Mathematics: Is the taught Order of Operations wrong?

There are a number of Maths puzzles doing the rounds on social media and many are based on the following theme:
X ÷ Y(A ± B)
The current one on Facebook is 16 ÷ 4(2+2) with people arguing over whether the answer is 16 or 1. I am writing this article because the “strict and literal use” of the PEMDAS or BODMAS mnemonics does not always give the correct answer.
However, it is possible to use the order of operations to solve to the correct answer of 1 in all situations, even with this deliberately ambiguous mathematical expression.
