MMWC 2026 - Master Category (Ages 9-11) Webinar

[00:00:09]Hello everyone.

[00:00:19]>> Good good afternoon sir.

[00:00:22]>> Good afternoon sir.

[00:00:32]Good afternoon.

[00:00:36]>> Good afternoon.

[00:00:37]>> Good afternoon, sir.

[00:00:38]>> Good afternoon, sir.

[00:00:40]>> Good afternoon, sir.

[00:00:43]>> Good afternoon.

[00:00:48]>> Good afternoon, sir.

[00:00:50]>> Good afternoon.

[00:00:50]>> Good afternoon, sir.

[00:00:52]>> Good afternoon.

[00:00:53]>> Good afternoon.

[00:00:54]>> Wait, we have to open our camera. Hold on. Give me a second.

[00:01:00]>> Where's my camera?

[00:01:03]>> All right. It's so nice to see all of you here for today's session the for the webinar of the mental math tips and tricks for the mental math world cup. Um are you all excited to be part of this session?

[00:01:16]>> Yeah.

[00:01:20]>> Wonderful. Wonderful. So >> and and I'm sure all of you are working towards uh your preparation for uh the the round one that is going to be happening between the 1st to the 5th of August. I'm sure all of you will do well but you know >> it >> wonderful. So that's great. So today today essentially the session is going to be about metal mat tips and tricks for the master category. the 9 to 11 year old all of you are here and we have participants uh from all over the world uh you know and you know we also have people who have who are logging in from uh as far as uh you know the south of Americas u and it's very early there but you know I really thank you all for for taking your time and making sure that you're available for today's session u What's before we start the session I just want you all to read the instructions that are that are here that can be seen over here you know in in some time we will obviously mute all of you so that we start the session and then if we have any you know topics that we would want you to interact with us at that time we will unmute you we will ask you to interact with us so please make sure that you you know whenever we call out your name and you respond on to our our questions. Uh it would be great to be to have this made this into an interactive session. U if you all cannot hear us or for some reason you cannot see us uh the video, >> I would suggest that you you put off your own video just in case that could be because of your your network issue because of which you are not able to see us or hear us. So putting your video off may improve your hearing ability and you'll be able to watch us. uh uh clearly properly u if you have any questions you can drop them on the chat box uh uh and we'll we'll try to answer as many as we can.

[00:03:28]I hope everybody is ready with a pen and paper uh because there's there'll be a lot of uh you know valuable insights that we are going to receive from our our coach Daniel Tims who's there on this session. So please make sure that you're you're you know capturing all the pieces of wisdom that comes from him today.

[00:03:49]Also I'm sure all of you have a lot of questions about the competition that is going to be coming up the mock test the round one. I am sure you have all of all of those questions. If you do uh today is not the session for that you need to drop your queries or questions on contactiveml.com which is our email address >> or drop a WhatsApp on + 918291027238.

[00:04:14]>> All right. So you can ask us any question about the competition by emailing us or or setting us a WhatsApp.

[00:04:20]Today as I said is I'm just I'm just muting everyone.

[00:04:31]Okay, today as I said is it's all about uh the mental math tips and tricks webinar which is going to be led by none other than Daniel Tims. Mr. Tims is very very uh known personality in the world of mental mathematics. He he wears many hats. He's a renowned mental math expert and coach. He specializes in practical mental math and psychology of calculation. He is actively involved in providing workshops, training, stage performances and training materials for mental math including international competitions. Daniels also runs the world mental calculation website offering news and resources for advanced competitive mental math and he is here today to share his uh his knowledge with all of us. So let's make sure that we are here fully focused with your pen and paper ready to ab absorb everything that Daniel has to offer today. All right for all the important topics that are going to be covered for during our for our competition. Daniel thank you for joining us and you know you can take this take this ahead.

[00:05:38]>> Well thank you very much Avanash for the introduction. I'm really happy to see so many of you joining the workshop today from all around the world. If you have any questions, then you can write them in the chat. So, just to get using the chat, can everyone type which country are you from? Which country are you representing? Send me a message in the chat to tell me this. And um in the in the public chat, okay, we have Bahrain, we have UI. Is um can the participants write in the public chat or is that only for the hosts? Aanash.

[00:06:18]>> It's so it's a public chat. They can write directly to you.

[00:06:23]>> Okay. Uh okay. So we have Bahrain, we have the UAE, we have India, we have many people from India. Um India always very strong with mental maths. Yeah, I see lots of people from India. From the Philippines. I was in the Philippines in um March actually in Manila and Barakai um Australia. Oh, very far away. Syria, Germany.

[00:06:50]Um so many messages. Really cool. Um a lot of people from Bahrain. Okay, cool.

[00:06:55]I can't see all of your messages. Oh, Saudi Arabia, Qatar, India, Vatican City. Probably not the Vatican City. I think probably from India. Um, okay. Sri Lanka. I was in Sri Lanka in October as well. Uh, okay. Very cool. So, uh, introduction to me. Thank you for the messages. Introduction to me in for this workshop which is going to be covering some of the important methods that you that you need for the mental um, the mental math world cup this year. And this is delivered by me, Daniel Tims. I am from the UK, from England. I'm currently in Oxford today and I studied mathematics at university and worked as a software developer until in about 10 years ago I decided I didn't like the cold weather in England and I wanted to travel. So I've been doing that since and I've been to some of the countries that you are in as well. And some of the reasons I've traveled has been for mental calculation competitions, mental math competitions in various countries. And so if you get good at mental maths, you have the opportunity to represent your countries uh to represent your country in competitions such as the ones organized by live MCL who are running this workshop today. and the competition that you're already preparing for.

[00:08:27]And so here are some of the competitions that I've done. I'm a mental math coach.

[00:08:31]That's why I'm here today. I do this in other places as well. And as Avanash mentioned, I'm the author of the world mental calculation website, which you may have seen. It's the black and white website with information about different mental math uh techniques. And uh some of the more advanced methods [snorts] you can learn on that website. Today we are going to be focusing on oh it didn't display everything properly, but the top one is supposed to say addition, subtraction, and multiplication. We also have having doubling and tripling mean which is uh another way of saying average square numbers profit and loss and we may have some time for questions and answers.

[00:09:21]I want to repeat something that Avan said. You may have questions about the competition itself. I am not the person to ask. Those questions should be sent to Avenache and the live MCL team. But I can ask you questions about the I can answer your questions about the mental maths.

[00:09:44]>> I'm going to be mostly doing it from the whiteboard.

[00:09:49]So, >> hey Daniel, before you move ahead, just just one quick check. Uh you know, I'm getting a some of some participants who are asking they're saying that they can't hear us. U I just want to make sure everybody you can hear us right you can hear us loud and clear can I have a thumbs up from all of you if you can hear us >> wonderful so I you know whoever is not able to hear us please make sure that you log out and log in again could be a problem with your device please please have that checked out thank you okay so both of you can hear us good check okay we're going to start off with multiplications And for your competition, you need to be good at multiplication of a two-digit number multiplied by a one-digit number.

[00:10:39]For example, 47 * [snorts] 6.

[00:10:46]So, what would be 47 * 6? A few ways to solve this.

[00:10:52]I would recommend that you start with the 10 digits.

[00:11:04]So for fast mental math what I would recommend is start with um know that 47 means 40 and 7.

[00:11:16]So calculate first of all 40 * 6 which is 240.

[00:11:25]This is like 4 * 6 = 24 with a zero at the end.

[00:11:34]Then we do 7 * 6, which hopefully you know is 42.

[00:11:43]Then we're going to add them together which gives us 240 + 42 is equal to 282.

