Posted by MathBard on October 18, 2002 at 11:58:15:
In Reply to: about the commutative properety of multiplication posted by T.Gracken on October 18, 2002 at 10:02:36:
:
: : : so if we have (1/2)x [but don't use parenthesis; as when writing with pencil], then we also have x 1/2 [commutative property of multiplication].
: : NOPE. The communative prop. applies to moving around TERMS. In the above above example you didn't really (although it SEEMS the same) commute the terms. there IS the procedure about stating the coeeficient BEFORE the variable for the very reason of avoiding the confusion to which you allude.
: : : does this mean that one half "x" is the same as "x and a half"?
: : I am an English teacher who got stuck teaching Algebra (because i can).
: I certainly can't argue correct English, but I do know the commutative property of multiplication.
: for your reference: the commutative property of multiplication is: if each of A and B is a number, then A*B = B*A
: so in my example, (1/2)x = x(1/2) IS justified by (none other than) the commutative property of multiplication.
Um i DO understand the commutative property and i am NOT arguing that,or saying that you didnt. Everyone knows that "5a" would have the same mathematical value as "a5" but are we going to use dipense with proper notation just because it will be an equal mathematical value. We have specific notation to avoid the very confusion you are pointing out. What's next? Rearranging the order of operations.
PS WE need a life if this is what you and i do with out spare time. I tip my sliderule to you in salute!