 Welcome to your second session of your second semester. Basic numeracy session, facilitation session. Please remember to complete the register. I've just posted the link in the chat. And always remember if you have any technical issues, you need to send an email to CTMtatt at unisa.ac.za. And if you have any content related to your BNU or QMI module, send an email to eboyem at unisa.ac.za and ccctmtatt at unisa.ac.za so that they have some visibility in terms of the queries that we receive. Okay, so today's session, we are going to look at ratios and proportions. And the last week of August, which will be next week Monday, same time we're going to look at differentiation. Are you all doing QMI? Or are you doing BNU? Are you doing BNU or QMI? BNU, both of you. Okay, then I will have to change the schedule because differentiation is mostly for QMI and I don't want to cover something that you guys don't do. So we'll have to find another topic that we'll do on Monday because the QMI students are not here. I must just apologize. I'm just recovering from hay fever and flu. So my voice is still husky and I'm going to be clearing my throat so often as well as we go along. Are there any questions, comments before we start with today's session? Any query? Okay. And then it's fine. Then we can just start with today's session. Like I said, today's session we're going to be looking at ratios and proportion. There are interlink. And we are going to also maybe if we have enough time, we can look at percentages. I'll wake up late percentages. And then I had some little bit of other concepts that I wanted to include in the session as well, but they were more relating to QMI than to BNU. So since they are not BNU students or QMI students, so I'm not going to cover that section. So we only going to do ratios and proportion and a little bit of percentages as well. So a ratio is a value that we use to compare things. So if we want to compare two or more numbers, we use a ratio. And especially if we want to create something new, sometimes you need to balance things. For example, you all know ores. In order for you to take the concentrated ores and make nice juice, they always tell you that it's one part orange to four parts water. In order for you to make a perfect drink. So that is the ratio. The ratio of taking the concentrated product and adding the four parts of water to it to make nice juice. And that's the other way of using ratios as well. So we're going to compare the differences between the two numbers as well. And also with ratios, you try to highlight certain things. If there are more of them than the other, you are able to use the ratios to highlight those things. And a ratio, we always denote it by one is to four, or you can write it as one over four, or one out of four. So with the ratio, because you're finding a ratio of this value to another value, the difference is with the two. It almost works like a fraction. And the two tells you which value will be at the top and which value will be at the bottom, or which value will be on the left and which value will be on the right of the dot. So if we say one is to two, one is to four, then it means we're finding the ratio of one to a four. So this is very important. The two tells me that the one will be at the top. If this is a fraction, it will be one over four, or one out of four, we can write it as a fraction. So the one will be at the top, the four will be at the bottom, or the one will be on the left and the four will be on the right because of these two. So the two is very important. It tells you how you're going to set it up. So let's get an example. A company hired six females and 24 males. What is the ratio of females to males? There again, our important letter, two letter widths, two females to males. So in this instance, they are telling us we want to find the ratio of females to males. So we can write it in this manner, or you can write it as females is to male, or you can write it as females out of males. And that will give us the ratio of females to males. But we need to be able to write it in number because they have given us the actual numbers. So let's do that. So we know that we have, we are given six females to 24 males. And we can simplify it even further by writing it in a fraction format, to say six divided by 24. And it gives us one over four, which means there is one females to four males. One is to four. In terms of ratio, we say it, the ratio is one to four males. One females to four males. So we can even simplify it further because if we want to know how many females, for every one male that they hire, how many more females do they hire? They hire actually 0.25 females for every male that they hire in this company. If I'm working at this company, I will know that if there were more females and if there were females and males coming into the interview, the chances of a female being selected will be 0.25 as compared to for a male, which will be 100%. So we know that 25% of the time they will select a female by 100% of the time they will select a male. So we can use also the ratios to calculate proportion because like I said, in order for us to balance out things or make things equal, we can use the ratios, but ratios alone don't give you that much. Therefore, we can use proportions to make things equal. So what are the proportion? Proportion is a statement that gives you two equal ratios. Right? So let's begin this example. If we have Peter and Grace selling veggie soup for the total profit of 50,000 for their shop, they need to share the profit according to the ratio of number of soups they've sold. Peter sold only 15 and Grace sold 32 soups. How much should each receive? In order for us to pay them, according to the amount of work that they put in, we need to split the profit equally against the ratio of the number of products that they have sold. So Peter sold 15, so they cannot split this 50-50 because someone sold more products than the other. So Grace sold more products, so Grace should be getting more profit. In order for us to determine how