Anomalous cancellation

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An anomalous cancellation or accidental cancellation is a particular kind of arithmetic procedural error that gives a numerically correct answer. An attempt is made to reduce a fraction by canceling individual digits in the numerator and denominator. This is not a legitimate operation, and does not in general give a correct answer, but in some cases the result is numerically the same as if a correct procedure had been applied.[1]

Examples of anomalous cancellations include 64/16 = 64/16 = 4/1 = 4, 26/65 = 26/65 = 2/5, and 98/49 = 98/49 = 8/4 = 2.[2]

The article by Boas analyzes two-digit cases in bases other than base 10, e.g., 32/13 = 2/1 is the only solution in base 4.[2]

[edit] References

  1. ^ Eric W. Weisstein, Anomalous Cancellation at MathWorld.
  2. ^ a b Boas, R. P. "Anomalous Cancellation." Ch. 6 in Mathematical Plums (Ed. R. Honsberger). Washington, DC: Math. Assoc. Amer., pp. 113-129, 1979.