How have you been? Good. Yeah, all good in your worlds. Any exciting news to report? Alrighty. Okay, well, let's get started. So we've been doing lots of mix number arithmetic. We're going again, you're both getting really good at this. We're going to again, just return to this idea of simplification and cross simplification before we then move on to something that knew. If I Jack, asks you to simplify three over twelve, what would that simplify to? Sorry. Simplify? Yeah lify, Yeah what would it simplify to? Good one over four, absolutely and stellar. If I ask you to simplify five over 25, what would that simplify to? One over five, absolutely very, very nice. And if I if we use these same numbers, Jack, if I said work out three over 25 times, twelve. Sorry, five over twelve. Could you use the cross simplification method? Now you don't have to do this, but I really would love you guys to show me that you can do it if needs must. So the cross simplification method, remember, this works by simplifying diagonally. When you have a multiplication question, you're allowed to simplify diagonals before answering. Could you use the cross simplification method to solve this question much more easily? Me. Wait. Is that right? Okay, well you haven't quite cross simplified it. So remember that I didn't use these examples above you know for nothing. Three times twelve and twelve, 25 times. No, no. So remember it's called the the methods. There are two methods to doing a question like this. Let me let me just outtwo methods. So the first method. The normal way. Is multiply the top by the top and the bottom by the bottom. So in other words, here. Three over 25. Times five over twelve is going to become 15. Over. 300. So 25 times ten is 250 2510 item then item because I saw I thought it was like you do the things like this like this I saw you you let me to like to do five times 25I three times I'm confused at the line right so that's this is the second way of doing it. So this is the normal way. The problem with this way is that when the numbers get big, your job in simplifying becomes much more difficult because we go, okay, 15 over 300, they're probably both divisible by five. Actually, you can spot they're both divisible by 15 if you're really paying attention, because 15 goes into 30. So 15 therefore goes into 300. So we could call this one over 20, and that would be your answer. But it's a little bit tricky to get from here to here, and sometimes it's much easier to use the second. Method, which is called cross simplification. Now you can't always use this method, but sometimes you can. So and the way that this works is you simplify the fractions diagonally, which is why I drew those lines. So the way that we're doing this now, I copy and paste. That's her. Is. We're going just as you did before, three over twelve is one over four. So in exactly the same way that just a second ago, Jack, remember you said three over twelve equals one over four. So here I'm doing that, but I'm doing it diagonally. I'm going top left, bottom right. And exactly the way that you stelllar just a second ago said that five over 25. Was one over five. I'm doing the same thing here. I'm cross simplifying, diagonally simplifying, and that becomes one. This becomes five. Now I do it the way that I normally do it, and it's super easy. One times one is one. Five times four is 20. And you can see I get exactly the same answer. But I would argue the second way of doing this in this particular case is much easier. Now you're not always gonna to be able to do it this way because sometimes you you look at your diagonals and you go, Oh well, I can't simplify. And in that case, you've just got to do the first method. But when you can simplify, this method is an amazing method to use. Is that all clear? Is it making sense, guys? Is there are there any doubts as to what what I'm talking about here or how to do it? Stella, you nodded your head there. Was that a nod of I understand or yes, I don't know what you're talking about? Okay. I'm going to take that as an I understand. So let's try and do another one, which again can be simplified so through 21 over 33. It's not very good example actually. Let's do 21 over 35. Times. Still not a very good example. I'm going to get it right third time, 21 over 55. Times 77, let's do 88. Over and. 35. So this is a question that is infinitely easier, is really hard. This question, if you do it the normal way, because the normal way involves doing 21 times, 88, you know, good luck working that out. Oh my God. So it's still hard to write on my bluwhat. I really don't what it's I know that you can do 21 times 88 stelllar, but I want you guys to try to do it the other way just to show me that you can and to see hyou the first do this. Can I first do this and I do that, okay. If you wanna do that, sure. Finish good. And now you've got to simplify that because it's an unsimplified answer. So okay, good luck. Incredibly difficult. I'll give you a clue. They're both divisible by seven. Okay, fine. I'm kind of do the second message. You're gonna do it the second way. Yeah. I mean, it's really hard to spot now, isn't it? We're we're in this mess. This would get you sort of half Marks because you have that is right. It's just unsimplified. It's incredibly, incredibly difficult to see. The 1848 and 19 hundred 25 are both multiples of seven and eleven actually very, very hard to spot. But they are we can do this quickly. 