Last time we did multiplication when multiplier is 999 9999 and we did anti so it was 10 100,000 and then we did when multiplier is 9 99 and so on. Now today yes first of all any doubts in this any question you have Yes, good sir. 9 into 7 and 9 into 63 9 into 7 into 63 into 9 into 6 into 7cess. - 7 - 1. So 9 - 6 4 sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry 93 33 sorry sorry 62us 62 3 - 1 6 2 individual 9 - 6 3 9 - 2 7 9 - 2 7 or Okay, that is what I'm saying. Neither you watched video. [Music] 9 7 8 5 into 4 9 on a time. Sir 97 840 215 97 84 0 215 Got it. Thank you. So today we'll start with a new topic that is multiplication with series of one. Now this means 11 which we have already done but today we'll focus on 31's 4 1 5 1 6 1 and Anything there multiples? So multiples will be double2 to 9, triple 2 to triple 9. 4 to 4 9, right? Now so 11 you remember or you forgot? Yes. Multiplication with 11 numbers. Amazing. Remember, so let's check uh two three questions. What is 78 into 11? No use of paper and pen. Try mentally. 958s. Yes. 858 85858 858 Yes. 858 sir. No, I'm here. So answer 858 94 into 11. Uh it is 1 34. So two digits we can do correct. Three digits. 1 95 into 11. 2145 1 4 5 215 214. Rakkesh. Yes sir. 2145. 2 145. Yes sir. Okay. 396 into 11 4356 4356. Again four digit 6 7 pushp. Are you getting? Yes sir. So give me this answer. 6 7 7 8 into 11. Others don't give. Tell me. Tell me. 748 745. Yes. Got it. Good. Okay. Last 98765 into 11. Yes. Aruna sir. 108 6. Good. 415. Very good. So I think 11 is clear to everyone. Any doubt please ask 11. So 11 was because we practiced also and now we understand that fact that we are just adding the numbers coming next and then after we did some questions on multiples of 11. So what are multiples of 11? 22 33 up to 99. So if the question is 3 26 into 33 what will you do first? Multiply by 3. Multiply. Yes bou. Sir first we do multiplication with three then by 11 sir. Very good. So what is the answer? Now try try doing multiplication with three mentally because that we can do with the help of table format. So try. So 10758 is 978 is multiply by 3. Mhm. And then multiply by 11758. 10758. Yes. 10758. Okay. So now it up till here it is clear. Sir. Yes sir. Okay. Uh there we were. 4976 into 88. 437 437 88 88 8 Okay. Very good. So 4 * 9 into 4 * 7. How will you do this? So which method you will apply? Yes. Hey, which what are you using? Why? Yes. So that was verbal. It was verbal. 77 76 26 37 74 22 22 22 22 22 22 22 22 22 22 22 3. Yes sir. So why why so much of time? Why so much of time then? Oh yes. So 7776. So but you took so so much of time. Yes. Aruna Kyani. Why I got confused? This was the last So this was the last topic we did. Yes. 7776 222. So we have to be very clear if the topic is from nine that is the easiest method right. So now this was all for multiplication with 11. All of you are clear in that. Now what is the difference between 11 and triple 1? Now the first question you should have asked me is sir why we are let's say this is this was a question why we are making pairs nobody asked this question because we are busy cramming the things see why don't you understand that students will ask you they'll always ask such questions why Why not more? Because this question arises when you are shifting when you from 12 you are shifting to 2 three when you're shifting to 3 4. So this question arises that moment. Yes or no? Yes. Aruna question. See, you have to understand this. Hello. So what was the reason? Because also we are doing no I I I'll tell you I'll tell you see I I'll tell you in balancing line when we talk about first what we understood was place values that every position only one one and I gave you an example like a student is sitting on one chair correct that was there but time will come I think we have not done that scaring in one concept scaring I'll show you two two digits at every position but now you are talking about nikum multiplic nikilum is on the basis of reference Okay. So reference has to be taken care of. If reference is 10, we are following one one digit because it is on the basis you can take it like it is a dual sofa and a triple sofa. See if in a hall there are all double sofas. So what will you do? Will two people not sit? So that and that this point I cleared that time