DAY 27

Added: 2026-06-03

[00:00:21]Good morning students.

[00:02:13]Okay.

[00:02:21]Did you complete yesterday's worksheets which was uh posted in our WhatsApp channel?

[00:02:56]So if you have doubts ask me or else you can continue this concept.

[00:03:24]base method multiplication different bases.

[00:03:48]So till now we have learned we have discussed about base method multiplication concept uh with same basis right above This same basis in same basis above base below Place mix above and mix it means one uh one number is above and one number is below. Either it is multiplicant or multiplier mixed above base, below base and mixed. And second different basis we have to learn this.

[00:05:01]Is it clear? We are here.

[00:05:05]We have learned. We have discussed about same basis concept above base, below base and mixed.

[00:05:15]And now different bases clear.

[00:05:47]like this base must have same first digit means here we have first digit one here we have or else like This first digit of basis means 1 minute.

[00:06:29]See if you have to take basis here.

[00:06:33]You have to take basis for this number.

[00:06:35]Base for this number is 1,000. Base for this number is 100. See check base first digit must be same.

[00:06:46]First digit first digit. Here 300 has to be base. Here 30 has to be base. Now base is first digit must be same. This is the only one condition here. That's it.

[00:07:01]you know how to take base for the for a number. So in this case if you have different digits in base this method is will not applicable. Okay is that clear everyone?

[00:07:15]So for example do one problem you will understand.

[00:07:38]So in this also above basis, below bases and mix it we have same like um base method multiplication with uh same basis. See I explained just now same basis when we are having same basis for both multiplicant and multiplier we have three kinds above base below base mixed in different bases also we will have three cases above base below base and mixed okay so multiplication with different bases bases must have same first digit Okay, here is the same process with very little changes.

[00:08:27]See multiplicant into smaller based for example 109 into 7. Okay. See both both are above bases.

[00:08:42]See if you want to take base for this numbers you have to take 1,000 here and you have to take 100 here. Okay.

[00:08:54]Both have same both bases have according to this rule both must have same first digits.

[00:09:03]So both m here 1,00 has one as it is as its first digit. Okay, clear this is the single rule or condition for this. Okay, now follow this uh answer method or answer format multiplicant plus base smaller base difference. See what is the difference here? Here 9 here 7 clear.

[00:09:44]So 109 is 9 more than base. Base is here 107 is 7 more than 100 which is base. So now multiplicant generally we call is above number as multiplicant. This is multiplier. So multiplicant plus smaller base difference. What is the smaller base? 100. Here difference is seven. So multiplicant here 109 plus smaller base difference. Smaller base is 100 and difference is seven plus with extra zeros. Here one different concept is there. You have to add smaller base with extra zeros means what is the difference between zeros of bases. Here smaller base has two zeros.

[00:10:47]Here bigger base has three zeros. What is the difference? One zero is the difference.

[00:10:53]One two zeros. One two zeros. One zero is the difference. that zero has to be added to the difference. That is the thing. Multip multiplicant first smaller base difference with extra zeros.

[00:11:06]Okay. Into first number of base. That is the main reason. First number of bases means bases must have same first digits.

[00:11:14]That is the main reason to give this condition. Bases must have same first digit that is into one.

[00:11:22]We have basis 1,000 and 100 here. So that is the reason we don't have any other problems. If you multiply by one any number becomes same number. Okay. This is first part.

[00:11:36]Second part as usual product of differences out into G of smaller base.

[00:11:41]Same as the case with base method multiplication with same bases. Okay.

[00:11:46]What is the product of differences?

[00:11:49]Product of differences. 9 7 are 63.

[00:11:53]According to zeros of smaller base, we have two zeros here. So, we have to write in twodigit twodigit format.

[00:12:03]So, 9 7 are 63. We got 63 directly.

[00:12:08]So, we don't have any other problem. If if it is three zeros, if it has smaller base has three zeros, we have to add zero in front of 63. Not after 63. If you put zero here, it becomes 630. That is the reason you have to keep zero here. 0 63.

[00:12:26]So we have two zeros. Excuse me.

[00:12:30]We have two zeros. So how we have to write two-digit format here? 97 63. We got already twodigit format. We don't need to we need not add any zeros here.

[00:12:42]So what is the answer? 1 09 + 70 into 1 means it will come same answer 109 + 70 1 79 and this 63 this is the answer you can check your answer using digital root We are here when both are above basis.

[00:15:09]1 minute.

[00:16:06]Did you understand everyone? This method 107963 or else you can do another example to get more clarity.

