 Hello and welcome to another session on speed mathematics and continuing with our series on multiplication Now we will learn how to multiply two numbers which are very close to thousand So like in the case of hundred we will be doing in three three phases first when both the numbers are less than thousand Then when both the numbers are greater than thousand and in the third phase Where either of them one of them is greater than thousand and another one is less than thousand so the problem statement is we have to multiply two numbers a into b and a and b both are less than thousand, but they are very close to thousand, right? So they're like 990s and 980s and things like that. So how to do it? So the best way is to learn through examples here. We will be You know dealing with three digits at a time because it is getting multiplied by thousand So keep that three in mind. So we will be dealing with set of three digits at a time Okay, in the case of multiplication with hundred we were dealing with set of two digits at a time here We will be dealing at a time with three digits. What is meant by it? Let's see with an example So let's say I am multiplying 999 Okay, and I am multiplying with 991. So this looks like a very big TDS multiplication See with this technique how quickly you can solve this now So you have to reserve three digits for the hundreds tens and units place hundreds tens and units place like that Okay, and how to get this HTU. Okay, so like what we did in hundreds case here How far this 999 is from thousand now thousand. So clearly it is minus one of it Okay, it's less than thousand so minus one and this one minus nine of it Am I right? So this is minus one and this is minus nine away Okay, so now you again do the same thing multiply minus one times minus nine is Zero nine only nine right so that you write here zero and sorry nine and let's say there are no other digits Accompanying it so simply write zero zero nine Okay, and your job is done and now again as we did in hundreds case. Just do this operation 991 Minus one. So basically nine nine zero So if you have a you know calculator or if you want to do it through a proper long division process You can see the product indeed is nine nine triple zero nine. So how quickly we could do this Calculation isn't it? Let's take another example and understand it another one is nine nine two And again, so let's say very close similar 991. We are doing 992 991 okay, so as I told you what do you need to do reserve HTU? Okay, now this is just for your understanding later on once you are having habituated Once your practice is enough. You don't need to do all these steps so you can do it mentally, okay? So just to illustrate I am writing all those steps now here It is minus eight away and here it is minus nine nine eight So how much minus nine into minus eight is 72 so write 72, but then one place is empty So write zero that's it and simply this 991 minus eight is 983. So this is the product. Tell me, you know, isn't it fast enough? You are doing the calculation so faster once you are thorough and familiar and quite, you know in practice You will be able to do it much faster than me. Okay So this is the process nine eight three zero seven two is the product. Let's take another example and understand So this was example number one two and Example number three now so here it is 997 Into 996. Let's do this again for your understanding sake. I'm writing HTU H2 you I will not be writing it for our calculation or whenever we I am doing the calculation But once you are also familiar with the process, you also need not do it Okay, now how much is this away? So minus three and how much this is of a minus four So minus three times four is 12. So right well put a zero because third digit was missing and Simply this or that whichever so 997 minus four clearly 993 C. So 993 012 is the product Right, isn't it amazing very easily you are able to do. Let's do another one. Let's take another one 999 999 and 998 Right huge number. So hence it is minus one minus two product So you'll get only two but you have tried to do zero zero like that three HTU hundred stents and units and Perform this operation 997 done This is the product Okay, one more one more. Let's say now we we will be seeing its Importance in terms of a bigger number right or bigger difference numbers on 991 and Let's say 984 More realistic now. This is minus nine away. This is minus sixteen away now sixteen times nine is 144 So you don't have to do anything just simply write 144 and now do the operation 984 minus nine is 975 so hence 975 144 is the product. Can you do this fast while you're doing a Normal process. So you'll have to write all the steps one by one and add and all that is it? Let's take another one right, so it is 982 and 988 Okay, again. Yes. The only thing is you want to throw with tables of table still 20 at least So that will make it much faster So this is minus 18 and this is minus 12 away from thousand Okay, now 18 20 18 times 12 Let's say you don't know 18 times 12 is 216 then you can always they do 18 times 10 Which is 180 plus 36 that is 216. So clearly this is 216 three digits are already available So I don't need to do anything now 982 minus 12 looks so easy to do 970 So this is the product Okay, so in this in this method What did we learn exactly similar to what we did for the case of hundred we found out how far it is from you know visit or The number thousand did the multiplication did the operation of addition and then simply wrote them side by side keeping in mind that the product has to be The product of the differences which you are doing has to be a three-digit number If there are not no three digits three digits you have to fix zero so that you compensate or you fill all the three slots and This operation very easy right 975 done So I hope you understood this process in the second series second phase We will see how we do it when the number is more than thousand and exactly similar Process we will be following what we did in case of hundred