 Hello friends and welcome again to another speed math session in this session We are going to learn another very effective technique and that is multiplication of two numbers near hundred So first of all, let's identify which two numbers are we going to multiply? So numbers near hundred mean means like 97 98 or even 85 so which is not that far from hundred on the other side as well You can have 1 1 1 not 1 1 not 7 Or 1 1 2 how far you can go and depends on how much you know tables you have already Remembered right so let me explain the technique so you can decide how far you can go for multiplication of such numbers Yeah, so let's first take case one case one is both are Both numbers we are going to multiply two numbers near hundred but less than hundred so numbers are a and b let's say and a and b or a and b are both less than hundred Okay, so a is less than hundred and b is also less than hundred and both are near hundred So we are not going to take a 49 47 48 51 76 like that No somewhere near hundred that is around 90s and 80s only okay, so let's start with an example So here is one example 97 and let's say you're you're to multiply this with 93. Okay Now see how far 97 is from hundred so it's actually minus three away y minus three because it is lesser than hundred So write minus three like that and how far is 93 clearly it is minus seven Isn't it now what you need to do is you simply? Add this column or sorry multiply this column. So if you multiply this column, what will you get? So you multiply with signs. Okay, so when you multiply you will get minus three into minus seven 21 Isn't it now what you need to do is you just? Do this operation 97 minus 7 right that means you will get what you will get 97 minus 7 is Right 9 0 2 1 so hence the answer is 9 0 2 see such a quick Method now you could have done this as well 93 minus 3 as well was 9 0 so either of that So it will become much clearer if I take another example So let's say example number. So this was one Let's take example number two So example number two is let's say 94 and 96 near hundred both of them How far is this number from hundred minus six away this one minus four? Isn't it now what you need to do as I told you product multiply these two numbers You will get 24 plus 24 and then either of this either you do this one or you do this one So 94 minus 4 if I do I will get 9 0. So this is the product of these two numbers 9 0 2 4 You can quickly check. Okay, another example. Let's take Another one. Let's say 97 already taken a 97 and 96 Okay, so again, how far is this number so minus 7? Sorry, this is not minus 7. This is minus 3. So this is minus 3 away 100 So minus 3 from 100 and this is minus 4 from 100 isn't it? So if you see this is minus 3 into minus 4 is 12 and Then 97 minus 4 so 93. So how quickly you can do the calculations? Now what happens when let's say you don't get a two-digit number when you multiply the unit's place What I mean is example number for it will be clear from here. So let's say if you have you have to multiply 98th and 99 So how far is 98 minus 2 and 99 minus 1 from 100, right? So if you multiply guys minus 2 times minus 1 you will get 2 But be careful. You don't you can't write only single digit. You have to place 2 digits while doing this Product now you will ask. I am getting only 2 so what to do So basically then you have to affix a 2 0 before that 2 so it becomes 0 2 not 2 Okay, so you have to fill 2 slots 2 digits, right? So 2 into 1 is 2 and then 0 2 I have to write and then rest is same. So 98 minus 1 is how much 97 so product is 9702 You can take another example. Let's say you have 98 and 97 now. So how far minus 2 how far minus 3? So if you product it minus 2 into minus 3 is plus 6, but you have to write 0 6 Is it and then 98 minus 3? 95 so this is the product. So this is how you can go on calculating now. What happens when Let's say You have the the first when you plot, you know multiply the units digits Then you get more than 2 digits. So let's take that example as well. So this is fifth 6th one so example like 91 times 87 Okay, 91 times 87. How far is this minus 9? Is it and this one minus 13? Is it a minus 13 and minus 9? Is that okay? So now you multiply this 13 9s are 117 Okay, so now you have to write the only 2 digits of 117 13 9s are 117 You have to write only 17 and let this one be here. Okay, and now do the similar operation 91 minus 13 We'll give you 78. Is it it 91 minus 13 is 78 plus this carry. So 79 so product is 7917 you understood what to do in case of a Multiplication giving you more than 2 digits. Let's let's understand with another example. So let's say you are multiplying 93 and 84 Okay, now. How far is this minus 7 200 and this one minus 16 200 now? Let's multiply 16 and 7 minus 16 times minus 7 is 112 correct. So you have to remember those tables as well. So 112 so but I will write this one as a carry I will write the 12 Tens and the units place digits there like as as it is But I will carry the hundredth digit hundred place digit now do the same thing. So this is easier calculation So 84 minus 7 is 77 so 77 by this calculation and this one so hence it becomes 78. So the product is 7812 I hope you Understood this part Okay, now we will take up what happens when the numbers are Greater than 100 so that will take up in the next session