now last time we started with digit sum so clear yes sir any doubt in this digit sum digital root be junk or namashes now we started with the application where we will apply this and the we saw that it was used to verify addition multiplication subtraction So any doubts in these three yes anyone has any question regarding these three yes kalyani I need to check the YouTube sir this one about this but uh till here the multiplication yesterday what you had before the class what you had explained about this tables that everything I have completed the homework too but this ban about this I need to check once again in the YouTube class Yeah but try to always check before the next class because what happens you the more you'll be asking me queries more doubts should be cleared right no no actually little busy about the stage level competition for that uh by 29th I will be free completely okay right so now we'll be doing further yes gurit Sir and sir quite out nice sir all clear table is clear this uh regarding digit sum how to check the answers now yes Harish what happened late what's up man just Harish in the morning also you are late uh evening class I just 8 8:45 I come to home sir just I I am also a human being yeah but I I always try to be that because when we have given time to someone I also take care yeah getting delay in office that's right as you wish okay so now fourth we'll start with division now division is of two types generally we are calculating we are finding division in two ways one is where we are finding the answer in question plus remainder format and second is where we are looking for final answers so two types of division we are generally doing I'll tell you both when you're going for question and answer format in actual this is already explained in class 3 book what is there dividend divisor is equal to divisor into quotient plus remainder this is already explained this is one one way which has been given there and it is correct i I don't say it is wrong but the point is there we are taking total number i'll give you an example let's say I have a number Just giving an example 98 796 and if I say okay I'll write down this question here 98796 if it this is to be divided by 36 can you tell me what is the quotient and what is remainder Huh yes what is the question and what is remainder is it hello Hanji good evening sir good evening just started with so 98796 divide by 36 yes what is the question what is the device uh reminder Too much of time 2744 okay and what is the remainder 12 sir correct so that means if 36 is your divisor then 2744 was your remainder and 12 sorry quotient was 2744 and remainder so what we were doing is to check we were doing this way again a long calculation but here in Vic maths what we are checking we are just checking with the digit sum what is the digit sum of this 15 and 6 21 means three yes or no three is the digit sum and here it is nine So whatever is this it will remain nine but you can check eight so that means this part is 9 + 3 so that is again three so see what is simpler to calculate if you have done this long division a student has done that complete tree he has found that 2744 is a divisor and 12 is a remainder again start multiplying is it easy if a number is bigger it's never easy but with digit sum it becomes that very simple we're just finding the results and we get the answer yes is it clear a very small example if I take let's say 279 divided by 3 now quotient comes is 90 and remainder is zero again if you see the digit sum okay first I'll place so here digit sum is nine here 3 into 3 is 9 finish got it yes anyone ask any question any doubts regarding this no sir but this is one way this is one kind of division you are doing when you are finding the answer in question and reminder format but there are other types what you call as when when I say you are looking for the final answer then you have either terminating decimals or you have recurring or or non-terminating So here it was applicable in case of question and answer format digit sum is 100% applicable but in the case of final answers when we are talking about terminating and non-terminating digit sum is applicable here but it is not applicable here i'll tell you why let's consider uh first talk about terminating let's say 1 by 2 so what is 1x 2.5 now this is terminating correct but if I talk about 1 by3 this becomes 33 33 33 33 this is non-terminating right now let's uh apply in some formula some question let's say uh the question is very simple I'll take first 23x2 2 and 23 by 2 the answer is 11.5 correct how to check this yes though we all know this by heart but we just taking as a sample as a for a big numbers how to check so first you need to understand what is 23 you cannot work with digit sum in the base in the uh denominator so you have to write like this so you'll say this will be a big trouble it will not be we will understand how it can be done right so 23 into.5 now what is the digit sum 2 + 3 is 5 here also dot can be ignored so 5 into 5 is 25 which is nothing but 7 now this is your question part and when you'll talk about answer part again ignore the dot 2 + 5 is 7 right so this is when you're talking about decimals but for this you have to remember certain things for example 1 by 2 is 0.5 this you should be aware 1x4 it is nothing but 25 this you should be aware 1 by 5 it is.2 2 you should know 1 by 8 it is.125 this you should know so first this should be clear half of this is this half of this is this and this is very easy right so this is how if you know these four five values then you can do anything then division is you can verify division very easily easily correct but now this is a case of terminating so same example let's say 6 3 4 27 divided by 4 okay find out the answer let first you give the answer then I'll tell you you take take your method later we will also learn how to divide by four in a single line that will come but right Now divide by four you you can use your old method right now the question is 18,856 okay quotient question is 18,856 okay and what about remainder please three six three okay now I I sir 15,856,856 15,856 sorry oh no issues and we we don't want an if I want an uh decimal this we can do it we have already checked that we can do this if I want the final answer H because it is if it is to be divided by a even number then it is always terminating so what would be the answer so it would be you will learn I'll teach you how to do this we'll learn in halfing so it is 15856.75 correct so we'll do this so don't worry about it you don't know now when we'll be going for halfing you will be able to do within seconds so same thing if you