So the problem is two-fold: first, order of operations as most people are taught it is a lie, and second, the original problem is written very ambiguously.
Letâs drill down into that first point.
PEMDAS! Parentheses, exponents, multiplication, division, addition, subtraction. Everyoneâs taught to do operations in that order! Except thatâs not really right. As a math teacher of mine put it, âit works for now, but youâll find out I was lying in a few years.â
The problem is that multiplication and division are the same operation, and addition and subtraction are also the same operation. Division is really just multiplying by a fraction, and subtraction is just adding a negative. With that in mind, it doesnât necessarily make sense to do some multiplication arbitrarily early in the problem before the rest! As a result, hereâs the bottom line for that point:
Well, that brings me to the second point: the expression is written very ambiguously, so as to maximize confusion! Itâs also why I donât like using the division symbol when a fraction will do just nicely.
Observe two other ways we could write this expression:
The first one resolves to 8/8, which is 1. The second resolves to 4(4), which is 16. Both are right, only because the original expression is vague.
The sad thing is that everyone hates fractions, when actually they make life so much nicer!
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