Multiplication by 9,99,999...

Multiplication with 9,99..

We will use a method ‘Ekanyunena Purvena’ for multiplying any number with 9, 99, 999, etc. This is a subset or derivative of Nikhilam method. We will take a simple example to begin with.

8x9

Step 1: subtract 1 from digits to the left of 9.

Step 2: Subtract the remainder of step 1 from 9.

Step 3: Combine the digits from steps above.

8x9 = (8-1) / 9 = (7)/(9-7) = 72

Answer: 8x9 = 72

73x99

73x99 = (73-1)/ 99 = (72) / (99-72) = 7227

Answer = 7227

6x99

6x99 = (6-1)/99 = 5/(99-5) = 594

Answer = 594

643x999

643x999 = (643-1)/999 = (642)/(999-642) = 642357

Answer = 642357

53x999

53x999 = (53-1)/999 = (52)/(999-52) = 52947

Answer = 52947

If you observe, we have taken examples where both the operands are of same number of digits or the number we operate on has lesser number of digits than our 9s set operand. Now a question arises, what to do if we number we operate on  to be of higher number of digits?!! We will see VM handles such cases.

738x99

Step 1: Split the number with right side having same number of digits as 9s set. =>7/38

Step 2 : Subtract from number (738), one more than the left hand side digit => 738 – (7+1) = 738 – 8  = 730

Step 3 : Find the Nikhilam of right side digits => (100 – 38)  = 62

Step 4 : Combine the steps 2 and 3 => 73062

Answer is 73062

43967 x 9999

43967 x 9999 = (43967 – (4+1))/(10000-2967) = 439627033

Answer is 439627033

Simple and amazing!!! Is n't it? If you have suggestions or questions please post it here.