see here you could have easily checked using remainder and this but sometimes the answer is calculated in decimals so that time also we should be aware so 6 3 4 27 I can write it as.25 so if this is there let me check 6 and three gone 7 and two gone so it is 4 into 2 2 and 5 means 7 28 means 1 correct let's check this eight gone 5 and 1 2 3 15 and 13 so again 28 that means again one see now is it clear see actually it is difficult to find decimals like this but for all these even numbers 2 4 8 16 32 you can do it in a single line you will learn in uh coming top uh days you'll be able to learn this done up till here yes okay now this was terminating so that means it had a answer it had some terminating or fixed answer but there are cases when we don't have the answer for example I told you 1 by3 now if the answer is 3333 how can you find the digit sum so one one person can write the answer as 33 so digit sum becomes six if you write it as 333 digit sum becomes 9 and if you write four times digit sum becomes three yes so that's why digit sum cannot be applied for non non-terminating or recurring answers 1x 7 so 1x 7 is.142857 1 142857 so it cannot be done because you are not sure how many times you will be considering 1 by 9 it is.1 one one or 2x 9 or 5 by 9 7 by 9 8 by 9 it is.88 right so such numbers you should know what comes when you divide by 1 by3 see I'll give you 1 by 2 you are clear 1x 3.33 1x 425 1x 52 1x 6 Yes what is that what is 1x 6 it is.16 6 6 66 6 something 1 by 7 I give you.174285 and continuously 1 by 8 it is.125 and 1 by 9 is.1111 right so this is how you can use this knowledge right but you should know these things 1x 2 1x4 1x 8 will come across in halfing and doubling three 1x 3 1x 6 1x 9 will come across when we'll be doing uh square roots at that time you generally use this but overall you should know yes Harish any question no sir second thing so one is you cannot use digit sum in non uh non-terminating or recurring on another sometimes you you take approximations for example I'll give you it is written 3.9 into 3 and the answer is given something 11.7 and so if you're using like the same if you're taking the values as same so this is nothing but three this is nothing but three so 9 and 9 it's okay but there are instances when you say okay take 3.9 as 4 uh take approximate value right for example in case of pi it is given now pi value is 22x 7 that is 3.142857 but sometime it is written take only 3.14 So that time we cannot get the correct answer right because if you take 3.9 y so if you take 3.9 This one so now if you take here four then answer will go all wrong because 4 into 3 will be 12 not 11.7 right so approximations when when you are considering approximation that time digit sum may not work right it depends how you are taking the values any doubt now regarding division yes Aruna harish pushpa you came late So any question you have no sir see you have to ask questions pushba and particularly pushpa harish aruna and why I'm saying because I'll not issue certificate the way same way so like I am teaching you I'll be asking you the questions also later so whatever doubt even a minute doubt is coming please ask everybody's we we all are teachers right so don't worry what other person will think whatever is coming in your mind you can ask right so now so first four arithmetic operations are over these are what when when you start teaching so if you are giving uh classes to class third fourth fifth then these four operations are sufficient totally sufficient but one more important what we have to teach them because in sixth standard there are all olumpied exams all NTSC C National Talent Search Examination as well as Senic Vidyales exam and most of the parents they are applying for Sanic Vidyala's NTSC Olympiads now here that means we come across MCQs how do we solve MCQs we solve in the normal way and if a student is solving in a normal way they are taking much more time i'll give you one example that will clarify all your doubts 352 into 867 now this is a question it is a multiplication question so class third fourth fifth can attempt it but since four options are given though four options are given still what do we teach because when you are in classrooms in classrooms we are never teaching we are never working on MCQs we never teach them the way to solve these MCQs and we just tell them okay go by the normal routine method gupit how much time will take if you solve this three-digit into three digit five minutes sir and I think the first it's the first answer 305 why how much time uh it took me around 5 minutes only when you gave me the question only I wrote it so five five if you took 5 minutes first thing is it's too much but students generally take two to three minutes correct do you know when such questions are coming we are given only one minute second thing if you were asked to solve this why four options were given see if you were supposed to solve why four options are given did you understand my question yes anyone harish if you are have to solve or if you're supposed to solve why four options are given yes anyone aruna Arish Pushba using this summer so that will be faster no I'm I'm not talking about right now Vic maths it's it's like class 6 class 5th they get MCQs in every competitive exam every olympiad every NTSC there are MCQs if their aim is if they are expecting you to solve it why they are giving you four options to check spir how much perfect you are so that no try to understand this way that means they are not expecting you to solve they are expecting you to do in a smarter way and what is the smart way now here I'll tell you what is digit sum of 352 one what is digit sum of 867 three so that means digit sum of the answer should also be three because of the question part is three now check first three finish you can check with others also 8 1 so this digit sum is five this sum four six so please understand it is not that vic maths is not being used it is being used for since so many years all the competitive are using all the comp all the competitions they are being done but yes we were not promoting in this way so we were never taught in the school the and today you check with all the MCQs you have check all the MCQs regarding arithmetic can be solved with digit sum if it is a calculation if it is regarding arithmetic operations it can be solved so why do see you we need to address to this point we were not supposed to solve it rather we were supposed to do it in a smarter way i met few teachers they said check with the last digits two and seven it should be four i said okay sir now everywhere it is four now what to do this is I'm talking about