[00:11:56]So the method here is very simple. It is possible to do 7 * 6 first and then do the 40 * 6.

[00:12:06]I would recommend for small calculations like this, for ones that could be very easy to start with the 40 and then do the seven afterwards.

[00:12:19]So I'll look at some of your messages.

[00:12:21]Yeah, 282 282 uh people from the seells from Canada. Oh, very early morning for you. Good morning Greece.

[00:12:33]Very cool. So many so many different countries that you're from and uh correct answers many correct answers coming in as well from Bangladesh. Okay, very cool.

[00:12:47]So try try using this method for another calculation here. So what would be 63 multiplied by 8?

[00:13:01]And I will also invite someone who would like to explain how they solve this to tell us with their own voice in the chat. So, I'd like you to write the answer. And if you would like to volunteer to say it, then put in the message after your answer that you volunteer to share.

[00:13:36]Okay.

[00:13:40]Lots of messages coming through. Very cool.

[00:13:46]A lot of correct answers as well.

[00:14:10]Okay. And okay, so we have a volunteer with the correct answer. Adve D.

[00:14:18]Um, Avanache. Can we invite advice?

[00:14:41]Message for the host.

[00:14:43]>> Okay.

[00:14:43]>> Can we invite Adve Adwit Na? Right.

[00:14:48]>> Yes.

[00:14:49]>> Yes.

[00:14:50]Yes.

[00:14:51]>> Cool.

[00:14:51]>> Thank you for volunteering. Uh first of all, what was Yeah. First of all, what was your method? How did you solve it?

[00:14:57]And eventually then we will find the answer. What did you do?

[00:15:01]>> Uh uh sir, you told the matter like 60 uh into 8 which is equal to 480.

[00:15:11]>> Nice. Yes.

[00:15:13]>> 3 into 8 which is equal to 24. Then I did 480 + 20 which is equal to 500. Then 500 + 4 which is 504.

[00:15:25]>> Very good. Yeah. So 480 + 20 something gives us 500 and it's 24. So that gives us 54.

[00:15:34]Very nice. Cool. Thank you for sharing.

[00:15:36]So this is exactly the method I recommend. Some of you may prefer to do the 3 * 8 first. It's also okay. But I recommend for fast mental math to do the um 61st. Okay. Very nice. So we can do many examples but they are all the same.

[00:15:53]Later I will give you uh a special a special gift for people joining this workshop. Uh a way that you can practice this by yourself. I'm not going to give it to you now because it will be a distraction. But I will show you um I will show you in a moment another way you can practice this.

[00:16:13]Uh another thing I want to mention here is that uh in the competition you may have multiplechoice questions and if you understand about how the numbers are working sometimes you can identify the answer using a shortcut and I'll show you a shortcut that works for the multiplications.

[00:16:39]I'm going to give you a really difficult multiplication and I don't want the answer. I don't want you to tell me the answer. I only want you to tell me what is the last digit of this multiplication.

[00:16:53]Um this one. Yeah. So this multiplication here, what is the last digit?

[00:17:26]So yeah, what is the last digits for this really large multiplication?

[00:17:36]And also after you after you tell me the answer, if you would like to volunteer to explain, then say volunteer. This means I only ask somebody who would like to volunteer.

[00:17:48]I do see lots of correct answers.

[00:17:55]Okay, very cool. Can I can we ask a volunteer? Um, Suas Suhas. Yes.

[00:18:06]>> Yeah. Got him. Bet.

[00:18:09]>> Yes, sir.

[00:18:12]>> Yeah. So how did you you got the correct answer here. Can you explain to us please how did you know the last digit of this really large multiplication?

[00:18:21]>> Uh so like basically you how to just multiply like take both of the numbers and take the like the first digit. For the first number it is six and the second number is seven. So 6 * 7 is equal to uh 42. From there take the one's place digit and which is it is two. Good answer is two.

[00:18:43]>> Very good. Yeah. And this is because all of the other digits [snorts] so the the 3 4 5 6 7 4 75 this represents a multiple of 10. And in the second number the 2 3 6 725 is also a multiple of 10. So in the multiplication these digits they cannot affect the last digit of the answer. The only digits in the question that can affect the last digits of the answer are the last digits in the question which as Srias has mentioned are six and seven.

[00:19:21]So 6 * 7 = 42. So last digit is two digit before that we need we would need to do more work.

[00:19:42]So it doesn't mean that the answer ends in 42 but it does mean that the last digit is two.

[00:19:50]So if you're doing uh if you have a large multiplication in a competition and you have to choose in multiple choice, you can look at the last digits and this tells you what the answer must end in. So if the if the answers are um something ending in four, something ending in two, something else ending in four, and something else ending in um two, then you know it's got to be one of the ones ending in two, it can't be this one, and it can't be this one.

[00:20:30]And sometimes this means there's only one possibility. In other times it means you can check your answer.

[00:20:40]Let's do another question like this before we move on to a different topic.

[00:20:43]So again I will write a big multiplication and I would like everyone to tell me what is the last digit of this.

[00:20:59]So what is the last digit here? I don't I don't need a volunteer for this question. I just want you to type what's the last digits.

[00:21:09]So parto correct? I am correct.

[00:21:13]I have correct. Yes.

[00:21:18]Yeah. Lots of correct answers here. I can't read them all because I have uh more than a hundred people answering the the question here.

[00:21:30]Um, yeah. Also, please send me the message once. If you send me the message millions of times, then it doesn't it's just annoying for me. It doesn't mean I see your message any better.

[00:21:41]Um, okay. So, the answer is it's like 4 * 5, which this is equal to 20.

[00:21:55]So, it ends in a zero. is the answer.

[00:22:02]Later when you learn to do very large multiplications, there's an a way that we use the same logic here to calculate all of the digits starting from the left. And this is called cross multiplication. In the workshop today, we're not going to cover that. This could be a topic at a different time.

[00:22:21]Um, so if you want to know how to multiply uh really big numbers, then I will give you a resource at the end. so that you can learn to do it. In this workshop today, we move on to a different topic and we this is as far as we go with multiplications.

[00:22:39]Okay. Um the whiteboards as well for the hosts. We can save the whiteboards at the end. Um we can figure that out at the end. I'm now going to move on and have a look at additions.

[00:22:55]And additions are really important. Not just because in the competition you might have to do multiplications but because lots of mental math questions in even square roots fractions uh everything often they involve in the methods doing an addition or a subtraction. I'll give you an example of this. In the multiplication we just did in every question we needed to do an addition. Look at the light blue. The first example we had to do 240 + 42 and in the second example it was 480 + 24. So it's very normal that we have to do additions or subtractions even if the question looks like it's something else.

[00:23:42]And you will see in the competition you're preparing for the mental math world cup. There's many really many calculations where you have to do this.

[00:23:52]So it's not enough that we need to know how to do multiplications. We need to be fast. So what I show you today is some tricks so that you can be fast at multiplications. Sorry, fast at additions and subtractions.

[00:24:08]And I start with something quite basic.

[00:24:11]So, if I have an addition like 43 plus 85, here's an example.

[00:24:24]>> Hey, Daniel, I'm sorry to bother you.

[00:24:26]>> Sure. Yes.

[00:24:27]>> Um, I think I missed communicating that we will also be covering twodigit by twodigit multiplications also.

[00:24:35]>> Uh, you would like me to cover that today?

[00:24:37]>> Yes. Yes. Yes. I missed including that in our list of topics actually that that's my mistake.

[00:24:44]>> Okay. Oh, cool. Thank you for clarifying. So, we can also do the two digit times two digit and we can do that.