only in nicom multiplication you have to go as per the reference point so in 10 one digit in 100 two digits in thousand three digits but this place value also I will shift I'll say at one point of time we can have two also now the reason is if there is a dual desk two students will sit I so that understanding is basically what is as per the digits. Now when we are to uh talking about uh it will be too early to give you that example right now. Okay. But otherwise I would have taught because everybody will not understand. You have done once so you will understand basically. So let's wait another one one week. But but in nikulum it is because of reference right now. So yes. So what was the question key? Why two digits? Because number what do you mean by consecutive numbers? I am asking why pairing only why not three numbers were taken together in one two three why were three numbers not taken together? because two uh I'm guessing that because two digits are there in 11 so that is the reason we are adding two to get okay my understanding maybe in triple one we can add three three digits yes this is what the logic I'm getting sir yes so that but that logic is to be clear now this is we are uh you know you get the answer now you're trying to appro uh make the answer correction right when we see the answer from the answer key then We should try to mold out our question as per the answer. So that should not be there. I tend to like that. It's okay. We are actually removing all those things. No, that grammar and all we have to I taught my son trigonometry also. He's in 10th standard. So I I taught him the entire table of stand. So he understood otherwise he was also cramming everything. Now see so that was the reason because there were two ones so we were making the maximum allowed was two digits. So I'll give you two examples simultaneously. 1 2 3 into 11 1 2 3 into triple 1. So now 1 2 3 into 11. So this was first 1 then 1 + 2. Now since there are two ones so maximum this was my capacity I cannot add the third number together. And therefore we used to shift to 2 + 3 and the last three. But in the case next case now I have one 1 + 2 since there are three ones + 2 + 3 2 + 3 and one. So can be like understood like this one two digits then three then two one. Why do you want to why do you want to cram again? Means if there will be if there will be four digits then again make one formula one digit two digit three digit four uh then three digit I'm just trying to how to that is what I'm trying to No no no no no it is very simple explanation reach to the maximum reach to the maximum and come down the same way how did you how do you explain 11 how do you explain 11 what 1 then two then two so see I I'll tell you example so what is the answer this is 1 3 5 3 but here 1 3 6 5 3 3 sorry I have to write three so this six is extra now coming in between that is because all the three digits we have added Got it. Similarly background. So same if I take more numbers 1 2 3 4 into 11. What was that? 1 1 + 2 2 + 3 3 + 4 and last was 4. But if I take 1 2 3 4 into triple 1. Now this will change. This will be 1 1 + 2. These two are steps are same. But the third step changes 1 + 2 + 3. Now again the problem is I have reached to the maximum. I cannot add four. So that is the reason we shift and then start decreasing. Now it is clear. Find out the answers for both and then we'll practice. Yes. Kalyani. Is it clear? GRIT. Yeah. Yes sir. Tuna. Yes sir. Please. Yes sir. Pushba. You act like backbenture sir. I have to you act like backbencher. I have to ask you are you getting are you getting? You never ask yourself. Huh? Not like that. Sorry. First answer is 13574. Second answer is 136974. Got it? Yes sir. [Music] Can you please explain it again? What did you not understand? 1 2 3 1 2 3 4* 1 + 2 + 3 then 2 + 3 + 4 Yeah. Why? Because you you you cannot add another number. Now in that and so you have ultimately you have to move. If you have to add the other number you have to move because the maximum limit was two digit and then after three again you moved. Same as here after 1 2 3 what is the position you have to shift. So that it was 2 + 3 + 4 now all numbers are covered. So start reducing. Okay. Okay, let's practice some questions. 6 7 5 8 into triple 1 So 750138 750138 sir 750138 38 sir Sorry. 