Delhi i was in book fair Delhi book fair world book fair that time teachers told me this okay sir check with the last i said all the four are with four now now you have to solve so that means and just think these small small things if you are teaching to the students in the classroom itself they are getting to they're going to score something better i don't say key just by one method they'll crack the exam but at least better Gur did you understand what I did Harish yes this is how it has to be done it is not supposed to be checked right so if you are teaching class third fourth fifth then these five are sufficient means uh addition subtraction multiplication division and MCQs this is to be taught now if it is a senior student then we'll come across scaring cubing so scares I'll not go in depth what is a scare how to I'll just give you one or two questions let's see how do you do what answers you're getting and then okay let's what is 65 Five scale answer okay so so many of you have done this concept 425 correct this answer is perfectly correct but let's check it so what is 6 + 5 11 11 means two now two square we know it is four four correct here also if you check gone four so see easily you can check the scares but we are not aware one more easy first 999 scare so all those who know the trick they can give get this answer in one second and others you solve it but we'll learn this don't worry we will learn this very shortly we'll learn 99900 998 99800 Very good so now if this is to be checked Finish this is nothing but 9 9 square is 81 again 9 and here also if you check it is 9 let me take some other number because this is simple concept what is scare of 82 67 672 67 2 4 2 4 Okay yes harish you got the answer grie sir yes multiply yes 82 into 82 but we'll change the method so again 1 square because 8 + 2 is 10 10 means 1 so that is one here again check 10 means one see correct 52 square so it is 25 + 227 2704 I think 2700 sorry 274 yes 2704 04 So again if you see 7 7 square is 49 49 means four and this is also four four so it was so easy but non awareness see awareness should be there clear now any doubt left I'm not taught here how to do scaring we will learn that up till now whatever is your method whatever is your technique you go ahead with that we will do understand it in later now comes scare roots i'm not sure by which method you will be doing 1156 yes what is the answer the root of 56 34 okay okay yes git aruna 34 34 so how to check with this see in case of square root you just have to see this numbers not the under root sign so this is 7 + 6 is 13 means 4 correct and if you have calculated 34 that means you'll be checking square of that right because you cannot work on under root sign so this will be seven square means 49 means four right means try to understand because we we if we cannot work on so we are writing like this 1156 is equal to 34 square that's what I did reversed done yes done up till here yes no excitement no voice little bit confused what confused i have not taught see I whatever method you know I just want the answer right now i will teach you yeah about the squares only i had a little bit confused sorry square square root so no problem I we will learn just now I'm first making you we are working on only one point right now okay of digit sum but this is very easy if you want I can explain right now also for that okay give me the answers theni one square one two square four three square n four square 16 no five square 25 six square 36 seven square 49 eight square 64 9 square 81 10 square now this just see this is a table of first 10 squares correct but where will we use this we'll use this for bigger squares first thing suppose we are asked to find 88 square 89 square that time we'll use this table second thing we will use it for square roots third we'll use this for divisibility the same table now how just observe the answers see here it is ending with one here also it is ending with one here it is ending with six here also it is ending with six that means okay let's start from one if a number is one means any number you talk about let's say a 1 a can be zero a can be one a can be two a can be three if I find the square of this the last number will always be Yes or no yes sir are you understanding similarly if a 9 is there then also it is always one one now think reverse when will last digit come one it will come one when it is ending with one or nine or nine correct when it when it Okay now second C four so when will it come four when it is with two on eight two or eight correct similarly nine so when it will be nine three or seven three three or seven seven then six when it will be there either with four or six correct now when it will be five when it will be five only five only now this is to be understood so when questions are coming on square roots now let's talk about the question 1156 first thing is whenever square roots are there divide into two parts two and from your right side first should be two digit rest it depends on how many numbers are there for example if it if the question was only 156 if it was only 156 or let's say 756 so this was one and this was one combination right first Okay so here it is 11 and 56 now step one observe right hand side so it is ending with six when will the unit place be six tell me four or six either the number is four or six now before this it is two set of numbers that means the answer is two digit finish so either four or either six this is explained don't worry it is explained in uh book six step six very deeply it is explained so don't worry about it just understand over here because notes are the book in book every point is written nothing to worry about that but here you should understand first second step observe this 11 now where do we get 11 somewhere here between 9 and six that means 3 square and four square between three square and four square so we will always take lower side so that means my answer is 34 either 34 or 36 36 step three there are there are several ways to check this which is correct 34 or 36 one way is you can check using digit sum only your you will get the answer one is we check that three it comes between 3 and four square so I'll multiply three and four that is 12 my number is smaller 11 is smaller so I'll choose smaller side 34 if you get confused in choosing then you should have checked another way 115 6 is equal to 34 square let's say think this way so yes this is three sorry this is 11 and 23 means four if it is 7 square it is four if it is if we opted for 36 then it would have been nine so it is not possible this is the correct so this you'll learn in depth right so can you please explain