But, that's NOT how that works...
The P in PEMDAS means that you solve the equation inside of the Parentheses BEFORE doing anything else. PEMDAS is actually better written as PE[M/D][A/S] where the brackets mean that they are equal, but performed in left to right priority with the possibility of a reciprocal PE depending on the equation (IE: nested PE). So that means you end up with 6 / 2 * 3, not the nested thing I see just above. The fuzzy part is where you run into "Do I convert the division into a fraction?". Converting it to a fraction gives you the different answer only if the condition far below is true, but once you've completed the Parenthesis, then you're actually left with simple Division and Multiplication. In this case, the Division goes first.
Based on the provided equation, you'd get the following:
6 / 2(1+2)
6 / 2(3)
6 / 2 * 3
3 * 3
9
The key here is that anything adjacent to a Parenthesis is implicit Multiplication
What's throwing everyone is that at some point or another we were all taught that division can be rewritten as a fraction.
With that logic, you get the following:
6 / 2(1+2)
6
--------
2(1+2)
6
--------
2(3)
6
--------
6
1
But in reality, that only works if it were written like this where an additional set of brackets was originally included:
6 / [2(1+2)]
I tried to find the rule for this, but IDK what to search for.