Re: [Phys-l] How to divide numbers

[John Denker <jsd@av8n.com>]

On 03/05/2008 07:43 AM, Rauber, Joel wrote:

> Out of curiosity, the multiplication method, is it self-invented, were
> you taught it somewhere along the way . . .

I definitely wasn't taught these tricks.  My teachers thought
the tricks were somewhere between eccentric and stupid.

On the other hand, I can't possibly be the first person to 
think of these tricks.  The multiplication trick is not
completely the same but not completely different from the 
"carry save adder" that is sometimes used in computer hardware.
  http://www.google.com/search?q=carry-save-adder


> I like the look-up table method of division.  I don't see it as being as
> much different from the standard algorithm as your multiplication method
> (but beauty is in the eye of the beholder.)  The main advantage
> (difference) is the removal of guesses at the price of some beginning
> overhead.  But if one figures that in a large digit situation, one may
> make 1 out 2 or 3 bad guesses, not having to repeat the multiplications
> all the time for good and bad guesses pays dividends.  Plus it seems
> clear to me that it is less prone to error.

Yeah.

Which advantage you see as "the" biggest advantage varies from
situation to situation.

 -- For kids who are just learning long division, removing the
  guesswork has tremendous pedagogical advantages.  Just at the
  conceptual level, some kids are stuck on the idea that arithmetic
  should be exact, without any need for guessing.  I hope that
  eventually they will become good guessers, but the day we
  learn long division is not the time to press the point.  Let's
  learn one thing at a time.
 -- For multi-digit dividends, the speedup can be quite noticeable.
  (This is /not/ a good argument to use when kids are first learning
  the algorithm, because they are afraid of big multi-digit dividends.)
 -- Yes, I like to emphasize reliability and checkability.  It's
  one thing to tell kids to be more careful, and it's another thing
  to offer constructive suggestions on /how/ to be more careful.