much profit each one of them should get, we need to calculate the ratio of each of their products sold and then multiply that ratio to the profit, and that will give us the amount. So for both of them, we need to also calculate the total because it will be the ratio that we'll be calculating will be the ratio of the total of both of what they have sold. So we need to say 15 plus 32, which is equal to 47. So they have sold 47 products or 47 soups, right? So we know that in total, they have sold 47 soups. So we need to calculate the ratio of pitas so that we can calculate how much Peter will receive. So Peter sold 15, so the ratio of Peter will be 15 out of 47. Multiply that with the profit that they have made as a team and that would give us how much would Peter receive. And we can also, from here, because if we have the ratio of one, we don't have to calculate the ratio of the other we can take 50,000 minus 15,957 and that will give us how much should Grace receive. But because we're working with the ratios, we're just going to calculate the ratio. So let's calculate the ratio for Grace. So the ratio for Grace will be 32 products because she sold 32 products out of 47. So it's 32, 247, multiply that with the 50,000 and that gives us 34,000. If you add both of them, they should give you 50,000. There will be some little bit of marginal error that I have. I didn't take into considerations because I rounded off some of the values. So let's see. It should give us 50,000 if we combine both of them. I'm missing one round. So 34,042 plus 15,957 Yeah, I'm missing one round. So some way, let's see. 15 divided by 47 equals 0.31, multiply that by 50,000 and the answer is I think I should have 0.44 somewhere there. 0.45 should be 0.45 because when you round off the money you are going to drop off some decimals. And the same happens, 32 divided by 47 equals multiply the answer by 50,000 and the answer will be 0.55 So I could have just made this still 4,000 0.43 because it's 55,000 and then I wouldn't be missing that one round. But that's how you will calculate the proportions. Because I dropped the decimals that's why I don't get 50,000 I'm missing my one round. But if I kept my decimals and I rounded off correctly I should have for grace we'll get 34,043 That's how the proportions work. Let's look at more examples. Mary buys a box of 48 Fritos Zimba chips for 58 Rant at Giants. She sells two packets of Fritos Zimba chips for five Rant on a tray. How much profit would she make? Now, the first thing we need to recognize from here is that a box has 48 Fritos Zimba chips and they bought it so this is the cost. So the cost is 58 Rant that's what she bought for. She sells two packets for five Rant so it means two for five Rant. That's how much she sells the Zimbas. The question is we need to calculate profit. What is profit? Profit is your revenue which is your sales minus your cost. So it means from the 48 chips that she has in the box if she sells all 48 chips how much revenue will she be bringing? It will be because she sells two for five Rant or one so therefore it means one is equivalent to two Rant 50. So we can say two Rant 50 times 48 and it will give us the revenue and we subtract the cost. That's how easy it would be in order for us to find the answer. So then let's do that. Let's first find the ratio of two Rant to five Rant and the ratio of two Rant to five Rant is to two Rant 50 and that's what I just said. That's how you will find the ratio. So one packet is equivalent to two Rant 50 cents. Take in the ratio and multiply the two Rant 50 cents multiplied by the number of packets of chips that she has. She makes a revenue of 120. So the sale is 120. We need to take away the cost that is how much she bought this packet of Zemba 4. She bought it 58 Rant so we're going to minus from 120 which is our revenue which is our sale we're going to minus the cost of 58 Rant so 120 minus 58 gives us 62 Rant so she makes profit of 62 Rant and she can go and buy two more boxes now with the amount of money that she has made she can now afford to go buy two which will create more and more and more and more and that's business. The other way of using ratios when the question looks like this and they ask you how much profit and you can say we know the ratio of the packet to the amount or the sale so we know that two packets is sold for five Rant so the ratio of two to five Rant is the same as we know that there are 48 Fritos in the box but how much are we selling them for we don't know how much they would give us so that is our X amount that we don't know so we can calculate our X we can calculate the total amount of that so please crossing two will multiply with X and five will multiply with 48 then you will have two times X is equals to five times 48 and we simplify this five times 48 divided by two because we need to get rid of two we're going to divide by two and we make X the subject of the formula and five times 48 is 240 divided by two it's 120 so we know how much the 48 will make 120 but that is not what the question is asking the question was asking us how much profit then we do the same profit minus revenue profit is equals to revenue minus cost 120 minus the cost of 58 Rant would give us 62 Rant and that's how you can use the ratios to answer questions when asked this is your exercise I'm going to do one with you and then I'm going to give you time to do the other exercise I've got a lot of them a certain school has 1800 Lenas the ratio of the number of boys in the school to the number of girls is four is to five respectively how many girls are there in the school we need to go back and read the question and make sure that we understand what we are given a certain school has 1800 so these are total total Lenas within the school the ratio of boys in the school to base my other indicator so yeah I have boys to the number of girls and they telling us that it's five is to four so there are five in this group five boys to four girls right but in terms of ratio respectively how many girls are there in the school so we need to find out