1800 and. 40 eighths. Divided by seven is going to be two remainder four and that's going to be six remainder two and that's gonna to be four. So that's six, 264. Do you want to like just because you mentioned your division? Could benefit from a little bit more practice. Do you want to try and do 1925 divided by seven? I don't I don't actually, I don't know how to do it. You don't know how to do it. Okay, ack Jack, think how to do it. And I want another way. You've got another way. What's the what's the other way that you learned, Stella? But it's very dumb way. Just like do like seven you guess first like seven times, maybe seven times. Two seven times 200, 200 first and it's 1400. And then just go up in like very dumb way. Hey, Jack. Jack, because I think it's really important to be able to do this. Jack, how would you do this one? And I'll see. I'll try to make sure that I'm teaching a method that you both in use and there's no confusion between teaching methods. Oh, it is like this. Yep. 1452. Wait. And then. Hundred so let's just go through that bit by bit. So all that's going on, Stella, it looks maybe a little bit complicated. It's really, really nice. So all that Jack was doing now did it very, very well indeed. Okay, okay, things can you like like a question? Like I think I know this. The first step is like two times seven equals 14 because we need to do like if three times seven it's 21 but here's 19 so two times seven is 14 is like smaller than 19. We try to do like if can some can some number can time seven equals 19 but there not so the small the biggest is two so two times seven absolutely right. Brilliantly explains. We're looking for the the biggest number in the seven times table which is smaller than 19 that's 14 and two times seven is 14. So you just write the two there, you write 14 note under it. And then the next part is just a simple subtraction. So here we draw a line under that and we go, what is 19-14? I -14 equals 55. So we write five that the next step is this number here. Can you see the one? The next one that we're wrong because we're done with 19. We already did that. So this one comes down. Yeah, exactly. And we write that there. So the next thing that we're doing is what is 52 divided by seven? Now you look thinking about how close can we get to 52 without going over 52 in the seven times table. So also time seven because if we times eight it's gonna be 56 but seven is 49. So the the biggest one is 49. So yes, which I know about seven. So we go 49 and we do exactly the same thing. We're just repeating, repeating, repeating what is 52-49. 52-49 equals three. And again, this number drops down. So we write the five there. What's 35 to vote? Dict, there we go. And that's your answer. So that's all there is to it. And it's a little bit more. Okay, let me remember. Yeah, you can boto another example here. So we just worked out that this is 275. And actually both of these are divisible by eleven, believe it or not. So I'd like you both. Maybe, Jack, you can try on the left and with 264 divided by eleven. And Stella, give it a go on the right, 275 divided by eleven. The 49 here because 22 plus 27 it's minus you're minus in Oh okay. And so I need to put seven down right? So here 5757 divided by eleven equals. So remember so remember you're done with you can't do 55. Yeah. So put the aligit up. You won't get confused if you just line it up like that. So you know that the next number along is coming down. If you put the five over there, it gets confusing. Yeah, good. Wait, wait, wait, this is 49. Wait, I am confused. Okay, let's just go through this. So first of all, I got it. I got it. Yeah. Okay, let me try. I got it. Well, you don't need you're done now 55 divided by eleven. You don't need to bring down another 55. It's gonna be it's just gonna be five. There you go and that's it done. So just to again, just to go through that celelllar, what you should be doing is first of all, you go, what's two divided by eleven? No, I can't do that because it's going na be zero. You could if you want to, you could put a zero up there, but there's no point. So you go to the next one, you go, okay, what about 27 divided by eleven? That's two. What is two times? Eleven, 22, 27-22 is five. Then we bring down the next number, and we do 20, 55 divided by eleven. Jack, what about 264 divided by eleven? Mothat going to be. Two so 12. Four, 24. Good. So we get a final answer. 24 over 25. Now correct me if you think I'm wrong, but that was quite difficult, wasn't it? To get from here. Remember how long ago we started this question to here? Which is why I'm really encouraging you guys when appropriate, when you can see that your life would be made easier. Do it across simplification ways. So let's try that. Let's just put this answer somewhere so that we don't forget it and we'll see if we can get the same answer of 24 over 25. We should be able to using the cross simplification method. So remember that we're just simplifying as we would do a regular fraction, except we're doing diagonals. So think about what 21 over 35 would simplify to and think about what 88 over 55 would simplify to. Then we've got a new, much easier multiplication question, which we should be able to solve very easily. Jack, do you want to have a go? How conis. I go to get some water. Mm. We simplify it. So Yeah so you remember we're cross simplifying. So think about what 21 over 35, you can simplify really well. I don't know why for some reason. The diagonal elements is confusing, but what would 21 over 35 become? 