[Bill Verburg]

Originally Posted by island911

Yeah, those idiots who programed those HP calc's. ...and to think that NASA was so stupid to use those devices for alt landing program for the space shuttles.

the proof is right before your eyes, and you still try to deny it,
one of these is wrong

Originally Posted by island911

I should point-out that both the HP and Mathcad eqn writers give a graphical (non-ambiguous) representation of the entry.

and yet one of the above is wrong

Originally Posted by island911

No. They MAY be identical. ...but when it comes to writing logical mathematical groupings they are not.

In what classroom did you learn that little tidbit? It must have been the same one where you learned that in 48÷2(9+3) multiplication by 2 comes before the division by 2,

again there is no rule that tells you to do the binary multiplication on the parenthesis first,
there is a rule that says when operations are at the same precedence level, do left to right.
There is a rule that says perform all operations inside the parenthesis first.
There is a rule that says that unary operations like exponent on a parentheses are done first.

To reiterate, there is no rule that says to multiply by a parenthesis comes first, if you think there is find it in a credible source and post a link to it, I double dog dare you


adding the laws of logic to the laws or arithmetic and algebra to evaluate the expression does not change the result as there are no logical operators present in the given expression, merely the binary arithmetic operators and a parenthesis
2(3) and 2x3 and 2 • 3 are identical because they all simplify to the same result and they are the same as 3(2) and 3x2 and 3 • 2 because of the commutative law and are the same as 3^2 - 3 and 3^2 -(-2-1) etc.

Originally Posted by island911

If you want to stamp your feet and demand that everything anyone needs to know about math operations, they learned in the third grade, then so be it. ...but the OP eqn is intentionally ambiguous. And,this inconsistency in notation is nothing new. ...just as is the eqn 1/2x (read: is that .5*X ? ...or 1/(2x)

If they were taught correctly and learned correctly, yes. It's obvious that math was either incorrectly taught or learned by a lot of folks. There is nothing inconsistent or ambiguous about the notation, there is a lot of fuzzy headed understanding of the rules of arithmetic and algebra. There is no ambiguity in 1/2x either it is 1 divided by 2 times x and must be done left to right because multiplication and division are at the same hierarchical level, if it was other than that the explicit use of a parenthesis is necessary. If you do not understand that, then you do not have a good grasp of elementary math. I know that it is difficult to accept that but it is true

Originally Posted by island911

Demanding that "left to right" always takes precedence is simply short-sighted. (unless one is in the third grade)

the rules of arithmetic and algebra are independent of time or location. You do not get to make up rules that suit you own view and then claim others that do follow the rules correctly are wrong. I did not make up any of the rules nor did any of the posters that got the correct result, we simply followed the correct set of rules in the correct order. Many times you or others follow your muse and still get the correct answer, that does not mean that the rules you followed are correct, It merely means that in that particular case they worked. Following the correct set of rules in the correct order is the only way to always get the correct answer.

here is an example that I used to give my grad students,
64/16 = 4, the easy way(though incorrect to do in all cases) to get the correct answer is of course to cancel the 6 's in the division. then divide by 1 to get 4

It's obvious(though incorrect) that this must be correct because in (6x4)/(3x6) we can (correctly) cancel the 6s and get the result 4/3. This is correctly done only because of a quirk of algebra and is a valuable trick to know.

Originally Posted by island911

Again, engineers and math geeks often use notation beyond the third grade rules. Sure, you can claim they are "not right" to do so, but we also don't speak the Queens English, now do we?

I don't know about 'the Queens English' but I do know a thing or two about Math, using the rules correctly gives the simplified result 288 any other result comes from the misapplication of the rules,

if the rules were correctly taught then they are applicable to any one, at any time, there are not different rules for different folks when it comes to math, each level is a super set of the preceding level. There is obviously a different level of comprehension among the various respondents that has been exposed by this thread.