how many girls do we have in the school so if we take this ratio and assume that this is our then how many number of girls we have so we can combine the two ratios and create the total of nine in terms of ratios so this is the ratio total right so we'll have nine we have nine but we can calculate the ratio of girls to the total ratio right to the total ratio that we are given now that we just created so we know the ratio of girls so we need to oh sorry not what I'm writing here ratio of girls to total so how many girls we have we have four out of nine then we can apply the proportion multiply that with the total number of learners we have in the school and that will give us the number of girls we have in the school in order for us to find the number of girls we need to calculate the ratio of girls to the total ratio which the total ratio will be combining the ratio of boys and girls which gives us nine dividing the ratio of girls which we know that it's four is to the total so four will be out of nine multiply that with one thousand eight hundred and the answer we get four is to nine multiply by one thousand eight hundred and the answer is we have eight hundred girls in the school therefore it means we have one thousand boys in the school and that's how we calculate the ratios are there any questions if there are no questions I'm going to give you an exercise which looks almost exactly the same let's see but then okay we'll do this one also together to some extent or maybe I should give you a few minutes to see if you can get it so the profit of four hundred and thirty six thousand five hundred of a company is shared between three partners A, B and C in the ratio of three is to two is to four how much is partner C going to receive from this remember it's almost exactly the same so if you think about this how much is partner C is the same as how many girls are they one thousand how much they will receive in terms of the amount so I'm just going to give you time it seems like you all got the same answer let's see so we need to add the total of the ratio so they are three plus two plus four which is nine so C is four so it will be for C it will be four over nine multiply that with the total profit of four hundred and thirty six thousand five hundred and when you calculate that you get four divide by nine equals multiply the answer by four hundred and thirty six thousand five hundred you will get the answer of hundred and ninety four thousand easy right so sometimes ratios you get them even when you calculate measurements as well so let's simplify the ratio of two hundred and fifty centimeter to fifteen meters now you must pay attention to what you are given in terms of units we did this last time so you need to at least convert one to the other so are you converting from centimeters to meters or meters to centimeters so let's assume that meters to centimeters and working with centimeters because they didn't tell us in terms of the ratios which units we can choose whichever so we are going to choose fifteen meters convert that to centimeters so let's do the unit conversion do you still remember that so meters two centimeters so we have fifteen meters we want to convert that to centimeters so we need to multiply by the number of tens remember so to convert from fifteen meters we multiply by a hundred which then means we are going to have two hundred and fifty centimeters two one thousand five hundred centimeters equals one meter is equals to hundred centimeters so we are going to multiply meters by centimeters to get it two centimeters now what is the ratio the ratio would be two fifty divide by one thousand five hundred and two fifty go into one thousand five hundred it goes how many times it goes six times so the answer here will be one over one over six and therefore it will be the same as one is two six and you can see that some of them they didn't in the same direction but pay attention to the two which one comes first so the two fifty is the smallest so you need to pay attention to that so our answer will be G another exercise relating to ratios the picture is sixty centimeters wide and one meter long also pay attention to the units the ratio of its width to the length in the simplest form would be so it means we need to change from centimeters now we are moving from centimeters to meters so since we have centimeters on the left we are going to keep the centimeters we are going to just change our meters so let's convert meters so we are going to convert from meters to centimeters so we have one meter is equivalent to hundred centimeters as we said we did it in the previous time one meter is equivalent to hundred centimeters so we just multiply with the number of tens so we'll have sixty centimeters two hundred centimeters therefore it's the same as sixty divide by hundred are there any values that can divide into sixty and divide into hundred twenty can right twenty goes how many times into sixty twenty goes three times into what other number can go into sixty and go into hundred as it is or not sixty and zero cancels out we are left with six is to ten and that's the lowest that it can go because if I look at all this there is no other number that will give us six and will give us ten so sixty to ten will be the lowest simplification of this we can rewrite it therefore we can rewrite it as six is to ten which one looks like that number two that will be the ratio of its width to the length in the simplest form so there are other ratio calculations I'm not gonna do all of them so I'm just gonna give you a time can take a screenshot of them so that we can move to percentages otherwise no we don't even have to rush let's do this one because I think we have one more exercise and then we go and do the percentages and then we are done a school has thirty teachers if the ratio of the number of female teachers to the number of males in the school is three how many male teachers are there at the school let's see 18 the answer is 18 let's see the ratio of males we know that we have the total of thirty teachers and the ratio