嗯。Is three Yep three over. Five. Yeah so that's what we're going to write there. We're going to write instead of 21 here and 35 there, we're going to write 35. Good. But hang on. No, no, no, no, no, no, Jack. But it's not three over five. But we're just using this to demonstrate the point that this simplifies in the same way that a regular fraction does. It doesn't become three over five because 21 is here and 35 is here. So they stay in the same position. But with simplifying diagonally, that's the method. So again, for the next one, you're imagining atover 55. What would that simplify to? Remember, we're not actually simplifying. Atover 55 is just to help us. Right eight over five girds. So again, exactly. Goods ds and now on top, there you go. Very, very good, Jack. Excellent. And can you see just how much easier that was? We get exactly the same answer that we got just a second ago. Yeah but it was it was like a fraction of the time that was taken to do the other one. So it's a really, really powerful trick to have up your sleeve if you understand how to do it. And it looks like you do understand how to do it just while Stella's getting a getting a glass of water or whatever she's doing. So if you can do another one, let's do 15. Over 49. And times how good to see back times 28. Over 27. So again, we're going to do try and do this the same way. This is a I'm designing these questions so that they can be cross simplified. They're much more difficult to work out without cross simplify. So Stella, I think Jack's got this now we're just discussing the fact that when you cross simplify. Imagine you're simplifying a regular fraction with the diagonal numbers. So first of all, start thinking about what 15 over 27 would simplify. Two, what is 15 over 27 simplified? It's 15 over 27 simplified. I think you've got your microphone off stelella, in case you're talking. I don't know. Oh, five over nine. Five over nine. Excellent. I saw I was saying like three times that and I saw my back Corthis. So and again, we've just done this to help ourselves out. What we have not done is actually simplified 15 over 27 here because we're remembering the way that this works is diagonally. So rather than a 15 here, I'm going to write five, and rather than a 27 there, I'm going to write nine. So it works in the same way that a regular fraction would work, but you don't then write the regular fraction. Use the diagonals. So Jack, same thing for 28 and 49. What would the 28 and 49 become? You told me. 20. Yeah, four over seven. Absolutely. So where are you going to write the four and where are you going to write the seven? Back to the original question. Excellent. And what's going to be the answer to this now having cross simplified. Good. 20 over 63, fantastic work check. And again, you can see this has just saved us so much time. We didn't have to work out what 49 times 27 was, what 15 times 28 was. We didn't have to do a whole bunch of work then simplifying that enormous well fraction with enormous numbers on the top and the bottom. So it's really, really time efficient to do it this way. Stella, is the method making sense? I think yes, it is. Okay. So I'm going to give you two. See if, Jack, you can work on the left. Stella, you work on the right. So Jack's question here. Instead as question here. Stella, see if you can do. 25. Over 44. Times 88. Over. Sorry, that's right. 45. And. Check, see if you can do. Hmm. 5 man。Over. 27. Times 33. Over 28. Yes, it is my mom's. All right, see if you can do these, okay? Okay. Oh, no. Wait, no. 没。Finish. Okay. So Stella, you're saying 110 over 99? Yeah. Check what's your answer? Okay, I'm going to stop you guys there because I think I think it's both Jack, you've slightly did from the path now I don't really understand what's going on. You cross simplified and then decided to do it the normal way, which was odd. Stella, you nearly nearly got this. There were just a couple of silly mistakes made. Remember you let's start with you, Stella. Remember that you are simplifying diagonally. So the one that you nearly got right is this diagonal here. So you're imagining what would 88 over 44 simplify to? What would it simplify to? Simplify to 4440Oh Oh so 44 and 2044 and 22 and then more as gonna be. Eleven and Oh wait, wait, wait wait the last one is 22 over eleven. Last one. And then it's eleven over one, eleven over one. What are you doing? Eleven? And one is not well, it's eleven divided by two. With hell you can't exactly it's not in the two times table. So you can't divide by two. You've got to divide by eleven. So what's 22 divided by eleven? Two. What's eleven divided by eleven? There you go. So two over one is your answer there. So where there was an 88, we're going to write two. Where there was a 44, we're going to write one. That's half the work done. Next bits we're looking at this diagonal here, the 25 and the 45. So again, we to help ourselves, we imagine the fraction 25 over 45. And we simplify that. What's that going to simplify to Stella? It's going to be. Five over nine good. Straight in there and we can't do better than that, can we? So again, instead of writing 25 there and 45 there, we're gonna to write five there and nine there. Now we have something really easy that we can solve five times two on the on the top, one times nine on the bottom. What's that going to simplify to? Oh, what's it