 Good afternoon or good evening everyone. Hello. Can you guys hear me? Might be that you can hear me. Yes, I can. Why when I greet you guys you don't talk back? Are you angry with me? Yes, you can hear me. Can I also ask, is your module a year module or semester module and if it's semester module, when are you writing your exams? It's a semester module and you're writing on the 11th. Of June. The 11th of June. And this is QMI or BNU? BNU. And then those who are doing QMI? We're writing on the 18th of June. 18th of June. Okay, which makes my life a little bit difficult in order for me to support you guys. I don't think I will manage to get through most of the content that you might require. So what I will suggest is because we do have a schedule that I've drawn up before, I realized that oh, it's May this month and then you will be writing exams very soon. I want you to tell me which are the concepts that are difficult in your module that you want me to assist you with in the next couple of weeks coming. Reason being is today we're going to do fractions, but the whole of May we're going to dedicate it to financial meds, but I know that there are other components in your module that you might find them difficult because you're already submitted to assignments, you already looked at your content, so you know which area you are struggling with. If you can find concerns on the WhatsApp groups and send me the topics, then instead of me concentrating on the topics I've set out for May, I can change them to accommodate you so that you are ready to go write your exam. Because there's no use for me to go through the content and you are still struggling with some of the things and I might be doing things that are easy, like for example calculating simple interest. It might be easy that we don't even have to cover that section in detail, but there might be some pressing section that you want me to cover. So please, please, please do so so that then I can prepare and then also be able to assist you. The other thing as well, since you all write online your assignments and all that, so I don't have your assignment, so I don't even know how your lecturers ask questions, but if they do send them to you as PDF, please share them with me so that we can use them closer to when you write your exam. We will have one session where we do exam preparation, so I will want to use some of those questions just to show you how to answer them, especially the ones you found them to be difficult, how to answer them. And also when we do some activities in class now, then we can use those questions as well. So please do so. That's it. So let's start with this week's session. So today we're going to deal with fractions. There is a register in the chat. For those ones who joined late, then you are unable to see the register. I'm going to repost it on the chat and you can complete it as well. Let's have a which WhatsApp group. I will share the WhatsApp groups later on after we are done with the session as well. So you must just stick around because I need to go and find the links. They are somewhere. Okay, so let's look at this week's session. So like I said, because it's our second week, we're going to look at fractions in May. Those were the topics that I thought we can do, but if they are not pressing an important, we'll rather change them because we have at least six weeks to work through your content. The other thing next week Monday, it's a public holiday because the first of May is a public holiday. It's on Sunday, therefore Monday, it's a public holiday. You must let me know if you want to continue with the classes next week, otherwise then that session will not happen because I don't want to come online and nobody is here. So let me know if you still want to continue or you're taking a break because I know Wednesday is it Wednesday or Thursday? Wednesday is a public holiday this week and next week Monday. Some people might take some holidays in between, but just let me know. Do you have any question, comments, query? Oh, while we get to the comments, question and query before I even forget, the first session that we attended there was a person named Landla. He stopped or she stopped the recording and I sent on the WhatsApp to say that person must provide us with access to those recordings because at the moment we are unable to access the recordings to upload them. So you might not have the recordings for the first session because of that reason. So next time you join the session, please don't stop the recordings. Don't stop the recording and start the recording because then it complicates life and you go into disadvantage other other students as well. Do you have any questions, any comments? Before we start, silence means there are no questions. And you guys, you need to talk to me. I can't be the only person talking the whole session. So like I said, we're going to look at the fractions. We're only going to concentrate on how we use our calculator in this session. But also remember, you must always remember that what must rule anytime, every time you work with meds. It's very important. So what are the fractions? Fractions are a number that represent part of a whole. Like for example, if you have a pie or a pizza, the whole circle is a whole. It's part of a whole. And the slices, they are those part that makes up the whole pizza or pie. If I take away three slices, then it means I'll be having other slices. So if this pizza had seven slices, eight slices, if this pizza had eight slices and I take away three, then I'm left with five. Therefore it means I'm left with five out of eight slices. But if I want to know how many slices I have taken out, I've taken out five out, sorry, three out of three out of the eight. So that is a fraction. With a fraction, it consists of two values, a denominator and a numerator. A numerator is the value at the top and a denominator is the value at the bottom. And that's how we represent a fraction, a numerator divided by a denominator. There are different types of