of females two females two males which is three two and we know that the total of the ratio will be five so in order for us to find how many males we're going to find the ratio of males which is two males out of five multiply that with the number of teachers which they are thirty that will give us two divided by five multiplied by thirty multiplied by thirty is twelve and let's see if you did go and fix Juliet unless I am reading your previous question the answer should be twelve because there are the ratio of males females to males is three is to two so there is two males to total of five which will give us the proportion of two over five times thirty is twelve so there will be twelve males there should be more females because you can see if you say there are eighteen males then it will not be correct because there are one more female than males in this school the last question a school has eight hundred and eighty people if the ratio of the number of boys two girls is seven is to four always pay attention to two it resembles the same thing as the double dots how many more girls would need to enroll if the school authority wants the ratio of the number of boys to girls to be one is to one so they want the same number how many girls and boys should be how many more girls you will need to enroll in the school if we want the ratio to be one to one so first you will need to calculate what is the ratio of females to boys and calculate how many boys or girls we have in this school that will give you the number of girls that we have in the school so in order for boys and girls to be the ratio to be one to one how many more girls needs to be enrolled in this school let's first calculate the ratio of girls to the total so seven plus four is eleven so therefore we will have four out of eleven multiply that with eight hundred and eight and that will be four divided by eleven multiply by eight hundred and eighty and that will give us three hundred and twenty girls in this school right how many boys are there in this school remember these are girls how many boys are there in this school it will be eight eight eighty minus three twenty should give us the number of boys so boys we have five hundred and sixty boys in this school now how many more girls would you need to enroll if the school authority wants the ratio of the number of boys to girls to be one is to one how many more girls how many more girls should we be enrolling let's see what you have in the chat two hundred and forty yes correct because if we have three hundred and twenty so the authorities can just enroll two hundred and forty more girls into this school two hundred and forty more girls then the ratio will be two forty plus three twenty will give you five sixty and the ratio will be one is to one if they want to enroll more girls so they will need two hundred and forty girls to make the ratio one is to one so how did I get to two hundred and forty you calculate the ratio of girls we know what the number of girls would have been out of the ratio of seven is to four so there are five hundred and sixty and three hundred and twenty and the gap which is the difference between the number of boys and the number of girls will give you the difference of how many more females or girls you need to enroll to make it a one to one the last twice like I have more than last question so this one is truly the last question you can also do this one on your own we've got okay we've got ten minutes to do this suppose a school has nine hundred and sixty two learners enrolled the ratio of the number of boys to girls is five is to eight so we know the total we know the ratio of boys to girls so boys girls is five to eight so there are eight girls to five boys or five boys to eight girls find the difference difference means subtract so some way we will have to subtract find the difference between the number of boys and the number of girls enrolled at the school so we need to find the difference so it's easy to do because we can find the ratio of boys and the ratio of girls and then subtract the answer of how many number of girls and how many number of boys there are there five plus eight five plus eight is thirteen so it will be thirteen divide by five for the boys multiply by nine hundred and sixty two and this will be boys right so how many boys are there at the school they are five divide by thirteen multiply by nine sixty two they are three hundred and seventy three seventy boys and I can find girls there are nine I don't have to calculate the ratio because I can just take nine sixty two minus three seventy two that will give me the number of girls so nine sixty two minus three seventy will give me the number of girls they are five hundred and ninety two girls now the difference which is what we need the difference between boys and girls is five ninety two minus three seventy five ninety two minus three seventy which is two two two which is there are because the girls are more right there are two hundred and twenty two two hundred and twenty two more girls that boys in the school and that's how you will answer the question when it comes to ratios that's a correct yes Leslie now let's move to the last session the last part percentages I just added percentages to the mix so a percentage is a fraction of a full part of a part right we split the part in different fractions a fractional part of a hundred is called a percentage and it's denoted by the sign percentage so sometimes if you don't know how to use your calculator when we see a percentage you just divide the percentage value by a hundred and it will be a decimal and you can use it to do calculations for example like when you see in your questions the way you have sixty five percent you cannot just write fifty five multiply by something and hope to get the answer you will need to divide this sixty five because sixty five percent is a fractional part of a hundred there are zero point six five of that whole part of one so sixty five percent will be sixty five divide by hundred which will be zero comma six five we always in