Sutra - All from 9 and the last from 10 (Explained)

This is an explanation to one of the 16 sutras of Vedic Mathematics. This sutra is popularly known as "All from 9 and the last from 10 ". This sutra (Original name- Nikhilam Navatashcaramam Dashatah) is helpful in making subtraction easy.


NOTE: This sutra is useful in cases of subtraction where a number is subtracted from a number being 10ⁿ   (example- 10, 100, 1000 and so on..)

RULE: All the digits of the number should be subtracted from 9 and the digit in the last place should be subtracted from 10. (Easy, isn't it?)

Starting with an easy example first:
Subtracting  1 0 0  -  5 3 

So, the answer becomes 47 . This was a example where the number we subtract is of same number of digit as the number of zeros in the number we subtract from (In our case, 100 has 2 zeros, and 53 is of 2 digit).

Now, what if the number of zeros is more than figures of the number being subtracted. Taking the same example as above,
Lets subtract  1 0 0 0  -  5 3 . 
In this case we simply suppose 5 3 as 0 5 3 :

So, the answer becomes  9 4 7.


Let's take one more example to make things more clear.
Now we'll subtract  1 0 0 0  -  2 6 7  (We see that no. of zeros and the figure in the number we subtract are same, similar to the first example)

So, the answer becomes 7 3 3.


Now, You must have found it very easy to understand. Why don't you try to solve some of them yourself?

Self-Exercises :-

a) 1 0 0 - 2 8             =
b) 1 0 0 - 7 6             =
c) 1 0 0 0 - 4 6 3       =
d) 1 0 0 0 - 6 3          =
e) 1 0 0 0 0 -  4 6 3 1 =


Answers: a) 7 2 (b) 2 4 (c) 5 3 7 (d) 9 3 7 (e) 5 3 6 9.