fractions. There are what we call a proper fraction, which with a proper fraction, it means the number at the top is lower or it's smaller than the number at the bottom. For example, how many slices I'm left with, there are three out of eight slices. So three is smaller than eight. This is what we call a proper fraction. We also have what we call an improper fraction where an improper fraction, it means the value at the top is bigger than the value at the bottom. So we know that this has four slices, this pizza, regardless of whether there are two of them and so forth. There are four slices of pizza out of those that are remaining out of seven. Because four plus four, when we go and when we start looking at how do we simplify fractions by applying the basic operations, you will learn that four plus four is the same as four when it comes to fractions. It will be the same because we're looking for the lowest common denominator, even though there are two of them. But the slices, we're going to count all of them. We also have what we call a mixed fraction. So when you have an improper fraction, that is not the lowest form of a fraction. A lowest form of an improper fraction is what we call a mixed fraction. We used a mixed fraction to simplify or to visualize the simplest form of an improper fraction. The other way, when you have an improper fraction in your equation or expression, you need to convert the mixed fraction into an improper fraction before you can use it. So it means you move from improper to a mixed fraction when looking for a simplified solution. When you are working out and applying the basic operations and so forth of fractions and you are given a mixed fraction, you need to move from a mixed fraction and work with an improper fraction. So it means convert your mixed fraction into an improper fraction. How do we then get this improper fraction into a mixed fraction? We say four goes so many times into seven. It goes one time. The remainder will be four times one is four minus seven, so the remainder is three over four. It's a mixed fraction. This is a mixed fraction. A mixed fraction is the whole number plus n a proper fraction. Hi Lizzie, it's Adele. Yes Adele. Sorry while you are cleaning your throat. Can I quickly just make an announcement to the students? I'm sorry to interrupt you. No problem. Thank you. I have just posted a message in the chat about May, June exams regarding data that students will get for the examination. The importance of that message, it is on your Mayu Nisa but I posted the link for you where you will also be able to read the message. The importance here is that they give you only until Wednesday that if your cell phone on our system at the moment is not your current cell phone number where you should receive the data for the examinations then you will not receive the data and it means then that you have to go on to Mayu Nisa and in this announcement they explain the steps that you should follow for you then to change your cell phone number. But please also focus on the section where it says if you get more than 30 gigs on a contract per month that you then have to give an alternative number on the system and it doesn't mean a second number just change your current cell phone then to that new number that should be a recurred number in order not to lose your data that you if you have a top-up that's a capped amount of data that you can have per month. Be very very careful of that because very often during exams times students are very unhappy that they haven't received data but it's due to us not having your correct cell phone number on the on the system. So please if there are any queries about that make sure that you send an email to and I'll put that address in the in the chat as well. I can't see any previous chats in the history I just want to make sure can someone just say yes they can see the the message that I've posted in the chat. Yes thank you Adele. Okay thanks so much okay I will leave the city in touch email address but they've got a telephone number there that you can call to make sure about your about your data if you have any queries. But now don't don't phone and and ask them how this works read the the announcement properly carefully and make sure that if you have a contract you contact your cell phone provider and tell them that UNISA is going to give you 30 gigs but it's only 10 gig daytime and 20 gig for nighttime and if they then say no no no then you're going to lose that data please make sure that you change to and or give it get a new number and change on the system to that number. If you struggle to change your number on the system then you send us an email to city in touch then we can help you. Okay Lizzie thank you so much I'm sorry to have interrupted you. No problem Adele. Yes next week Monday is a public holiday I've asked them to come in because they are writing on the 11th of June and we only two days of a second session. So it's not going to be a problem right? No you are self-sufficient so you can carry on with your session. Thank you very much. Pleasure. If you want me to send out a reminder email for Monday just let me know. No problem we will communicate thank you. Thank you Lizzie. No problem. Okay so we wait yeah by the mixed fraction so we said you can change your improper fraction into a mixed fraction because that is the simplest or the the last answer you will give. You can't leave your answer as an improper fraction but you can also the other thing that you need to be aware of is what options did your lecture give you. If the answers are mixed fraction therefore it means you need to go you need to once you have your improper fraction you need to go and change it into a mixed fraction and we said a mixed fraction is a whole number and a proper fraction together and I've already done that. Okay so now let's look at how do we then use the information we just learned now in solving fraction questions. So we're going to start first with addition and subtraction because remember with BOTMA's addition