mathematics we work with this amount than with a percentage but if you know how to use your calculator there is on your calculator a percentage sign on most calculators let me look at my one percentage why am I not seeing a percentage sign on this oh they they is so a percentage let's say sixty five percent mine is written in orange so if I write sixty five percent I must go and call the shift button because I'm using a case show you go and find the shift button and you write it and you will see you'll write sixty five percent and that is sixty five percent if you know how to use your calculator you can use the percentage on your calculator which will be the same as sixty five divide by hundred and you can use that percentage to calculate something so let's say we want to calculate the percentage of a number when we say a percentage of a number and off is the same as multiply so we need to say we need to multiply sixty five percent of something and sometimes when we apply a sixty five percent of a number we either use it to mark down or mark up or we do this count whatever the other values that you can find in terms of reducing or adding more with the original value so we use a percentage so let's look at an example if we need to find a percentage of three hundred and sixty thousand let's say I'm buying a car and they say in order for you to buy this car you need to pay a deposit of twenty five percent of the original purchase price so how do I calculate the deposit that I need to put on it is twenty five percent of the three hundred and sixty thousand divided twenty five percent by a hundred we get zero point two five multiplied by three hundred and sixty you get ninety thousand so you need to make a down payment a down payment of ninety thousand if you know how to use your calculator it will still work the same you do shift you say sixty five oh sorry I'm still on sixty five you say twenty five shift percentage you press the multiplication button and then you put the three hundred and sixty thousand and it will give you ninety thousand so you just need to know how to use your calculator correctly otherwise if you don't know how to use your calculator you just divide the percentage by a hundred it gets to a percentage and then you multiply that okay that's easy straight forward not as easy and straightforward like this but they might give it to you in a question and ask you example thirty five percent of students at the university are made how many male students are there in total of one thousand two hundred students body that we have at this university is the same thing they are asking you what is thirty five percent of one thousand two hundred you just go and calculate thirty five percent times one thousand two hundred is zero point thirty five times one thousand two hundred which is equals to four hundred and twenty what if the follow up question says how much more how if we want to increase the number of student body by an x amount how much more how many students should we register the university expects fifteen percent increase from those one thousand two hundred next year they increase the number of students for the following year to increase by fifteen percent how many students do they expect so that they can make some arrangements so we need to find the increase from the original and edit to the original because they want to know how many students they expect next year to have been registered at the school so it will be the old one plus the new ones how many are they to calculate the percentage increase so you can use the same formula for increase or decrease decrease it means you will be minusing increase will be adding so for percentage increase we use the previous value plus the percentage of the previous weight because we adding a certain percentage from the previous weight so our previous value we know that we had one thousand two hundred students we need to calculate fifteen percent of one thousand two hundred which is the new number of students that we are getting and fifteen percent of one thousand two hundred is one hundred and eight plus the one thousand two hundred gives us one thousand three hundred and eight and that's how you use percentages to answer questions and let's look at more examples because sometimes the examples don't just come as straightforward as I give you as examples so in the exam or in the assignment you get questions like this Mr Singh sells his house for five hundred and eighty five thousand the total commission is six point five percent of the selling price for which the broker receives three quotas and the sales person receives the rest the amount that the sales person receives is how much so the first thing you need to do is you need to calculate the commission from the selling price the price is five hundred and eighty five what will be the commission and then from the commission we need to calculate what the broker is receiving and what the sales person is receiving but we all actually want the sales person's number so we can calculate the ratio of and divided by or multiply that ratio with the total commission so let's first calculate the commission what is six point five of five hundred and eighty five so we need to find six point five percent of five hundred and eighty five thousand that's what we need to find zero point zero six five because this is six point five six point five divide by hundred will be zero point zero six five five eight zero point zero six five times five thousand and the answer is three eight oh two five that is the amount now we not done because they said the broker receives three quarters and the sales person receives the rest what is a three quarter a three quarter so we know that if we have an equal part of four a three quarter will be three over four right that is a three quarter so if the broker receives three quarter so that is the broker therefore it means the sales person receives one hundred one over four of that because a three quarter plus one over four will give me one right if I add them together they will give me one so if I know