How you doing? Hello. But I have seen to say it's like the today I have some business, so I need to go in like 45 minutes. Is that okay? That's okay. That's fine with me. I'm just going to see if I can get a bit more light. My face very dark here very early in the morning in the uk, eight in the morning over here. What is it for you guys? It's what time is it? You're seven hours ahead, aren't you? So what is that? Is that like three, three in the afternoon where you are? It's five. Is it five? It's five in Okko. Oh, you're in Tokyo. That's so cool. Are you on on holiday there, Stella? No, I'm learning the English in Tokyo. Wow, that's really, really cool. What about you, Jack? Whereabouts to you? You're in China, presenno. Oh, now I'm, now I' M London in China. You're not in China. Whereabouts ts, see you, Jack. Hi. Whereabouts to you, Jack? So now I'm in the. Japan. Are you both in Japan? Wow, there we are. I had no idea. Very interesting. All right, well, let's have a quick recap of some of the stuff that we were doing last time on mixed number arithmetic. So jumping straight into it, Stella, do you want to start off with I'm a little bit forgetting, but if I will remember some, well, what? Okay, I'll tell you why. Actually, let's warm up into this. Can can you remember Jack, how to convert from three and a quarter into an improper fraction? So at the moment, this is what mixed number mixed number is when it's a mix of a whole number. Oh, maybe I know. Is there 13? Good. Over four. So this on the right is an improper fraction. Over on the left, a mixed number. And what about Jack? Two and a fifth again as an improper fraction. Eleven over five. Eleven over five. Fantastic. So doing that really, really nice and easily. And what about if we go the other way with I give you an improper fraction, and then I ask you, what is that? Improper fraction is a mixed number. What would 25 over four be as a mixed number? Stellar. Gonna be wait, let me think. Oh six and wait can I have a pen? Yeah of course. Sorry you can pen six. Wait six for all. Okay, wait here must be six gonna be here 641 good six and a quarter is absolutely right. And what about Jack? 34 over five? What would that be as a mixed number? Good 64 fifth fantastic. So we were looking then at a little bit of mixed number arithmetic. So Stella see if you can remember how to do this. You had your own way of doing this which is fantastic. 24 fifths plus one and a quarter. How would you do that? Okay, so I need to this one we to do equequals ten 1410 over five plus plus six over four. Is it going to be six over four? Just double check the six style. Oh Oh no one times for five Yeah good five over four. Five over 45 need this one times. Wait, I'm a little bit forgetting how to put them to us. Same like things. Same like here is saying I forget how to put this here. Yes. So remember you're thinking of the smallest number that's in the five and the four times table. So if we think of a five times table, we've got five, ten, 15, 20, 25, 30, blah, blah, blah, blah, blah. With four we've got four, eight, twelve, 16, 20. So we've already come across it. It's 20, just the first numbers featuring the four and the five times table. So that's going to be our denominator. 20. So 20, 20Yeah gets you do it in here. 20 and up we're gonna be times four. This one is times four and this one is gonna be times five is so four is gonna be so it's 14 times four, right? Okay, so t 56 okay. And then five times five equals 25. So the answer is. Answer is seven, 81 over 20. 81 over 20 is exactly right. And depending on the question, sometimes they might say, leave your answer as a mix number, or they might say, leave your answer as a as an improper fraction and you just tailor your answer recording ding. So if it's improper faction that 81 over 20 is perfect, what would it be if they ask you to leave your answer as a mixed number? Stelllar? Mixed temper, you mean like this one? Yeah, exactly. Okay. So I think. I'm how to do it 20 times four. So it's gonna be four. And here's 20, here's one. Good. Absolutely right. And again, just notice, nothing wrong with the way that you did it. I really like it. If you wanna keep doing it that way, no problem whatsoever. You can also get to the same answer just by doing two plus one is three, and then four fifths plus one quarter is going to be the same thing as what we time we get a common denominator of 20. So we want times the first one by four. So that's 16 over 20 and then plus five over 20 which gives us 21 over 20 which is one in a 20. Yeah I like doing the first one very good. So don't veer from your preferred method of solving in that case. So only you can just add those two together to get the same answer for Anna twentieth. Excellent, Jack. Let's go to a little bit of subtraction now. So what about 33 fifths -15 eighths? Mm mm. And again, do it whichever way feels best. Nice. Great. Yeah, good. Some quite tricky arithmetic here, but doing really well. Good. Yeah, excellent. Very good. Good, fantastic work, Jack. And again, what would 79 over 40 be as a mixed number? That's absolutely fantastic. Really, really well done, Jack. Difficult piece of arithmetic there and done perfectly. All right. On multiplication, same methods. Both of you both like doing it that way. So keep keep doing it that way. And the nice thing about this, as