Mathemagic - Magical Methods Of Quicker Calculations

 

 CHAPTER 1

Nikhilam Method

Let us begin our journey into the magical world of Vedic Maths with a very simple technique - Nikhilam Method for subtraction, one of the easiest operations on numbers. Some of the important techniques in the following chapters are based on this technique.

Subtraction :

Subtracting one number from another is not at all difficult. One can easily do it using any of the normal methods learnt in schools. But if we have to subtract from numbers like 100, 1000, 10000,..... it can be made easier by using Nikhilam Method from Vedic Maths.

For Example : Consider the following subtraction.

10000 - 7368 = ?

Normal Method : 

    1 0 0 0 0

    -  7 3 6 8

————————

       2 6 3 2

We borrow 1 from the left end1 and continue doing so till wer reach the right most digit; leaving 9 in each column and 10 in the last column.

Then we subtract the unit's digit 8 from 10 and write down 2 as the unit's place of the answer. The second last digit 6 is then subtracted from 9 to get 3 as the second last digit of the answer.We continue the process till the left most digit is subtracted.The borrow operation (carry) used in this method is bit time consuming.

Nikhilam Method :

This Vedic method of subtraction is based on the sutra "निखिलमऽ नवतः चरममऽ दशतः" which means "Subtract all from 9 and the last from 10".

           1 0 0 0 0

          -   7 3 6 8

        ——————

Here we have to subtract the last digit 8 from 10 and the rest three digits 6, 3&7 from 9.

     (9-7) (9-3) (9-6) (10-8)

        2       6       3         2

The last digit is subtracted from 10 and the rest from 9 and the result is 2632.

Do it from left to right or right to left, either way it's equally easy and comfortable.

Example 2.  100000 - 85437 = ?

Subtract the first four digits 8, 5, 4&3 from 9 and the last digit 7  from 10 to get direct answer.

    (9-8)  (9-5)  (9-4)  (9-3)  (10-7)

       1        4        5        6          3

And the result is 14563.

100000 - 85437 = 14536.

Example 3.  50000 - 2754 = ? 

This subtraction is same as  10000 - 2754. The only difference  is we borrow 1 from the left most digit 5.

    (5-1)  (9-2)  (9-7)  (9-5)  (10-4)

       4        7        2        4          6

And the result is 47246.

Example 4.  7 - 0.1832 

Here, write down 7 as 7.0000 and rest everything is same as in Example 3.

            7.0000 

         -  0.1832

       -----------------

Borrow 1 from the left most digit 7. Subtract the three digits 1, 8 & 3 from 9 and the last digit 2 from 10 as follows,

  (7-1)  (9-1)  (9-8)  (9-3)  (10-2)

     6        8        1        6          8

And the answer is 6.18168.