Algebric Proof for NIKHILAM NAVATAS’CARAMAM DASATAH (all from 9 and last from 10) — Vedic Mathematics

Posted: September 16, 2012 in Mathematics
Tags: , , , , , ,

This rule is applicable for multiplication of numbers which are near to multiples of 10..

General Format :

N1          D1

N2          D2

—————-

(N1-D2) or (N2-D1) / (D1 X D2)

Example:

97 X 94

Here base is 100

97          -3

94          -6

—————

( 94 – 3 ) / ( 3 X 6 )

= 9118

Proof:

Let the two numbers N1 and N2 be less than the selected base say x.
N1 = ( x – a ), N2 = ( x – b ). Here a and b are the corresponding deviations of the
numbers N1 and N2 from the base x. Observe that x is a multiple of 10.
Now N1 X N2
= ( x – a ) ( x – b ) = x.x – x.b – a.x + ab
= x ( x – a – b ) + ab
= x [( x – a) – b] + ab = x ( N1 – b ) + ab —————(1)
or
= x [( x – b ) – a] = x ( N2 – a ) + ab ———————(2)
x ( x – a – b ) + ab can also be written as
x[( x – a ) + ( x – b ) – x] + ab = x[ N1+ N2 – x] + ab —————-(3)

By following anyone of (1),(2) or (3) we can get the answer..

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