Order of Operations in an Equation

Date: 9/13/95 at 16:57:1
From: Anonymous
Subject: Algebra

We have a controversy here at our high school math department over a very
simple question.

Let c = 4.  Find: 16 divided by 2c.  (Place a division symbol where the words
divided by appear, since that key is not on my keyboard.

Is the answer 2, since 16 divided by 8 is 2, or is it 32 because order of
operations tell us to multiply or divide from left to right?

Date: 9/13/95 at 17:16:3
From: Doctor Steve
Subject: Re: Algebra

Here's my fairly informal response off the top.
     
The order of operations is for evaluating expressions but 2c is a number,
not an expression.  Another way to put this is that there's an implied set
of parentheses around 2c.  You could rely here on the definition of number
which should include some phrase such as "a continuous string . . ." and 
this would make clear 2c's status.

-Doctor Steve,  The Geometry Forum