The simple math problem that stumped the Internet DOES have an answer

Apparently, Twitter is all a-twitter over a simple-looking equation, 8÷2(2+2), which no-one can agree on. Some say the answer is 1; others say 16. Even math graduates can't agree on it.
Some say that it all comes down to which system you were taught for the order of operations: BODMAS or PEMDAS. BODMAS stands for Brackets, Orders, Division, Multiplication, Addition and Subtraction; PEMDAS stands for Parentheses, Exponents, Mutliplication, Division, Addition and Subtraction. The USA tends to use PEMDAS, while the UK (and most of its ex-colonies) tends to use BODMAS (Canada and New Zealand typically use the hybrid BEDMAS). Now, given that parentheses is just another way of saying Brackets, and Exponents another way of saying Orders, the two methods are essentially the same, except that Division and Multiplication are in a different order. Thus, under BODMAS (Division before Multiplication), the sum becomes (8÷2)(2+2) = 4×4 = 16. Under PEMDAS (Multiplication before Division), it becomes 8÷(2×(2+2)) = 8÷(2×4) = 1.
The conclusion might then be that the problem is poorly framed, and should make use of more brackets (parentheses) to make the meaning clear. Except that ... I think that this interprets both PEMDAS and BODMAS wrongly. My understanding, backed up by Wikipedia, is that, under both of these systems, the Division and Multiplication operations actually have the same level priority, as do Addition and Substraction. So, whether we are talking about PEMDAS or BODMAS, they are better written as Division/Multiplication and Multiplication/Division. If there is any ambiguity - for example, consecutive Multiplication and Division, as is the case in the problem originally quoted - then the convention is to go from left-to-right, i.e. as it reads. Therefore, under either PEMDAS or BODMAS, the sum becomes (8÷2)(2+2) = 16. Unambiguously. Definitively.
My confidence is boosted by the fact that my calculator gives the same answer. My daughter, however, thinks I am wrong because it relies on a rule or convention that many people don't know about. This does not seem to me to be a valid objection: math is full of rules and conventions that the average guy on the street doesn't know about, but that in no way invalidates them.