and subtraction have the same priority we move from left to right but also when it comes to the fraction they've got the same similarities in terms of when we are adding when we are adding or subtracting fractions there are things that you need to be aware of you need to look at your denominator and ask yourself do I have the same denominator which means are my values at the bottom common are they the same if they are common what you do is you just add or subtract the values at the top and keep only one numerator so let's look at this one we have four over two over four minus one over four they've got the same common denominator so which is four and we can just subtract the numerator so it's two minus one which is equals two one over four because two minus one is one over four what happens when they don't have the same common denominator like yeah they've got different denominators it's two over five plus one over ten in this instance where they do not have the same denominator we need to find the common denominator and what a common denominator is which is the lowest common denominator it is that number that both of those two numbers can divide into so both can divide into and not leave a remainder so it means the answer that both of them when they divide into that number it should be a whole number it cannot be a decimal so five and ten can go into ten so that is our common denominator sometimes when you work with large numbers it might sometimes become very difficult to find the common denominator in other some people what they do they use vectors or multiples or they multiply the two numbers and that will be their common denominator so find them I cannot go through all the methods that we can use to help you I'm just for this one I'm just going to show you only one way of doing it so we find a common denominator which is ten and we say five goes how many times into ten it goes two times and because at the top the numerator is two we multiply by two ten goes one time and multiply by one so it will be two times two it's four one times one is one four plus one is five and that is the answer but this is not the simplest form remember when we work with fractions you always have to simplify the answer to its simplest form five can still divide into ten so therefore it means I'm going to say five goes how many times into five it goes one time and it goes how many times into ten it goes two times and that is your answer you cannot leave it as such you must simplify it to the simplest form after I have just said everything let's look at this one where we have mixed fraction and different common denominators and here we have addition and subtraction we know that in terms of bot mass rule they have the same priority so I can work from left to right because addition and subtraction have the same priority so before I can simplify this there are methods that you can use to simplify the whole equation without even changing it from a mixed fraction to an improper fraction but I don't want to confuse you those who have a casual calculator as well these things are easy to calculate on your casual calculator you just use the fraction button which is that the bloggy button on top of the bloggy button there is the one where it is a whole bloggy and two blockies this is for an improper and a proper fraction and this is for mixed fraction you can use this to work out your equations but because this is numeracy let's just do things skills-based the way we know how we need to first change the mixed fraction into a improper fraction so two times one is two plus one so we multiply two with the whole number and then we add the numerator so two times one is two plus one is three over two so we keep the denominator now we have the numerator at the bottom here all of them they are the same they are not the same they are different so we need to find a common denominator and a common denominator in terms of all three of them is six obviously so we're going to say three goes I mean you know two goes how many times into six it goes three times three times three and six goes how many times we need to keep the minus six goes how many times into one it goes uh one time one times one plus three goes how many times into six it goes two times two times two and the answer we get is 12 over six our answer is in an improper fraction this is an improper in an improper fraction we need we don't need an improper fraction we need to simplify this to the lowest form six can go into 12 and it goes two times into 12 and the answer will be equals to two and that's how you will simplify fractions in terms of addition and subtraction this is your exercise simplify the following as far as possible that is your question simplify as far as possible you can write the answer in the chat when you're done you can even take a picture and post it on the chat if you want us and then once you are done we go into give feedback and look at how we answer the question you have three minutes how are we done I see four over ten two over five and four four over five add num we so if your answer is four over ten you it's not the lowest four you will still need to simplify that the other thing as well if someone has posted an answer and you agree with that answer you can like there are emotions there you can use that let's make that last interactive let's make that last interactive by using all our tools at our disposal so if we agree with one we like that one and then we see that the majority have the same answer okay right anyone who wants to try to answer it to help those who might be lost remember not everyone is on the same same page so let's do it together who wants to try it tell us how you did it hello hi Lizzie can I go ahead yes you can walk it thank you okay I chose 20 as the LCD because it can go into four and it can go into five and it can go into two which is the denominator so 20 divided by four equals five so that's five times two for the first fraction minus four times three because 20 divided by five is four and then 20 