Multiplication

Sutra : " Nikhilam Navatashcharamam Dashataha "

Meaning : All from 9 and the last from 10.



Upasutra : "Aanurupyena "

Meaning : Proportionately



This simple sutra teaches us to do multiplication of numbers which are close to a BASE or Aadhara such as 10, 100, 1000, 10000 etc.





Consider the example given below

8 * 13



Step 1 : Since 8 and 13 are close to 10 we shall consider 10 as the base.



8 - 10 gives -2 and

13 - 10 gives +3



Step 2 : Write the problem as below



8 -2

13 +3



Step 3 : For the first part of the answer add diagonally.

i.e. 8 + 3 Or 13 - 2 == 11



Write it as 8 -2

13 +3

11 0

( One '0' is added because the base is 101)



Step 4 : For the second part multiply the number in the RHS column and put it below zero and total to obtain the final answer.



8 -2

13 +3

11 0

-6

10 4



Hence the Answer is 104.





Example 2 :



Consider 945 * 1005



Here the base can be considered to be 1000

Therefore the problem is written as



945 -055

1005 +005



By Diagonal Addition

945 + 005 == 1005 - 055 == 950



945 -055

1005 +005

950 000

By linear multiplication of RHS

-55 * 5 = -275



945 -055

1005 +005

950 000

-275

949 725



Hence the answer is 949725



Aanurupyena



An Upasutra or Sub Formula of Nikhilam is Aanurupyena which means 'Proportionately'.



Here we consider multiples and sub-multiples of the Main Base as the Working Base.



Consider 53 * 57

Let us consider the working base to be 50, which is a sub multiple of the main base 100.



Let 'x' be (Main Base) / (Working Base)



Here x = 100/50 = 2

Write the numbers as in normal Nikhilam



53 +3

57 +7

60 00

(Two '0' s are added here as the Main Base is 100)



Now divide the first answer by x , here 2



53 +3

57 +7

30 00

Now do the second part as in normal method



53 +3

57 +7

30 00

+21

30 21



Hence the Answer is 3021.