Quote:
Originally Posted by island911
I just trudged thru this thread, and it does have some redeeming value - now we know the stiffies who will demand that the eqn. as written, is w/o ambiguity because "  third-grade rules always dictate mathematical syntax! . . .damnit! "
btw, Dari (you strange old fart) I did plug the eqn in to both my HP calc and into Mathcad (both eqn writers) and both gave 2. --the mult next to the bracket forces priority multiplication in the denominator. |
This pic shows the isse w/ using technology to get answeres rather than knowing the rules of math
if the person that wrote the calculator code doesn't know the rules he will get the wrong answer
2/3 and 2÷3 are identical
2(3) and 2x3 and 2 • 3 are identical too(I know it looks like a dot product which is something else but it was either that or use a *, I chose the lesser of 2 evils)
2x3(4) is still 2 multiplications that by rule are done left to right unless another rule allows something different(
there is no rule that says that 3(4) takes precedence over 2x3)
6(4)
24
in this case the commutative property of real #s under the multiplication operation allows the transposition of 3 & (4) & 2
(4)3 x 2 or (4)2 x 3 are the same as 2x3(4)
apparently everyone remembers that a parenthesis alters the operator precedence, but only for operations that occur inside the parenthesis and have no operator on the outside of the parenthesis so there is no debate as to the first operation here. Some would be confused if there was an exponent on the parentheses, but if it is remembered that the exponent is a unary operator that only operates on the inside of the parentheses no issues will result. note that multiplication is a binary operation whether it is implicit 2(3) or explicit 2x(3), and if it is paired w/ another operation 2+2(3) 2(3) is done first because multiplication takes precedence over addition, if it was 2÷2(3) the division takes precedence because when 2 binary operations are at the same precedence level the left to right rule is in effect
48÷2(9+3)
48÷2(12)
we are now left w/ an expression that has 2 hierarchically identical operators, division and multiplication which must be done left to right by rule
24(12)
now there is only 1 operation, multiplication which removes the parenthesis
288
here are the rules
1) perform all grouping operations, Grouping Symbols:
Perform operations inside first.
( ), [ ], { }, square root, fraction, absolute value (yes, square root and fraction are grouped operations)
2) multiplication and division from left to right
3) addition and subtraction from left to right
commutative, associative and distributive properties when properly applied can alter the precedence.
the issue as I see it is that some people that don't know the rules as well as they should seem to be applying an associative property incorrectly
they want to make this
48÷2(9+3) into this 48÷(2(9+3)) the only rule that allows the addition of a grouping symbol is the associative property of addition or the associative property of multiplication which says that 2x3x4 is the same as 2x(3x4) or 2+3+4 is the same as 2+(3+4)
the associative property does not work for division or subtraction and so the addition of the explicit grouping is not allowed for 8÷2(9+3)
8÷2(9+3) does not equal 8÷(2(9+3)) because the associative property only works w/ pure multiplication or pure addition