 To the second lesson of NSSEO mathematics in a series of two lessons the topic of this lesson is ratio, proportion and rate. The objectives of this lesson are to define ratio, simplify ratio, define rate, divide a quantity into a ratio, solve direct proportion problems, solve indirect proportion problems. Let's switch over to hear what Sam and his family have to say. Sorry to disturb you, Sam, but I am moving for the electricity bill. Sure, sir. Go ahead. What is the problem? I have a mathematics assignment that I have to hand in next week. So what's wrong? I don't understand half of these things, Anne-Sara. But what is the topic of the assignment? Well, it deals with ratio, proportions and rate. I understand the ratio part, but the rest is completely Greek to me. So what are you going to do about it? I don't know. I'm not sure. Okay, let's do this. You work more on your stuff and then I'm going to talk to Aunt May's daughter to come help you with it. She's a mathematics teacher. That's my favorite people. Evening, dear. How was your day? Fine. Very fine. So, what is Sam? Sam is having a big problem with his mathematics assignment. He's in the study. Come on. Sam cannot have a problem with mathematics. He's so good at it. I know. I think you should have a talk with him. And I've even asked Aunt May's daughter to come help him tomorrow. Yeah, that's a good idea. Now what? I think I will go check up on him. Okay. All right. And now get supper ready. Good. Hi, Sam. How's it have been? Hi, Uncle Dave. My day hasn't been good at all. This assignment is completely Greek to me. What is the topic of the assignment? It deals with ratio and proportions. Yeah, I think we've got a problem there. You know what? Your aunt said that she phoned Aunt May's daughter. She's a mathematics teacher to come and help you with this. Or I think you should rather go to her tomorrow then. Yeah, sure. So, I'll just leave this for now and continue tomorrow. Yeah. And you know what? For now, let's do my favorite subject. Yeah? Let's go eat. Oh, okay. Gotcha. Must be Sam. Hi, Mr. Thompson. Yes, I'm Sam. Have a seat. Mr. Thompson, thanks again for helping me with my assignment. It's a pleasure, Sam. Now let me hear what the problem is. Well, we've been given a math assignment that we have to hand in next week. It deals with ratio, rate and proportions. The problem is, I have to show my working as well as my solutions. Okay. Now let's start with ratios. What do you think the word ratio means? Um, I'll try. Ratio must be the comparison of things. Yes, Sam. You're halfway right. Ratio is the comparison of two or more quantities of the same kind. Let's look at an example. There are 26 girls and 12 boys in your class. The ratio of girls to boys would be what? That would be 26 to 12. Yes, that's right. But you must always give ratio in its simplest form. What do you think it would be in its simplest form? Well, both of these numbers can be divided by two, so I'd say it's 13 to 6. That's good, Sam. Let's move on to rate. What do you think the term rate means? Um, rate must be the comparison of quantities of a different kind, isn't it? That's spot on. Speed is an example of rate. You compare distance with time. Can you name some other examples of rate? Sure. Um, the amount of money we pay per minute when we make a phone call is also considered as rate, isn't it? Yes, Sam. That is correct. Now, let's look at the definition of proportion now. Proportion is a statement of equality between two ratios. Four quantities A, B, C, D are said to be in proportion if A over B equals C over D. But before we go on dividing a quantity into a ratio, let me get us something to drink. Okay, thank you. It's a pleasure, Sam. I hope that ratio, rate, and proportion is clear to you now. But you know that's only the beginning. Next, we are going to look at how to divide a quantity into a ratio. Are you ready to start, Sam? Um, sure. Okay, I have a problem I want you to work out for me. Let's start with the following. Three girls, 9, 12, and 15. The father gives them $600 to divide in the ratio of their ages. How much do you think must each one get? Okay, I'm done with Thompson. Okay, now explain to me what you did. I took 9 divided by 12 and multiplied it by 600. That will give me the amount of the first sister. Then I took 12 divided by 15 multiplied by 600 and that is the amount of the second sister. To find the amount of the third sister, I just added the amounts of the first two sisters and subtracted it from 600. Unfortunately, Sam, that is not right. You must first write the ages of the sisters as a ratio. That would be 9, 12, and 15. Now you simplify the three ages by dividing them by 3 and it will give you 3 to 4 to 5. Then you add the simplified ratios together. That would be 12. Then you calculate the amount each sister will get by taking the ratio divided by 12 multiplied by 600. For example, the first sister will get 3 divided by 12 and multiplied by 600. That is $150. Now you can do that for the other two sisters. Okay, Ms. Thompson, the second sister will get 4 divided by 12 and multiplied by 600 and it will give you $200. The third sister will get 5 divided by 12 and multiplied by 600. That's $250. Is that right, Ms. Thompson? Well done, Sam. Is there anything else you need help with? Yes, Ms. Thompson. I have a problem with direct and indirect proportion. I don't quite understand it. Okay, let's start with direct proportion. Direct proportion is when one variable increases, the other one will also increase. That means if one book costs $5,000 and we increase the amount of books, the cost will also increase. I see. It's not that difficult though. That means that indirect proportion is when one variable increases and the other one decreases. That's right. Can you give me another example of indirect proportion? Yeah, if 10 people build a wall in 3 days, I would expect 15 people to build the wall in less than 3 days. That's if they work at the same rate though. While, Sam, it seems as if you understand everything just perfectly. Now I'm going to give you some examples on direct and indirect proportion to work out. Sure. The first problem is if a machine prints 8 books in 25 minutes, how many books will be printed in 2.5 hours? The second problem is as follows. 8 people can dig a trench in 6 hours. How long will it take 3 people if they work at the same rate? You can do this problem so long while I finish preparing my supper. Okay, Ms. Thompson. While Sam is busy completing the problems, let us look at how we should solve them. In order to solve the first problem, we make the unknown number of books x. We then take the x divided by 8 and equal that to 150 divided by 25. Do you know where the 150 comes from? Yes, that's right. It is the 2.5 hours that is converted into minutes. Then, we calculate x by cross-multiplying 25 with x equal to 8 multiplied by 150. That gives us an answer of 48 books. To solve the second problem, we make the time x now. We will then have x divided by 6 equal to 8 divided by 3. Did you notice that we inverted the 8 divided by 3? We do this because we are calculating indirect proportion. Now you can find how long it will take 3 people to dig the trench. Then, we calculate x by cross-multiplying 3 with x equal to 8 multiplied by 6. That gives us an answer of 16 hours. Let's hope Sam could solve the problems easily. Let's now recap what we've learned today. Racial is the comparison of two or more quantities of the same kind. Always give racial in its simplest form. Rate is the comparison of quantities of different kinds. Direct proportion means when one variable increases, the other will also increase. Indirect proportion means if one variable increases, the other one would decrease. This brings us to the end of today's lesson. Goodbye.