B R TR R Y

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40 THE FASCINATION OF NUMBERS

roots of the individual numbers, then the total number is in-
correct. In other words, all additions can be checked by
checking the digital roots.

Thus, 64321 Root=%
13679 » =8
5032 N =i

Add: 83032 16 (Reducing to 7)

The digital root of 83032 is 7, and the total of the individual
roots also reduces to 7.

Before proceeding further, it is to be noted that this is not
an infallible check for additions. Although an addition can-
not be correct if the roots are not in the right relationship, it
does not follow that an addition is necessarily right because
the roots are correct. Because all negroes have curly hair, it
does not follow that all people with curly hair are negroes.

In the example:

5432 Root=5
1618 . ==y
Add: 7005 Add: 12

Final Root g 3

the roots agree but the addition is incorrect. This is because
the digits in the total are correct but in the wrong order. The
correct total is 7050 and this obviously has the same root as
7005
In the same way, the extraction of digital roots will not
reveal any error where the difference between the correct
and incorrect totals is a multiple of g, since we have already
noted that the number x will always have the same root as
% plus or minus q.
Subject to the same qualifications, subtraction can be
checked by deducting roots.
64321 Root =%
12120 & 6

 

Subtract: 52201 Subtract: 1