48÷2(9+3) = ?

[JMJones0424]

It doesn't matter "how you see" the operation, because as this thread demonstrates, there are different "ways of seeing" it. Perhaps you didn't notice the link to the wikipedia article on order of operations in CraigD's reply or the link to Wolfram's article on precedence in C1ay's, both are provided again for your convenience below. Under normal mathematical rules, there is only one answer, 288. The correct way to write the problem and end up with the answer 2 would be 48/(2(9+3)).

 

Please note that [math]48/2(9+3)[/math] does not equal [math]\frac{48}{2(9+3)}[/math] , instead it equals [math]\frac{48}{2}\times(9+3)[/math]

 

http://en.wikipedia.org/wiki/Order_of_operations

 

http://mathworld.wolfram.com/Precedence.html

[CraigD]

The answer depends on the precedence of the calculator’s (human, electronic, or whatever) operations.

Just calculators? I recognize this as the standard precedence I learned in school.

By “calculator (human, electronic, or whatever)”, I mean any person or thing that performs a calculation.

 

It's what we were taught is the 'right' way to do it and it's the order that has been consistent throughout my math texts.

While electronic hardware and software-controlled calculators follow rules programmed into them, humans likewise are “programmed” by textbooks, teachers, and experience.

 

C1ay's statement is a clear description of this.

 

When would it be right to use these other orders of precedence?

As a general rule, when doing so is useful. A great strength of mathematics and computer programming is that its notation is very flexible, allowing it to be tailored to specific uses.

 

Specifically, the order: { (); *; +,-; / } is not uncommon, and may be used intuitively by most people when encountering special whitespace renderings. For example:

 

“A +B/C +D” would be interpreted by most as “A+(B/C)+D” or [imath]A+\frac{B}{C}+D[/imath], but

 

“A+B / C+D” might reasonably be interpreted as “(A+B)/(C+D)” or [imath]\frac{A+B}{C+D}[/imath]

.

If I ever used them in the past my teacher marked my paper wrong. Is precedence in mathematics really ambiguous?

With flexibility comes the need to clear when one is deviating from the usual, avoiding ambiguity. Operation precedence, the operations themselves, and the glyphs and codes associated with them, change, between specialties and individuals, and over time.

[Qfwfq]

It is wise to distinguish between the two topics: Mathematics and Mathematical Notation. ;)

 

In any case it is not considered excellent practice to write an expression such as a/b*c even in a context where notation is well defined, such as programming languages where the BNF univocally determine the matter. Good programmer texbooks recommend using more parentheses than strictly necessary, in order to improve readability and thus avoid mistakes during the overall process of development and maintanance of source code. I myself, once more of a C syntax freak, currently tend by experience to write either (a/b )*c or a/(b*c) according to my actual intent; although superfluous in the first case, the ( and ) can avoid wasting plenty of time.

 

#include <stdio.h>

int main(int argc, char**argv){
printf("TEST: 48/2*(9 + 3) = %d\n", 48/2*(9 + 3));
}

Wow!!!!!!!!!!!!!!!!!! It really does write TEST: 48/2*(9 + 3) = 288....:P

Edited May 30, 2011 by Qfwfq
unwarranted smiley

[zoysa1234]

I`m trying this sum according to BODMAS theory.

 

 

48÷2(9+3) = ????

First remove the brackets.

 

48\24=2

 

 

 

 

 

link removed

Edited June 17, 2011 by sanctus
Additionally to spam link you can't even do math :-)