers there on the board that I've given. So feel free to look at those, but there are absolutely loads here. So I hope you've had a really good mess with it. That's the end of today's lesson. So thank you so much for all your hard work on dividing into a ratio. I hope you've learned a lot. Please don't forget to go and take the end of lesson quiz so that you can show me what you've learned, and I'll hopefully see you again soon, bye.

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The angles in a triangle are in the ratio 1 : 1 : 1. What type of triangle is it?

The ratio of Adam’s height to Tony’s height is 7 : 9. Adam is 154 cm tall. How tall is Tony?

The ratio of Adam’s height to Tony’s height is 7 : 9. Adam is 154 cm tall. How much taller is Tony?

Dividing into a ratio quiz

In this lesson, we will review how to divide amounts into a ratio and find part or whole amounts from given information.

Maths

Y9 Maths

Key Stage 3

Year 9

Miss

Dividing into a ratio

Ratio review (9.7a)

Geometry

THEME

UNIT

Representing ratio

Ratio problems

I draw a rectangle and the side lengths are in the ratio 5:7. What fraction of the perimeter are the longer sides?

I have a bag of pink and brown cubes. 5/11 of the cubes are pink. What is the ratio of pink cubes:brown cubes?

A triangle has side lengths in the ratio 5 : 5 : 3. What fraction of the perimeter is the shortest side?

A rectangle has side lengths in the ratio 4:3. How long would the longer side of this rectangle be, if the shorter side is 24m?

A box contains caramel and toffee chocolates. 3/10 of the chocolates are caramel. What is the ratio of caramel to toffee chocolates in the box?

At a bake sale 25% of the cupcakes on sale are chocolate.  3/5 of the cupcakes are vanilla and the rest are peanut butter. What is the ratio of chocolate:vanilla:peanut butter?

The ratio of roses to violets is 3 : 4.  The ratio of violets to daisies is 6 : 5. What is the ratio of roses to violets to daisies, in its simplest form?

Lesson overview:Dividing into a ratio

Core Content

Ratio review (9.7a):