 Let us learn the method of multiplication, which is very quick by finding out The base of the number so multiplication using the base of the number when we say we have to use the base of the number We also have to use the supplement of a number. So what if we were given two numbers like this? So we had 98 times 93 now how we can find out the multiplication of these two numbers So the first step is to write these two numbers like this. We will just quickly write the base of these two numbers in a small bracket the Base of both these numbers is 100. This is kind of a mental math procedure So you don't always have to write 100 But just need to remember that the base of both of these numbers is going to be 100 But we have to ensure in order for this method to work base of both the numbers should be same Now what we are going to write on the right side right hand side of each number is The supplement of both the numbers so supplement of 98 is going to be Minus 2 since supplement is basically number minus the base. So the supplement of 98 is going to be minus 2 The supplement of 93 is going to be 93 minus 100, which is minus 7 now once we have written this We are ready to get the answer and I really like this method a lot because it gives the answer very quickly So what we have to do is that we have to multiply The supplements together and write it down when we multiply the supplements we get minus 7 minus minus 7 times minus 2 which is 14 then we'll put a slash and then we combine Either pair of a number and a supplement of the other number So we could either say 98 minus 7 or 93 minus 2. So basically Both the things give us the same thing which is 91 and we just have to ensure that This is a two digit number because our base is 100 Consider we have two places to put our value here If this number was a three digit number carry will overflow on this side But in this case there is no carry. So our answer is 9,114 let's quickly do another example. So now let's multiply 105 and 113 let us quickly write down the base of both these numbers in a small bracket So that we can mentally note that down now What we need to do is to quickly write these two numbers like this vertically and then write the supplement of these two numbers The supplement of 105 is 105 minus 100 which is 5 And then 113 minus 100 which is 13 Now the next step is that we'll multiply these two numbers or the supplements Let me just put a positive sign here so that we know that the supplement is positive And the multiplication of the supplements is 65 We'll put a slash then we will perform one of the operations 105 plus 13 or 113 plus 5 In either case we get 180 note that since our base was hundred we have secured two places on the right-hand side There is no overflow and we can safely write our answer as 11,865 which is basically the multiplication of 105 and 113 I'll encourage you to verify this answer using a calculator or any conventional method that you know Again note that in order for this method to work Bases that both numbers have should be equal. Let us take one more example. So this example is 998 times 996 Let's quickly write down the basis which are closest to these two numbers Of course, these two bases need to be the same and the basis thousand year Now let's write down these two numbers in a vertical arrangement like this And then we will write the supplements on the right-hand side. Let's write the supplements in green So supplement of 998 will be 998 minus thousand which will be minus two and supplement of 996 will be 996 minus thousand which is minus four. Let's multiply minus two and minus four and we get eight But remember our base is thousand So the places available for the result of this multiplication are three So we will have to write zero zero eight in this case and then we'll put a slash and now we will combine either 998 and minus four or 996 and minus two both of which give us the same result which is 994 and so the answer in this case for the multiplication of 998 and 996 is 994,008 Now there is another explanation of why we put zero zero eight instead of just eight here So consider that the two steps that we do one is the multiplication of these two numbers and other is the Combination of the numbers at the end of the cross are separate results the multiplication of two three digit numbers is Going to be either a five digit number or a six digit number So whenever we have this result on the left, which is obtained by the the combination of say the numbers 998 and minus four Where we have 994 we are padding three zeros Because we want to add the result obtained by the multiplication of the supplements So we are adding this result into this number and the result is eight And that is why the answer is 994,008 Again from where these three zeros come from why not two or two zeros or one zero The multiplication of two three digit numbers is going to be a six digit number, right? The half of the result of this six digit result is obtained here by the combination of supplement and the other number So rest of the three digits are kept as zero and then the rest of the result is added to it I hope this explanation is clear