### 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 10^{n } (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.

## 7 comments:

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It is awesome .... thanks

itz fun learing...things so easily

The best easy methods for hole life maths problems

Really Good

To learn these is the best way to revere old Rishi s.

Thanks...

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indian geniuses had been so great that they gave us such amaizing formulas

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