[00:24:49]>> Um, we'll do that [snorts] >> a I want to do that after the No, I'll do it now. I'll do it now. It makes most sense. Okay. So, >> yeah. Yeah. multiplication two digits times two digits.

[00:25:09]So for for these there's lots of quite advanced techniques to do them. So even if you tell me the question and I don't have it written down I can get the answer in 4 seconds because I practiced this specifically for the competition you're doing. You have a couple of advantages. First of all, it's allowed if you write p if you write something on paper although it's better if you don't because it makes you slow and the second thing is the the you also have multiple choice. So that gives you some idea of the answer. So here are some tricks that you can use before doing the calculation.

[00:25:49]So uh question for everyone if I I I have thought of a twodigit * two-digit multiplication like AB multiplied by CD.

[00:26:00]I want to know how many digits are in the answer.

[00:26:08]How many digits would be in the answer?

[00:26:16]Slightly trick question.

[00:26:19]How many digits would be in the answer?

[00:26:32]And if and if you would like to volunteer to explain why for this one, you can tell me afterwards that you volunteer and I'll get somebody with the correct answer who volunteers. [snorts] Okay. Uh, so can we have a Samsung SM P619?

[00:26:58]I'm sure that's not your name, but can we have this person? Maybe you can change your name so we know what your name is, but in any case, to answer the question, can we invite Samsung SM P619 to explain this?

[00:27:12]>> Hello. What's your name?

[00:27:15]My name is Vian.

[00:27:17]>> Vian. Cool. Thank you for volunteering, Rian. So, how many digits are in the answer?

[00:27:23]>> The answer would be three to four digits because if you multiply such as 45 uh * 40.

[00:27:34]>> So, uh if you multiply 0 * 5 0 and you keep going, it could the answer would be in three digits. But if you do such as 90 * 99 that could be a fourdigit question answer.

[00:27:49]>> Good. Yeah. So the highest it could be was 99 * 99 which is 9,8001.

[00:27:54]This is four digits. What example did you have for a very small one? What's the smallest it could be?

[00:27:59]>> Small one. 45 * 40.

[00:28:03]>> 45 * 40. What would this be?

[00:28:06]>> This would be >> maybe I can help you. So it's 1,800.

[00:28:11]This is also four digits. What's the smallest twodigit * two digit we could have?

[00:28:18]>> The smallest time two digit we could have is 10 * 10.

[00:28:22]>> Very good. Yeah, 10 * 10. And the answer to this is clearly 100, which is three digits. And I can do another example here. Maybe we have like um 21 * 29. And this here is going to be um 69 which is also 300.

[00:28:46]>> Yeah, I would like to correct my name.

[00:28:48]My name is not Vian. My name is Van.

[00:28:51]>> Oh, sorry. Sorry, I misheard you. Vian, thank you very much for volunteering, Vian. And you're exactly correct. for two-digit times two digits. If the numbers are quite small like 10 x * 10 or 21 * 29, the answer will be three digits. [snorts] And if the digits are quite large or even medium like 45 * 40 or 99 * 99, the answer would be four digits.

[00:29:16]And so you can tell from the size of the number whether it's going to be three digits or four digits in the answer or maybe if the numbers are kind of medium then you're not sure. Um thank you very much for that. In general if I have so question for everybody I'm going to expand this to uh something a little more challenging just for a moment. If I have this is not typing multiplication of let's say okay multiplication of 10 digits times 20 digits so really really large multiplications how many digits are going to be in the answer 10digit number multiplied by a 20digit number. And again for this one I will take a volunteer.

[00:30:28]So if you want to volunteer, you need to tell me the answer beforehand.

[00:30:45]I'm looking as fast as I can for the answers.

[00:30:53]Um, you've sent me too many messages, so I can't actually see what the thing is.

[00:31:08]Okay, lots of good answers coming in. I haven't had any correct ones yet though.

[00:31:14]I think this is maybe a difficult question.

[00:31:21]A few people say 30 to 40. It's not 30 to 40. Something slightly different.

[00:31:30]Hey Daniel, I think we have a volunteer Jayen Fonka.

[00:31:37]>> Was it is it with the correct answer?

[00:31:39]>> Uh, did I tell [snorts] you the answer?

[00:31:42]>> I'm looking for someone for a volunteer who has the correct answer.

[00:31:51]So, I've seen lots of answers. None of them correct. Actually, I haven't had any correct answers to this. a lot of good guesses. So, I'm very happy for people to guess even if it's not correct.

[00:32:05]Okay. Had a um yeah, so we have a a first first correct answer. I think this is a very difficult question. So, it's from um Aberh i. So, abh i r a rau.

[00:32:24]Very good.

[00:32:25]>> Okay.

[00:32:27]Yes, Abra.

[00:32:30]>> Yeah, good evening.

[00:32:33]So, what I basically did was that I took an example.

[00:32:39]>> Okay.

[00:32:40]>> And then I tried solving it. So, it came in like 29 digits.

[00:32:46]>> Okay. Very nice. Yeah. So, it could be 29. Yeah. Sorry, please continue. I sorry I interrupted.

[00:32:53]>> Okay. So like it could be 29 to 30 digits because we are multiplying 10 to 20.

[00:33:03]>> So like basically the it'll vary between the numbers you choose.

[00:33:09]>> Exactly. Yeah. So the largest we could have is like 99 * 99. Imagine if the >> if the 10-digit number was all nines and the 20digit number was all nines. Then the maximum we could that's the maximum we could get would be 10 + 20 is 30 digits but could be one fewer if the initial digits are smaller.

[00:33:37]So the answer is it could be 30 digits or only 29. Those are the only possibilities for this.

[00:33:44]So if you remember this rule then it helps you understand the size of the multiplications for the ones you need to do. It's twodigit time two digits. So the answer is going to be four digits or sometimes only three digits.

[00:33:58]Thank you um Abdag for the um for the explanation there. You are correct uh for the most difficult question so far today.

[00:34:07]Okay.

[00:34:09]Next thing is what is the last digit? We know how many digits are in the question, but what would be the last digits? So, we have an example here in blue, but one of the digits we can't see what it is.

[00:34:28]So this is going to be yeah a number that ends in four multiplied by a number that ends in seven is going to be um what is the last digit of this going to be?

[00:34:49]What is the last digit of this?

[00:34:53]And again for this one I can take a volunteer.

[00:35:18]Okay. Uh, can we have um I I take a different one.

[00:35:30]Uh, okay. Let's take um Archets, please.

[00:35:35]Archet has the correct answer.

[00:35:43]So my idea was multiply 4 by 7 and then the answer is 29.

[00:35:55]>> 28, sorry. And I then I type the last number of of 28. It's eight.

[00:36:04]>> Very good. Yeah. So, uh, you're exactly right. We're looking at the last digits, so this must end in eight. Cool. Thank you for sharing. This is correct. Now, we're going to do another example putting um something else together. So, it's going to be um 50 something multiplied by 60 something.

[00:36:35]How many digits are there going to be in the answer? And this time we know how many digits there's going to be.

[00:36:43]For the last one it could be 29 digits or 30 digits. For this one we know how many digits it will be answers and also volunteer.

[00:37:04]Very good. We got some got some correct answers coming in. I could only take a volunteer if you told me the answer in the previous message.

[00:37:16]And so it needs to be the correct answer.

[00:37:22]Okay, I've got a range of answers coming in. Okay, not all of them correct. It's good. I'm very happy everybody is trying to guess these.

[00:37:34]Okay, can we have Zoroa?

[00:37:36]Zorawa Zawa Kalia they have the correct answer.