divided by two is 10 so that would be 10 times one and then I simplified then that would come to 10 minus 12 plus 10 um divided by 20 and then I got eight over 20 and then um I divided four into 20 to give five and four into eight to give two so that would be two over five yes that is correct um others might have let me see if I can get this one the other way around so I can see the common denominator and let's say for example the numbers when you look at them they don't the lowest common denominator doesn't come to mind as quickly as possible so what you can do alternatively is to take the denominator and multiply them by each other so you'll say four times five times two which will be 20 times two which is 40 you can use that as your denominator so that will be your denominator will be plus 240 and you just say four goes how many times it goes 10 times and you multiply that by two and subtract five goes how many times into 40 it goes eight times yes eight times and you multiply that with three minus two goes how many times into 40 it goes 20 times 20 times one and you simplify 10 times two is 20 minus eight times three eight it's 24 oh sorry on my pen it's 24 20 times one sorry yeah it's plus it's plus plus 20 divide by 40 20 minus 24 it's minus four plus 20 it's 16 over 40 a number that can go into 16 and also can go into 40 is eight eight goes how many times into 16 it goes two times it goes how many times into 40 it goes five times and that's the other way you can answer the question and there are the options that we were asked to find the answer would be option three that's the easy part doing subtraction and addition of fraction it's easy i'm not going to ask you to do this one let's go to multiplication so when we work with multiplication of fraction there are several methods that you can do to answer the question so let's let's start with one so i'm going to show you all of them so the first method is to simplify the numerator and the denominator of the first fraction of the first fraction if they are able to be simplified you can simplify them and then work with them the other one is to simplify the numerator and denominator of different fractions so numerator of the first fraction and denominator of the second fraction will simplify numerator of the first denominator of the first fraction and numerator of the second fraction will simplify the other way we say what what we do with multiplication we can multiply what is at the top with what is at the top, what is at the bottom with what is at the bottom. So let's look at this. We're going to look at all of them. So we have 1 over 4 multiplied by 2 over 6 and we apply the last method that I just explained. Whatever is at the top, multiply with whatever is at the top. So 1 times 2 and 4 times 6 and that gives us 2 over 24 which is the same as 2 can go into 24. It goes 12 times. So the answer will be 1 over 12. That is the first method. Easy. Straight forward. You don't have to worry about other things. The challenge with this first method is that at the end here, if you have big numbers, you will be working with big numbers. This method might be easier to use because with this method it says when I have the fractions and its multiplication, I can just simplify the values first. So at this instance, I'm applying the second method. The numerator of the second can simplify with the denominator of the first. So 2 can go into 4. It goes 1 time into 2 and it goes 2 times into 4. 1 and 6, we don't even have to worry about that because 1 goes 1 time into 1 and it goes 6 times into 6. And now we can go back to that method of whatever is at the top, multiply with whatever is at the top at the bottom with what is at the bottom. So 1 times 1 is 1 and 2 times 6 is 2 and that is 1 over 12. That is another one method that you can apply which makes it easier to work with. The last method is the first method that I just spoke about which says let's simplify the numerator and the denominator of each fraction. So we have 1 over 4, it will stay the same as 1 over 4 but 2 can go into 6. It goes into 2 1 time and it goes into 6 3 times. Multiply what you see at the top with what you see at the top. So 1 times 1 and 4 times 3 is 1 over 12. So choose whatever way of solving it but always remember that it only works with multiplication. You can do the criss cross simplification when you have addition and subtraction. That is multiplication of fraction. I'm not going to ask you to do that, we're going to go straight into the division. Now with division, division and multiplication have the same priority we work from left to right. So therefore it means if the equation has a division and it has a multiplication regardless you just work from left to right. So how will you work from left to right if you have a division? You need to take care of the division first. You need to take care of the division first. How do you take it? How do you take care of the division? We applied the method you will see. If you remember kfc you will never forget this. The method is keep the first, change the sign and flip the second. You can see that that is kfc right but it's kcf. Keep, change and flip. Keep, change and flip. Keep the first fraction. Change the sign from division to a multiplication. Flip the second equation which means the numerator and the denominator they swap places. It's only on the fraction that is close by. If I had a multiply by 1 over 2 it has nothing to do with that multiplication there. Only that one. So I only use the kcf for where I have a division sign. Always remember that. So let's do that. We're going to keep, we're going to change and then we're going to flip. We keep the first. We change the sign to a multiplication and we flip. Whatever was a numerator becomes a denominator. Whatever is a denominator becomes a numerator. And we apply the multiplication. Please cross. If 6 and 7 can divide we could have simplified it. If 14 and 3 can divide we could have simplified it. But 7 and 14 can divide into one another. 