But no, yes, glad to hear. Hang on, let me just. Make sure my headphones are connected. Okay, it should be better. All right, let's get into the swing of things. So quick recap of some of the mixed number arithmetic that we've been doing recently. Stella, do you want to jump in with two and a quarter plus 34 fifths? Good. And just double check the seven there, the nice good. 你说有困难，你没空给你关一下。Is it like times the. Wait, let me think I'm a little bit forgetting, okay? Four times four. To not get absolutely. Yep. Nice. Nice Yeah and and it's gonna to be just if we do 45 plus 76. So five plus six is 21? Yeah, yes, absolutely. 121, fantastic. 121 over 20. Perfect. Very, very nicely done. Stelllar and Jack. What would three and a quarter -25 sevenths b. Be careful not to. Follow the trend of the last question. We're doing a minus question now. It was all correct. It's to see wrote plus, not minus. Everything else was. It's good. Listen. Nice. Yeah. Good. 15 over 28. Perfect. Very, very, very good. Jack and Stella, back to you. What would two and a fifth times, three and a half. Very, very good. Seven, seven out, ten. Again, sometimes theyask you to leave your, your answer as a mix number, but if they ask you to leave your answer, wers an improper fraction. Seven, seven over ten. Perfect. And Jack, what about three and an eighth? Divided by two and a third. Remember division? Remember how leatudivision you've got two? It's a division. It's no. Can be. So we've got 25 over eight divided by. Seven over three is perfect, okay? Sure. If you want to do it, do it that way. All make sure it's right times. Mm mm. What number is that there on top? What's this? Number eight? What? But is it eight? Or are you misreading your own handwriting? Now why would it be eight? Remember, two and a third is the same thing as seven over three and then you flipped that fraction. So it should be three over seven. That's a three of that. There you go. Yep. Absolutely, 75 over 56. And so that's a real case. I think there's a case to be made for not skipping out any steps. There's nothing wrong with you know writing this out as 25 over eight divided by seven over three, which you can then converts. Now we keep change flip, so equals 25 over eight times three over seven, you're much less likely to make a mistake like that where you get a little bit confused as to what the original fraction was that you're flipping. I would recommend it, but do what you want. Stella, one of those for you. What about 32 sevenths divided by. One and a fifth. Finish. Good, very, very good. Nice 126 over 35. Excellent work. Really good. Okay. So next question would be, although sorry, I've just spotted a mistake. Sorry for that dramatic thing. Just be careful of the 21 here. What should that 21 be? Oh, it's gonna be four. Yes, three, three. Yeah, 23. We've got to do seven times. Three is 21 plus the two. So 23. Times six, and that's going to change our top number. Should our top number be who's. 138, 138. Very, very good. And jacack again. Another one of those is two, 13 eighths divided by five sixths. Just be careful to simplify your answer here. You're going to get an answer which is not simplified, simplified. Good or perfect so far, remember, you can chip away at it if you want to. You have to do it all in one. Got two even numbers, 66 and 40. What were all even numbers divisible by. Such really the definition of an even number. Row two, two exactly. So one, if you did divide them by two. Good. Yeah, absolutely. 33 over 20 and actually we can't really do better than that cawe 33 and 20 not got any common factors between them. Okay, good. We're going to get to some worded problems in the second half of the class. But again, just because some papers will test this method, again, I always say this, I'll say it again, it's not always necessary that you do questions this way, but it's a lovely trick to have up your sleeve when questions get very difficult. And I'm going to deliberately give you some questions now which would really benefit from using the cross simplification method, or just again, recap when and how to use it. So the cross simplification is specifically for multiplication questions, and this includes division questions, where in the second part of it you've turned it into a multiplication question. It has to be a fraction times another fraction. That's when you use this. You never, ever, ever use it when you're adding or subtracting. Stella, see if you can remember. How to solve a question like this by kind of taking that a sneaky shortcut by not doing it the long way routes. So I'm going to say 999 over 22 times, 44 over 333. Oh, Oh, so I just need to time like butterfly things does. Okay so so first 22 times so this one gonna be 88 so 8822 times 44 equals 88 okay so that would be two times 44I just I also just want to clarify what how this works because I think it's slightly better you are absolutely right with the so we're we're cross simplifying you can't always do this but in this question you can and it's gonna to make it a hell of a lot easier because 999 times 44 and 22 times 333 it's a bit it's a they're big numbers and then we're going to have to simplify after and it's going to take us forever so what you want to do is you want na just imagine that you have a fraction of 44 over 22 and think about what that would simplify to what would 44 over 22 simplify to if you kept on chipping away at it? She knows Stella 44 over 22. It's going to be times. Four it's all going to be equals 88 like times two when I when I say simplify, I mean when you've got something like twelve over 15 and you go, Oh Yeah, they're both in the three times. Oh, Oh okay, okay. All over five how about you? They are kind about too. Yeah then equals to first it's equals 22 over 22 over. Eleven Yep, there is going to be. We think eleven can divide by Oh, then just divide by eleven. Then here is one and here is also two. Fantastic. So that's what he writes. 