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70 THE FASCINATION OF NUMBERS

similar manner. Thus, to divide by any number ending in g,
divide by that number increased by 1, and proceed as before.
In other words, to divide by 19, 39 or 79, divide instead by
20, 40 or 8o respectively and make the necessary adjustments
at each stage.

If the divisor ends with the digit 8, the principle may still
be employed, but with a difference.

100-98=1 and 2 XTI over
600+-98=6 and 2 Xx6 over
x¥(100)=-98=x and 2x over

Therefore, to divide by 98, we can still divide by 100, but
this time each quotient must be doubled before it is added to
the remainder to form the carry-forward.

To divide 123456789 by 98, proceed as follows. Divide 123
by 100, giving 1 and 23 over. Write the quotient 1 in the
answer. Double this quotient and add to 23 (=25) and carry
this amount forward. Divide 254 by 100 and proceed as
before.

25 58 o5 g 6

4 1 30
9Pt & 3 ¢ 5,00 9. 8 gl
1ot g g ah g tand ER . Over)

 

 

Similarly, to divide by 97, we can divide by 100 and obtain
carry-forward figures by trebling each quotient before adding
in the remainder. Again, to divide by g6, divide instead by
100 and quadruple each quotient before adding the remainder
to find the carry-forward.

If the divisor ends with the digit 5 or a smaller digit, the
same principle can be utilized if both divisor and dividend
are both multiplied by 2 or 4. Thus to divide 1234 by 5,
divide instead 2468 by 10. Similarly, to divide 1234 by 22,
multiply both by 4 and so divide 4936 by 88 (i.e. divide by
go and make the necessary adjustments.)

To divide by 101 it should be noted that the divisor can
be written 1001, in the same way as 99 can be written
100 —1. It is logical therefore that, to divide by 101, it should
be possible to divide by 100 and make adjustments.