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GS Chandy
Posts:
7,866
From:
Hyderabad, Mumbai/Bangalore, India
Registered:
9/29/05


Re: How to simplify an expression ...
Posted:
Oct 3, 2012 10:29 PM


John Lee posted Oct 3, 2012 12:17 AM (GSC's remarks follow): > > Dear Colleagues, > > I've noticed through the years that many students had > considerable difficulty simplifying the expression > below > on a test in Intermediate Algebra: > > [ (6 r^8 t) /(3 r^2) ]^3 > > I'm interested in seeing how you think students > should > approach this problem, and detailed steps they should > > take, along with precise assumptions/formulas they > should know and be able to apply correctly at each > step. > Thank you in advance. > > John Lee > Thanks, John  herewith some thoughts:
[(6 r^8 t)/(3 r^2)]^3 = [(N)/(D)]^3 {where N stands for Numerator and D stands for Denominator} = N^3/D^3 Difficulty!! Does the Numerator want to mean 6*(r^8)*t OR 6*r^(8*t)?
On the face of it, it could be either: i.e., the expression is ambiguous (as I believe the exchange between Dave Renfro and Peter Duveen has already indicated).
Where there is no ambiguity, the HOW? is easy enough. I'm pretty certain I can resolve almost any unambiguous expression more or less correctly  but I believe John had actually wanted to pose a couple slightly different and more complex issues:
HOW to teach this to a class of (questioning) students?
How to convince them that THESE particular steps will lead to a correct result, and THOSE steps are likely to lead to 'difficulties'? How to lead them through the many doubts they will surely encounter?
i.e., what John actually requires are the "WHYs?" involved: i.e., why we do It THIS way and not THAT way.
Sorry, at the moment I can't quite get my mind around that. I shall try and recall just how my school math teacher took me through the many doubts I must have had on this to throw some kind of light on the issue that now enables me to be able to do this kind of stuff reasonably well ... that's the best I can do  sorry about that!
However, I do believe the test expression put up for simplification should deal with a few plus and minus phrases in N or D or both.
(By the way, I am SO glad at this point that I'm not a schoolteacher with the HUGE responsibility of having to take young questioning minds through this!)
GSC ("Still Shoveling Away!")



