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68 THE FASCINATION OF NUMBERS

The procedure for dividing a number by g is as follows:

(1) Divide the first two digits by 10, giving an answer
‘@’ and a remainder ‘5’.

(ii) Write the number ‘a’ as the first digit of the quotient
in the usual way.

(ii1) Add the numbers ‘@’ and ‘4’ together and carry this
total forward to the next digit of the numerator,
giving the number ‘¢’.

(iv) Divide ‘¢’ as in (i) above and proceed as before.

The working is:

6
9)2 35 I I7 1 (2567 and remainder 8

We first divided 23 by 10. This gave 2 and a remainder of 3.
2 added to g gives 5 and this is thus the carry-forward to the
next digit, 1. We then divide 51 by 10. This gives 5 and a
remainder of 1. 5 added to 1 gives 6 and this is carried for-
ward to the next digit, 1.

It is true, of course, that in the ordinary way, division by
9 can be carried out mentally without recourse to this
method, but the value of the foregoing demonstration is in
the fact that the system can be applied to much more com-
plicated divisions with equal facility. By its use we can divide
by numbers like g9 or 999 in only one or two lines of working.

The usual way of dividing is:

99 ) 123456789 (12 ... etc.
99
244
198
465
etc.
and this takes up 13 lines of working.
It is easier to proceed by the other method as already
shown, and the following explanation will clarify the reasons.
If we divide by g9 into 100, the answer is 1, plus a re-
mainder of 1, and it will be found that any number of hun-
dreds, when divided by g9, will always give an answer equal