7 goes one time into 7 and it goes two times into 14. 3 and 6 can simplify. 3 goes one time into 3 and it goes 2 times into 6. Then I multiply whatever is at the top with what's at the top. So 2 times 2 is 2. And 1 times 1 is 1. Therefore my answer will be 4. You can write it as 4 over 1 but it doesn't make any difference because any number 2 divided by 1 is the same as that number. It's one and the same thing. 4 over 1. So therefore it means if you have a fraction where they ask you, let us assume that here it was 6 divided by 3 over 14. Let us assume that it was the equation. Always remember that 6 is the same as 6 over 1. Always, always, always. So that you don't get confused. Otherwise if you have a casual calculator then life becomes easier. Okay, so now let's look at how we solve multiple fractions. Here we have mixed fraction, division, multiplication. So there are a couple of things that you need to always remember. We are going to have to change, before we do anything, change there. We need to change the mixed fraction into improper fractions. And then we need to apply the keep flip, the keep change flip on the division. So let's start with our first method. Changing everything to an improper fraction. 3 multiplied by 1 is 3 plus 1 is 4 over 3. Divide by 2 multiplied by 4 is 8 plus 1 is 9 over 4. Multiply by 3 over 16. Now we need to apply KCF. Keep the first, change the sign and flip the second and multiply by 3 over 16. Now we have, now we have, I want to change the color of my pen to blue. Now we have multiplications and we can simplify. If 4 and 3 can simplify, we can simplify that. If 4 and 9 can simplify, we can do that. If 3 and 16 can simplify, we can also solve that. Since we know that they can't simplify each other, what else? We can do the criss-cross now. We can look at numerators and denominators. Now, if you look at this, there are, for example, 3 fractions. That 4 can divide into that. And if it's still, there are some things that still needs to be simplified can also go and simplify the other thing as well. This 3 can cancel out that 3 as well, because they are all multiplication. So it doesn't have to be the one closest. So let's start with the simplest one. 3 and 3 can cancel out because 3 goes one time into 3 and they will cancel out. 4 and 16, 4 goes one time into 4 and it goes how many times into 16? It will go four times, right? Because 16 divided by 4 is the same as 4. Now, even if I have divided that 16 by 4, I still have a 4 at the bottom and I still have a 4 at the top, I can still continue and simplify. And that's the beauty of this, of division and multiplication. Actually, I need to use another color, the beauty of a multiplication. So 4 and 4 can cancel out because it goes one time and it goes one time into 4. Now, I'm left with simplified equation. So let's simplify it. 1 times 1 times 1 is 1. 1 times 9 is 9 times 1 is 9 and they will go. And that's how you do multiplication and division of fraction. And there and my me talking and talking and talking now is your time to do the work. Any question? Any comment? Anything you want to say? You want to ask? Let's see. Anything in the chat? KCF. Yes, KCF. Yes, yes, yes, yes, yes. Okay. Absent of question? Yes, your question. Simplify the following expression as far as possible. When you're done with the answer, start putting in the chat so that I can start monitoring the chat to see if you guys are done. It should be easy. Okay, so it seems as if you guys are on the road. So let's move on because I think if I see 4 answers that are correct, therefore it means the majority of you unless someone is still busy. How do we answer it? Anyone? You know, I always say these sessions are for students by students because I just I'm just here to guide you and then I just guided you and you just need to show that you understand the work. Anyone help each other? Yes. Hello. Okay. Okay. From the first part, we will apply the KCF. So we keep the first one over three. Then we change the sign to a multiplication. Then with this fraction to seven over six. Multiply by three, divide by one. Then from there, we can see that we can then cancel what we can. So effectorize three and three can cancel each other and one and one, leaving one and one. So and then one can cancel the other one and one. So we will have seven over six and we know we can leave it like that. So ask how many times does six go into seven? It goes once and then it leaves a remainder of one divided by six. And the answer will be that. Okay. So the next one. So ask yourself, what do you have here? Before you answer this question, look at the options very carefully. Right? Can you see the options? The option doesn't want you to solve the entire fraction, the entire equation. It says, do some things, but leave it somehow unfinished. That's what the expression, the options are saying now. You need to remember we use the Newman error prompts. We first identified what the question actually is asking us to do. We did that in our own understanding. Number two, need to ask yourself, what is it that I am given here? I'm giving mixed fractions. I am giving multiplication division addition. So therefore it means I need to change my mixed fraction. I need to also do something with my bot mass because multiplication division comes before addition. So it means I must work with multiplication and division. So on that note, you can then solve the equation. So you'll just solve one part of the equation. Are we winning? Let's go check the chat to see others. Are you winning? Still business. All right. Are we winning? Okay. Lee says they are a bit stuck. Okay. We will help you. We will unstuck you. Don't worry. I'm glad that you raised that. All right. Let's help Lee. Let's show Lee how to answer this question now. Anyone? All the answers that I've seen they are correct. So therefore it means someone should be able to unmute and take us through the process. Time waits for nobody. Come on. Come on. Come on. Come on. Anyone? Lucy, I will go ahead and explain how I got to my answer. Because time is ticking. We don't have a lot of time. All right. So what I did first was the improper fractions are turned to mixed fractions. And then so the first one came to 25 over 9 times 3 over 4 divided by 25 over 8 plus 10 over 3. Then only simplified first without going to the plus because we first have to do the multiple positions first. The 9 of the first fraction goes while 3 divided by 9 for the first fraction equals 3. And then this also was 3 for the next fraction on top. So that was then 3 goes into 3 one time. So then the first fraction is 25 over 3. Also note that... Sorry. Sorry. Sorry. My plan is top 20. 