```Date: May 16, 1995 8:59 AM
Author: JansonEdit@aol.com
Subject: re: order of ops

>>4(3 + 2)   =   4 x 3 + 4 x 2>> 4(5)  =   12 + 4 x 2>>20   =   16  x  2>>20  =  32 >4(3 + 2)  =  (4 x 3) + (4x2)>      4(5)  =  12 + 8>       20  =   20It's a matter of semantics.  The associative property (for example) stillholds; it's a property of the operations, not the notation.  However, astudent may need clearer wording of the property.  After all,ShariV@aol.com's solution (the first one) may not be how one student mightthink of the associative property, although it's perfectly valid--because ofthe order of ops conventions.  jsuggate@chch.planet.co.nz's (the second one)is another way to think of it which will work as long as you know tocalculate the parentheticals first; but because of order of operations, bothwill work.   If we throw the conventions out (not that I think we should!),we simply may have to reexamine how we have stated things.Of course, if we removed the standard order of operations, it seems unlikelythat we would write something like 3A + 2, as I believe someone used in oneargument.  It seems more likely that we would write 3 x A + 2; the closenessof 3A makes it more natural to want to do that operation first.  It seems tome (although I have not done any research) that at least some of our notation(such as exponents, removal of multiplication signs, and of courseparenthesis or lack thereof) is useful *because* of the order operationsconventions.Eric E. KarnowskiMathematics EditorJanson Publications, Inc.
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