Nothing to brush up on. I’m right. Anybody that comes up with 288 is wrong. Thanks for the advice, though. Not according to the rules.
x = 48 / 2 x (9+3)
Parentheses (evaluate what's inside them)
Exponents
Multiplication and/or division from left to right
Addition and/or subtraction from left to right
And the EXAMPLE: 9 ÷ 3 × 3= 3×3= 9
Multiplication and division are performed at the same time...working from left to right....after the parentheses and any exponents. Thus:
x = 48 / 2 X (12)
x = 24 x 12
x = 288
The rules...and I ask you to simply go anywhere you wish to look them up...are when you get done with parenthesis and exponents you begin working on all the multiplication and division in the problem....and you work from left to right.
Your error is you are doinging all the multiplication FIRST...then starting over from left to right with the division. And that is the error of many. That is not what the rules say:
Not necessarily an error. Just a competing methodology that is in dispute. I love this debate. The "2" people (including myself) are subscribing to the view that the 2(9+3) demonstrates a multiplication by juxtaposition which would take precedence over "normal" multiplication.
I provided an earlier cite for this at
Ask Dr. Math where he states:
The closest thing I have found is the convention used by the _Mathematical Reviews_ of the American Mathematical Society (AMS), at
Mathematical Reviews Database - Guide for Reviewers http://www.ams.org/authors/guide-reviewers.html
that "multiplication indicated by juxtaposition is carried out before division." Thus, in general, for any variables a, b and c, we would have a/bc = a/(bc) (assuming, of course, that b and c are nonzero).
However, the ams link is dead and I didn't track it down any further.
It's actually fascinating to see such debate at physics forums and math forums about this very issue...an issue that one little "(" would solve. To me, the 2(9+3) represents a 2 that was factored out of the 9+3 originally, so would be represented as ((9*2)+(3*2)).
The juxtaposition angle is something I'm going to keep looking into, I can't believe I've found a math-related argument so interesting.