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===Casting out nines=== {{main|Casting out nines}} [[Casting out nines]] is a procedure for checking arithmetic done by hand. To describe it, let <math>f(x)</math> represent the [[digital root]] of <math>x</math>, as described above. Casting out nines makes use of the fact that if <math>A + B = C</math>, then <math>f(f(A) + f(B)) = f(C)</math>. In the process of casting out nines, both sides of the latter [[equation]] are computed, and if they are not equal, the original addition must have been faulty.<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Casting Out Nines|url=https://mathworld.wolfram.com/CastingOutNines.html|access-date=2020-07-22|website=mathworld.wolfram.com|language=en}}</ref>
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