[00:37:50]>> So it could be three to four digits. We know that you have the correct answer though. So basically what I did was uh uh so I took an example as 50 into 60 which is uh 3,000 and that's like one of the smallest numbers. So I thought it would be four digits.

[00:38:10]>> Very good. Yeah. So the answer is just more than 50. It's going to be more than 50 times more than 60 which is got to be more than 3,000. So it has to be a four-digit number. And we know that two digits times two digits it can only be four digits or sometimes three digits.

[00:38:26]So logically we know that this must be four digits.

[00:38:30]Okay. Very good. Thank you for sharing.

[00:38:33]So now I'm going to make another example. And I think now you see what I'm doing here.

[00:38:39]If I have 54 multiplied by 67, we know that the last digit is an eight because it's like the dark blue example. We know that the answer is four digits because it's like the light blue example. So now my question is what's the answer? Who knows a method for solving the entire multiplication?

[00:39:02]And again for this one I can take a volunteer to explain the methods. This one is a little more difficult of course.

[00:39:44]So your answer must your answer must be a a four-digit number. We know that's true.

[00:39:54]We know it must end in an eight.

[00:40:00]Okay. I've had two I'm doubting myself here. I'm getting lots of people with the same answer, but it's different to my answer. Okay. Yes, some people with the same answer as me.

[00:40:14]That makes me less worried.

[00:40:17]Did I make a mistake?

[00:40:22]Also, message to everyone. Don't send me the same message multiple times because it doesn't make me see it more.

[00:40:30]It just means that I can't find your um answer later.

[00:40:36]Okay, we have a um make sure you send the message about volunteering after your answer so I know that it's this question that you're volunteering for.

[00:40:49]Okay, I'm still looking for a correct answer with a volunteer.

[00:40:57]It's not 3,028.

[00:41:00]I've had lots of answers. 3,028 is actually not true. Um, okay. We have a volunteer with the correct answer.

[00:41:08]Revance, please. Revanch Mashwari.

[00:41:17]>> Um, uh, good afternoon. Good afternoon, sir. Um, >> good afternoon. For uh for 54 into 67 um my method is to first take the on's place into on's place 7 into 4 which is equal to 28.

[00:41:37]Then uh then we take the when then we do 5 into 7 + 4 into 6.

[00:41:52]Good. Yeah. So, we've got the 350 and this is thinking about the 10 >> and then and the last step we just multiply the 10's place into 10's place which is 5 into six.

[00:42:04]>> Very good. Yeah.

[00:42:06]>> So, we get the answer 3618.

[00:42:15]>> Um Okay. Okay. So you don't So um you got the So just to be clear, you're thinking of 28 here and then when you do um what are you doing with the 10th digits? Just to be clear exactly what you're doing.

[00:42:37]>> Uh yeah, Revanch to continue.

[00:42:41]>> Uh what?

[00:42:43]>> Yeah. So you have the 4 * 7 = 28.

[00:42:48]>> Yes.

[00:42:48]>> And the 10 you have the 5 * 7 and the 4 * 6. What do you do immediately afterwards? What's your next step?

[00:42:56]>> And then last step is 5 into 6. We take the 10 into 10. 5 into 6 which is 30.

[00:43:03]>> Okay. And how do you put all of these together to the correct answer?

[00:43:08]>> Yeah. So in the first we got 28. So we write 8 in the answer and two in the carryover.

[00:43:16]Then we got the answer 59.

[00:43:20]So 59 + 2 61. So in the so in the actual answer we'll write 1 and six in and six in.

[00:43:33]>> Yeah. And >> yeah.

[00:43:36]>> Okay. Very good. Yeah. So we start with the in this method here we're starting from the right and this method is called >> cross multiplication.

[00:43:53]You may all you may have seen this at school as something called foil. This is foil. Um foil you can do in a few different ways. So this is foil from the right.

[00:44:09]So uh this is the method that you're using and you're exactly correct here.

[00:44:14]So we're starting from the the right. We do 4 * 7 is 28. This means like [clears throat] before the last digit must be an 8. We know that for sure. So we can write down the 8 in the answer and figure out the other ones.

[00:44:33]And so the two here represent two tens like 20. And then we have a look at the other parts of the question that contribute tens. [snorts] And this would be the 50 * 7. So how many tens is this?

[00:44:46]5 * 7 as revant as you were saying to us. And I'm going to give a little I'm going to do a small change to your method. This is my special trick that I use for cross multiplication.

[00:44:58]I start with the carry. And the benefit of this is that now I don't have to remember the carry later when I'm busy thinking of the calculations. I know that I already have the carry. So I start with the I start with the carry 2 + 5 * 7 and then I already have 37. So this is something that I do differently to what Revanche explains and I think it will help everyone here if you practice doing it like this. So you start with the 2, you add the 5 * 7 and that gives you 37. Then you add the 4 * the 6 and that gives us the answer that Revanch told us 61 and this is counting the tens.

[00:45:43]So Revanch at this point what digit can I write down >> after eight? We we can write uh as you showed 61 we can as it is write 61 and multiply 5 6R which is 30 and remove zero and write 3618 as the final answer.

[00:46:04]>> Good. Yeah. So we can't almost correct.

[00:46:06]So we can write the one down. So now our answer ends in 18. And if it's a multiple choice question you could look to see which answers end in 1/8. And if there's only one option, then you already found it. It's also possible.

[00:46:20]And the carry digit is then the six. So now I'm looking at the the hundreds. And I start with my six. I add the 5 * 6.

[00:46:31]And this gives me then 36 36 what? 3600s.

[00:46:40]So uh at this point I finished. So the answer is going to be 3600 110 and 18 which is the correct answer.

[00:46:49]So I make a very small change from what was described here because that was the um one of the things I wanted to mention as part of this. So yeah, thank you very much for explaining that. This is a a more advanced method called cross multiplication.

[00:47:06]So there a few ways that you can think about this. So I will show you a couple of illustrations of how this how you might think about this and then whichever way makes sense to you is how I recommend to think about it. So first of all I'm going to write the number very big. So I'm going to do a big diagram.

[00:47:28]So 54 * 67 and then the first step is to start from multiplying together the units. Let's use a very bright color. Let's use a bright green, the brightest green I can find. So, I'm multiplying four times the seven. And that's what happens on this line to give me the eight.

[00:47:52]The next thing I did, I'm going to change the color. Let's do um orange. I did 5 * 7 like Revanch told us. 5 * 7.

[00:48:01]That's not a That's not what I wanted.

[00:48:03]Sorry. Uh I guess I wanted a straight line. Here we go. So I did a 5 * 7 and then we also did 4 * 6 and this makes like a big cross a big cross in the middle of the diagram and this is representing this step here.

[00:48:23]This is why it's called cross multiplication by the way.

[00:48:28]So this here is representing the big cross. And the last thing I do is look at the last digits over here which is the 5 * the 6.

[00:48:46]So for a 2x two this is three steps and [snorts] if it is uh a larger multiplication like 20 digits time 30 sorry 10 digits time 20 digits there would actually be 29 steps and it would take you a very very long time. Luckily in the competition you don't need to do this. You only get questions which are twodigit times two digits. But when you get fast at this you find that you can quickly get you can quickly multiply four digits times four digits. For me it takes me about 22 seconds to do fourdigit time fourdigit. And some people practice a lot and they can do eight digit numbers multiplied by other 8digit numbers in less than 1 minute.

[00:49:27]sometimes less than 30 seconds [snorts] with practice using this method.

[00:49:34]I said I would illustrate this in a few different ways. So, pay attention to this one. When we start off, I'm going to put a star above the digits we're looking at, which are the four and the seven. So, I'm multiplying the four by the seven.

