Is the Order of Operations Always Clear-Cut in Math?

[Corosus]

If you take 48/2(9+3) = 288 and re arrange it like so:

48/2(12 )= 288
48/2(12)/12 = 288
48/2 = 288/12
24 = 24
See, legitimate

But if you rearrange 48/2(9+3) = 2
48/2(12) = 2
48/2(12)/12 = 2/12
48/2 = 2/12
24 = 0.1666...
So why would anyone even say 2 or is this just completely stupid and just doesn't work?

 

[ngc1333]

This is a true statement: if 48/2(9+3) = 2, then 24=0.1666 ...

The statement A implies B is true unless A is true and B is false. In this case, A is not true. You cannot conclude from this (true) statement that the conclusion, 24=0.1666 is true.

 

[pwsnafu]

So why would anyone even say 2

$$\frac{48}{2(9+3)}= 2$$

but

$$\frac{48(9+3)}{2}=288$$

The same expression was parsed differently by different people.

 

[snipez90]

If you take 48/2(9+3) = 288 and re arrange it like so:

48/2(12 )= 288
48/2(12)/12 = 288
48/2 = 288/12
24 = 24
See, legitimate

Um you forgot to divide both sides by 12 in the second line. More amusingly, you're committing the same logic as proponents of 48/2(9+3) = 2 in your derivation, i.e., you do not perform multiplication/division from left to right.

Also guys go solve the problems I posted https://www.physicsforums.com/showthread.php?t=71315&page=16"

 

[Hurkyl]

https://www.physicsforums.com/showpost.php?p=3237510&postcount=117