9408 1044288. Yes sir. Yes other. Yes sir. Same. 98. Huh? An sir. 1044 288. Good. Okay. Check check check using digit sum first because everybody forgot digit sum. No no it's clear what I know. No no no check check using digit sum. See you are clear but when you'll start teaching then students you have to make them remind every time oh check using digit sum. It should be a part and parcel of life. This same digit sum is n. Yes sir. N digit sum is n 9 9 into triple 1. 1 0 9 8 6 7 8 sir. 1 0 98. Okay. Uh 678. Perfect. 1098 678. Correct. Yes. Pushba. Tunit. Where are you? I'm here. 1098678 sir. Good. Good. Good. Definitely two classes. I'll prove first. answer and sir digit sum is three. Good. Now we'll we'll have one more and then we'll shift five digit into triple 1. In the next class I'll give you one more method. Uh Aruna for you. Yes sir. You are getting confused now. Two digit three digit why this is shifting? I'll give you I'll give you finish for this 122 but not today because then you'll not practice this you have to practice this because this is again easy that is for kids that is quite uh so I don't want you though the sutra Da manta and you'll be very amazed that how it was derived. It's very okay I will do the homework from Monday sir. Tomorrow I'm busy completely. I that is the reason I'm not posting anything in the groups. I will do it started from Monday because I'm running one camp tomorrow. Good. I'm completely occupied with that. Very good. 18 7 9 2 into Okay. Not 1 four triple one last this. Sorry. 91 5 42. So 51 912 5 415 912 That is it sometimes. Okay. Now same if it is into triple 2 again first you'll be multiplying with two and then triple 1. So first you'll be getting 2 7 4 and then this will be triple 1. Correct? Yes. So you have to remember if you know 11 so there should be no that you don't know triple 8 or double 8. Correct? You have to visualize these things. It should not go off their brain. No, we learned only 11 and triple 1. No, because we cannot do every question 22 33 or triple 2 triple 3. But that should be in your minds. Every time you get these numbers, the first multiply single digit then go for that. So two questions on this then we'll move further. 5 8 7 6 into triple 2. 13472. Yes sir. 13472. Yes sir. 1 13472. Sir, any doubt left? Okay. 1092 into 7. Thank you. 848484. Sorry, come again. 2484840 8484. No, it is 848484 848484. Sorry, wait for 848484. So how how this happened? Huh? Actually sir instead of seven I wrote one. Okay. Okay. Okay. That's what I was thinking. How you did wrong? This should not be there. Okay. Now any doubt in three uh triple one or its multiples? Yes sir. Yes. No sir. It's very simple. Instead of two digits we can three digits. Yes. Um questions cannot be mentally done like 11 because we have not practiced. Once we'll train our brain then we can do it. It is possible but takes time. Now similarly going on the same pattern if it is four ones that means now you can add four numbers together. But before this if it is 36 into triple 1 then what you'll do? Yes. 03 then we follow the thing. Yes. So balancing it see balancing there are two things one is balancing line what I follow one is every time you should balance because this will make clarity otherwise if you remember if this was being done by ura sutra also then also we get confused we don't know where to multiply because 1 into three you will be able to multiply but what will be in the case of second we get confused so these small small things you need to understand just by putting zero all confusions are gone. So same here 03 6 means first you'll take 0 then 03 same number then 03 6 same number then 3 6 same this and this is same and then last six but there is no confusion at all. Clear now? Okay. Now same process four numbers I'll start from bigger number so what is going to change now we have the ability to add four numbers together we got that you can say you got that permission earlier you were shifting from here 1 2 3 4 you shifted to 2 3 4 now not required because you can add the fourth digit together. So if this is being done then next would be 2 + 3 + 4 3 + 4 and 4 finish. Yes. Any doubt on this? Tell me any doubts on this. No. Okay. If no doubts, please give me the answer. 