[00:49:50]But the this is for the green one. The next step, I'm going to move the star at the top across.

[00:49:59]So now we're looking at the five multiplied by the seven.

[00:50:06]And while we're doing that, I'm going to imagine that the stars are moving in opposite directions.

[00:50:13]So this star starts at the top, starts from the left and moves to the right.

[00:50:18]And at the bottom, it starts at the right and moves to the left.

[00:50:22]So after it moves one place then it's above the four and beneath the six.

[00:50:28]And this is a way of finding all of the ones for multiplying the 10. We have the 5 * the 7 and the four * the six.

[00:50:38]And then finally we for the last one we can't move the top star any further. It's stuck. We moved it so far to the left. There's no more numbers. So we have to move the bottom one and now it's above the five and the six.

[00:50:54]So this is the way that I think about it. So I show it to you as another way of thinking about this question.

[00:51:03]And I'm going to give one last way of thinking about the same question which is 54 means 50 + 4. Actually I'm not going to write it like this. I'm just going to write it like this. So this is like 54 multiplied by 67.

[00:51:26]So I'm going to start off multiplying together.

[00:51:35]Uh how to do it? Yeah. So I'm going to start together. I start by multiplying these numbers together. The four times the seven.

[00:51:45]After that, I'm going to make the these two arcs beneath it. And I'm going to finish off with this.

[00:52:02]And it looks a bit like a smiley face.

[00:52:04]You've got a big mouth in orange. You've got a little nose also in orange. And you've got a green eyebrow and a pink eyebrow.

[00:52:13]So this is if you learn this in school, this is the like the foil diagram. It's showing the same methods.

[00:52:22]I'm showing you the same method in different ways, just different options for how you might think about it.

[00:52:31]I'll put this back also to show you it moving for the tens. And then yeah then we have here actually four different ways of thinking about the same multiplication and actually the same methods. This is all the same methods just different ways that you might think about it. Not only this but we saw two shortcuts. One shortcut was how we knew that it must be a four-digit answer and the other one is how we knew it must end in eight or after one stage how it ends in 1 eight. And this means that we can uh short um several shortcuts to make it faster to find the answer.

[00:53:15]So okay, that was lots of talking.

[00:53:18]Let's see if we can solve a similar question.

[00:53:24]So try to use the same methods for this one. I'm I'm not going to ask for a volunteer, but you can type me the answer.

[00:53:34]What would be 43 ultiplied by 78?

[00:53:55]I give everyone a minute to try this.

[00:55:24]Okay. Lots of answers coming through.

[00:55:28]Lots of lots of answers. Very good. Uh some people say they don't understand.

[00:55:33]That's okay. If you don't understand, you can also send me a message to to let me know. And I um yeah, good also for me to know. I will give you some resources to help you with this later as well.

[00:55:58]Okay, this one I said I I wouldn't need a volunteer, but I'm very happy to see we have lots of correct answers here. So I will just quickly explain the method that I use. So the units we have our three multiplied by 8 which is 24. So we write four carry 2.

[00:56:26]So in particular I can already write down the answer is ending in a four. We also know because it four is quite 40 is quite big and 70 is quite big. We think it's a four-digit answer. Four-digit answer that ends in four.

[00:56:43]The 10, we have the two. We're going to add the Which way did I do? This way.

[00:56:52]Um, okay. Okay. So, we do uh 4 * 8 and that gives me 34. And then I'm going to add the 7 3 * the 7 and that should give me 55.

[00:57:14]So, at this point I can write down five and carry the other five. So the answer is something something 54.

[00:57:23]Then the hundreds I have my five that I carried. I have to do the 40 * the 70.

[00:57:31]So the digits are 4 * 7 and that gives me well solved it equals 33. And so the answer is then 3354 which is the correct answer.

[00:57:45]It is possible to do this starting from the hundreds and finishing at the units.

[00:57:49]Some people prefer to do that. I recommend for this one or like my preference is starting from the left and working to the right. If you want to do from the right and move to the left, some people working with Sorban, they prefer to use this. It doesn't really matter as long as you are consistent when you uh solve the question.

[00:58:09]Okay.

[00:58:10]So now we've finished talking about the u two-digit times two digits. [snorts] I'm going to actually skip ahead and look at square numbers next. We will do additions and subtractions again later and everything else I mentioned. But I want to move on to the square numbers because the the technique works very nicely actually the the same method works very nicely when we look at square numbers.

[00:58:40]If I get a new board somehow. Here we go.

[00:58:46]Let's think of how we would solve square number 50. Uh, don't want that one.

[00:58:52]Let's um, let's do 47 squares. So, what does 47 squares mean?

[00:59:01]It just means 47 multiplied by itself.

[00:59:08]So the little the little two it means that we have this number two times all multiplied together. If I have 47 cubed this means 47 * 47 * another 47.

[00:59:27]So this would be the cube of 47. This is much more difficult. We don't have to solve this, but just to help you with the notation, um, put it there. Okay. So, how would we find 47 squared?

[00:59:46]So, there's several methods here.

[00:59:50]Method one is cross, cross multiplication or foil.

[00:59:57]So try to use this methods for solving 47 * 47.

[01:00:09]And for this one I'll I will accept a volunteer So now looking for a volunteer with the correct answer.

[01:01:49]Someone says we can use algebra. Yes, we can. That's method two.

[01:02:02]So, if you have the answer, make sure you tell me that you can volunteer, that you'd like to volunteer as well.

[01:02:15]Okay. Not many correct answers actually.

[01:02:32]Okay, I'm just looking for a volunteer with the correct answer.

[01:02:47]This is uh taking me surprisingly long.

[01:02:50]Yeah. Okay, I see some correct answers but not from people who are volunteering and I have some volunteers for who don't have the correct answer and a lot of messages I haven't seen yet.

[01:03:13]Do let me know if you want to volunteer.

[01:03:18]Unfortunately, Zoom gives me all of the conversations separately, so I can't It takes It's very slow for me to check through everything that you've been writing to me.

[01:03:52]Okay, I see some of you have got uh very good methods here.

[01:04:03]So, if you want to volunteer, send a message saying volunteer, but only if you have the correct answer. I see some people um I see lots of correct answers, but somehow no one with a correct answer wants to volunteer.

[01:04:18]But I've seen I'm looking through your messages as quickly as possible.

[01:04:25]Maybe next time we can do the messages differently.

[01:04:34]Okay, I think I'm just going to go through the answer myself.

[01:04:42]Otherwise, it might take me too long to find the answer with someone who is volunteering.

[01:04:49]So, the answer is just over 2,000.

[01:04:56][laughter] Okay, so what has changed there?

[01:05:01]Um, I like that you changed your changed your name with the answer to I love refrigerators. Yes. Okay. Um, okay.

[01:05:15]I'm just going to I'm just go through the answer because I don't find uh um Okay. Okay. Finally, we have one. Zion.

[01:05:21]Z A Y A.

[01:05:24]I find Zion. Please, can we have a Zion invite to explain the method, please?

[01:05:48]For the host, are we able to unmute Zion? Z A Y A N Are we not able to?

[01:06:14]Okay. Somehow.

[01:06:20]Yeah. The hosts, we need to unmute Zion.

[01:06:23]Zam Siddiki please >> sir. Uh I am I use cross multiplication to find the answer. Like first I multiplied uh 7 into uh first I multiplied 7 into 7. Uh I got 49 then I took 9 and put four and carry over. Uh and then after that uh I I just did the same thing with all the times and then basically my answer uh uh came 2209.

[01:07:02]>> Good. Yeah. So what do I write for the tens? I'm starting with the four from my curry and then what?