25 over 3. Yes. And then the second one would be I've got the 4 divided by itself. So that's 1. And then also divided by 8 which is equal to 2. So the third fraction would be 2 over 25. Right. So the first one is 25 over 3 times... Wait. Wait. You still have a division. 25 over 3. Oh yes. I'm sorry. I still have a division here. So it's 3 over 4 for the second fraction. And then... You simplify 3 to be 1. So it means on the second one you have multiplied by 1 over 4. That's what you have right now. If the first one is 25 over 3, that's multiplied by 1 over 4. Yes. Then we need to take care of the division. Yes. So for the division, I would flip the 25 over 8 to make it 8 over 25. But then the division turns to multiplication sign. Yeah. And then the fourth one would stay as 10 over 3. Okay. The 25 in 25 divides into each other. So the first 25 divided by 25 is 1. And the third fraction is the bottom 25 divides into itself also one time. And then the 4 divides into itself one time. And then 4 divided by 8 for the third fraction is 2. 8 divided by 4 is 2. Yes. Yeah. And then I got... So that would equal to 1 over 3 times 1 over 1 times 2 over 1. And I first did those multiplications. So at times 1 times 1 times 2 equals to 2 divided by 3 times 1 times 1 equals 3 plus the plus 10 over 3. Which is the last one. Yes. Option 4. Yeah. So when you get to questions like this, where it gets a little bit complicated with so many things happening, ignore the multiplication as yet. Look at the things that you have. Remember that multiplication and division have the same priorities. So if you can flip the division, you will be able to use multiplication and multiplication and simplify the whole equation. So let's look at this in this way. So you would have had 25 over 4 over 9, multiply by 3 over 4, divide by 25 over 8 plus 10 over 3. Now we can change the division. Say 25 over 9, multiply by 3 over 4, change, keep the first change and flip 8 over 25 plus 10 over 3. Now the next thing you need to do is remember, we need to simplify. Now I can do the simplification. 25 and 25 goes one time. 9 goes one time. Oh, sorry. 3 goes one time and it goes three times into 9. 4 goes two times. Oh, gosh. 4 goes one time into 4 and it goes two times into and the answer you will have will be equals. 1 times 1 times 1 is 2. 3 times 1 times 1 is 3 plus 10 over 3. In the exam, you don't have to follow step by step by step by step by step. You can take shortcuts because you're writing multiple choice questions. It's just that when you are practicing and when you are in a hurry, you tend to make a lot of mistakes. So by doing things step by step, it also helps you to make sure that you don't commit little mistakes or little errors when you're doing the calculations. So pay attention to those small details. Minimize where you have to spend so many or so much time doing one equation and see where you can reduce the amount of time for an activity that you are busy with, but without compromising the quality of your answer as well. Okay, so sometimes in your questions, especially those who are doing BNU, they might ask you, given a mixed fraction, change it to an improper fraction. So you can do all three of them. A, B, C. Change them. The first two, A and B, change them to A an improper fraction and C change an improper fraction to a mixed fraction without using a calculator. Possibly they would have said that in the exam paper. Should be easy. Are we done? Are we done? Are we done? Are we done? Okay, anyone? It should be easy. You can just give me. Anyone wants to try this? First one, A. I will do it. The first one, the answer is number four. You say four, multiply it by four. You add the one. So it gives you 17 over four. Yes, thank you. Number B is 29 over, this is number four, 29 over three, the correct answer. But how do you do that? You say three, you divide 29 by three and then the answer will be, you know, we say nine times three. Nine times three, you add two, which is 29 divided by three. Thank you. And number C, anyone? Can I also do it? Yes, you can do it. The correct answer is number three. Same as number two, save or not same. You say 13 divided by four, which is three, then you are left with one, then it is three into one over four. Yes, that will be that. Easy, right? Very easy. That's easy stuff. If in the exam they give you a question like this and they say simplify the flow in fractions, are you going to panic? It's too complicated. Sorry, I'm not laughing, but I'm laughing because you're thinking that it is complicated because it's something on top of the other and top of the other and top of the other. So it's easy to do because there are two fractions. What do you say when you see this? You say one divided by two, right? That's how you say it. So you can also write it as one divided by two. So this is one, if I'm working with fractions because it says simplify the flow in fractions. So take this as one, take this as two. So therefore it means it's eight over nine divided by seven over, seven over 15. That's how you will solve it. So you can rewrite it as eight over nine divided by seven over 15. And does it look much better? Are you able to do it? So that is your question to answer. Are we winning? Are we winning? Are we winning? Still busy with trying, but I don't know if it's still business. But I see the answers popping up. I'm finished, but I think I should give out