Glossary
order of operations
The order of operations is the fixed sequence for evaluating an expression: parentheses, exponents, multiplication and division left to right, then addition and subtraction left to right.
The order of operations is the agreed sequence in which the parts of an expression are evaluated, so that the same expression always yields the same value. Work through parentheses first, innermost out; then exponents; then multiplication and division, left to right as they appear; then addition and subtraction, again left to right. The left-to-right clause is where most errors live, because multiplication does not outrank division and addition does not outrank subtraction: in 8 − 3 + 2 the subtraction runs first, giving 7, not 3. In 6 ÷ 2 × 3 the division runs first, giving 9, not 1. A fraction bar and a radical sign act as brackets over everything they cover, and a negative sign applied to a whole expression behaves the same way. Write one intermediate line per step rather than doing it in your head, and the question is usually a formality.
Taught in
Related terms
- exponent — An exponent states how many times a base is multiplied by itself, so 10³ means 10 × 10 × 10, and for a power of ten, each step moves the decimal point one place.
- decimal — A decimal writes a fraction using place value after a decimal point, so 0.75 means 75 hundredths, and the alignment of that point governs every operation.
Source: The math guides in this course (ratio and proportion, measurement and conversion, dosage calculation): every definition and worked value above was written for this course, because arithmetic and unit conversion are not a publisher's prose, and each guide shows the method worked. Elsevier's own HESI A2 page, which names math among the areas the exam covers, is the exam-side source. (Elsevier HESI A2 page accessed 2026-10-23; definitions written 2026-10-27)