[01:07:09]>> I got 16. So uh I did 16. I put 16 in six and I put one like that and multiplied it and it uh and my answer came to uh 01.

[01:07:26]>> Okay, good. So, we start at for the 10 we have the the four * the 7 and that's going to give us 32 and then we have to add the 7 * the four and that is going to give us then 60.

[01:07:44]>> Yes, sir.

[01:07:47]So I'm going to write down which digit do I write down Z.

[01:07:52]>> So we have to write zero and carry over six.

[01:07:57]>> Very good. Yeah. So you write the zero and carry the six. So this is going to give me something something 09 and then I start with my carry digits.

[01:08:08]I add the four times the six. And what does that give me Zion?

[01:08:13]Sir, uh, 4 * 6 makes 24. Yeah.

[01:08:19]>> Uh, >> oh, sorry, I wrote the wrong thing. You said four * 4. I wrote the wrong thing.

[01:08:23]>> Uh, then we'll get 16. We'll put six and carry over one.

[01:08:30]>> And we need to remember the six at the beginning as well, which I think you did when you calculated because you gave me the correct answer.

[01:08:37]>> Yes, sir.

[01:08:38]So 6 plus the 16 like you said this gives me 22 and now I finish so I can write down the whole answer which is 2209.

[01:08:48]Thank you very much Zion.

[01:08:50]>> This does give us the correct answer with cross multiplication.

[01:08:54]Notice here that the 4 * the 7 and the 7 * the 4, they're the same because it's the same number multiplied by itself. So what I can actually do here is I can get 4 * 7 and just double it. So double of 28 is 56. 4 + 56 is 60 which is a shortcut.

[01:09:17]So this is the way that always works for multiplications including for squares.

[01:09:22]And now I show you a trick that's going to happen for um a trick that will work also for the um for square numbers specifically.

[01:09:36]So what I can do, this is method two, but the same one.

[01:09:43]Step one, let's call it step A. Step a round to a nice multiple of 10.

[01:09:56]For example, I round it to 50.

[01:10:00]I could also round it down whatever I like.

[01:10:13]I now adjust the number the opposite way the same amount. So what does this mean?

[01:10:21]47 up to 50 is + 3. So I need now 47 minus 3 which gives me 44.

[01:10:32]That's for step B actually.

[01:10:36]Step B is to adjust the numbers like this.

[01:10:40]Step C is then going to be.

[01:10:54]So we have two numbers close to 47.

[01:10:59]Need to multiply them. So this would be 44 * 50. And 44 * 50 is very easy because one of the numbers ends in zero.

[01:11:11]So we can just do like 44 * 5 which is 220 and not forgetting the zero.

[01:11:20]Step D, we add the square of the adjustments. So 2,200 + 3^ 2 gives us 2,29.

[01:11:36]So when I'm multiplying square numbers, this is a method that I prefer. For me, it's faster.

[01:11:46]So I I don't want to go into too much detail so we have time for everything we want to cover in this workshop. But this is something you can maybe look at later and will help you with the square numbers especially for something like 47. It's much faster to do it this way.

[01:12:04]There's also a couple different ways that we can solve the same question. So I could also do 47 and round this down to 40 if I want to.

[01:12:17]If I'm doing that, then this here would be um subtracting 7. So I would want to do 47 + 7 because the opposite of subtracting 7 is adding 7 and that would give me 54.

[01:12:33]Then when I multiply then I'm doing 40 * 54 which is equal to 2,160.

[01:12:42]I need to add on my 7 squared and this is 2,160 + 49 which is equal to 2209.

[01:12:52]So I can do the method in um I can always do the method in two different ways. Sometimes there's even other ways of doing it.

[01:13:01]So, this is like a bonus special trick that you might want to look at later. We haven't got time to do lots of examples with this today. Um, maybe we maybe we have time for one example. Actually, we have time for one example using method two.

[01:13:21]So using method two specifically what is 63 squared?

[01:13:34]So answers in the private chat using method two. What is 63 squared?

[01:13:55]again. I can take a I can take a volunteer for this one.

[01:14:00]>> Look.

[01:14:21]Okay.

[01:14:27]So, uh, by the way, with the messages, there's more than 300 people in the workshop. So, I don't see many of the messages. Especially if you send me the same messages lots of times, then I I don't see. So I I only see a small sample of the questions. So if I um if it feels like I'm ignoring you when you have the correct answer, I'm sorry about that. I I just cannot see with the um >> Yes. So I I would request everyone, you know, just just type your answer once.

[01:14:59]Please do not keep entering the same answer again and again because you're blocking the entire chat and we are not, you know, we not able to cover everyone.

[01:15:07]In that case, I would request everybody to please follow what Daniel is telling you.

[01:15:14]>> So good. I see some correct answers coming in. Also say volunteer after you give me the correct answer as we have with can we ask HR I um please you have the correct answer and you're volunteering.

[01:15:36]And thank you to everyone who is volunteering. Uh even if somehow I didn't see that you volunteer. So could I what do you suggest for this?

[01:15:47]>> So um sir first we have to um round off 63 to nearest 10.

[01:15:56]So the nearest round when we round off 63 by 10 the answer is 60.

[01:16:04]And the difference between 60 and 63 is three. So we have to add three with into 63.

[01:16:15]So the answer is 66. So now we have to multiply 66 multiply by 60.

[01:16:26]>> Very good. Yeah.

[01:16:28]So first we can remove the zero and multiply 66 * 6 which is 3 96. Then we can add the zero and then the remaining three we can square three square. So the answer is 9.

[01:16:53]So then we add 9 into 3 960. Answer is 3969.

[01:16:59]>> Very good. Really good explanation.

[01:17:01]That's exactly exactly the right thing.

[01:17:04]Um, very good. Thank you for that.

[01:17:08]So, this is the easiest way I would say of calculating 63 squared. I would I would use method two if I actually I would use method three which is a little cheat. But if I couldn't use method three, I would use method two exactly as Fredai has just explained for us.

[01:17:27]So if you're practicing with square numbers, I would recommend practicing using this method so you get used to it.

[01:17:34]So what's method three? What's method three? So method three is just memorize them all. So this is what I've done. I have learned by memory all of the square numbers up to 99 squares.

[01:17:52]So for this reason when someone was explaining earlier about the sizes of the numbers I knew 99 * 99 because I've um I've memorized this before and when you do other competitions that have square roots of big numbers and other calculations the squares it's very useful to know the squares. When you get to the grandmaster level of the mental math world cup, then you will have to do square roots of small numbers. And they might look like they're very scary, but if you if you know the square numbers, they're actually, I would say, the easiest questions really.

[01:18:29]And so, uh, there's lots of techniques that we can use for memorizing the square numbers. I don't want to go into a lot of detail about those today, but I will cover that tomorrow in the um uh yeah I I I think I cover that more detail tomorrow in the grandmaster workshop when we look at square roots.

[01:18:51]Uh given it's a multiple I do want to say one thing about this though which is helpful uh given it's multiple choice.

[01:19:06]The last two digits of square numbers there's only certain possibilities.

[01:19:11][snorts] So some numbers can end in 0 0 and some numbers can end in 25. I'll give an example.

[01:19:29]30. Let's do um 60^ squar = 360 0 0.

[01:19:35]I've got some random other character here. Hang on.

[01:19:39]Equals 360 0. Example here would be 65^ 2 is equal to 4225. So it ends [snorts] in 0 0 or 25.

[01:19:51]The other possibility is it could end in 1 six 36 56 76 and 96.

[01:20:04]So examples would be something like 2116 3,136 256 676 and 1,296.

[01:20:21]So those are some examples for um for those.

