Ambiguous PEMDAS (source collection and paper)
by Oliver Knill · Harvard University Department of Mathematics
Harvard mathematician's dossier on order-of-operations ambiguity, collecting Cajori's 1928 notation history, Lennes's 1917 Monthly article, ISO 80000-1, archived AMS guidance, and how calculators and computer algebra systems actually parse 2x/3y. Includes a short paper.
More resources on Order of Operations
Khan Academy - Order of Operations
Free Khan Academy arithmetic unit of short videos and auto-graded practice sets on evaluating expressions with parentheses, exponents, multiplication, division, addition and subtraction. Learners finish able to simplify multi-step numerical expressions in the conventional order and check their own work.
The PEMDAS Paradox
Explains why 6÷2(1+2) has two defensible answers: two competing conventions for implied multiplication. Argues the expression is not well-defined rather than commonly misread, and shows when parentheses are mandatory.
mathsisfun.com
MathIsFun.com is a beginner-friendly math site that explains concepts with clear, step-by-step lessons and interactive activities. It covers topics from algebra and linear equations to geometry, fractions, data, and more, with practice problems, worksheets, and quizzes.