 welcome back guys so let's complete this process of multiplication of two numbers near thousand so in the previous sessions we have seen two numbers lesser than thousand then two numbers more than thousand and we tried finding out our easier technique of multiplying those two numbers now in this case what we are going to do is we have two numbers again we have to perform this multiplication but it's given that a is less than thousand and B is greater than thousand so two numbers are there they are closer to thousand closer to the number thousand but one is less than thousand another one is greater than thousand so let's see how to work with those kind of numbers so again as we have been doing we will be taking up lots of examples to illustrate and then you will be doing a lot of practice on our LMS and you will you know make yourself perfect in this okay so let's take example number one so the numbers are 997 and I want to multiply this with 1 0 0 3 so again we have to find out the deviations from thousand so this 997 is minus 3 from thousand and this thousand three is plus 3 from thousand so now the next step is to multiply these two to get the hundred stents and units place so minus three times three is minus nine but like what we did in hundred we can't have a negative number in the product of two positive numbers so in this case we simply add one thousand to it one thousand okay and write the number one here because of only one thousand you are adding hints just for your understanding right now just write that one separately now perform this so it is much easier to perform and this is 991 very easily so you don't need to write into it but because I'm illustrating it to you all the steps so hence it is necessary for me to write everything but when you are doing the calculations you don't need to write anything you can do it mentally now the only thing which is remaining is just do this perform you know operation so thousand three plus minus three is thousand but you have to now take care of this one as well like we did in the case of hundred so what you need to simply do is whatever is the sum here you just reduce it by one so the sum here is thousand reduce it by one you will get 999 write it here this is the product okay so product of 997 and thousand three is triple nine double nine one okay let's take another example and once again so I'm writing it very very slowly and you follow all the steps okay so let me say instead of 991 I will now take 996 and 1004 1004 okay so clearly this is minus four this is plus four the deviations from thousand the product is minus 16 add thousand write my right plus one here just to you know just one no plus or minus just write one so that you have to you know you can accommodate this one later on how we have already shown we'll show it once again so minus 16 plus thousand is nothing but 884 isn't it and then you do this operation thousand four minus four is thousand and subtract this one so 999 this is the product the only difference here is you have to subtract one while you are performing the diagonal of diagonal operation so this is let's say diagonal operation so while you are doing the diagonal operation either of them you can do the result is same you have to just reduce one from that let's take another example okay we'll do a little faster in this case let's say 991 and let's say 1019 okay so what is the difference 9 here and 19 here is it now the numbers are a little bigger but not to worry 19 times 9 I know it is once minus 171 because there is minus n plus so minus 171 I will add thousand though I'm writing here while I will be doing it I will be not writing that in the paper I will be just doing it mentally so if you do thousand minus 171 you will get 829 right and now what keep this one aside and then do this operation so 1019 minus 9 is 1010 and subtract this one you'll get 1009 so what all steps did I do so I first wrote minus 171 plus thousand I'll get 1829 now I have to do this sum which gives you 1010 and you reduce this by this one here you'll get 1009 829 okay let's take another example to illustrate it much you know and once again once again so 984 and 1012 okay now this is let's say minus 16 this is plus 12 correct now 12 times 16 if you do the calculation comes out to be minus 192 yep minus 192 correct so minus 192 you have to add thousand to it because it's a negative number so adding thousand you'll get 808 so I hope you have seen the video on how to add negative and positive number quickly especially when it is multiple of tens correct so 808 and now 808 is my htu so what do we need to do I need to perform this so 102 1012 or rather this one will be easier for you to do so 984 plus 12 is 996 but this one will be subtracted so 995 is the product so 995 808 is the product okay one more one more 978 times 1009 okay so 978 how far from thousand minus 22 now this looks little bigger but very easy to calculate let's see how plus nine so 22 times nine is minus 198 in this case negative and positive add thousand you will get 802 quickly 802 so you got the three digits of htu 100 stands in units place now what 109 or you do this is better so 978 plus nine is 987 then you have to subtract one from it so 986 so the product is 986 802 so the difference between the same or both greater than thousand and both lesser than thousand numbers is simply this that you have to first of all you'll get a negative number you have to compensate that by adding thousand the moment you add thousand in the next step when you are doing this operation you have to just keep in mind that you have to reduce one from the result so 109 minus 22 was 986 sorry 987 and then you have to reduce this one from that so 986 is the other three digits so the total product is 986 802 this is how you can multiply numbers near thousand so so after this I would recommend that you take the you know practice sessions multiple practice sessions so that will make your understanding clear as well as faster so hope you understood this process