Order of operations

The order of operations is the convention that tells everyone how to evaluate a mathematical expression the same way. Without it, an expression like 3 + 4 × 2 would be ambiguous — is it 14 or 11? The rule says multiplication comes before addition, so the answer is 11.

The standard sequence is remembered with the acronym PEMDAS: Parentheses first, then Exponents, then Multiplication and Division, then Addition and Subtraction. Two details trip people up. First, multiplication and division have equal priority and are performed left to right as they appear — in 12 ÷ 3 × 2, divide first to get 4, then multiply to get 8 (not 12 ÷ 6 = 2). Second, addition and subtraction likewise share a tier and go left to right.

Grouping symbols extend beyond parentheses: brackets, fraction bars, absolute value bars, and radicals all act as implicit parentheses. In (8 − 3)² + 6 ÷ 2, work inside the parentheses to get 5, square it to get 25, divide 6 by 2 to get 3, and add for a final answer of 28. Negative signs deserve care too: −3² conventionally means −(3²) = −9, while (−3)² = 9.

The order of operations underlies nearly every algebra question on standardized tests. The ACT tests it directly in pre-algebra and implicitly whenever you isolate variables, the SAT relies on it throughout equation solving and manipulation, and the Praxis Core math exam tests it within number and quantity problems. Fluency here prevents the small arithmetic slips that cost easy points.