Most common ambiquity is the order of precedence for implicit multiplication operation, for example as in 18/3(1+5).
If it is written as 18/3×(1+5), the most commonly accepted rules state it is equivalent to (18/3)×(1+5), as multiplication and division have the same precedence and are applied from left to right. Many people disagree about the precedence of the implicit multiplication operation, because they may associate it as part of the parentheses. This
is ambiguous, because there is no universally agreed upon interpretation of this notation.
The ambiquity is more pronounced when the 3 is replaced by a variable, say
y, and moved immediately after the parentheses, as in 18/(1+5)
y.
I myself always treat implicit multiplication as explicit multiplication; or rather, essentially inserting all implicit operators first into the equation, before examining it. This does avoid any precedence issues, but it is not –– as far as I know –– universally accepted interpretation of the notation.
I do not claim it is the correct one, either; it is just the
simplest one that makes sense, among many.
This is why I feel questions that rely on this are dishonest. Their authors definitely know this is a notation interpretation issue, and nothing to do with math per se. For example, if we instead used
RPN or postfix notation, no such ambiquity would be possible. (Instead, each valid expression could implement more than one sequence of operations, yielding more than one scalar result, so
other ambiquities would be possible then. Simply put, any notation we choose, we need to define and agree the rules for. If we miss details or disagree on some rule, that's our fault, and nothing to do with the actual math the notation is supposed to express.)