MULTIPLYING BY 11, 12 & 15

 VEDIC MATHEMATICS
MULTIPLYING BY 11
Antyayoreva (sub – sutra)
only the last 2 digits

Nought Placed at both ends.

Add the final digits 

Continue to add adjacent digits

For Example:

13423 x 11

0134230

0+1     1+3    3+4   4+2    2+3    3+0

147653 

43211 x 11

0432110

0+4    4+3   3+2   2+1   1+1  1+0

475321

MULTIPLYING BY 12

sopantyadvayamantyam

The ultimate and twice the penultimate

Nought sandwich

Ultimate digit is 0

Penultimate digit is 4

The ultimate plus twice the penultimate is 

For Example:

65214 x 12

Ultimate 0652140

0+8 = 8

4+2 = 6

1+4 = 5

2 +10 =12

5+12+carry 1 =18

6+0+ carry 1 = 7

782568

Multiplying by 15

Multiplying by 15 can be broken down into a multiplication by 10 plus a multiplication by 5. Multiplying by 10 is just a matter of adding a 0 on the end of a number, multiplying by 5 is half of a multiplication by 10 as above e.g.

15 x 33 

= [10 x 33] + [5 x 33] 

= 330 + [(10 x 33) / 2] 

= 330 + [330 / 2]

 = 330 + 165 = 495

e.g. 

to multiply 15 x 27 

you first multiply 27 x 10 giving 270, 

then 'add half again',

 i.e. half of 270 is 135, 

add this to 270 to get 405 

and 

that's your answer

 

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