44 comes a two and 22 becomes a one. Done. We move on to the next part now, which is 999 and 333. What would 999 over 333? Again, you don't need to write it out like I'm writing. It's just to demonstrate that we are simplifying as if you had not by three, yes, three, three, three. And here is one, one, one, one, yeand, then here is gonna be one, and here is gonna be one, one, one. Well, if if you technically what you're doing there to get an answer of one on the bottom, you're dividing by 111 111 divided by 111 is one what's 333 divided by 111 if you think about it? Okay, it's going to be one, 333 divided by 111Oh, three gso. We we say this is one, this is three. And suddenly the question has become ludicrously easy. From being very, very difficult on the top, we now have just three times two, which is. Six which is six the 61Yeah six over one equals six and Yeah six. So so that's it. Again, I know I keep going on about it, but it's just to really, I can't hammer the point long enough. You do not always have to use this method. This is a little trick that it's sometimes really helpful to use, but you don't the way that you're doing multiplication questions as it stands is perfect. It's just sometimes examiners will throw you a curveball or sometimes you'll have to answer a really difficult question quickly. Where this method may, it will save you ten minutes. It's a little shortcut that you sometimes want to use. Check, see if you can do your toilet. Yes, you can see if we can do 21 over 56 times. 800. Over 14 again, do I just need to do it? I'd love you to try to use the cross Yeah try to do it like that just just for the fun of it, just so that you know that you can. Hmm. So like sim multiply. So remember that Yeah the way that it works is we're looking at our diagonals and we're imagining this is just again, it's not because they actually are this. We're just imagining that the 800 goes over the 56 and we're going, okay, well, what if that was the case? What would these simplify to now? What is 800 over 56 going to simplify to? Good. 100 over seven. Fantastic. So that's what we can write there, 100 over seven. And we're doing the same thing for the 21 and the 14. We're imagining it's not actually, but we're we're going, what if we had the fraction 21 over 14? What would that simplify to. Yeah, absolutely. Three over two. And now we're laughing. Suddenly this question is quite easy. Three times 100 on top, seven times two on the bottom. What's our final answer are going to be? So 100 over seven claws, three over two. Or times no, you just do that. You just times it now. So you've you've prepared the question and you're just doing it on the top. You've got three times 100, which is. So you just you just multiply them out now Jack, three times 100 until is Yeah yes. Very, very nice. 300 over 14 is the unsimplified answer. And can you simplify that? You, I have to do it. It's only one more step. Remember, they're both even numbers 314, so they must be divisible by no. Good. We hundred divided by two half of 300. 450. It is 150 gears. So let's do a couple more of those so that again, you're just you're not afraid of this method. It's something that you have at your disposal. Again, it's not always something that's worth using. Sometimes you find that the diagonals can't be simplified, in which case you can't even use this method as completely useless. But sometimes you will have questions thrown at you that really encourage you to use this little trick. It's worth having up your sleeve stellar. See if you can do the next one. Let's do. 84 over 55. Times 77. Over 96 can going to be a lot easier. If you can cross simplify here, you don't have to. You could do it the other way. But my God, is it going to be easier? Okay, you're choosing not to. Wait, I did. There was a tiny, tiny little mistake made on this. Let me just check. So five times four, 25 times eight, 40, plus the two. Five times 4:20. By times 8:40 plus two. And then I've tathat item. Oh sorry, it what the hell am I doing it? You were doing 55 times? 96, right? Four, 20. I think it should be 5000. What? Yeah, no, this bottom one, I think I think there was a mistake made on that possible. Oh, I thought you was helping me doing a top one. Confusing the numbers makes so five times six, 35 times nine, 45. Plus the three is going to be 48 and we add zero five times six. Again, 30. And thoughts on that four, five. Yeah, sure. I'm getting. Okay, I know five, six, 28, 5000, 600, 28 over 5180. Well, it's it's 5280 on the bus. Okay? And 200000 top. I'm getting 6000, 6000. No, it's going to be 5000. Okay, well, let's do this quickly. But we're proving Stella arenwe, how much more difficult a question like this is if you don't do cross simplification, and you know we would not have to go into any of these lengths if we did it using cross simplibut. We're gonna to do that after. Let's just do this quickly, 84 times