Recipricals and Division
Why do we have to use reciprocals in dividing fractions?
At first glance this question, "Why do we use reciprocals in division?"
seems rather trivial. However, after some reflection, the question really
raises two very fundamental concepts: "What are 'numbers'?" and "What are
'mathematical operations'?" Consequently, to answer the question properly,
the definition of these terms must be laid out precisely.
To do this it was necessary to append my answer in a "msworks" document
because e-mail does not give the necessary flexibility of choices of letters
and characters needed.
It's a little spooky, I had a very similar question asked of me on a
take-home exam in freshman calculus many years ago!
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Update: June 2012