that inversely also square root digit uh square root is not uh tell me tell square root of 1156 is equal to 34 we have done it in a squaring way you know but this square root we have taken opposite side that's it right side we have taken so I I'm actually requesting you to tell us about this square root method digit sum is applicable in this square root also or we have to do in this way only the second step what is the difference hey you tell me if I do if I do 1 + 1 5 + 6 Okay uh what it will come 11 12 13 then square root of 4 it is two agreed so at some position it may it if it is coming seven then what you'll do that is what I am asking so how so it is it is very simple thing now it is understood see square root of four is two correct this much is clear so what do you mean by four is nothing but two square it is the way to represent so same I have represented this makes you easy at some points at some point at here you you were getting think this has 11 + 2 13 so then 13 means four four means two agreed but then this is seven then now tell me there now it is wrong then that is no so that is a reason we have to we have to take the reverse it is a way to a check right understood okay solve one more this is very simple but I'm getting water yes tell me 125 now this was very much clear if you know the rule of five scales of numbers ending with five so 12 into 13 was 150 right so same thing 1 5 6 2 5 so 10 means 1 so 125 square 8 square 8 square is 64 64 means 1 clear any doubt yes kalyani Harish no means tell me how much where is the problem tell me let's solve it you said between three digits you have put the line now sir 15 16 i say you want to solve this so you don't remember 125 square is 15625 you want to get the answer of 15625 i got it i got it sir yes what is your doubt problem yeah get confused in all the things correct so then we'll deate from the topic topic that is how to check what is what do you know see at least we we are expected that we all have done 10th class so we can take time but we we know what is square root or what is care if somebody says I don't know what is scare like Harish is saying so I cannot help him you you need to understand that and okay if you want this now see this is one this is two but 1 5 6 I am I can do three also together why now here it is very simple five means only five possible where do we get 156 so 12 square is 144 13 square is 169 so that means it lies somewhere here so directly put answer 125 finish otherwise we we also have one property when number is ending with five then this number is multiplied with the next yeah school that is a long procedure that is called division method correct but everything comes with time but yes don't worry about that okay uh cubes 12 cube what do you mean by cube very first thing well written three times correct so multiply then we'll show you how vic maths will be easy so if I'll show you now what is basic math then entire journey 12 into 12 is 144 into 12 is 1728 normal way I want the answer from your side so don't math we'll learn don't worry it is very easy we'll go step by step first we'll learn addition then subtraction then multiplication So that step is defined 1728 sir 1728 yes I so again check what is 12q 3 cq means 27 so 27 means 9 and here also it is nine nine got Okay simple 21 cube but then 21 will come same answer 31 cube 29791 uh Kabu uh can you repeat Harish 29 29791 sir no 721 sir 7 91 sir 29791 2979 Yes 29,791 correct this only no different answer yes 29 29791 is what I got sir good this is correct answer but very we have a different way not the way you are solving i'll give you that different way now here again 4 cube now what is 4 cube it is nothing but 64 4 into 4 into 4 is 64 that means 1 and if I check this all gone one i completed that got it yes I got it sorry sure some of you have done basic Vic maths some are very fresh to vic maths so that is also one point you need to understand so I had a confuse for the abacus and for this also sir so that I completely separated the abacus from this i'm trying in your way only sir in your way okay no no i I I'll ask you up till what what operations you do which arithmetic operations tell squares squares squares five arithmetic operations and And how much time you take so visualations it will take more time to me how much time um sometimes uh 4 minutes 3 minutes or 2 minutes how many years to learn for a student it will be 12 to 13 12 to 13 months no no sir for Okay it will take four years for child four years now now just just understand Kalyani if a child is in class third or first now if you if they join you and now they are in seventh yeah yes do you do you think that is a reason of dropouts why because they start feeling that we are not getting anything new yes we are just cramming i totally understand that it is it it it benefits but to the younger one when the child is in KG but when since it cannot be inculcated in the school slabs can you inculcate no and now talk about senior student so why Vic master I am training all the backers trainers UC mass I have trained more than 100 trainers of UC mass what is that why because you are not getting students after class third yes and once you have taught them four years if you take them for 3 months only you are getting to get more now yes I can surely tell you because my son completed it will take no he started in second class now he just now completed the abusers the whole program but what is the use now because in the school they have started algebra yeah yes but it's not a a use for the high higher classes I nothing see in in in Vic maths first thing all eight operations we'll be doing in 3 months only and not with do with the students also with class 3 4 5 6 also you can do 3 months is sufficient for total program as per their level of school education see what is the main aim of a parent that my child should be good in extracurricular but at the same time they should score good in uh school also huh if they're doing if they're topping in uh abacus and they are failing in school will they continue yeah no that is the biggest thing so all the eight arithmetic operations first thing second thing it is tool based now can you take the tool everywhere no no correct yes you become master after 3 years what about that struggle between the three years that time you have to carry the tool then only you can do visualization does not come immediately but with Vic maths it is just understanding and second thing again you are giving one way it is same like mathematics one way to do one approach that is enforcement basically you are cramming the things you are keep on doing the same practice 100 times 