Bridge-tied load

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 rare cases the result is numerically the same as if a correct procedure had been applied.

Examples of anomalous cancellations which still produce the correct result include:

${\frac {64}{16}}={\frac {\!\!\!\not 64}{1\!\!\!\not 6}}={\frac {4}{1}}=4$

${\frac {26}{65}}={\frac {2\!\!\!\not 6}{\!\!\!\not 65}}={\frac {2}{5}}$

${\frac {98}{49}}={\frac {\!\!\!\not 98}{4\!\!\!\not 9}}={\frac {8}{4}}=2.$

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.

References

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