Vedic Maths – Sutra 2. Nikhilam Navatashcaramam Dashatah ( All from 9 and the last from 10)


The sutra basically means start from the left most digit and begin subtracting ‘9’ from each of the digits; but subtract ‘10’ from the last digit.

To subtract 4679 from 10000, you can easily apply the Nikhilam Navatashcaramam Dashatah sutra ("All from 9 and the last from 10"). Each figure in 4679 is subtracted from 9 and the last figure is subtracted from 10, yielding 5321.

Examples

1. 1000-457

(9-4)(9-5)(10-7) = 543

2. 1000-54 = 1000-054 = (9-0)(9-5)(10-4) = 946

NIKHILAM APPLICATION: MULTIPLICATION – SPECIAL CASE – (Taken from N Sreenath’s Article)

In the following examples let us take two numbers and illustrate how to multiply them in a very quick way using Nikhilam sutra. Even though this technique works for any pair of numbers, we will look at a special case when the numbers are near a base such as 10, 100, 1000, etc. Let us start with a simple example.

Example : To multiply 8 and 7. Apply Nikhilam sutra “All from nine and last from ten” to the number 8 to get ‘-2’ (since there is only one digit so subtract by 10), and for the number 7 to get ‘-3’. Now write the following:

8 -2

× 7 -3

___________

• Multiply (-2) and (-3) to get ‘6’ and write it down as below.

8 -2

× 7 -3

________ 6_

• Next we ‘cross-add’. That is add 8 and -3 to get ‘5’ or add 7 and -2, to get ‘5’ as shown in the picture below. Note that in either of the operations you get the same answer that is ‘5’.

8 -2

7 –3

• We find the solution by combining the numbers we found by the above operations as:

8 -2

X 7 -3

__5_____6_ So the answer is ‘56’.

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