going to multiply out to? Sorry, final answer. So it's gonna be nine ten over nine, ten over nine is your final answer. And that's it. Is that all making sense? Yes. So good, Jack. You were doing good work. And then it all just kind of disappeared. I don't know what happened, but so we started off with. Trying to simplify 14 over 28. Now remember to try to simplify as fully ly as possible. If you can, 14 over 28, you divided them both by seven, which is fine. That gives us two over four. But we can go even further than that, can't we? What is two over four simplifies. One over two, right? So instead of writing 14, we're going to write one. Of writing 28, we're going to write two. Good. Next bit, 33 over 27. We imagine what that would simplify if it were a regular simplified two, if it were a regular fraction. Is this number really can simplify? Yeah, they're both in the three times stable we table. Good, excellent. In celeating 33 we write eleven. Celeating 27 we write Yep, good. And what are we left with? Eleven over 18. And that's it. Is there anything about this guys that's not making sense? You're going to be about to do another on both of you. So do let me know if there are any doubts, any bits of confusion, it's absolutely fine. But just let me know. Doesn't look like there is you both feeling confident to do another. Okay, there's going to be the last one that we do. So let's see if we can go out with a bang and then we're gonna to move on to something else again using the cross simplification method because it's gonna to make your life so, so much easier if you do. Jack, can you try and do 30. Over. 77. Times 99. Over. Five. And Stella, can you try and do 21? Over ten. Times. 15. Over 49. Have a go, both of you. So you can do it using the cross simplification method that we've been practicing. So both number can simplify, right? Finish. It's not right, Stella. So you might want to just go back and really check what you did. I was a bit confused. Is it ten and away? Is it five over ten? Just really talk yourself through it. Remember, the first thing that you're doing is you're looking at this diagonal and write the fraction out. Why not write out 21 over 49 and think about what that would simplify to whatever it simplifies to. Those are the new numbers that you're writing this correct? Let me just check 79. That's good. 61 54 over seven is perfect. Well, excellent work. Good. So hang on, hang on, hang on, hang on, Stella. So having done that three over seven, now you're writing that here, this becomes three, this becomes seven. Does that make sense? So that that working down there was to help you with the question above. You don't need to write a new question. 21 over 49 does simplify to three over seven. So you're done there. Those two numbers are done. Next, two numbers, 50. Again, imagine what 15 over ten would simplify two just to help you. 35, 32, 32. Good. So we write three there and a two there. Now you have the much easier question. 99 over 14 nine over 14 is correct. Makes sense. Okay, let's in the last four minutes just do a little bit of worded questions because I promise that we were going to and move we've kind of gotten a bit stuck on course multiplication. That's gonna to be the last time that we looked at that for a while but hopefully some of it has sunk in. Jack, if I ask you what is 57 ens of 49. How would you work that out? Any idea? Me, Yeah. Okay. So I'm going to I'm going to just let's just break down a few really, really important ground rules here. So generally. In worded questions, a worded fraction questions, the word of. Can be translated to multiply. Or multiplied by. So for example, if you're asked. And we'll just use this question here. What is five sevenths of 49? Really? The question means. Five over seven times, 49 over one. Because 49 is the same thing as 49 over one. Hopefully you guys are familiar with that idea. You can just turn a whole number into a fraction very easily that way. So we write that out five over seven times, 49 over one. Again, if you're quick to spot it, you can see that we do have a diagonal here that can be cross simplified. So I'm gonna to change that to a seven and I'm going to change this to a one again, that makes my life infinitely easier. I do five times, seven on the top 35. I've got one times, one on the bottom one, and that gives me a final answer of 35. So again, if I ask you what is how actually we're slightly running out of time, but let's do one more question. What is two thirds of maybe something that's not divisible by 325? Again, really the question means two thirds times 25, which we can write as 25 over one. So we work this out two over three times, 25 over one. This time we check our diagonals. Actually, we can't cross simplify, can we? 20 53 nowe don't have any common factors there. 21 doesn't work. So we've just got to do this the regular way. And we end up with two times 25 as 50. And three times one is three. So 50 over three is our answer. If you wanted to convert to a mixed number, you could do that. It doesn't really matter. But this this is where I want us to go next time. So going from the pure maths, which both of you have gotten pretty darn good at, into some slightly more difficult worded problem solving. So let's leave it there for today because I've got to rush off to another class and we will pick up from where we left off next time. Have a wonderful week, guys, and I'll see you next Monday. Take care. Bye.