[00:16:18]We are here both are above basis. For example, um 2 0 0 7 into 2.5.

[00:16:34]So here bases are we are both bas are above bases we are at both bas are above bases. So that is the reason I'm giving you this kind of basis. this kind of multiplicant and multiplier basis here 2,000 we have to take 2,000 here we have to take 200 here okay what is the difference 7 is the base here difference base difference from base five is the difference from base so follow this format okay multiplicant plus smaller base difference what is the smaller base 200 so multiplicant this is multiplicant this is multiplier Remember in multiplication this one is multip multiplicant this is multiplier. So multiplicant multiplicant plus smaller base difference. Smaller base difference means smaller base 200 difference is five. So 27 + 5 with different zeros. See smaller base difference with extra zeros. What is extra?

[00:17:42]Here bigger base has three zeros, smaller base has two zeros. So difference is 1 zero. You have to add one zero here. That's it.

[00:17:56]Did you understand? And as usually first digit of base, what is the first digit of base? Two. So that is the reason bases must have same first digit. If you find two different first digits that is confusion thing or else this method will not applicable.

[00:18:17]So product of differences according to product of differences 7 5 are 35. Here what are the zeros?

[00:18:28]This smaller base has two zeros. So 7 5 are 35 is the two uh twodigit number. It has two zeros. That is fine. We need not add zeros here.

[00:18:42]So 2007 + 50 20 57 into 2. Remember this you should not forget this first digit of base into first digit of base. Remember this. So 2 7 are 14 four here 1 carry over 2 5 are 10 + 1 11 2 0 fine 2 2's are 4. So 414 35 is the answer.

[00:19:19]41 4 3 5 You can check your answer.

[00:19:40]Okay.

[00:19:42]107 963. Okay.

[00:19:46]Fine.

[00:19:49]Gokada 411435. Yes. Correct answer.

[00:19:53]Yes. Rohit. Yes. Red Lakshmi.

[00:19:58]Yes, Nissant. You're right.

[00:20:14]Okay.

[00:20:17]Kulasawi, right answer. Okay. Fine. If you if you understood just do this.

[00:20:43]Do this. Do this multiplication.

[00:20:48]Every everyone must get same answer.

[00:21:15]Double one.

[00:21:18]41135 Yes. Nissant do this 4,7 into 43.

[00:21:25]Do this multiplication.

[00:21:36]Okay. N >> go to next problem.

[00:21:44]Don't stuck there.

[00:21:55]So first is the answer 40,7 into 43.

[00:22:03]Note the uh format answer format not Okay.

[00:22:42]This is the answer format and round of circle circle.

[00:22:56]This one answer format.

[00:23:19]Deluxe me got 1601 4821.

[00:23:28]So bases what are the bases there 40,000 this is 400 base okay 40,400 what is the difference is 7 from 40,000 3 from 4,000.

[00:24:01]Now 40,000 7 plus smaller. See smaller base difference with extra zeros. How many zeros are vary here? 40,000 has four zeros. 400 has only two zeros. So you must add these three with two zeros into first different first digit of base. What is the first digit of base?

[00:24:27]Four. This is one part. Another part 73 is a 21. It has two zeros. Smaller base has two zeros. Answer is 21 is fine.

[00:24:41]Now add this 40,7.

[00:24:45]That means 40,000 300 and 40,7 you have to add 40,000 37 into 4.

[00:25:09]4 7s are 28. Eight here, two here because four zeros are zero. 4 3's are 12. You can write 12 because we we have zero here. 4 is 16. So 1 612 8 and 2 1 answer is 612 is the answer.

[00:25:41]Yes. 16 Nissant bot. Correct answer.

[00:25:49]And uh 160 4821.

[00:25:59]So 160. Where did you get that zero?

[00:26:05]Check your answer.

[00:26:10]1612821 is the answer.

[00:26:17]Only one student got correct answer.

[00:26:26]Yes, Rohit you got correct answer.

[00:26:41]This is the correct answer for this problem.

[00:26:48]Okay.

[00:26:51]So we have completed both our above basis. Remaining cases you can do as we did yesterday.

[00:27:01]If you practice more, you will get more clarity and uh you can do within no time.

[00:27:10]Yes, Jam Jam Satyam. Right. Red Lux me now corrected it. Very good. Yes. Wasabi.

[00:27:20]Very good.

[00:27:22]1612 821 I think typing mistake.

[00:27:41]Okay.

[00:27:45]Now both are below basis.

[00:28:55]Now both are below basis. That means um like this.

