the division in the casting out nines is not clear to me. In the given example he got a 8 and a 4, and later he got an 8 and a 3. Shouldn't it be an 8 and a 4 (or 3) in both?
casting out nines: division
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$\begingroup$
arithmetic
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0The tag "division-algebra" ought to mean something different. – 2011-04-04
1 Answers
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The example seems to be:
$275462 \div 877 = 314 \quad \text{ r. } \quad 84 $ which which can be checked by casting out nines and verifying $\quad 8 \quad \quad \equiv \quad 4 \quad\times \quad 8 \: \quad + \: \quad 3$ (modulo 9).
In fact what is being checked is the equivalent multiplication statement
$275462 = 877 \times 314 \quad + \quad 84 $
which could also be written as
$(30606 \times 9 + 8) = (97 \times 9 + 4)\times(34\times 9 +8) +(9 \times 9 + 3)$
and (modulo 9) all the $\times 9$ terms are equivalent to 0.
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0Ow, I got it, the 4x8+3 is for checking the division.. I think I was too asleep to other day.. XD Thanks! – 2011-04-10