[01:20:26]The other possibilities would be and notice that in 1636 up to 96 the 10's digit is odd. So I can't have 26. I can't have 66. It's only um odd number one six. Odd number 36. What happens if the 10's digit is an even number like zero? Well then I can have 01. I can have 04 and I can have 09.

[01:20:57]I could also have 89, 69, 49, and 29.

[01:21:03]24, 44, 64, and 84. And maybe you can guess what's going to happen. 81, 61, 41, and 21. And I'm not going to give 15 examples of these. Maybe I'll just give one example of an example would be um let's do 6889 the 83 squared.

[01:21:30]Uh so this is really nice when you have multiple choice because if a question says you have some square number and the answer equals either let's say it's 1 2 3 4 2 3 4 5 3 4 5 6 or 4 uh 567. Which is the only possibility? Well, it can't.

[01:21:53]The only one that makes sense would be 56.

[01:21:57]This is the only one that could be a square number because no square numbers end in 34. No square numbers end in 45 and no square numbers end in 67. So it would have to be 56.

[01:22:11]Actually none of these is a square number. Um but three um yeah so this would have to be a different number.

[01:22:22]So you can use this in the multiple choice for finding the the specific square numbers for finding which ones could be square numbers and if there's multiple possibilities then you can either have them by memory in which case super easy to select the correct answer or in case there's multiple possibilities then you can use the method two. If you don't know the square numbers this is, then you can use method two, which is the fastest way. Or if you find this is complicated and you didn't learn method two yet, you can use method one, which is working for all two-digit multiplications.

[01:23:00]So, okay, it might seem that we spent a lot of time today working uh multiplications, but that's because this also covers the the square numbers which are very important and it's the the most impactful topic that we can cover today.

[01:23:15]What else are we going to do to finish?

[01:23:17]I just want to make sure everyone is clear on the definitions of a couple of words that you see in the mental math world cup.

[01:23:29]And then I'm going to I promised you that at the end of the workshop or actually I didn't tell you when but I promised you at some point I would give you a couple of gifts [snorts] and so I will give those at the end of the workshop which is finishing in about 10 minutes. [snorts] So this slide is about several different categories and [snorts] I'm going to call it important words in the mental calculation world cup. So one of them is mean.

[01:24:04]So in advanced mathematics there's lots of ways of calculating the average.

[01:24:09]There's lots of things you can mean by the average. And in the mental math world cup you need to calculate the mean.

[01:24:15]Can I have a volunteer to explain what is meant by the mean? When it says calculate the mean, how do you do this?

[01:24:23]Type um type volunteer mean if you want to volunteer to explain what the mean is.

[01:24:37]So volunteer mean have to be volunteer mean. Okay. Can we have um Marian Marian Mail?

[01:24:57]Thank you for volunteering.

[01:25:02]>> Yes, Marian.

[01:25:05]>> Yes.

[01:25:08]>> Yeah. Marian what what is the meme?

[01:25:12]>> Uh actually mean I think it's like getting the answer like in the in the sheet in the practice sheets we can like get he gets me some numbers and I have to add them and then divide them on uh by three like 45 50 uh 15.

[01:25:34]Okay. Yeah.

[01:25:38]So what do I have to divide by?

[01:25:41]>> By three.

[01:25:43]>> Why by three? You are you are correct.

[01:25:44]Of course >> I actually do it like uh I carry up them and I made like five + 0 + 0 if not if it's not possible to divide the numbers by three. Uh I I do a um a circle m a circle method like I I add them and I do like three circles and I keep uh putting on points in them to calculate it and if there is remainder I like minus it or add it uh according to my to my answer.

[01:26:22]>> Okay, very nice. Thank you for sharing and you're exactly correct. When it says find the mean of some numbers, it means you add them together and divide by how many numbers there are. So in this case 45, 10 and 20, there are three numbers.

[01:26:35]I add them together, the sum is 20 uh 75. I divide 75 divided by 3 and I get 25. So the mean of these numbers is 25.

[01:26:52]And to check whether it's correct, the mean should feel like the middle of the numbers. So here we've got 10, 20, and 45. 20 is in the middle. 45 is a lot bigger than the other numbers. So it feels correct that in the middle of all of these numbers, we have something that's like 20 or 30 or something like this. So when we calculate that the answer is 25, this seems correct. If we do the calculation and we get for example uh 15 that's not correct and it should feel incorrect because 15 is very small within 10 20 and 45 it feels like it should be something bigger. So that there is the mean different words for the most common way of doing the average for profit and loss question. Um what what types of calculation are these?

[01:27:48]Answer in the um if you want to volunteer type volunteer profits.

[01:27:53]Volunteer profits.

[01:28:20]Okay. So, make sure to write volunteer profits so that we um so that I know that you're volunteering for this question.

[01:28:30]What does EG mean? EG means example.

[01:28:33]Okay. Can we have iPhone? I mean that's not your name but someone who is here as iPhone.

[01:28:42]>> Okay. We have three iPhones here.

[01:28:44][laughter] >> Okay. Um I'll pick somebody else with a unique name. It's a purple iPhone if that makes sense.

[01:28:53]Purple iPhone.

[01:28:54]>> Purple iPhone.

[01:28:55]>> Yeah. On my screen it's purple. Maybe it's not the same on your screen. I don't know how how it's working.

[01:29:00]Meanwhile, I'll see if um if that makes sense. We can have this iPhone. If not then we can have um man we also have a volunteer from man.

[01:29:10]>> Yeah.

[01:29:11]>> Okay. Goddess man.

[01:29:17]>> Yeah. Uh so oh so find uh to so to find the profit of like uh for uh to find the profit we need to check we need to like we need to see if the selling price is higher or low we can like we can choose if it's a profit or loss from an object if the uh if the selling price is higher or lower than the cost price. So uh in the example you have given me the cost price is 100 and the selling price is 80. So we are having uh uh so uh we are having loss. So the loss will be of 20.

[01:30:02]>> Very good. Yeah. So in this question here if the cost price is 100 and the selling price is 80. It's like imagine you have a shop and you buy something for 100 and you want to sell it for more than 100 so that you make a profit.

[01:30:17]In this case the selling price is less.

[01:30:19]So you didn't make a profit. You lose money. How much did you lose? We need to do subtraction. 10 minus 80 is 20. So in this case the the answer would be a loss of 20. And the question would say what is the loss? [snorts] So everything with profit and loss, selling price and cost price, it's just an addition or subtraction, usually a subtraction. So read the question carefully, practice with the resources given to you and then the profit and loss, it's just a a way of asking you to do addition and multiplication, but with lots of words.

[01:30:58]So these are some of the u main things we need to know very quickly.

[01:31:05]Having or half means divide by two double.

[01:31:17]This means we need to multiply by two and triple.

[01:31:33]This means multiply by three. So you need to know what these words mean and then it's just simple multiplication.

[01:31:44]I want to go back now to a comment with the squares. So we had method three which was to memorize the square numbers. This is um not it's a medium amount of work. You have to have some dedication if you want to do method three sometime to memorize them. But one thing that everyone can do is memorize some of the simple values that often appear for doubles, halves, and triples.

[01:32:10]You also need to memorize the multiplication tables like 4 * 6, 7 * 6, 8 * 3. So, uh, we now come to the end of the workshop where I give a couple of gifts that you can use. [snorts] And these are some um special tools that I made on my website that allow you to practice some of the things that we worked on today.

[01:32:39]So, can I ask the host first of all?

[01:32:41]Actually, no. I'm going to save the screenshots. Just remember that after the workshop we need to take a screenshot because I can't do it. Uh screenshot so that we can send the whiteboard to the volunteers. Is that the best way of doing it?

