PEMDAS
PEMDAS is a word built from first letters to help you remember the order of operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. Some learners say the phrase “Please Excuse My Dear Aunt Sally.” In Britain and elsewhere the same idea travels under the name BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction).
The mnemonic works, but you must read it carefully. The MD and the AS are paired, not ranked. Multiplication and division share one level and are done left to right; addition and subtraction share the next level and are also done left to right. PEMDAS lists M before D and A before S only because a word needs some order — that ordering is not a real precedence.
Treat PEMDAS as a reminder, not a recipe. Better is to picture four tiers: grouping symbols, then exponents and roots, then the multiply/divide tier, then the add/subtract tier. Within each tier you simply read left to right. That mental picture avoids the classic mistake of thinking 6 ÷ 2 × 3 equals 1.
8 ÷ 2 × (2 + 2): inside parentheses first, 2 + 2 = 4; then left to right, 8 ÷ 2 = 4, and 4 × 4 = 16.
MD and AS are tiers read left to right, not a strict M-before-D ranking.
Because the multiply/divide and add/subtract levels are left-to-right, 6 ÷ 2 × 3 = (6 ÷ 2) × 3 = 9, and 10 − 4 − 2 = (10 − 4) − 2 = 4. Reading the wrong way is the single most common PEMDAS error.