Glossary
order of operations
The order of operations is the agreed sequence for evaluating an expression: parentheses, then exponents, then multiply and divide left to right, then add and subtract left to right.
The order of operations is the fixed sequence in which the parts of an expression are evaluated, so that everyone reading the same expression gets the same number. Work through four levels, in this order: anything inside parentheses first; then exponents; then multiplication and division, left to right; and last addition and subtraction, also left to right. Multiplication and division share one level, and so do addition and subtraction, which is why they are read left to right rather than one before the other. The common error is to work strictly left to right, so that 2 + 3 × 4 is read as (2 + 3) × 4 = 20 instead of 2 + 12 = 14. A mnemonic such as PEMDAS names the levels but not the left-to-right rule inside a level, so it is a reminder, not the rule itself.
Taught in
Related terms
- percent change — A percent change is the amount of change divided by the value you started from, written as a percent: (new − old) ÷ old × 100.
- ratio — A ratio compares two quantities by division, written with a colon or as a fraction — 2 to 3 means two parts of one thing for every three of another.
Source: OpenStax Prealgebra, Elementary Algebra and College Algebra, first editions (CC BY 4.0); NIST SP 811 (units). Each definition restates the two Mathematics guides in this exam, which carry the per-source citations on their own pages. (OpenStax 1e and NIST SP 811 accessed 2026-10-07)