The amount of math-turbation in here is insane!

All I can say as an engineering graduate student is: Why does the equation matter, where was it derived from and search from there...practicality >> theory.

 

I don't understand. Care to elaborate?[/quote]The title of the thread is "48/2(9+3)".Standard order of operations interprets that as (48/2)(9+3), not 48/[2(9+3)].It isn't a numerator of 48 and a denominator of [2*(9+3)]; it's a dividend of 48, a divisor of 2, and a multiplicand of (9+3). Any other interpretation requires additional parentheses/brackets/braces, such as you supplied.
[/quote]

Incorrect. Standard order of operations aka PEMDAS say that you add whats in the parenthesis, then multiply, then divide. Hence the answer should be 2

 

I don't understand. Care to elaborate?[/quote]The title of the thread is "48/2(9+3)".Standard order of operations interprets that as (48/2)(9+3), not 48/[2(9+3)].It isn't a numerator of 48 and a denominator of [2*(9+3)]; it's a dividend of 48, a divisor of 2, and a multiplicand of (9+3). Any other interpretation requires additional parentheses/brackets/braces, such as you supplied.[/quote]
Incorrect. Standard order of operations aka PEMDAS say that you . . . then multiply, then divide. Hence the answer should be 2[/quote]
Um, no.

Standard order of operations has multiplication and division at the same level of precedence; operations at the same level of precedence are evaluated left to right.

To be clear: multiplication does not have a higher order of precedence than division.

 

I got 288 the first time..

plus even google calculator says (48/2)*(9+3) = 288 after you only type in 48/2(9+3)

I took AP calculus by 11th grade so I'm not too stupid at math either..

 

48/2(9+3)

bracket stuff first (9+3) = (12).. but only because "if a mathematical expression is preceded by one operator and followed by another, the operator higher on the list should be applied first." (there are only 2 different operators here).. things IN the bracket. not the things IN the bracket and all the stuff touching the bracket already (like multiplying it by 2 already)

48/2(12)

after the bracket is done.. "It is helpful to treat division as multiplication by the reciprocal (multiplicative inverse) and subtraction as addition of the opposite (additive inverse)." and also... "The commutative and associative laws of addition and multiplication allow terms to be added in any order and factors to be multiplied in any order, but mixed operations must obey the standard order of operations." which means that the order of operations doesn't apply anymore (there's only one operator left-multiplication and division). and you go from left to right.

24 x 12.. =288..

B. E. D. M. A. S. which is: brackets, exponents, division & multiplication, addition & subtraction.
division & multiplication = same level
addition & subtraction = same level
4-1+2 does not equal 1, it equals 5
4 / 2 x 3 does not equal .66, it equals 6
[[For those who think the order is multiply, THEN divide. not a fraction either]]
it goes from left to right

"Parentheses outrank exponents, which outrank multiplication and division (but multiplication and division are at the same rank), and these two outrank addition and subtraction (which are together on the bottom rank). When you have a bunch of operations of the same rank, you just operate from left to right."

 

you didn't say anything about "explanation"?
and btw (thread hijack just for Magician), check out freakonomics. Good reading.



anyhoo, this reminds me of the Constitution. The writer made it vague so the people fight over the interpretation.
we are fighting over semantics. A couple more parentheses would be so effective here.

 

I've now realized why there's two answers, it's a syntax error.

The op posed the question to us, and asked for the answer of 48/2(9+3).

Since he asked us for the answer, we are assuming we're solving for an unknown answer.

48/2(9+3) = X If solving then
48 = X(2(9+3))
48 = 24X
2 = X

If you're asking what that expression represents it's 288. That's why this is so debated, it's all in what you're asking for. It's not an issue with math, it's an issue of language, and magician you should know better. The OP asked for an answer, not the representation of an expression.

 

You should solve left-to-right, after resolving the parenthesis. In your solution above, you solved for the "2(9+3)" first to get the 24 in "24X".

I think it should be done this way:

48/2(9+3) = X

resolve the parenthesis,
48/2(12) = X,

then if you must shift such a simple equation to solve for X, then you must shift only the 12 over, leaving left-to-right order intact,
48/2 = X/12,

simplify further,
24 = x/12,

and solve for X,
288 = X

 

You would multiply X by 12, and have 24/12 = 2... Why would you divide? You multiply both sides by the inverse...

 

PEMDAS works from left to right. Multiplication and division are considered the same as with addition and subtraction.

The problem is the way in which it's written.

Technically, if you were forced to apply the basic mathematical principal I mentioned earlier it would go like this:

*note: for people adding brackets from the beginning of 2 and the end parenthesis, your making up your own problem at that point ...

1. Work from left to right after parenthesis are taken care of.

48/2*(9+3)
48/2*(12)
48/2*12
24*12
288

Like I said before, PEMDAS works from left to right. The way people are imagining it is if it were as followed:

48
______

2(9+3)

That would be the answer 2 if it were written in that method, but since it's considered one whole equation not over another... then the latter is correct and 288 would be the answer.


The key is working the PEMDAS from left to right w/ multiplication to division and addition to subraction.





EDIT: I just realized Chiung explained this and showed the simplication evidence also, whoops!