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A cancellation fallacy (Posted on 2013-01-18) |
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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).
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