What is the order of operations?

The convention, taught as PEMDAS in the US and BODMAS or BIDMAS elsewhere, is: parentheses or brackets first, then exponents or orders, then multiplication and division, then addition and subtraction. The part people misremember is that multiplication and division sit at the same level and are performed left to right as they appear, and the same is true of addition and subtraction. PEMDAS is a memory aid, not a strict sequence of six steps, and reading it as one is the source of most errors.

This is exactly what the periodic viral equations exploit. An expression like 8 divided by 2 times 4 is unambiguous under the convention, work left to right, giving 16, but people who treat multiplication as outranking division get 1. Expressions written with implied multiplication next to parentheses, such as 8 divided by 2 open paren 2 plus 2 close paren, are genuinely contested, because some conventions in mathematical writing treat juxtaposition as binding more tightly, which is why mathematicians tend to respond to these puzzles by saying the expression is badly written rather than by picking a side. That is the honest lesson: order of operations is a shared convention for reading notation, not a law of arithmetic, and any expression that requires an internet argument to parse should have been written with more parentheses in the first place.