Order of Operations: Common Calculator Mistakes to Avoid
Standard order of operations evaluates parentheses first, then exponents, then multiplication and division (left to right), then addition and subtraction (left to right) — commonly remembered as PEMDAS — and the most frequent mistake is treating addition/subtraction as always coming before multiplication/division, when the actual rule is that multiplication and division are evaluated first, regardless of their left-to-right position relative to addition or subtraction.
This single rule explains nearly every case where someone gets a different answer than a calculator, and it's worth understanding rather than memorizing by rote.
The most common actual mistake
People often evaluate strictly left to right regardless of operator type, which works for pure addition/subtraction or pure multiplication/division chains, but breaks the moment the two are mixed — 2 + 3 × 4 is 14 (multiply first: 3×4=12, then add 2), not 20 (which would come from evaluating strictly left to right).
Where parentheses remove ambiguity entirely
Adding explicit parentheses around the operation you intend to happen first removes any ambiguity about intent — writing (2 + 3) × 4 forces the addition first, giving 20, which is exactly why parentheses are the standard way to override the default order when a different sequence is genuinely intended.