200 times thousand times we cannot But yes it is very structured i I am totally you know satisfied the with the business proposal who initially gave the people who initially started a backers they earned like crores and crows because they structured the program in this way i also have 11 set 11 levels of books my company is running but not me because I totally understand that this is not because what is what should be what is the major aim extracurricular is one thing but if you're failing in school not doing good in school then the overall depression starts and the child lags behind so you have to understand that also right and vic math can be inculcated in the school's slivers Abacus cannot yes and now after NEP national education policy it has to be implemented it is yes slow procedure is going on certain schools have implemented today also one of our teacher from this no from tritometry back she called me up and that one school is approaching for Vic mas so can you share me the letter and details i shared already we are having so many school tie-ups in India Nepal so I'm having so many where it is thoroughly implemented any so any doubt you can always ask now last arithmetic operation is your cube roots now see you cannot do roots right in 8 standard you they have square roots cube roots and that that is not possible even cubes is not possible algebra is not possible trigonometry is not possible correct here everything is possible whatever is mathematics that is possible the only thing is uh till now see why why Vic mass is lagging behind or why it has not gained that the way a gain because it is time management seeas came uh around 30 years back 20 years back vic math has just started and second thing is all the vicacas trainer they they took proper training they took proper training that time but now in Vic maths what happens people learn two tricks from the net and they start writing Vic maths international trainers just give me one second right so that is what you need to address to so thorough knowledge of the subject is very important we are trying to cram vic maths but vic math is very vast very vast you see if you understand using concepts you'll never go wrong but if you'll try to cram then you cannot succeed because the parents also have so many queries they have already done a backus very first thing freshers are not coming who is coming parents who have already invested in a varas and now they want to continue their students to vic mass or they want to update righters are also there but they also everybody is aware now social media is very strong people ask so many queries and so many tricks are available online when you'll see entire course 3 months I'll not use a word trick because no there is no trick at all it is all concept you need to understand from the basics that is the reason I start from very basic things people often say why why you are teaching addition first but that is required if your addition is not clear how can you do other and you uh when we'll start with addition you'll understand it is taken from our Vedas what are Vedas vedas are our holy books now one sutra you know one sutra will deal it will reflect how you behave now what does that mean okay if your child kic if your son got 90% marks what will you say yeah try to more to get like that you can you know that the this sutra it relates with the human tendency to re to compare with the wholeness please understand the sutra it relates with the human tendency to compare with the wholeness means you are never satisfied even if he scored 95 you'll say five or you should have scored 100 you will not say you scored five more than 90 you'll say five more to reach 100 because we always look towards the wholeness wholeness means the completeness so when we learn addition now see how much knowledge is there in Vedas one sutra today I'll discuss all from nine last from 10 you know that is used for money transaction across the globe for every money transaction for every money every money means you talk about any country all money transactions can be done with that one line all from nine last from 10 Now see how much foresightness was there or let it be foresighteness or later let's say all the countries or everybody dwell the money in the same way whatever you can say see this is our way to think but this is the thorough knowledge we'll do that today we'll start with certain uh sutras today not sutras exactly I would Okay uh the terminology used in Vic mass then you'll understand okay and now it was cube root again cube root I I don't think anyone all the all of you would be able to solve all those who are not done through Vic math so that was really difficult and the problem with cube root is you cannot find on calculator also normal calculator will not give you the 77 how much 77 wrong multiply 77 into 77 into 77 on your calculator or find the cube of 77 what is cube of What is cube of 7 bhan it's 343 sir 343 correct so 47 sorry sir 47 again wrong so let's let's check it finally 30s don't worry yeah don't worry for this refer make the table of cubes yes then you'll get the answer within second 653 now three comes when the number ends with seven so here you get the answer what is 50 now you are looking at 7 square 49 correct that was your mistake but 3 cube is 27 4 cube is 64 so 37 was it was a verbal answer but if somebody has done vicas it's one second answer no issues don't worry at all those who have not done we'll cover up and you'll be better than others don't worry so don't think that much oh I'm not able to answer the last one you can explain it again yeah where you had done I mean 653 that which 653 ends with seven from there okay and now tell me cube of one cube of two eight cube of three 27 cube of four 64 cube of five 124 125 cube of six 216 216 cube of 7 34 343 Cube of eight cube of nine cube of 10 now here see the best thing is only one one digit see 1 8 7 4 5 6 3 2 1 no digit is matching like in scares it was two two options here it is one option only so when I said 5 0 6 what was that 53 correct now you have first three then this you were making double here triplet so it is ending with three where are you getting three tell me now seven cube so that means this is seven where do we get 50 here because 3 cube is 27 4 cube is 6 so 37 is the answer see this is how easily you can do in Vic maths otherwise this process it takes minimum 10 minutes in division method 10 minutes I'm talking about not before 10 minutes you can solve so again if I have to check 5653 is equal to 37 cube so 37 means 1 cube is equal to 1 and if you check this now so this is 19 19 means 1 clear now okay thank you no issue see we