you mentioned last time, stellar, is if you do it that way, you don't have to remember another method for multiplication. And division is the same idea. You just convert, but then it's a multiplication question or it's a division question. So Stella, see if you can do two and a quarter times, 32 thirds. Okay. Times so it's equals. Two times four equals eight, nine, nine over four. Times eleven over three. Equals four times. Okay, so it's going to be twelve fyear. Ptimes. So this this is the difference. Remember remember now that when you're doing multiplication, what you don't need to do is find a common denominator. It's actually much easier. Oh Yeah we don't need to. You don't even need to do that. It is gonna be it. Oh Yeah I forget. I thought it's Yeah so big action. Okay, so it's equal als twelve. 99, excellent. 99, right? And now you want to be asking yourself, can this simplify? Often with these questions, you're going to end up with an answer that can be simplified. This is one of them. Can you think of a way to simplify 99 over twelve? Okay, I think it's eight times 80. 16. Maybe eight. So that what you're doing now is you're converting to a mixed number, which which is fine if that's what they want you to do. If they say leave your answer wers a mixed number, perfect. I to let me to make clear Yeah. Wait, it's going be three. Three good. And you've just got them this slightly mixed up. Remember the denominator is gonna to be twelve. The whole number is but Yeah good. And again, see if you can simplify three over twelve is not a bulsimplified fraction quite yet. Wait, how did do the same play fraction? So remember if you've got something like five over 15, you're going, okay, I see that both of those numbers are divisible by five. So rather than times in top and bottom by a number, I divide both by five and I end up with a simplified version one and over three. That's a little bit hard. So it can be over twelve. Yeah so it can it's Oh, it can divide by three then. Yeah, it's going to be 33. And four good that's sy three of the 45 fraction. Yes. So that can't get also can divide by 14. The thing about dividing by one though is it just gives you the same answer. Oh no, that's all. Maybe one is 33. Four divided by one is four. So you don't move it this. So if they ask you to give leave your answer as an imfraction, it's 33 over four, perfect. As a mix number, it's going to be eight and a quarter. And again, when you're simplifying here, this is the bits that you're thinking of simplifying. So three over twelve, one over four or 33 over four. Good though. Stella really, really goes. And Jack, what about two and an. Times one and a third. Same thing. Yeah, it's really, really good. And again, just being careful that you fully simplify your answer, but that's fantastic. Remember, if everyone not in doubt, you can always just divide by two. That's a really nice way of getting it a little bit smaller when you've got two even numbers. Maybe. Yep, 34 over twelve is right. And then how how are you going to get that even smaller? They're still both even numbers. So if you want, you can just divide by two again. 17 over six is correct. Well done. Also, just returning to this idea that we discussed last time, guys, again, this is not something that you have to do, but it can be really, really handy. When you're doing multiplication questions, you are allowed to cross simplify. So cross simplification means looking at your diagonals and just checking if any of those diagonals can be simplified in exactly the same way that you would simplify a regular fraction. So 84 you can see, can be simplified as a regular fraction. If you divide both by four, you would get 21. 17 and three can't be because there are no common factors of 17 and three. But having done that, it's just a lot easier, isn't it? 17 times one is 17. Two times three is six. So you get the same ansas 17 over six but like that. So it's a really handy trick. Again, it's not something that you have to use, but it is a great trick to have up your sleeve if you want to do it that way. Good. All right, let's do a division question quickly. Stellar three and Oh, fifth, divided by one and a third. So we need to do the these things two times, and then change, change this one. Yes, well done. Keep change. How I change one. So same thing as before. First, convert to improper fractions. We write it using top heavy fractions. Is it like. Well, one and a thirds is equal to four over three, remember. So just rewrite it first. I would forget about this to begin with. Just rewrite it as improper faction. So we're doing three and a fifth is equal to 16 over five. And one and a third is equal to four over three. And then now you can worry about keep change flip. So always convert first, just as you have been doing. Oh okay so this is gonna be time this is. Good. Yeah. Yeah. Good, very, very good. 48 over 20 is the correct answer. And again, just simplify if you can. Brilliant. Brilliant. And can you go even further than that? And so it's equals five. Good. Absolutely right. Twelve over five as an improper fraction. If they ask you to leave it as a mix number, that's going to be 22 over five. Very good. Well done. And again, just notice if you wanted to, you don't have to. But I'm just showing you so that you're not confused. If ever this comes up, you are