another chance to answer. Okay. Okay, we don't have much time. I'd like to give it a go. Okay. You can? I was still looking at the chat. Okay. Yes, I'm here. Okay. So the one thing would obviously to get rid of the many division lines that we see and would be eight over nine divided by seven over 15. If we apply the KCF method, we will keep the eight over nine multiplied by 15 divided by seven. And that will give us 120 over 63. We divide the numerator and the denominator by three. That gives us 40 over 21. And 21 goes into 41 with the remainder of 19 over 21. Hey, you were on fire. Like you're driving on a, driving on a 250 kilometers per hour. Okay. So yes, that's how you will answer the question. Let's see if we have more questions. We've got 14 minutes left. This should be easy to do. Let me just see if there is a complex one. Nope, nope, nope. Yes. This one. Try this one. You're telling me that you already have the answer. So there's nothing too difficult for you guys. Anyone? The first thing that you need to do with this is look at the basic operations given. You have a division, addition, and multiplication. Both must say division and multiplication have the same priority and they come before addition. So it means you can do the left hand side and do the right hand side, leaving the addition in the middle. So on the left hand side, we can change the sign. Eight over three, change. We apply the KCF over five, over eight. And on this side, we can just simplify already from here. We will have one and one. So one times three is three, one times two is two. And we are left with simplifying the side. Eight and eight cancels out because it goes one time each, one times five is five, one times one. Three times one is three, plus three over two. Now we have addition of fraction. What do we know? They have different denominators. So we need to find the common denominator, which is six. Three goes how many times into six? It goes two times, two times five, plus two goes how many times into six? Two times. It goes three times, three times three from the numerator. And therefore we have two times five, ten, plus three times three is nine over six. Then the answer will be 19 over six. Nine goes how many times into 19? Oh sorry, six goes how many times into 19? Three. It goes three times. The remainder will be one over six. Because three times six is 18 plus one is 19. So that is fractions. The more questions I have are about addition and subtraction of fractions. So you can do the last one in the last 10 minutes that is work since we still have a little bit of time. Remember addition and subtraction. We first find the common denominator. If they have different denominator, we need to go find the common denominator. Finding the common denominator, we can find it by looking at the multiples or we can look at the highest common vector between all three of them. Common multiple. And always remember, both must rule, addition and subtraction have the same priorities you work from left to right. While you are busy finalizing your answers, those who are still working out, please make sure that you complete the register, especially those who joined late. I'm posting the link on the chat for you to use. Those who are looking for the WhatsApp numbers or whatever they call them now, links. I'm also posting them both on the chat. Make sure that you join the right group so that you don't get confused when you are in the group already and you start discussing wrong content or questions relating to the wrong module. I've posted two WhatsApp links, join the correct one. If you're doing both modules, you can join both. How do we answer the question so that then we can wrap up and do a check-in? Anyone? No one. So we need to find the common denominator. Finding the common denominator here, it's going to be very challenging because then it means we have to go and find out one of the multiples of 11, of 2, of 3 and find which one is the common, highest one between the three. Otherwise, we can say 11 times 2 times 3, 11 times 2 is 22, 22 times 3 is 66. Am I right? 11 times 2 times 3 is 66. Yes, I'm right. For 11 goes how many times into 66? It goes 6 times multiplied by 6 plus 2 goes how many times into 66? It will go 33 times, multiply that by 3 plus 3 goes how many times into 66? It will go 22 times 5. I hope I'm doing it right. Minus 3 must be minus 22 times 5. Okay, so what is the 6 times 6? Have you played the game? 6 times 6 is 36. Have you played that game before? 6 times 6 is 36. I just wanted to distract you a little bit, plus 3 times 33 times 3 is 99 minus 22 times 5 is 110. 110 is over 66 and we work from left to right 36 plus 99 minus 110 is 25. It's 25, over 66. Happiness is the motto of the day. And that concludes today's session. I hope you have learned something and now you are able to work with fractions or answer questions that have fractions from now on going forward. And now you know how to draw a teddy bear using 6 times 6. So let's recap. Remember, when we work with fractions, there are multiple types of fractions and we have proper fraction in proper fraction and mixed fraction. When we have fractions and we apply the basic operation, especially addition and subtraction, we first check whether do they have the common denominator. If they do not have the common denominator, we find the common denominator. A common denominator is that value that both of the two values, the denominator values, can divide into and not leave a remainder. If you are unable to find that, you can just multiply the denominator in order for you to find the common denominator. When it comes to multiplication, there are multiple ways of solving it. You can do numerator and denominator simplification or you can cross the numerator of the first, divide by the denominator of the second or simplify the other way around. Or you can just use the multiplication always says multiply what is at the top with what is at the top, divide what is or multiply what is at the bottom with what is at the bottom. With