this I'll really know my ratio so I can calculate using this so for the sales person I will just add multiply by three eight oh two five and that will give me from the ratio of a sales person times the amount of commission that they would have made I will know how much the sales person will receive because the sales person will receive one out of four multiply by the eight thousand and twenty five and it means the sales person only receives nine thousand five hundred and six and twenty five cents that's what the sales person receives if they were asking you to find the how much the broker receives so you will just multiply this with three eight oh two five or you can just subtract three eight oh two five minus nine thousand five hundred and six and that will give you how much the broker would receive and that's how you will use percentages percentages and ratios to answer questions in the exam or in your assignment let's see oh three quarter six seventy five yes and the other one is twenty five I could have just used zero point two five here for a the sales person three quarter six seventy five you are right yes definitely on point okay so that is the first exercise second exercise let's see if you can get this one bargains for you sells a washing machine I'm gonna assume that is one thousand three hundred I'm not sure it's not clear but it looks like three it looks like three so bargains for you sells a washing machine for one thousand three hundred and twenty excluding vet remember now excluding vet we assume vet is fourteen percent if you pay cash they offer a discount of five percent how much will you save if you buy this washing machine in cash so they are selling it excluding vet and we assume that vet is fourteen percent do we add vet or no vet because they don't say if you pay cash they offer a five percent discount so you're going to pay the amount based on the five percent or we need to also include vet how much will you save if you buy the washing machine in cash okay I can assume from what they telling us bargains is selling the washing machine for this much excluding vet so vet is not included in this so we don't even have to calculate it assuming us that we need to assume that vet is fourteen percent but it's not included in the price of the washing machine if you pay cash they offer a five percent discount so what will be how much money you would have saved if you buy the washing machine cash very tricky right yes it will be okay here is the catch it will be correct if we don't include vet in the washing machine the answer will be that excluding vet if you are including vet the answer will be that but because they didn't say that we need to include vet because they told us that they are selling it excluding vet so we're not going to include vet so the answer is sixty six right now this one is also the same they are asking excluding vet so as you were once to buy a microwave the cost of the microwave is one thousand seven hundred and fifty excluding vet we assume that that is fifteen percent if he pays cash the company offers a five percent discount how much will he save if he buys the microwave cash and I guess this is the same do do do do do the same challenge if we include including vet that will be the thing if we excluding vet that will be the amount so because it will be one thousand five hundred multiply by zero point zero five that will give you the discounted amount which will be the amount that you are saving if you are including vet maybe I should do this way one thousand seven fifty times zero comma zero five for if you are excluding vet if you include in vet it will be one thousand seven hundred and fifty plus you need to also add the vet which is one thousand seven hundred and fifty times zero comma one four and close the bracket and multiply that zero comma zero five and that would give you nine point seven five but they didn't say it includes vet so that will be the answer a school had one thousand two hundred lennas in twenty seventeen oh sorry in twenty sixteen in twenty seventeen the enrollment increased by fifty percent determine the number of lennas enrolled in twenty seventeen would we get a mark if we calculate the excluding vet in the exam I don't know right because now I'm assuming because they said they're selling it excluding vet then we don't have to include vet in our calculation if they would have said including vet and vet is this much then we will calculate the vet we will include vet okay so let's see they were one thousand two hundred in twenty sixteen they increased by fifteen percent how many more students are there so we need to find one thousand two hundred more students multiply by zero one five fifty percent of one thousand two hundred is one hundred and eight determine the number of lennas enrolled in twenty seventeen okay we need the number of lennas enrolled so it will be one thousand two hundred plus one hundred and eighty that it means they are one thousand three hundred and eighty lennas who are enrolled in twenty seventeen and that will be the answer so we calculate in the increase I think this is the last exercise I'm not going to cover the next section suppose a the normal price of a certain pair of shoes excluding vet is four hundred and fifty assume that the vet is fifteen percent the pair of shoes is on sale for a discount of ten percent what does the pair cost including vet there we go can you see that they have included it so now you need to calculate including vet and that is your exercise are we winning? it's four seventy two option two let's see if it's option two or four seventy two someone said option three and then the other answer is four seventy two okay let's see so in order for us to calculate the cost so what does the cost of the shoe is including vet to calculate that we're going to take our original price of four hundred and fifty and we're going to add the vet right because this four hundred and fifty exclude vet and we know that the question is asking us to calculate the cost including vet so we're going to add four hundred and fifty