Is division inherently the last operation when using fraction notation or is the order of operation always PEMDAS?

Question

Are parenthesis needed when adding or subtracting in the dividend or divisor when using fraction notation to divide, or is it inherent that division is the last step using this notation?

$ X = \frac{n}{a - b + c} \\or\\ X = \frac{n}{(a - b + c)} $

Answer 1

So if $$X = \frac{n}{a - b + c}$$ does not mean $$X = \frac{n}{(a - b + c)},$$ what could it mean? Could it possibly mean $$X = \frac{n}{a} - b + c?$$ If so, then you should just write that. There is ambiguity only when you must put everything on a single line, e.g., X = n/(a - b + c), as you might, for instance, when programming a computer.

Answer 2

Fraction notation always implies that the expressions above and below the fraction bar are completely evaluated before the division. So for instance, $\frac{n+m}{a-b+c}$ always means $(n+m)\div(a-b+c)$.