first understand we have not learned how to do square cube square root cube root we have not learned till now addition subtraction also we have not learned multiplication also we have not learned we have just seen the however we got answer maybe whatever we learned in class 1 to 10 or right now with a calculator whatever answer we are getting how to check that so the target was just how to check the answers how to verify that it is correct so with time when we'll do all the exercises you'll not ask me is this the answer now you'll say this is the answer and it is correct then see the confidence coming back to you so from today onwards you can start taking the classes but only condition is up till class third and fourth don't uh maximum fifth not go beyond that because then there would be a cross questions so class third fourth fifth these three topics will take minimum six classes six classes means at least two to three weeks if you're taking two classes a week then three weeks otherwise two three classes a week then two weeks and then in the meantime we'll go go ahead right any questions till now in all the three classes yes harish no sir b no sir nothing h yes uh tuna aruna greedit no sir no sir one I can ask like 31 cube we have done no 31 into 31 is 961 that is two digit two digit multiplication only uh like in terms of tables like 961 * 31 uh-huh so how to write in terms of table what we know multiples so now again you you you are trying to you can do this also but is it possible for you You have done that one but this is correct this is correct i have done that huh so you can do it but see this is when you are thinking in other way but it is not ideal way now not correct way things can be done see place values actually we didn't understand the value of place value that's why I gave the name balancing line and you'll see now everything can be done with that balancing line every topic will do with that so here also you could have done see now 21 31 lines 31 6 3 1 correct now but this is taking time so instead of that what you can do you can go for the other method that is your uh uda sutra no cross it is cross so let's start terminology i'll we'll just start with certain uh important terms which we'll be using but the first three topics they were related to speed then second confidence gaining what we did today the digit sum is for confidence gain because the student will get that feeling yes I can correct and they'll be always correct and the third was removal of that burden of tables i think everybody can write tables now and always when you are taking a class if it is online then there is a separate way to ask but if you are taking some offline class initially ask the students up till which number they know or if they are entering in the hall if it is a big session then always ask and then ask them before they leave and then see the smiles on their faces they'll be excited right so the these three things are very important okay so first sutra or the first term we generally use is We used this last time also in the last class i have why I have changed the color so that you can break and remember otherwise sometimes you say oh Sanskrit we we we find it difficult to remember the Sanskrit names or to pronounce it so a means one ad means more means then purvea means previous so the translation says none more than the previous yes so this we did earlier but I today I'll do more on that how many wherein where we can use this sutra one more than the previous and mathematically it means add one to the previous but you know the method could be different also it's not like every time you have to add only sometime add and find the product also it can be I'll show you two three examples today so first application we use in tables we saw right we did all the tables of all the numbers ending with nine this is the first application which we saw another is finding scarce of numbers ending with nine oh sorry ending with five now within five minutes you will remember all the numbers how now what is the formula i cannot give right now because you need to understand how it is derived but right now it it I'll make it very clear to you what are the numbers 15 square 25 square 35 square 55 scale 65 square and so on so we need to understand whenever it is ending with five the answer is into two parts the right side is always 25 because five square is nothing but 25 right and whatever is this number let's say it is a so you have to multiply with a + 1 means the next number so if it is one that means 1 into two see here also we are applying ikadena but not like the way we did in nine multiplic 9 table there we were just adding and then we were adding here we are multiplying and how this formula is derived that also we will learn because you should have that basic knowledge how formula is derived so this is nothing but one into two i'll write one answer and then for others we'll follow here 2 means 2 into 3 and 25 so that is 625 yes gurit sama pushpa yes sir of course you have done kalyani yeah yes sir so what is 35 square 1225 1225 yes others you have to speak there are n seven students so you have to speak 90 20 what is 55 square 30 25 30 25 what is 65 square 40 to 25 what is 75 square 5624 56 85 square GPI what is 95 95 square 95 square 902 95 square is 9025 25 9025 Got it 95 It is 9 0 9 025 What is 105 square 1 102 1 2 5 1 2 Correct so see how simple it becomes what is 115 square 121 to 5a what is then 11 into 11 12 again first first question we did 11 into 12 was 132 132 rest ban 11 into 12 132 first question it was 1 + 1 yes 1 + 2 not 1 + 1 1 3 2 5 see this basic you have to understand okay what is 125 square just now we did 12 into 13 so 12 into 13 is 156 625 correct what is 135 square so 13 into 14 is 182 18 to 4 correct what is 145 square 14 into 15 210 25 yes is it clear now this is where you apply even even it is not only for scares there are certain other examples where we will be using in multiplication also but in multiplication other combinations are also there so this becomes a very small part for example I'll show you and that is again a part of this only so we'll we'll do with anura uh noturupena and dash 10 multiplication that time we will do so even multiplication this is coming we'll be using this for finding one more technique is there when numbers are ending with nine for example 19 square if you have to do directly 29 square if you have to do directly so it is nothing but a 9 into a + 1 minus a + 1 and 1 so you will do this i'm not going in depth in this very important what you'll be learning is during fractions now 1 by9 2 by 19 or 29 these are called as vulgar functions because they do