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 A cancellation fallacy (Posted on 2013-01-18)
Sometimes an arithmetic procedural error produces a correct answer.
An accidental cancellation is reducing a fraction by canceling individual digits in the numerator and denominator.

In some cases the result is equal to that obtained by a correct process.
Examples:
16/64 = 16/64 = 1/4;
26/65 = 26/65 = 2/5;
266/665 = 266/665 = 2/5;
49/98 = 4/8 = 1/2 etc.

Try to find two-digit cases in bases other than base 10,(e.g. 13/32 = 1/2 ( the only solution in base 4).

 No Solution Yet Submitted by Ady TZIDON No Rating

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 re: computer solutions -a partial errata | Comment 2 of 3 |
(In reply to computer solutions by Charlie)

CH,

e.g. in base 10

13/65=1/5   10         ok
15/75=1/5   10    not 1/7
16/32=1/2   10    nothing to cancel
16/64=1/4   10    ok
16/96=1/6   10    not 1/9
17/85=1/5   10     nothing to cancel
19/95=1/5   10    ok
26/65=2/5   10    ok
27/54=2/4   10    nothing to cancel
38/76=3/6   10   nothing to cancel
39/65=3/5   10  nothing to cancel
49/98=4/8   10   ok

Another example :.... different triviality, that can't come up in base 4 is exemplified by the decimal 21/42, where ....

Should be 1/2 not 1/4

Your output apparently lists cancellations that not necessarily produce the right answers...

Please check other bases as well.

 Posted by Ady TZIDON on 2013-01-18 19:38:23

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