[00:29:26]So basis are you can take basis as here 3,00 because 2,998 is nearest to 3,00 difference from base is 2. Here 300 difference from base is three. Okay, remember you have to check the multiplicant and multiplier first to take the base. You have to take exact base or nearest base to get your answer correctly. So these are the differences but here negative see this multiplicant has two less than base its base. This multiplier has three less than its base.

[00:30:14]Okay. Now as usual multiplicant plus smaller base difference with extra zeros. What is multiplicant here? 2,998 2,998 plus this negative number but with extra zeros. How many extra zeros this bigger base has? One zero extra. So you have to add this 1 zero you have to add here. That is the reason multiplicant plus smaller base differences with extra zeros.

[00:30:55]Smaller base differences with extra zeros. See the smaller base has one less zero than bigger base. That is the reason we have to add one zero here into first digit of base. You should not forget into first digit of base. Both base has three as it is first digit.

[00:31:13]This is one part of the answer.

[00:31:17]Remaining part product of differences. What is the product of differences? Minus2 and minus 3.

[00:31:31]So 2 3's are 6 negative number into negative number gives you positive number. But product of difference according to zeros of the smaller base. See we have smaller base 300 300 has two zeros. So you have to write twodigit format here. You have to write 06 not six not not just six. You have to write in twodigit format because the smaller base has two zeros. Okay. So what is the answer?

[00:32:06]2 98 minus 30. So when you are adding one positive number, one negative number, that becomes subtraction. 2 9 8 9 8us 30.

[00:32:22]What is the answer? 8 9 - 3 6 9 2 Simple subtraction into three. This first digit of bases into first digit of base 3 is 24. Four here two carry out 3 6 are 18 + 2 20 0 again 2 3 9 are 27 + 2 29 9 again 2 3 2's are 6 + 2 7 8 here 8 9 04 is the answer in first part.

[00:32:59]Second part is 06.

[00:33:04]So complete answer is 8 9 04 06.

[00:33:13]8 9 04 06 is the answer. See this is four digit and this is three digit. So answer will be in either six digit or seven digit. We got sixdigit answer. You can check using digital route also.

[00:33:55]Did you understand students?

[00:34:14]Yes.

[00:34:17]And Ro.

[00:34:20]Great.

[00:34:22]Good. D. Great. Great.

[00:34:27]Fine.

[00:34:29]Do one more problem.

[00:34:36]Do this problem.

[00:34:55]Do this problem.

[00:35:04]4 62 72821.

[00:35:07]What is 462 7281? What happened? Uh uh Rohai, which answer is it? It is.

[00:35:28]Which answer it is? Rohoxai through uh 362 72 821.

[00:35:36]I think you X 89046.

[00:35:44]Okay, move to next problem. Nissant, don't be smart. Move to next problem.

[00:35:53]89406.

[00:35:57]Okay, Wasabi, complete this problem.

[00:36:02]Do this problem. Everyone 4,995 into 497.

[00:36:24]Okay.

[00:36:27]I don't know who who is it. Who is it?

[00:36:32]Okay. complete that answer.

[00:36:39]Excuse me.

[00:36:55]So both are below basis.

[00:37:02]So base is here 5,000 here 500 both are below bases difference is it has five less than its base it has three less than its base. Okay.

[00:37:49]Okay.

[00:37:53]Now follow this format.

[00:37:57]Answer will be in two parts.

[00:38:01]First part is multiplicant plus smaller base difference. What is the multiplicant?

[00:38:08]4,995 plus smaller base is negative number.

[00:38:16]Okay.

[00:38:17]With difference with extra zeros. What is the difference here? Difference in zeros. It has three zeros. You have two zeros. You have to add this one into multiplication of first digit. First digit of bases. What is the first digit of base is five. This is first part.

[00:38:34]Second part is multiplication of differences. -5 into -3 and answer has to be according to smaller base zeros. So it has two zeros.

[00:38:45]53 is a 53 is a 15. Negative number into negative number gives you positive number. 53 is a 15 is the answer. So twodigit format it is okay. It has two zeros. We wrote here as twodigit. We got two twodigit answer. That is clear.

[00:39:02]Fine. Now complete this 4,995 + 30 means this 30 is -30 bar 30. So subtract 30 from that.

[00:39:15]So 5 - 05 9 - 3 again 6 9 4. So 4 965 into 5 multiplication you should you should not forgot this first digit of base you have to multiply by first digit of base. 5 are 25. Five here. 2 carry over. 5 6 are 30 + 2 32. 2 here. 3 carry over. 5 9 are 45 + 3 48 8 4 carry over 5 4 are 20 + 4 24. This is the answer.