not terminate immediately it may take 28 terms 18 turns now this takes 18 turns so up till 18 digits you cannot do with your normal division because your page can have only five to six eight and that is the reason it we find it difficult but with ikadika proven concept we can do this kind of fractions using multiplication also and division also see this is scarce so this is one uh we'll be learning then it is also used in cubes finding cubes in cubes we have the formula a² into a + 1 d into a + 1 3 b² a and b cq so you will do this correct so all so that means you are using it in addition also we can say you are using in multiplication you are using in scaring you are using in cubes you are using in fractions the these are these would be the applications which we'll be understanding correct now the second terms is exactly the opposite means one less than the previous So mathematically also subtract one from the previous number now where do we use this predict which one predecessors that is what she is predecessors and predecessors are there predecessor okay okay we we will be using this measure in multiplication of 9 series very important when you'll go with fast multiplication or specific multiplication when you multiply with 99 9999 or 4 * 9 and so on at that time you will be using this so calculation becomes in seconds for example this is a number now in normal process you may take 2 minutes but if you apply this minus one so answer is 1 2 3 3 and then 9 - 1 8 9 - 7 uh sorry 2 7 9 - 3 6 6 finish so here we use Any questions till now sir can you please explain this uh 9 - 18 see this is when you have specific multiplication of series of nine that is if you're multiplying with 9 99 triple 9 or 49 like this now let's say first case is when you have same digits so I'll I'll take this that only right now if it is 9 into 6 or 99 into 16 or 9 into let's say 121 correct first the first step is whatever is the second digit other than nine series subtract one from that means find a unit of that so 6 - 1 5 is here 15 here 120 clear now subtract from here 9 - 5 4 4 9 - 1 8 9 - 5 4 4 So 1584 here 9 - 1 8 9 - 2 7 9 - 0 - Yeah and but but but this is not all this is I've just explained you the general case here also there is three types of numbers one is when the number of digit digits are equal to number of nines second is when the number of nines are more than the number of digits and the third is when the number of nines are less so three conditions three cases yes you have to study the case studies when we'll do uh base multiplication at that time also there is case study because until unless you'll do case study you'll not be covering every topic correct and that is where we generally make mistakes right yes any other Okay now the third important term very important uh we use it purak complement or we also call it as the second sutra nikilum sutra I'll give you the complete name also Now what do you mean by purak or compliment and what is the definition of nikulum this these all are three are same now the complete name nikilum is we are just sutra we are giving a smaller name but the complete name says yes harish what is the complete sutra kilam sutra it is not nikilam sutra sir best method of multiplication sir what is the complete name yes Aruna said that what 10us 3 10 - 7 that's this is wrong harsh one one one last time I'm saying you don't complain about any teacher he taught this so are you you don't have mobile you don't have Google you don't have chat GPT sir then don't say this thing see take any teacher as a reference and Then do some efforts huh don't complain he didn't teach he didn't who knows what you're going to say after me everybody this is this becomes a habit don't say this thing now it is caramel dash see this is a complete name yes some some some of may say chamom so see Sanskrit is a language which it is difficult to pronounce and everybody has a different way to pronounce correct so because we generally see from English version so sometimes we say chs ch sometime c correct so it is like this and what does this means means all from nine and last from 10 now this is one word one phrase for this sutra but here also there is one small change which we'll bring down to understand i I'm not going to change the sutra of course but for your understanding there is something missing in this mathematically it is so this is your translation mathematical meaning is all digits are to be subtracted from nine and last digit from 10 right so every week just every class Harish try to pronounce one sutra there are 29 weeks in 29 weeks you'll remember 29 sutras okay not big thing now how to what does this mean we have written but what is the answers what how we will be applying let's come there let's talk about any singledigit number so what are the singledigit numbers 1 2 3 4 5 6 7 8 9 So I said yes but what zero zero is a single digit number zero is a single but zero we don't count I I we'll give you the reason in that because here we are trying to get the what will you do anything plus 0 is nothing change anything minus 0 nothing change so we are here to calculate some things so that's why you're not you're not talking about zero right now right now I said all the digits are to be subtracted from 9 and the last from 10 now this is the last only it's only one so what what is 10 minus one 9 correct any doubt up till here we got the answers let's talk about the double digit numbers if it is 21 so 9 see how will you look now 9 - 2 7 and 10 - 1 9 so 21 nilum is 79 if it is 35 so 9 - 3 6 10 - 5 5 If it is 38 so 6 2 If it is 45 44 so that is 5 and 6 if it is 98 then 0 and 2 correct are you getting so this is this is for double digit i'm getting how I got 65 how I get yes gurupit Kalyani Pushba Harish yes sir sir 9 - 9 - 3 six sir correct and take try try from left side only please don't go from right try left then you'll be faster now let's come to three-digit numbers 1 2 3 so it will be 9 - 1 8 9 - 2 7 and 7 correct 145 so 8 5 791 so 9 - 7 2 0 9 9 Let's take one or two three four-digit numbers 1 2 3 4 So 9 - 1 8 7 6 7 six and six correct so this would be your exercise in your teacher's book first exercise is this but now first understand this now just observe this is your number and this is we we said I said dulum or this is also called as complement purak now why I'm calling it as compliment also purak also see if you combine these two answer is 10 combine any singledigit number answer would be always 10 and combine any double-digit number answer is going to be 100 check every then only you will be correct otherwise you are wrong check three-digit number it will be always 1,000 check four-digit