Re: [MLUG - DISCUSSION] Lost knowledge (was: Broadband besides DSLor cable)

[Mike Miller <EMAIL:PROTECTED>]

On Tue, 1 May 2001, Mikhail Kovalenko wrote:

[snip]
> Jonathan King wrote:
>
> > Now, I was *shocked* to find out the other day that today's undergrads
> > were never taught how to perform the procedure we were taught as "casting
> > out nines".
[snip]
>
> Would you like to explain a bit more here?


I'll just add that I might have forgotten it, but I don't think I ever
learned "casting out nines" either.  On the other hand, I certainly
learned enough to be able to see immediately how it works.  I did learn at
some point in grade school that the remainder for a number after division
by 9 was always equal to the remainder for the sum of the digits of that
same number after division by 9.  So..

     3,451,236 has the same remainder as 3+4+5+1+2+3+6 = 24
and         24 has the same remainder as 2+4 = 6.

Thus the remainder of 3,451,236 after division by 9 equals 6.

This fact leads pretty easily to the "casting out nines" method of
arithmetic checking, but I'll leave verification to the reader.  :-)

Mike

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