1374. Yes. Uh, Aruna. Do [Music] 136974 134. How six turna? This is six. What about the carryover? Okay. There will be a carryover also. No. Yes sir. So we can write first 1 3 6 then 10 then 9 then 7 then four. So this 10 will go here. So 1 13 7974. Clear? Yes sir. Yes sir. See the method is easy but still we have to be very careful because Yes sir. 6154 into 41's So 68379 794 683094 683794 683 094 094 683 7094 Yes. Yes. 63794. [Music] Got it. Yes, sir. Now, and the digit sum is three. Digit sum is now for you to check. Yes sir. Because that will make you confident. Now like last time you gave wrong answer so you have to you will cross check your answers. 65174 into 4 1's. 724 8314 2 8 1 7 1 4 7 7248314 72 72 4831 Yes 7 48 314 sir 7 23 4314 Math Carol 6 5 1 74 4 1's to 7 2 4 0 8 3 1 4 Clear answer sir my answer is 7 2 3 4 314 wrong 10. 6 6 11 Yes, sir. 12 19 then. Okay. 17 was wrong. Then 12 then 11 then four. So 4 1 3 8 20 means zero 2 means 4. Correct. Then 2 7. Yes sir. 19 wrong. Done. Okay. One more. Five digits. Okay. 98 76 5 into 4 once. Uh 10972785 1 97 109727 915 915 sir at the last Yes sir. 109727915. Okay. Your internet problem now for any doubt. Okay. Let's 1 2 3 4 into So The 2741 948 7419 2741 948 2741948 Okay, Clear now? Yes. Aruna. Yes sir. Yes. Any doubts? No sir. Just printing the numbers. That is what I Yes. Solve it. 22753724 22757724 Correct. 81 818 into 4 * 8. Last question. Pushpa. 72 719 A384 7271 98 Very good. Calculation fast. 727198384. Correct. 727198384. Very good. All are doing good today. So I think after three once, three, four ones you are clear. Even if five ones come, so things will not change. Same. First one, then 1 + 2, then 1 + 2 + 3, then 1 + 2 + 3 + 4, then 1 + 2 + 3 + 4 + 5 because five 1's are there. So all depends on this second number right the series of one or series of 2 or 3. Now it will we will we cannot call it as series of one only. It is now series of any number. Then 2 + 3 + 4 + 5 then 3 + 4 + 5 4 + 5 and five. Yes. Any questions on this or is it clear to you? Tell me. Is this clear? Anyone has doubt please ask 1 131 65 295 Second 1371 65295. Okay. Yes. Others ara tuna gorrit same answers [Music] name. Who is not there now? Taruna 131652 13165 25 295. Yeah. So now it is clear. Huh? So, let's solve only two three questions so that you get 4 581 28752 Two 458 1 28752. Okay. Checka. Yes. Move on. 458 1 28 752. Correct. 1 2 six is digit sum. Mhm. Answer. Yes sir. Okay. 6 1 5 4 5 into 5 * 2 1367 65 2990 same 1367 6 52990 correct? Yes. Bhan Aruna sir, same answers. Good. 1 2 3 6 7 6 5290 now any question any doubt you have anyone has any doubt any questions Yes. Clear. Any doubts? No sir. Okay. Now yes anyone has any question. So that means we can do with 11, we can do with triple 1, we can do with four ones, we can do with five 1 and rest anything can be done. And similarly with the multiples 22 to 99 in particular here we can also do 121 because that is very easy to understand. Similarly here we can do with four two triple 2 triple 3 up till triple 9 though triple 9 will not use because triple 9 will go for that concept that is much easier. So up till triple 8 will do here also same. So any questions any doubts you have now? Yes Aruna Talyani Kushba any question? Gor priit your connection was disconnecting again and again. So you have any doubts tell me anyone has doubt. Ya shocked. No sir. All doubts. Yeah. No doubt. Shall. So let's do one more topic now. Very interesting. Very uh one of the easiest topic multiplication with 101. If you remember in the last class we did 99. Now 99 was one less than 100. This is one more than 100. So one approach could be very simple. Let's say I have a number 146. If that is to be multiplied by 101 I can say 14600 and adding to this 146. This is correct but it is not possible mentally. Why? Because we are not in when you when you calculate mentally you are not able to understand the digit the place value and it is we don't try because we are not sure that it will be correct every time. But with Vic maths with the balancing line Aruna. Yes sir. Now you'll again say I'm contradicting myself but no again 101 is near base 100 or more than 100. So again if this is the number 146 what I'll do is from right hand side I'll make a pair of 1 and whatever other numbers are in this. Now what do I mean by this is if it was 146 46 was one pair and one is if it is 21 46 then 46 is 1 and 21 is there. If the number was 1214 6 then 46 was 1 and 121. If it is 1 2 3 4 5 6 7 8 even such long number then also the last two digit this much is clear first thing. So it is because two digits the then we are taking correct. Yes, you can say near the base 100 near the base reference also begins. Now this will impact in the calculation on the balancing line. That means you have to have two digits at every point. Correct? Let's solve two three questions. 