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 = 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 valid--because 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.