I am embarrassed to admit that in over 50 years of doing mathematically-related work I have never used or encountered the PEMDAS rule, which establishes the order of operations in an expression to be: Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. The rule allows the writer of an expression to use fewer parentheses to identify the order of operation. (I never realized parentheses were such a problem.) Following are some examples of my understanding of how the rule works.
Evaluate \(4/3*2\).
Without any parentheses, the evaluator would be at a loss as to how to proceed. So this is where the PEMDAS rule comes in, which dictates that multiplication is to be done before division....Well, not in this case....There is another rule (not given in either the Reference Manual or the Math Journal) which states that "in expressions that involve ... multiplication and division only, ... the operations are done in order from left to right." This rule overrides the PEMDAS rule. It adds to the list of things to be remembered, but you can't have everything.
Evaluate \((2^{2}+3)\).
The PEMDAS rule specifies parentheses first, exponents second....Well, in this case you have to reverse the order....A slight modification, but one has to be flexible in these matters.
Evaluate \(6/2/3\).
Using the Left-to-Right rule, the answer is \(6\) divided by \(2\) (equals \(3\)), divided by \(3\) (gives \(1\)). But suppose \(6/2/3\) was meant to be \(6\) divided by \(2/3\) (equals \(9\)). The PEMDAS rule then gives the wrong answer. Oh well, nothing is perfect.
Its hard for me to imagine that a formula for when to fire a missle, for example, would rely on the user of that formula to know the PEMDAS rule. We would be blowing up unintended targets all over the place. Perhaps Aunt Sally should be excused, ... from the cirruculum. I often wonder what was omitted from the cirruculum in order to include it.
John Schwarz