1 4 6. So this and this. Now this is as equal to A because we are taking B as a two-digit number and we just have to apply what we did in 11 A + B and B. So this is 1 4 7 4 6 finish. Now this can be done mentally. Mentally you can think that 1 + 46 is 47. So 1 47 46. See question is same if you are doing with 101 you are not able to decide the answer mentally but here you can think of it 456 so 4 656 is it clear yes sir any doubt of course perfect no sir okay but now I'll I'll I'll give you the routes 999. So it is 9 108 and 99. So now this is not correct because I cannot have three digits here. So this will give here 108 99. Now it is clear. Yes. Yes. Pushpa talani gurrita aruna. Oh sorry I have asked Rakkesh. No sir. Yes sir. Clear. So as we did 11 same is a concept. So mentally you can do otherwise 100 + 1 is always there. But what is the sutra behind this? Is there in samsutra or sutra? No nothing. Sutra nothing subutra nothing. It's all see it is what actually it is it is your urat sutras calculation in 99 also what you are doing uh please understand this let's say any number 9 correct so what you were doing you were subract minus one and here also it was uh 1,000 minus this one right so you were writing 8 7 7 7 correct. Now what you were doing in nine uh series 87 I I said subtract one from the number subtract one from the number and complement of that. Now listen listen see here I said subtract one. So if you do like this why you were subtracting one because the deviation of triple 9 was one. See this is just understanding when you will be doing scaring also that time there is a method called duplex method. It is also nothing but ura sutra but the point is some okay leave that everything 100 minus 13 it is the simplest thing subtraction but what why do we fail because we think we we start thinking that subtract first take a borrow then subtract see what is our thinking process or anybody's any child but what when you confirm someone when you Give them some assurance. You know you have to go this way. See now you have to go to some place. If you have Google, you get assured. Oh, I am assured that Google will give me the path. This is what otherwise there is no difference. Same is what is happening when when we said all from 9 last from 10. You got an assurance that I just have to do this. There's nothing I have to do more. So that assurance in you got that confidence correct here also now the calculation was same it is nothing different what is series of nine nothing mute it was nothing but it was just a simple understanding triple 9 has a deviation of always one or 9 has always one 99 has always one. So we used to subtract one. There is no logic other logic behind it. It is the way to make you understand in a better way. And when you you know when you have that asurances with you, you get quicker, you get confident and you are able to solve. Otherwise entire Vic maths, entire multiplication is only two things. One is niculum, one is udwoa, nothing else. Scaring is same, cubing is same. Everything is just linked. So this is just your way to understand correct. So here also we did that the same thing. Now if it is 101 please understand again. So what is that? That means every time you will be having one extra. So that only you will be adding. Yeah. No, no paper pen. Please solve it mentally. Solve it mentally. 94738. Yes sir. 94738. Yes sir. 1012 into 101 2212. So see simple 10 22 1 1 2 otherwise see we know that this is 100 + 1 we could have done this way also but here you are not able to think what digits to be added where it is the same thing now but logic the way of explanation changes everything the way of thinking changes basically People say what is the difference how Vic mas makes different it makes if you understand in that way if you're just cramming the things then then this is nothing a simple calculation No 370074 371074. Got it. Yes, Aruna. uh one I have missed because 36 + 74 is nothing but 10. So one will go and you can do so. So first thing is you should add the two numbers then move further then you'll never be wrong. 