number it will be always 10,000 so what what is purak you know we we say north pole and south pole they are opposite but they attract each other they are complete in itself i was talking key see how things are used purat means what do you mean by pur one that completes complement one that is opposite so purak here is one 1 + n they are so it is purak of each other because they complete and they are also complement so nikilam is called as purak also complement also got it but till now it is clear yes sir okay now coming back what is compliment or purak or niklum of 10 400 40 80 give me yes Harish what is complement of 10 yes Aruna what is complement of 10 10 sorry so 9 - 1 10 - Yes Harish B again you'll say hidden to every example nobody can get so give it give the answer yes so no one is sorry it is zero now so we have to do 10 - 1 and 10 - 0 yes anyone 10 - 9 10 - 1 and 10 - 0 because it is zero no so you have to do that 10 - 1 10 - 0 10 just I am not able to understand your language so please give me the answer 90 how can you explain one sir you said earlier sir if you add a 10 plus two-digit number then we will get the 100 so 10 + 90 becomes 100 sir the answer is 90 your logic is 100% correct but now see what they all were doing was all from nine last 10 and I said there is one loophole see every system has something missing this definition when it was derived they have they might have thought but you know a phrase is always a heading is so whenever the last digit is zero let it be this let it be this let it be this so last digit it will be kept constant zero as it is and your formula your term your that procedure all from n last it will start from here so 90 two zeros 6 6 0 2 0 but this does not mean tomorrow I'll give you 404 so don't say now second digit is so that is 6 9 and 5 got it but now since I have done some changes so this definition needs to be revised I cannot change that sutra but here all the digits are to be subtracted from last non zero digit got it if it is zero last then that remains constant this understanding should be there and secondly I was again telling two digits add up to 100 that also you didn't take it three digits add up to th00and that you should have taken 10 minus 0 is 10 only so that That way you will just wander here and there harish now is it clear if it is zero so now I have changed the d definition all digits are to be subtracted from nine but last non zero if it is zero that means you are moving to towards the next number so this thing is very important and this will play a very important role when you'll do questions on this now now any doubt so now if I ask you anything let's say 4 91 6 0 what is the digits what is a sorry complement yes harish what is the compliment first 5 0 8 4 0 Correct because zero was remains a constant correct so this is the exercise you have to do why we are doing this because we are in actual we are subtracting only we'll do the reverse of this also later you will understand that what we are doing when when we'll be doing subtraction see right now we are thinking we are just doing all from 9 last from 10 in the other way but later you'll be subtracting from that only 1,000 yes Gprit any questions no sir I got it if it is the last number is zero then move towards the next take next number as the first of your step yes bhan any questions any doubts aruna any doubt yes sir it is real no you because you are asking it's good neither harish is asking doubt is there yes you it's good now see then only clarification will be there otherwise it's always we will be confused every time right and after this there is one one term called vinculum now next class is most important because people leave that topic it is considered as tough it is considered like it cannot be done but without Vinculum you'll not be able to solve flag division you'll not be able to become confident in division in fact because even every nikilam division can be converted to parvarta okay I'm not giving the names division is very important uh scaring becomes very easy i I will not use more in subtra uh addition but subtraction is very much easy in vinculum and then simultaneous addition and subtraction is easy in with vinulum so vinculum is the topic which you have to understand right from scratch so that that day don't miss even first five minutes the next class would be like Saturday every minute will count and that we can do yes taruna any questions now anyone yes kalani anything you have in your mind thank you so no one has any questions it's very easy just go step by step everything is damn easy you know take my example uh Gurrit knows me gurprit is connected to me from around 8 years i she met me in Bangalore in my school oh so at that at that time I I I didn't know even zero uh a of maths M of maths i was always behind the scene never came on stage never anything so it is all practice it is practice your efforts right so what what was the reason you got confused or whatever carried away now do step by step so when I was writing books first thing came in my mind what should I write level one book one book two book three what should I write so then I thought whenever you have to move ahead you take the stairs now so that is step one step two step i made it step one step two step three and people used to ask me that time sir what is step why not level i said who gave level has government decided no so go ahead so that was the time initially 21 now though we like told us to start classes for third and third huh I have question here like for third and fifth whatever we have done multiples of 11 till 121 is it possible or we have to cut down on that you can uh you can do up till 99 don't take the example of 121 that's all only one cut down because because four standard they do double they they have done multiplication they have done uh double digit also they have done tables also and moreover they they'll be requiring four days for tables only because to them you have to make them verbally speak correct so they have to 399 so 2781 run that way they have to learn so balancing line you have to take 50 examples with them for with with you I took three examples five examples but there you have to take 40 I don't see it again I don't know God has gifted like that I I complete their slavers also in three months let it be class third or fourth I take only one or two days in tables that's all but you can take more not Asian because I take small batches for students i don't take more either more of them are one-on-one classes oh okay so no doubt then I'll share you the video before 12 right okay that we'll meet on Saturday i and uh that that topic is important right Answer