All from 9 and the last from 10

The second sutra "Nikhilam sutra" literally means " ALL FROM 9 AND THE LAST FROM 10 " helps in performing instant subtraction.

Before proceeding further, let me tell you about Place Value of any number .

The Place Value of 187

Place value of 7 is 7 units

Place value of 8 is 8 tens

Place value of 1 is 1 hundreds

For the number 1623

Place value of 1 is 1 thousands.

Now to our "All from 9 and the last from 10" sutra :

Example 1 :1000-687= ?

We have to subtract the last unit digit from '10 ' and the tens and thousands from the number ' 9 . Here our number is "687" in which the Units digit is 7 ,Tens is 8 and Hundreds is 6. So applying our sutra ,

7 from 10 = 3

8 from 9 = 1

6 from 9 = 3 ,we get the value 313.

Therefore , 1000-687 = 313

Example 2: 10000-5674=?

4 from 10 = 6

7 from 9 = 2

6 from 9 = 3

5 from 9 = 4 , We get the result as 4326

Therefore, 10000-5674 = 43264

With enough practice ,you will be able to calculate them mentally.So keep practising.

This sutra is effectively applied in case of multiplication of numbers near to base 10,100,1000 etc. (power of 10)

Case 1:When both the multipliers are lower than the base
Case 2:When both the multipliers are higher than the base
Case 3:When one number is more and the other less than the base

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