MULTIPLICATION WITH A DIFFERENCE 75

Superficially, the remarkable things about this method of
calculation are (a) in dividing, remainders are ignored, and
(b) the even numbers in the left column are always deleted;
yet the answer is always correct. This is to some extent ex-
plained by the fact that all even numbers are composed of
varying powers of 2, and that all odd numbers are, in reality,
even numbers plus 1. This will more clearly be seen from the
following table.

1=1I 5=2241

2 =2 6=2%42
3=2+1I 7=22+2+1
4=23 8=22

As the numbers increase, new factors appear at certain
stages. These factors are in order 1 (or 2°9), 2 (or 21), 22, 23,
etc. A few examples of simple multiplication are now helpful.
In

(a) 2 x10, the columns will be

2 10
I 20

To obtain the answer the second term only is taken.

(b) for 3 x 10, we have:

3 10
I 20

To obtain the answer,
the first and second terms are taken.

(¢) for 14 X 10, we have:

14 10
” 20

40

I 8o

To obtain the answer,
the second, third and fourth terms are taken.

Mo TS S

o R e AR R SRR TR oA

g

SR T

i

T
RIGHIR

R