division, always, always remember that multiplication and division have the same priority. If they appear in the same question, just work from left to right. However, when you have a division because a division is not a multiplication, but when you have a division, it means you need to change your second fraction and you need to change your sign. You need to flip and change your sign. So we apply the method KCF, keep, change and flip and then apply the multiplication rule. And that is how you work with fractions. And also remember the simplest form or the simplest form of a fraction is a mixed fraction. And you can toggle between a mixed fraction and improper fraction because when you work with or simplify an expression or equation, you need to change a mixed fraction into an improper fraction. But it's not always the case because some people have a method where you can work with mixed fraction, but I don't want to complicate your life this way. It's much better. Unless if you have a cashier calculator, then you can use the fraction sign on your calculator to calculate fractions. And when you are working with your cashier calculator, remember the SD button, change, you can change using that SD button. It can change from mixed to decimal and it can change from decimal to a mixed fraction. By pressing the shift, you can use the mixed fraction. So shift and the fraction button, you will see that you can swap the values. With that being said, I've posted the link to the water group on the chat. I've posted the link to the register on the chat. If you have any question, comment, you want to say something, feel free to say anything you want to say. The floor is yours. If there is nothing, if there aren't any comments or questions, yes. Which topics did you cover in the previous session? On the previous session, which I'm not even sure whether we're going to get the recording for that, we did the introduction into the basic numeracy. We looked at almost most of the things that I was talking about now, like the bot mass rule, we looked at the bot mass rule, we looked at the root power. So everything to do with the first section of your modules in a way where they talk about fractured roots, powers, how to simplify basic operations. What I don't cover is the distributive law and the associative law because with bot mass, you can do all those things. And I don't see it necessary because they don't ask you about them. They don't ask you whether you solved the equation using the distributive law or associative law. But if you use bot mass, it covers almost everything because it says brackets first, which is almost like with the distributive law where you will have to remove the bracket. So it means multiply with whatever is inside the bracket first. Okay, then we looked at or we looked at changing the subject of the formula. We looked at how we simplify an equation or an expression. What else did we look at? I think those were the things that we looked at. We didn't do much. It was just giving the skills in terms of things that we're going to be working on. Remember also now, I asked those who were here earlier. I know that most of you joined late. I said, we have a schedule. I set the schedule, but I didn't think that you are writing the exam. No, no, no, no, very soon. So now I need to change that schedule based on your priorities because your meta. I need to hear from you. Once we join the WhatsApp group, I'm going to give you. You don't have a lot of time because I need to send the updated schedule to UNISA next week. Or this week if possible. But it doesn't matter because that is for the administrative side of things. All I need from you is tell me which section of your module do you find challenging so that we can prioritize those ones in the next coming six weeks before you go write the exam. Those who are doing BNU, you said you are writing your exam on the 11th of June. So it means the six weeks will be on the dot and then we can also find a day somewhere where I can help you with the exam preparations. Those who are doing QMI, you at least have the six weeks plus the probably one week. One week and then the other week we can use it for exam preparation. But because you're writing other exams as well, I need to take that into consideration when we do all these sessions. But your input is very important in order for me to be able to assist you properly. You need to talk to me. So I'm leaving it in your hands. Any question? Okay. I just wanted to know are we going to get the schedule on the WhatsApp group or on the next session? And when will be the next session then if you are going to change the schedule? Remember, we meet every Monday. So the schedule it will be in terms of me telling you which topic we're going to be covering every week from now on. That is the thing that I need to communicate with you after I've received your feedback. I will also share it with you guys. Otherwise, I will share it next week, tell you next week we're going to cover this topic and then I will share the entire schedule with you. But the schedules are always loaded. Where you find the notes, where you find the recordings, they will be there. Once you join the WhatsApp group, if you're not in the WhatsApp group, let me not disadvantage those who are not part of the WhatsApp group and don't want to join WhatsApp group. There is, I'm not sure how you join the sessions, where you find the details to join the session, but there is a schedule that gets updated by UNICEF. I've posted the link on the chat as well. If you click on that link, it will take you to my module. What do you call this new system that UNICEF is using? My module. Yes, it will take you to my module, where they have the schedules. On the schedule, there are always two buttons. There is a button to join the session and there is a button to do what the other button is for what? Oh, the other button is for notes and recordings. So there's always going to be two buttons there. All right. Let me stop the recording because then I'm going over time.