seven, seven. So seven times four is. 20 87 times eight, 56, plus the 258 ths add a zero seven times four again 28. I'm going to get myself a little more space. Seven times 856 plus 258. So eight plus zero, eight, eight plus eight, 16, five plus eight, 13 plus the one, 14, five plus one, six, 6468 on top. But look at that. Look how difficult this question is going because now you're not even done yet. Now you've got to simplify 6468 over. So it's going on and on minutes. Oh, it can be divided by two. It can divide by two. Okay, do you want to give it a go? The first divide by two. So the first one divided by two equals three, two, three, four, three, two, three, four. It's very easy. First one and second one is gonna be okay. The second one is a little bit hard. So it's here it's 40 and here's one and here it's gonna be Oh, Oh wait. Is it like this? Let's do it quickly. 5280 divided by two. There are two. Oh, two. It's gonna two. It's two, it's two. Sorry, it's two, two, one, four, zero. Six. Oh. Oh, okay. And we're still it you can see. Both of those are even numbers, so they can be divided by. Bye by two. Yeah. I can't do the second one. It's second one. It's second one is and let me see, one, three, two, zero. Yep. And let's do the first one here. So we've got one, 23 remainder 16 twos and twelve, one, 23 remainder, one, seven. So that's gonna to be 1617 over. Thousand 320. Yep. And then we're gonna divide back to Oh no, not two because the seven is not even number. Oh, seven is not even number. So maybe we're gonna divide by seven. No, quick, it's not count if by seven. Well, I mean 1617 does divide by seven. 1320 divide it by seven doesn't divide by seven. I've got a feeling they're both divisible by eleven, but it's incredibly hard to see that they are, I think, both divisible by eleven. Yes, but how on earth are you gonna to spot that? Very, very hard to spot, but they are divisible by eleven. So let's do this. So 1617 divided by eleven. What would that be, Stella? That's gonna be, wait, my division is not good. I don't know how to do this. All right, well, that's good to know. We can definitely make a note of that. Jack, do you want to help Stella out here? Board thousand 16 hundred and 17 divided by eleven b. Yep. Yes, good. So we've got 140 7Up top and what would 1320 divided by eleven b. And we'll work on this stela later today. I'm not going to do it now because I think we should just try to focus on fractions, but six or zero. Yeah one, one, two, zero, 120. I mean you've got no remainder there. Do 20, 22 divided by eleven is two. And then Oh, it's a zero. Sorry, I understand your question now. So we end up with 147 over 120 and I don't think can it be divided? Yes, I think it can be divided by three now. So 120 divided by three is 40. And what do you know? 147 divided by three would be Jack. 147 divided by three. Longer 40 73. 40 birforty nine. And we finally, after about probably probably about 15 minutes, we finally get to an answer of 49 over 40, which can't be simplified any further. Now, am I being unfair to say, Stella, that that took us a really long time to do. Yes, Yeah, I mean, it did. It took a really long time. So let's remember this answer. I'm gonna to delete all of our working and I'm gonna to keep our answer of 49 over 40. And Jack, see if you can do this the other way that we've just been practicing using, not not doing 84 times 77 and 56 times 96. But spotting that in this question, you can take a shortcut by cross simplifying and let's see just how much easier the question gets if we do this. I like not the same as before. Not the same as before. We're doing cross simplification. So I mean, what you just did a question ago, Jack, imagining what 77 over 55 would simplify to. Can you see they're both in in the what time table? Five Yeah what's 77 and 55? It's not even it's odso. But can if you think about 22, 33, 44, 55, 66, seven, seven, what times metable is that you're multieleven goods. Absolutely. So that's going to go to 75. What about 84 over 96? What can you spot a times table you can do too, because they're both even. But there's even even there's a much bigger times table both of these numbers belong to. We're just going to get us there faster. Four. And also the twelve times table, aren't they? They are both in the four times table. You're right, the 84 and 96 on the twelve times table, which would get you there even faster. So 8:12 times watts is 84Yeah. T six divided by twelve. Twelve times what is 96? Twelve times seven is 84. And 96 is 20, twelve more than a year. So this goes to an eight. This goes to a seven. And we just do this now. What's seven times seven? So up top, we've got seven times seven, which is. Iseven. Odie nine. Yep, and five times eight. Okay. Now, is this not exactly the same answer that we got over here? But this one took us about three times as long. It was much, much harder to get to exactly the same answer using the method that we normally use. And this is why it's important to look out for opportunities where you can use that second method, the cross simplification method. Stella, does it make sense how to use this method here, the cross simplifying. We're going to do another one now. That was really good work, Jack. So you're really I would what I would say, let me just note this down so that you so when checking whether to use the cross simplification method. You want to see whether the numbers. Our