MULTIPLICATION WITH A DIFFERENCE 79

The principle of multiplication and division in successive
stages by the number 2 can be applied to division in exactly
the same way since the division of one number by another is
the same as multiplying the first by the reciprocal of the
second number. Thus 994 can also be represented as
99 X+ and we can proceed as before:

 

99 ¥

9 1

LV

® N
5w

3 4%

Lol

997 = 144

 

This method is, of course, quite impracticable for present-
day needs but was of very real assistance at a time when men
found great difficulty in multiplying large numbers. It is in-
cluded here mainly because it makes use of the knowledge
of how numbers are made up and serves to emphasize the
nature of that structure.

It is a well-known fact that the squaring of a number con-
sisting of a whole number and the fraction }, can be carried
out by adding # to the product of the whole number and the
next whole number.

Thus,

(73)*=7x(7+1) +}=56%
This is because:
(x+3)*=x+x+}
=x(x+1)+%
So that
(743)2=7(7+1) +} as above

The same principle can be applied to all numbers end-
ing in 5.

A PR

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B R R PR R TAORE

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