 Hello and welcome to another session on speed maps. And now we are learning how to multiply two digit numbers, which are near 100 in the previous two sessions. We saw how to multiply numbers which are just less than 100 or just above 100. So both the numbers were either just less than 100 or both of them were just above 100. In this session, we are going to take up the case three. And that case is when one of them is, let's say you're doing this multiplication where A is greater than 100 and B is less than 100, then how to do it faster? Okay, so examples would be, let's say you are multiplying 97 to 103. The process remains almost the same, right? So 97, how far or what is the difference between 97 and 100? And that is minus three. So you have to check the sign as well. So basically you're doing the number minus 100. Similarly here, 103 minus 100 is simply three, correct? So this is plus three away from 100 that 97 is minus three away from 100. So I understood, I hope you understand what it means. Now guys, when you repeat the process and I have to multiply these numbers, so minus three times plus three is minus nine. But then minus nine cannot be written in the product. So what to do? So the moment I see minus nine, what I do is I subtract nine from 100. So what should I add? Or if I add 100 to it, so just add 100 to this number. Just add 100. So the moment you add 100, you will get 91. Isn't it? 91, okay? Now, how many hundreds did you add? Just keep account. So you just made one, you added 100. So let me write this one here, okay? Now what? Now repeat the process. So 103 minus three is one, zero, zero. But since you have taken 100 out, so you'll have to just subtract, so whatever you get as a sum. So hence the sum is one, zero, zero. So you have to reduce this one from here. So it will be 100 minus one, that is 99. So this is the product, 9991, okay? I hope you understood. Otherwise, let's take another example for more clarity. Okay, another one. So let's say you are taking 96 and 104. Similar numbers, okay? Here you'll get minus four, and here you'll get plus four, isn't it? Now plus four, minus four is minus 16, right? It's minus 16. I just need to add only 100, right? To make it a positive digit, two digit number. So add 100, so write this one here. So add 100, how much you get? 84, isn't it? Now you do the same process. 96 plus four is 100, but since you borrowed 100 already, so you have to, so 96 plus four is 100. So I'm doing this. I will not be writing all the steps while doing it. It is just for you to understand. So 96 plus four is 100, but there was one one here. So remove that one, and you get 9984 is the product, right? Another one, another one. Let's say I have 95 multiplied by 104, okay? 95 multiplied by 104. So what do we get? You get minus five and plus four, right? Multiply minus 20, right? Add 100 to it, and this will be 80, and one you write here. Then you do this operation, 95 plus four is 99. Take away this one. So 98, so the product is 9880, okay? I hope you're following this. Another one, 96 into let's say 109, okay? So here minus four, here plus nine, correct? So nine into four minus 36, right? And then plus 100, you add it to make it positive, you'll get 64, right? 64 and this one has to be counted here because now when I'm doing this 96 plus nine or 109 minus four, whichever you your choice. So 109 minus four is 105, then take away this one from here. So 105 minus one is 104. So this is the product, 10464. Now what happens if the number to be added is more than 100? So you take, you learn that as well. So let's take an example of such cases. For example, I am doing 91 into 112. This is the multiplication I have to do. So 91 is nine away, right? And 112 is 12 of it. Now if you see 12 times nine is how much? One not eight, so minus one not eight, okay? Now if you add 100, still it will be a negative number. So hence minimum you have to add 200 out of it. 200 to it, right? If you add simply 100, you will get minus eight. So you have to add 200, right? So if you add 200, what will you get? You will get 92. These will become the last two digits of the product 92. But since you added 200, so keep two here. And now do the same process 112 minus nine is 103, but you have to take away this two from here. So 101, this is the product. Once again, what did I do? I multiplied nine and minus 12. So the moment I did it, I got minus 108, but I have to make it positive. I can't have negative number in the product of two positive numbers. So I have to add multiples of 100. So if I add simply 100, still it will not help. So hence I am adding 200, twice of 100. So when I add 200, I will get 92. 200, two, one, not eight, minus one, not eight will get you 92. But in that process, you have borrowed 200. So I'm just writing two here. And then I repeat the process where I add 112 to minus nine. So I get 103 and then take away this two from it to get 101. So 103 minus this two is 1019, right? And 10192 is the final answer, correct? Now, during understanding, it might take a little bit of more time to getting yourself acclimatized to the process. But if you do multiple number of times, I'm sure you will be able to ace it and you will be able to do it much faster. So after this, you can try the practice sessions on our plot LMS. And then you will be better equipped with these techniques.