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re: order of ops
Posted:
May 16, 1995 8:59 AM


>>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 = 20
It's a matter of semantics. The associative property (for example) still holds; it's a property of the operations, not the notation. However, a student may need clearer wording of the property. After all, ShariV@aol.com's solution (the first one) may not be how one student might think of the associative property, although it's perfectly validbecause of the 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 to calculate the parentheticals first; but because of order of operations, both will 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 unlikely that we would write something like 3A + 2, as I believe someone used in one argument. It seems more likely that we would write 3 x A + 2; the closeness of 3A makes it more natural to want to do that operation first. It seems to me (although I have not done any research) that at least some of our notation (such as exponents, removal of multiplication signs, and of course parenthesis or lack thereof) is useful *because* of the order operations conventions.
Eric E. Karnowski Mathematics Editor Janson Publications, Inc.



