For the past two weeks we have been discussing how to multiply numbers below and above a particular base. Today, we shall be dealing with some more special cases of Nikhilam Multiplication. Let us consider an example:

Base=100

                     

88-12

X 87-13

___________

76/56

nAt the very onset identify the base of the numbers. Then find the compliment of both the multiplier and the multiplicand. The third step involves multiplication of the compliments.12 when multiplied by 13 gives the answer as 156. But since the base is 100 and the same contains two zeroes, only two digits can be written at the right hand side. Hence, we write 56 and carry 1 to left hand side. The fourth step involves cross substraction. And finally the carry has to be added to the value that comes out of cross subtraction. Let us explain another one special case with the help of an example.

Base =100

       112 + 12

X 111+11

__________

124/32

nAt the onset the base was identified as 100.The next step involves finding the excesses with respect to the base of both the multiplier and multiplicand. The third step involves multiplication of the “excesses”. 12 when multiplied by 11 gives the answer as 132.But since the base is 100 and the same contains two zeroes only two digits can be written at the right hand side. Hence we write 32 and “one” gets carried forward. The final step involves “cross addition”(112+11 or 111+12) with simultaneous addition of the carry to the same. In the next issue, we shall be dealing with multiplication problems involving mixed bases.

Solve the following:1) 114x112 2) 15x16 3) 14x16 4) 109x112 5) 109x114 6) 18x18 7) 18x17

Answers to the questions asked in the last issue:

1)10608, 2)11130, 3) 132, 4)1008012, 5)1008007, 6)156, 7)11025

The author a finance professional, and one of the youngest faculty members of World Academy for Vedic Mathematics, and conducts workshops on the subject. He can be reached at dheuyertaale@yahoo.com