The rule
brackets, then exponents, then × and ÷, then + and −
Why it works
The order of operations is a convention, not a law of nature, but it is a universal one: without it the same expression would mean different things to different people. Brackets first, then exponents, then multiplication and division left to right, then addition and subtraction.
How to do it by hand
- Work out anything inside brackets first
- Then any exponents
- Then multiplication and division, left to right
- Finally addition and subtraction, left to right
What is worth knowing
The detail that trips people is that multiplication and division share a rank, as do addition and subtraction — they are worked left to right, not multiplication before division. That is why 8 ÷ 2 × 4 is 16 and not 1. The viral expressions that circulate periodically all exploit exactly this ambiguity, usually with implied multiplication next to a bracket, where the convention genuinely is not universal. The honest answer to those is that the expression is badly written: an extra pair of brackets removes the argument entirely.