MT 007.02 / SL 266.01
Ideas in Mathematics: The Grammar of Numbers

Exercise: Nikhilam multiplication

Multiplication rules:

1) choose as base a power of ten nearest to the numbers to be multiplied
2) put the given numbers over each other
3) subtract each given from the base and put the deficits on on the right with connecting minus signs.
4) separate the two parts of the product with a virgule (|) [or a slash]
5) multiply the defits to get the RH product
6) get the LH product in whatever is the easiest of four ways:

1. given1 + given2 - base
2. base - def1 + def2
3. cross subtract given1 - def2
4. cross subtract given2 - def1

algebraically:

• (x - a) (x - b) = x (x - a - b) + ab
• (x + a) (x + b) = x (x + a + b) + ab

1. Demonstrate the following multiplications, using the nikhilam method:
a) 8 x 7
b) 8 x 6

c) 6 x 6
d) 6 x 5

e) 88 x 96
f) 56 x 98

g) 88 x 91
h) 88 x 88

i) 96 x 98
k) 97 x 97

l) 598 x 998
m) 888 x 991

n) 99979 x 99999

2. Choose any two examples with a differing number of digits and demonstrate the applicability of the algebraic formulae to the calculations you carried out.