This doesn't do anything to resolve the debate. The distributive property doesn't *take precedence* in order of operations. It's just a mathematical truism.

>48 ÷ (2 X 9 + 2 X 3)

This step is only valid if you hold that the second and third terms are in the denominator a/k/a that the multiplication should be done before the division. The only reason you would believe that is if you believed that multiplication by juxtaposition (i.e., 2(a+b)) has higher precedence than multiplication with a symbol (i.e., 2*(a+b)).

Imagine for a second that you agree with the 288 people. You would have this:

48÷2(a+b)

The first step would ordinarily be the parentheses, but pretend you can't reduce any more and you're stuck with a+b. This shouldn't matter if the distributive property holds (it does).

What Stravinskian, Abby and the others are saying is that there's no reason to do the multiplication before the division according to standard interpretations of the order of operations. You would do the division first since it occurs first from left-right.

24(a+b)

Which would give you 288. You can see that the disagreement has nothing to do with the distributive property and everything to do with evaluating the precedence of 2(a+b) vs. 48÷2.

What I, and most of the people who are saying 2 believe, is that the lack of a multiplication symbol means that the 2(a+b) is meant to be interpreted as a single term.

See what I mean?