[01:32:53]>> Sure.

[01:32:54]>> Take screenshots at the end afterwards.

[01:32:57]>> Yeah, that that'll be best. Right, Ra?

[01:33:00]>> Okay.

[01:33:04]>> Yeah.

[01:33:05]>> Yes.

[01:33:06]>> So, we can do it now but maybe better at the end so people are not waiting. So >> the information there you can we'll see that again later and I'm now going to share if I can find it the yeah.

[01:33:31]Oh one of them I forgot to prepare. I'll get that for you in a moment. Anyway, so the this here is a tool on my website. That didn't do what I expected. Sorry. Uh here we go. This is a tool on my website. I will I will show you how to find this.

[01:33:52]And this allows you to practice multiplications of twodigit time one digit and two-digit time two digits. So the way it works is this. You select the answer the select the question size you want from the menu. Let's do some um twodigit times two digits. I type in the answer and press enter.

[01:34:13]And then it tells me that it took me 1.7 seconds and I [snorts] got so far um I've answered one question and I got it correct.

[01:34:23]Easiest way is to press the enter key on my keyboard. I don't press go. It's easier. Just press enter on my keyboard and I have another question. So, it gives me this one. I think the answer is this. And it takes me 5 seconds.

[01:34:40]Again, I can continue practicing this.

[01:34:42]So, 330.

[01:34:52]Uh what you notice here is that if you make a small mistake then it goes orange instead. So here this is an answer that you would get if you would take um if you slip the three for the four in the thousands when doing one of the methods for solving these. So notice here that the average time is 3.4 seconds. This is the average of the correct answers. Also the mean. This is how the word the mean becomes important in everyday life. And notice that this is the mean of the correct answers. And this one I waited longer before typing. So this one was not included. So you can practice this um as much as you want to [snorts] um to get good at doing this. And then >> we will make sure that we we share this with everyone.

[01:35:47]>> Yeah, I will share it's in a moment when I when I finish showing I share the links in the chat and then feel free to also share this in a different way if you would like.

[01:35:56]>> All right, >> we also have an easier one. Oh, the other thing here is the um 2x one. So this is a way of practicing the twodigit times one digit. If you're using Yeah, this is fine actually.

[01:36:11]So in this way I'm practicing these and let's get one wrong.

[01:36:15]It's working the same way. So I can use practicing twodigit times one digit. I think it's more important to be very fast at these before you worry about the twodigit times two digits. So unless you're very fast already at two digit time two digit, I would try to be fast at two-digit time one digit and then try and do these slowly. So 2 1,600 plus So it's 1,880 1,892 and not worry so much about the time.

[01:36:48]But for two-digit times one digit, then you want these to be fast.

[01:36:53]We have the same thing here for the additions. Oh, this is when I was playing with this earlier. So, it's doing the same thing but with additions.

[01:37:03]So, you get the question, you type in the answer, and then if you get one wrong, then it's working like this. And I have the same thing here, four subtractions.

[01:37:17]So, I'll drop the links so you can play with each of these.

[01:37:22]And there's another thing I wanted to but I didn't have it open yet. So, apologies for that. Uh, here we go. So, I said it was important to memorize.

[01:37:37]It's useful to know the square numbers and it's important to memorize the other um some of the other facts. So, I've made a flashc cards tool which works a little different and this is specifically the things that you need for the mental math world cup. For the master level, you don't need to worry um yeah, this this will include some cubes that you don't need to know, but you can practice for example the times tables.

[01:38:05]So, let's do the let's do triples because we haven't talked much about it today. This works differently. I press triples and then [snorts] it gives me these answers and I it doesn't give me much information. It just tells me correct. So, I'm going to keep going typing in these doubles. And you notice here that these are very easy for me because I practiced them a lot.

[01:38:32]And for you, you won't be so fast at the beginning, but when you've practiced, then these will also be easy for you.

[01:38:45]You after 30 seconds of these questions, then the trainer will stop. If you take a long time on a question like this one, it will tell you at the end that you were slow on that question. And if you get one incorrect, it [snorts] will also tell you here I got nothing incorrect and I got this one slow as a demonstration.

[01:39:06]So if you are getting scores of more than 20 then you know these very well.

[01:39:12]You don't need to get a super high score but if you can get a score of more than 20 then you know everything very well.

[01:39:19]If I want to practice something else now, then let's say everything mixed together, I just press this on the menu and then it gives me all of these questions and I just continue again until it stops. So these are some tools that you can play with.

[01:39:37]These are available on my website. This is the world mental calculation website.

[01:39:43]So, in the public chat now, I will drop you a link to all of these and feel free to play with them. So, this is the flash cards that I just showed you. This here is the multiplication trainer.

[01:40:01]This here is the addition trainer and this is the subtraction trainer.

[01:40:09]So, feel free to visit those. Now this is now the I think the yeah the end of the workshop everything that I'm going to share today. So no more information from me. Um just if there's any questions I mean there's so many uh people here I can't respond to to all of the questions here but for um Avanache is there anything else you think I should answer at the end of this?

[01:40:36]Daniel, I think you've covered all the important topics and uh yeah so so thank you for your time Daniel and kids today's session was more focused on ensuring that you the multiplications two 2x one 2x two are covered thoroughly because a lot of the other topics are dependent on on multiplications as such. uh when it comes to the other topics uh you know uh whether whether it's half doubles profit or loss all these topics have also been covered in the past if you want we can share we also have the recording of Daniel's previous sessions we can share that with the group again the recording of today's session will also be available tomorrow uh we'll be sharing the link with with all of you so you can you know at your own pace you can go through the entire session do remember what Daniel has done today has shown you methods of thinking about numbers in a different way. In our schools, we are taught mathematics in a >> I think you're muted at the moment.

[01:41:51]We're not getting the audio for the last 10 seconds.

[01:41:58]>> Yes, Daniel. Uh thank you for your time today. I I'll just kind of um wrap up here again with the the introduction. The the topics we had a look at today were the multiplication, addition and subtraction. And so we uh multiplication is used for a lot of these categories and um like for the for the mean and the average for the h havinging and doubling and tripling. Trippling and doubling you can do directly with multiplication and the addition and subtraction. We had the idea of working from the left of the number. These are basic skills that you will pra you can practice with the tools that I've given you using the method that you're already familiar with. And for two digit times for two digits plus or minus two digits, then these are quite simple. And the the profit and the loss again this is the same techniques but with special words for it. And the squares is like the multiplication but with some additional shortcuts that you can use because there are few enough questions that you can memorize the answers or you can use method two which is a a great shortcut for this. [snorts] Just to summarize the the topics that are part of this session.

[01:43:42]All right, Daniel. So if you're done with this, I think Ain has gone offline.

[01:43:47]So if you're done with it, uh then we can have everyone uh exit the call.

[01:43:52]Thank you everyone. Thank you for joining us today. I hope you had a good session. If you have any doubts regarding anything, please uh reach out to us on the following. I'm just sharing.

[01:44:13]Yeah. If you have any doubts regarding the competition, you can get in touch with us on contact at the ratelivemcl.com or you can WhatsApp us on plus918291027238.

[01:44:24]A recording of this uh entire webinar will be uh the link will be shared on the WhatsApp community and it will be also there on our YouTube page. So if you want to refer it at a later stage, you can. With that said, I would like to thank Daniel for the lovely webinar today.

[01:44:44]And uh yeah that's it. I hope uh everyone had a good time. So now everyone you all can just log out of the meeting.

[01:44:54]>> Okay. And thank you everybody for joining. And thank you for