allowed to check for cross simplification. You can see that the 16 and the four there actually can be simplified. So this would go to a one and the 16 would go to a four. And that just gets you to an answer that little bit quicker. Four times three is twelve, five times one is five. You get exactly the same answer. Again, don't have to do it that way, but it is an option. Good. Okay, we're gonna to do a few worded problems. Now I'm gonna Nick these questions from a Corbit math sheet. Let's start off with just some really, really simple worded questions that can nevertheless really throw students off. So three quarters of 36, Stella, any idea what that would be? Yeah, good. Of 66, what's that means of 1636, three quarters of 36. This means like. 36 can divide by three. Tand then also can. Divide by four, it's equals nine and then is gonna be twelve over nine. You slightly got it the wrong way around. I mean, one way of doing this certainly would be to think of what is a quarter of 36. Oh, here I. No, I know, but what is a quarter? Nine. Yes. So what would three quarters be, which is three lots of one quarter. Well, if you think if you think about it, you're saying if we've got one quarter. Which is nine, then three quarters is going to be how much. 27. 27. Exactly. So that's one way of doing it. That's one way of doing it. Well done. Another way of doing it, if you want to, is to think about the fact that the of in these questions, infraction questions and percentage questions, the of nine times out of ten means times. So what this really means is three quarters times 36. Now if ever you want to convert a whole number into a fraction, you can just put it as 36 over one like that. Again, we can do this. Now if you don't want to cross simplify, it would be a good idea to cross simplify a question like this. But if you don't want to, three times 36 is going to be 90 plus 18. So that's 108 over four. And then you can divide both those, both by two. Maybe that's going to give you 50, 59. Sorry, 50, does that write three times the two, six? 2:32 services ces down. Two plus 18. So Yeah, 54 over two. Which is going to be finally 27. So we get the same answer again. It would be wise to cross them, phone a question like this. You can get them much, much more easily. If you just spot it, this would go to a nine and that would go to a one. And you get the same answer three times nine, 27 over one times one. So that's another way of thinking about it. If you want to do it that way, first way also perfect jwhat. Would a third of 24 be. What is 24 over three? What would that simplify to? Good. Eight over one. In other words, just eight. Fantastic. And Stella, what would two fifths of 35 days be? How many days we've got there? Again. So it's gonna be way. It's. Five times. 55 times seven equals 35. Seven. And here two times. Yeah, 14 over seven. I think you're getting a little confused here. 14 is I mean, look, well, one, I think that the way that worked for you last time to think about it is think about what one fifth of 35 is. What's one fifth of 35? Oh Oh okay okay so here is seven Yeah and now what would two fifths two fifths so it's gonna be. So because you know, 250 ten. Well, again, if we just imagine a circle and we're saying one fifth, 14, seven, Yeah, so two fifths, it's going to be 14, it says seven and another seven. So 14, because two times seven equals 40, exactly. And it's as easy as that. So 14 days is your answer. Yeah and again, another way to do it, if you want to do it this way, is to think about the fact that two fifths of 35 literally means two fifths times 35, which we can put is 35 over one. That's going to give me 70 over five, which is equal to 40. Okay. I think the first way is easy as well. Which other works best for you, Jack? What about you're gonna to have to go quite similarly. So sneak some questions in. What about five eighths of 14 kilograms? I've said to use a calculator for this, but I think you can do it without one. Yealways simplify. They're never going to ask you to simplify. So if you spot the opportunity to just go ahead and do it. With even numbers, that's handy. 35 over four, very good. And we can't do any better than that. Excellent. Really, really hard question. Naidone perfectly. Okay, Jack, I know you've got to leave pretty much rout now, so feel free to go if you want to stelllar, and let's keep going with these. So some slightly more challenging words. Problems. Actually, this is a bmark question that we've got here, but let's see if we can piece it together. So it starts off by saying, James earns 800 pounds a month. He spends a quarter of this money on rent, and he spends two fifths of his money on food and bills. How much money has he left? So going I'm going to PaaS it over to you see, I don't mind which way you do it. There are a couple more than a couple of us. Yeah, go on. This one makes. What do you mean? What's what's that sign? What's that symbol? Right? Like is this a number of like answer like what this means that's pounds that's the unit of money that we use in the uk in in okay. Why is here so many dots? Well, that's just because it's where they want you to leave the answer. Generally that indicates your put your answer there. Oh, okay, that's what that is. Okay. So he spent one over four of this money on rent. James spent two over five of the money on