9 9 8 7 8 9 998 789 Yes sir. Now this please do mentally. 9 099 90 999 09 9 uh 909 clear okay five digits so do this rest let it be anything. 23 67 2 3 6 7 945 2 3 6 7 945 Okay. Okay. 6 7 9 47 5 4 8 7 8 8 Yes. Tell me. So 488 7588 4 927 588 2 7588 Yes sir. 4927588 6059 697. Yes sir. 5 969. How? 59. What will be? So 65 59 69 6 First you said 59 that's why I asked one more. Yes. Tell me. So 1246956. Very good. 1 2 4 6 9056. 12 46956. Now it is clear. Now see if it is a two-digit number 23 into 101 what will be the answer? 23 23. Yes. Yes. But remember even if you do 023 what will happen? 0 2 3 2 3. So every time see now the logic is every time see with 11 if you multiply a single digit number. So it was same number repeating 11 into 1 11 into 22 11 into 3 33 11 into 44 9 similarly I told you this is also the same as well same if you multiply any twodigit number into 101 so what happens same 2 3 2 Got it? If you multiply any number, any digit, any two digit, it will always remain the same. So you have to and if it is singledigit number, you know 303 finish. Now any doubt. Done. Now on the same pattern we'll do multiplication with one0. Now you'll have to have three digits. First as B. A could be anything. A could be one digit, two digit, three digit, fourdigit but this should be three digit. If this is three digit that means all values not all but at least these two these should have three three digits only. Got it? So this answer is very simple. Now a is 1. So 1 2 3 4 + 1 2 3 5 and 2 3 4 finish. See we cannot do this mentally. If I go with,000 I have to think twice where will be four adding to what? But this way it is smart shing. Okay. Now let's say 8 7 6 5 into 1 8773765 8765. So very first thing first first thing is we should add the digits 765 + 8. So that is 773. So that means 8 773 and 765 finish. Then 3 4 5 6 1 into 1 3 4 5 8 5 5 6 1 3 4 5 95 561 3 4 5 95 561 1 8 9 98 into 1 01 1 9 06 1 169 998 1 9 016998 triple 98 916 98 Yes sir 98 2 3 4 5 6 7 into 1 0 1 2 3 4 8 0 1 5 6 7 2 3 2 3 4 8 0 1 5 6 7 8 6 8 7 9 5 8 into 1 So 688 645 958 same sir same characters are same. So see six digits also worked. Let's take one seven digit. 2 0 0 87587700 875 clear now. Yes. Aruna are you able to do? Yes sir. Yes. Any doubts? No surp88 65877. Yes sir. So beautiful. [Music] Now see here if it is 235 into 1 what will be the answer? Same it is three digits. So 235 235. Why? Because even if we add zero it will not be happening. So any two any three-digit number same nothing changed 506. So 506 506 But if I take here two-digit number then what will happen 23 0 23 you can check because now what you'll do you will do 0 0 23 so what will happen 0 0 23 here it does not matter But it will matter here. So answer will be 2 3 023. Got it? So every two-digit number, every three-digit number. You can understand like this right from the example of 11 with 11 singledigit number with 101 doubledigit number with 1 01 three-digit number it behaves like the same. Clear? Any question you have now? Hel doubt any session. I a + c. Is there any logic behind this or you just arrive? What? What? What? Where? Which one? Two 20 023. So logic I have already given I've given you the logic now then how arrived like a a + b and b how how here it is what minimum digits are required three digits and to process one more we are taking now three would be the b what is a zero so logic is that Yeah, we are not just because minimum four numbers you'll be having. Then only you'll be calculating. Ju just give me one second. Yes. Is it clear now? Any any other doubt anyone has? Yes. Anyone? Yes Aruna any question Kalyani Pushba so any doubt in triple 1 4* 1 51 and then 101 1 0 1 do practice this and next time we'll be doing algebra multiplication and that very small topics too. I'm finishing we're going on going on very good speed. So if anyone is not able to chase you can ask your doubts. push right so I I'll not take any new topic now so you rest and I'll share you the video shortly right yeah thank you sir Okay. Thank you, sir. Thank you, sir.