Which is it??

[Kmp]

(First off, I apologize if this is in the wrong thread)
Hello, so recently someone gave me a problem as follows:
12/2 (6-7+4)×2
We each got different answers and keep arguing.
Here is how I did it:
12/2 (3)×2
6 (3)×2
18×2
36
Here is how he did it:
12/2 (6-7+4)×2
12/2 (3)×2
12/6×2
2×2
4
So which is it? I'm 99.9% sure it's 36, yet he is set on it being 4.
Plz help! TIA

 

[Romsek]

[MATH]\dfrac{12}{2} (3)\times 2 = 6(3)\times 2[/MATH]
Your friend incorrectly multiplied the denominator of first term rather than the numerator.

 

[Kmp]

[MATH]\dfrac{12}{2} (3)\times 2 = 6(3)\times 2[/MATH]
Your friend incorrectly multiplied the denominator of first term rather than the numerator.

Thank you!! This is what I was explaining, but he kept arguing haha. Thank you though!

 

[Dr.Peterson]

Some textbooks teach an order of operations rule in which the multiplication that is not indicated by a symbol is done before the division, so your friend would be right. This is therefore a potential ambiguity in the rules, and the expression really shouldn't have been written. (Mathematicians use a fraction bar instead of an inline division symbol for clarity.)

So your answer is standard, but your friend's is not entirely without merit.

Ignore such questions. They are just made to start arguments.

 

[Romsek]

Some textbooks teach an order of operations rule in which the multiplication that is not indicated by a symbol is done before the division, so your friend would be right. <snip>

Seriously? Why would they do that when it so clearly produces errors?

 

[Dr.Peterson]

It's like a different dialect. And in fact there are logical reasons for it -- if only everyone agreed.

I discussed this on my blog here and here, based on my long history of answering questions like this. And there is plenty of room for disagreement.