food and bills. How much money has he left? Oh, so he he have 800 now and he spent, wait, so we need to plus the one over 42 over five together first, right? Great. If you wanna do that way, that's fantastic. I love that. N eight equals. Because so here it's going to be 20. So 20. Plus. And here is five, here is eight equals 20. So 40 over 20. Well, 40 over 20. I'm a bit confused how you got to that last time to remember you're just doing five plus. Oh, sorry, I saw that time. I saw this time. So that's that's 13. Good 13 of fantastic Yeah and then we use Yeah 800-30 over 20. Well, it's not that's not quite what we're doing because what we're saying now because you added these fractions together, what we can say now is we know now. We know how they spend money in twentieth of his money on rent. Oh, so they have seven more seven, seven like so he has seven, twentieth of his money left. Very good stuff. And the question is because they asking for a fraction here, they're asking for an actual note also, are we just. So we just need to do like answer is just do seven over 20, right? I saw it's gonna be, number was like just the number, okay, no I know it's no it is gonna be just a number because seven over 20 is the proportion it's the it's the fraction of the 800 okay but that's not what they want. They want an actual number. So now we've got to work out what is seven tws of 800. And that's why this is a four mark question. Oh, we need you. Oh, so 800. 800 first. So 800 divided by 20 first. Yep, you can do that. You can work for 40. Nice. So 40. So each is 40. So 40 times seven equals 280. Good. So 280. Oh no, I know. 280 pounds. Absolutely right. Fantastic. Oh, so quite a few steps to that. I love the way that you did that. I thought that was really, really clever, the way you added the fractions together. Absolutely brilliant. Well done, Stella. Let's do another one of those higher marker higher mark fraction problems. We've got one here, they say, which is larger, a half of 280 or three eighths of 400 show you're working. So we need to figure out what both of these numbers are once you do this. So I'm just going to get a tissue. Good. No. Good. Very nice. Yeah, absolutely. 150 bigger than 100 courses. So 38 to 400 is the bigger. Number fantastic stireally really, really good work nailing. And let's do another one of these four markers we've got. Hannah has $900. Let me answer the question for us. Anna has $900. She spends a third of this money on books and two bits of the money on presenwhat fraction of the $900 has she left. So this is it's very similar to the last one we did, but just be careful of the wording of the question they're asking you for the fraction, not the actual amount of money. Well done. Excellent. Very, very nice. So she spent eleven fifteenths on books and presents. Again, just he really paid close attention to what the question is saying. They're not saying how much money has she got left? She's there saying, what fraction of the 900 has she left? Okay, you'll like the number first. And then I changed to the if you want to do it that way, you can. It's actually much easier than that because how I do like two fraction now, well, again, if we just write down what we did, you've said she spent eleven, 15 of her money on books and presents. So what fraction of her money does she. Okay, so she have four left like 44 over 15 left and that's it. Oh, that's again just to notice there's a slightly different wording. The last question which was saying how much money does she have left? This one that's saying just what's the fraction of money she has left? She's got four over 15 left. So simple as that. Really good on to the next see if we can sneak in and we can do one more now. Mark ker, Yeah. Question 15, I like doing those questions. Yes, that's it here. So bid is 80 years old. Yeah come on. His son max is five over eight of his age. His granddaughter, jje, I don't know, like blah blah, is one over five of his age. How many years older than Jane is max? Oh, okay. So the question asking is how old is like the max older than like how many years the max older than jyeah? Okay, want to work out both both of their ages. Okay, first we need to so we need to do the max age. His son makes. Okay, so 80. 喂喂喂喂。Five, eight equals ten and ten times. Five equals 50. So it's 50 years old. Max is 50. So 50 years old Yeah. Okay. And so Jane is one over five of so it's ten years old. Yeah this I think I think because because she achieved my best life Yeah but I don't think they're saying Jane is a it's 40 more it's 40 older than like the answer is 40 because 40 years old more than Jane I think in both cases when they say his age they mean bills age Oh that bills okay okay okay Oh so now I know so it's going be 80 divided by five equals wait. Eight another five. Oh, good question. So it's 16 wait, wait, wait, wait, wait. Ten Yeah 16 is good. 1616 so 16 is. It's James H. So 50-16 equals 34. Well done. And that's your four Marks. Finish very good Stella getting very confident with these complicated word ded fraction questions. They are not meant to be easy these ats and doing really really well on them. So that is absolutely fantastic to see what I hope you can to enjoy Japan. I'm very jealous. I've always wanted to visit Japan and I'll see you next week. Have a wonderful life in the meantime by Stella.