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This is not about the associative property. It's not about the actual mathematics. It's not about anything other than convention. The reason this is a problem is that some people use a convention that states implicit multiplication (juxtaposition) has precedence over division or explicit multiplication. That's it. That's the whole enchilada.
That is not a widely held convention but it is widely held enough to render the original equation ambiguous. Ambiguity is why the mathematics community debates the equation so ferociously and why the absolute consensus is that it should be written more clearly. Before you say it is not ambiguous, don't. It is, period. It's ambiguous for the same reason 1/2x is ambiguous. Because the intent of the author, the convention they follow, is unclear. Some authors will mean x/2 while others might mean 1/(2x).
You can say there is nothing to debate. But, clearly that is completely wrong as the debate rages on all over the Internet...
Scott
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