Re: HELP!! (implied multiplication)

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Re: HELP!! (implied multiplication)

>I am a high school teacher at Northern HS in MD.  Our faculty has been
>recently debating an issue that up until yesterday seemed quite simple.
>We would like your help in resolving the issue.
>
>The problem:  Evaluate   10/2x when x=4.
>
>Some of our faculty seems to think that 2x is like an understood group.
>Therefore, 10/8=1.25. ...
>
>On the other hand, according to the order of operations, mult and div go
>left to right, so 5*4=20. ...

I'm not sure this issue can really be "resolved" -- it's just one of those
bits of mathematics that is open to debate!

I think the breakdown is that the 80, 81, 82, and 85 all treat implied
multiplcation as having a higher precedence than "ordinary" (explicit)
multiplication (and division).  The newer calculators (83, 86, 92, and [I
assume] 89) all treat implicit multiplication the same as explicit, and
therefore follow the "usual" order of operations.

The scheme followed by the earlier calculators has its merits (and
devotees); for example, one might argue that 10/2x is a fairly natural (if
somewhat casual) way to write what might be typeset as

     10
     -- .
     2x

As I understand the story, TI abandoned this scheme because teachers
complained that it was confusing their students.  I can recall several
instances where I asked students to graph (e.g.)

     1
     - x + 2
     2

and then found students who got a hyperbola instead of a line.  (I would
have hoped that they would have known something was wrong when they looked
at the graph, but ....)

Now on tests and quizzes I make sure to ask students to graph 0.5x+2
instead, just to avoid the potential snags that those with older
calculators might encounter.  (I save the discussion of such snags for
class time.)

Darryl K. Nester                E-mail: mailto:nesterd@bluffton.edu
Assoc. Prof. of Mathematics        WWW: http://www.bluffton.edu/~nesterd
Bluffton College                 Phone: 419-358-3483
Bluffton, OH  45817-1704           Fax: 419-358-3232
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