first awkwardly big. So I if you have to times multiply 23 by 71, you're kind of going, Oh my God, this is, I'm going to have to write this out. I'm going to have to literally like do a, do a multiplication and figure this out if I'm not allowed a calculator. And secondly, you want to make sure that the diagonals have common factors. Those are the two criteria. If both of those things are, then it's probably better to use cross simplification. So for example, if I say, you know what's 121 over 49 times 56. Over 77 we're looking at that and we're going, Oh my God, you're joking. Are you really gonna to make me do 121 times 56 and 49 times 77? So that that feeling that the question gives you of that you can't surely are you're not making me do this. That's a first that's a first sign that maybe this question is going to be made a lot easier by using the little trick to the cross multiplication method. Then you want to check your diagonals, you go, okay, maybe I can make this easier for myself. Can 56 and 49 be divided by a number of 49 and 56 in a particular times? Metable, Yeah, they are. They're in the seven times table. So I'm going to divide both by seven. And that's now going to become eight. And this is going to become seven. And I asked the same question for the other thing. R 121 and 77 able to be divided by a number. Yes, they are. They are both in the eleven times table. So this becomes seven and this becomes eleven. And now eleven times eight on top and seven times seven, which is so much easier, ludicrously easier. So I've got 88 on the top, 49 on the bottom. And that's my answer. And I haven't had to do any of the heavy lifting of doing 121 times, 56 and 49 times seven, seven and then simplifying after all of that workhas been cut out just by spotting the cross simplification thing. Does that make sense, guys? So do you have any questions about this? No questions. Great. So Stella, see if you can do this one. Let's do 20. Oh, let's do 35. Over. I'm going to use similar numbers just so. See, I'm not going to do that though de let's do 22 over 56 times, 28 over. I'm going to, I'm to keep changing my mind. So 33 over, 56, 28 over smaller, what no, 99, let's do. But you're not, you're not going to do this, Stella. You're not going to do this the long way. You're going to use the shortcut method. We're not doing that again. So the, that thing that you just felt there of, no youplease don't make me do this. That feeling should tell you maybe this is a, this is a question that I can cross simplify. So check your diagonals. Can 28 and 56 be divided by a number? The 28 includes six and what number? Two Yep they can be divided by two and what would that give us? Oh and then 99Oh okay so this one is gonna be give us divided by two equals 28 and then 99 divided by 33 it's gonna be Oh no 19 it's gonna be three. Like diviby 3:19 nine divided three, it's gonna be 33. So. It's the biby street. And then what about the other ones? Well, you've done 56 divided by two is 28. You didn't do 28 divided by two or 33 divided by three. 33 divided by three equals eleven, and then 28 divided by two equals nine 90. Nine, Oh no, no, no, wait, 14, 14, 14. Now can you go even further? Are you done? Can you go even further? Check 14 and 20. 28 divided by two equals 14, and f 14 divided by two equals seven. And then 33. Oh, Oh. Eleven further than that. Stellar. Can you go even further than that? Oh, okay. And then. 14 divided by two equseven and seven is out number. So so seven doesn't divide by two, but what about if you divide by seven? Nokwe, 14 divided by seven is it's going to do one right? We've got 21 there. Good. And what about 33 and eleven? Can you go even further with that? Eleven just can be divided by eleven and the 33 going to divide by three equals eleven three, 33 divided by eleven 33 times eleven. Oh, so okay, how much zero is this? Now we've got. Yeah Yeah we've got one times one up top that's what equals one down to equals one. Two times three was six, one over six. And that's your answer. And even though it took a little bit of time, it would have taken honestly about five times as long to get to that same answer using the regular method. So Jack, again, just to round us off, another question which I'm encouraging you to cross simplify on. See if you can do this quickly before the end of the class. Again, I'm gonna to use similar numbers to the ones we've been using just so it doesn't get too complicated. Let's do 33 over 28 times, 14 over 77. See if you can finish this. To do the or the well, what do you think the numbers are big, aren't they? 33 times 14, 28 times 77? It's a tough question. So I'm deliberately giving you this tough question to try to get you to cross simplify, make it a lot easier. So starting off with 14 and 28, what could you simplify 14 and 28 to? Watching is. Ten minutes. Okay, so so look 14 and 28 both both divisible by seven. So this is going to be 24 and actually you can now simplify 24 to 12 and 30 37. Seven boats are visible by eleven. So that's going to become three. This is going to become seven. We've got three times one is 32 times seven, 14, three over 14 and that's your answer. So much, much, much easier if you can cross simplify. I think we need to practice that a little bit more. But you're beginning to get there guys, which is good. So well done. That's has done for today. Have a wonderful rest of your Monday and I'll see you next time. Bye.