times our vet of zero comma one five and they're also telling you that you get a discount of ten percent right which is a little bit tricky there because the we're not asked to calculate the discount to calculate the actual cost so how much will the actual cost be so we know that suppose the price of a four hundred and fifty assume that vet is fifteen percent the pair is on sale for a discount of ten percent what does the shoe cost on sale okay so we want the cost on sale so first we calculate the vet we include the vet so what will be the cost including including vet that's the first thing that we can calculate which is easy to do we just say four fifty plus into bracket four fifty again multiplied by the vet which is point one five and that gives us the cost of the shoe including vet will be five hundred and seventeen fifty now we know that it's on sale so what is the cost on sale this will be five one seven point five zero multiplied by we need to do a decrease so let's do this five one seven point five zero minus we need to take out the discount which is minus five one seven point five zero multiplied by zero point one zero discount and that will give us the extra cost of the shoe so five one seven point five minus into bracket five one seven point five times point one and that gives us the cost of the sale of the shoe on sale will be four hundred and sixty five seven five that will be the cost on sale I have another question last last one I have the last one so the price of a financial calculator is six hundred and forty five without a value added tax of fourteen percent what does the calculator cost if vet is included seven hundred and thirty five which is option four so let's see if it's option four the price of a financial calculator is six forty five without vet so how much is the calculator cost so cost will be six forty five minus zero point one four but we need to add because this is the value the value added tax we need to add it back to the six hundred and forty five and that will be equals two point one four times six forty five is ninety point three plus six forty five which then gives us it gives us seven hundred and thirty five right and thirty and the any questions comments please any comments if there are no comments or questions then we can summarize and conclude like I said I'm going to change what we are busy with so that it aligns to the BNU sessions so we're going to look at fractions but not just fractions variables how to find or how to calculate fractions where you are given variables how do we find the LCMs and so on so that's our next session on the twenty ninth unless if there is a pressing pressing other topic that you feel you need assistance with up to so far because I checked on on the schedule thing to look at the recordings they haven't uploaded the recordings from the previous years not the previous year but the previous semester so therefore it means you guys will not have access to those recordings unless if you go via the channel I shared with you because I didn't want to repeat the same content but since I see that here my students are not part of the discussion so we'll continue with more related BNU sessions I will change all the schedules so that then we focus on your area but please if there are any banning issues or banning questions that you or topics that you want me to address through the sessions we only have one month in September then because then your exam starts so let me know which topics are banning topics for you which chapters are giving you hard times so we concentrate more on those months and then I adjust the schedule a little bit you can send me a WhatsApp or you can send me an email just to recap in today's session we looked at proportions and ratios, set ratios are the way of comparing two or more numbers together and remember it's very important to always keep in mind the true a ratio of females to males it means males will be at the top females to males females will be at the top males will be at the bottom in terms of a fraction so they will be your numerator and your denominator I didn't want to introduce those kind of concepts because we haven't touched the fractions but you must just remember that with the two two will mean something will be at the top the other one will be at the bottom the one after the two will be at the bottom what we looked at is calculating the proportion where we make things equal so always remember when you're giving the ratios to add the total of the ratio and use those ratio total to calculate another new ratio in order for you to find the proportion that you are looking for and then we also looked at an additional thing which is the percentages where a percentage is a path of a whole it's a fractional path of a whole where when you are giving a percentage if you don't know how to use your calculator you are going to divide it by a hundred otherwise you can use the percentage side on your calculator and you to calculate the percentage remember that often means multiplication and you can calculate percentage increase or percentage decrease or markup markdown depending on how they ask you questions just read the question carefully make sure that you understand what you are given highlight the facts that are there in the statement and be able to identify the things that you will need to answer the question and remember we always apply the problem solving framework that we use and on that note thank you for coming through and have a lovely evening see you next week Monday bye is there a way we can start at 7pm hey if we start at 7pm then it means we are going to finish at half past eight I can check if you are on the WhatsApp group we can also continue this conversation on WhatsApp but I am not sure I think because I assume that we need some rest if we finish late in the evening it's very tiring but we can look at that the times can always change okay so I don't have to add you to the group you can add yourself to the group be a new right just hold on let me just stop there and then I will send you the WhatsApp detail on