[00:39:50]So answer total answer is 2 4825 and this is 15.

[00:39:59]This answer is 2 4825.

[00:40:03]This is 15. If you combine both answer is 2 482515 is the answer.

[00:40:10]Yes.

[00:40:12]Wasi right Rohit and Dit. Good.

[00:40:19]You can check using digital root also.

[00:40:24]248 2515.

[00:40:34]You can can anyone check answer using digital throat.

[00:40:49]Good.

[00:40:51]2 48 2518 question digital root zero. Answer digital root is zero. Okay, good. That's good.

[00:41:11]So now we can move to this mixid.

[00:41:25]We have completed both cases. Both are above basis. Both are below basis. Now mix it.

[00:41:41]Mix it means.

[00:42:02]So check concentrate here.

[00:42:11]basis. What is the base here? 6,000 base here. Here 600.

[00:42:19]Remember both bases must have same first digit. Okay. What is the difference?

[00:42:25]This is bar three. So 5,997 is uh 5,997 is having three less than its base and 63 is having three greater than its base.

[00:42:40]Remaining things are same.

[00:42:46]So answer will be in two parts.

[00:42:52]So follow this multiplicant plus 5997 plus smaller base difference what is the smaller base 600 that's difference is plus three we got three here pos number according to difference with extra zeros how many extra zeros it has bigger base has 1 zero 1 zero that's it next into first digit of base what is the first digit of base six is the first digit of Yes. And second part product of differences according to zero the smaller number. What is the product of differences? Three 3's are 9. Remember -3 into 3 that means minus number into plus number gives you negative answer that is - 9. We call it as bar 9 in our vic maths.

[00:43:48]So you have to write this in two-digit format because smaller base has two zeros.

[00:43:56]Is it clear everyone?

[00:44:00]So 09 in two-digit format but both are negative numbers. Okay.

[00:44:07]So I told you in de viculation process if you find zero you can write as you can put viculation uh bar on zero also. Okay, remember that.

[00:44:24]Now complete uh you try to complete remaining process and tell me the answer.

[00:45:28]Complete this here.

[00:45:31]5 9 7 + 30 7 9 + 3 12 6 0 to 6 0 to All right.

[00:46:16]multiply by 6. You should not forget that 42 6 are 42 2 here 4 carry out 62 are 12 + 4 16 6 here 1 here 6 0 0 1 6 30 So first part answer is 3 61 62 clear what we got Here manated format.

[00:46:51]This answer is 3 61 62.

[00:46:59]Did anyone complete this answer?

[00:47:02]Let me check.

[00:47:08]Okay, Darit, did you check your answer?

[00:47:45]Darit got correct answer 3616191 is the correct answer.

[00:47:52]Yes.

[00:48:07]So we have we get 3 6 3 6 1 6 2 0 9 but this is bar 9.

[00:48:25]Did you understand?

[00:48:29]Yes. 3 61 61 91 is the correct answer.

[00:48:33]Answer is 3 61 61 91 is the answer.

[00:48:53]Remember We have only one digit or you can take on two whatever you feel you can take or else only one digit the last from 10 10 - 9 is one. So predecessor 3 61 61 9 predecessor 10 - 9 1 9 - 09 predecessor of 361 62 is 361 61 is the predecessor whatever you feel easy you can do that. Did everyone understand this?

[00:49:41]361 6191. Yes. Jarati inant Rohit Gada Trinad. Good.

[00:49:51]Anyway, Darit did it first and checked it also.

[00:50:01]Okay, these are the this is the method of multiplication B base method. I did multiplication with different bases. Okay.

[00:50:32]Base method.

[00:50:37]Base method multiplication with different bases. This is the method.

[00:50:40]Okay. Fine. This is the base method. So base multiplic both both numbers are nearest to any base you can do this method or else if you cannot find bases use general method. Okay. So this is the multiplication con concepts in uh these are the multiplication concepts in Vic maths. We have other concepts we can discuss tomorrow. Till then that's it for today. Bye-bye. Have a great day and uh don't forget to practice uh uh work worksheets which was uh which are posting in our uh WhatsApp channel.

[00:51:26]Okay.

[00:51:28]Next class different kinds of concepts happy learning different concepts concepts and math basics different kinds of worksheets um summer camps which is very useful to the every student. Okay, that's it for today. Bye-bye. Meet you tomorrow.