--- title: Order of Operations description: The order of operations is a standard set of rules used to evaluate mathematical expressions. You will understand how to correctly sequence addition, subtraction, multiplication, division, exponents, and parentheses to solve complex arithmetic and algebraic equations. category: mathematics subcategory: arithmetic-and-pre-algebra difficulty: beginner, intermediate, advanced url: /subject/order-of-operations --- # Order of Operations The order of operations is a standard set of rules used to evaluate mathematical expressions. You will understand how to correctly sequence addition, subtraction, multiplication, division, exponents, and parentheses to solve complex arithmetic and algebraic equations. ## Available Resources 4 Websites ## Websites ### 1. 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. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.khanacademy.org/math/arithmetic/arith-review-order-of-operations **Tags:** order of operations, pemdas, arithmetic, evaluating expressions ### 2. Ambiguous PEMDAS (source collection and paper) **Author:** Oliver Knill 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. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://people.math.harvard.edu/~knill/pedagogy/ambiguity/index.html **Tags:** order of operations, pemdas, mathematical notation, implied multiplication, history of mathematics ### 3. The PEMDAS Paradox **Author:** David Linkletter Explains why 6รท2(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. **Difficulty:** Beginner | **Language:** English | **Price:** Free **Link:** https://plus.maths.org/content/pemdas-paradox **Tags:** order of operations, pemdas, implied multiplication, mathematical notation ### 4. 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. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://mathsisfun.com **Tags:** websites, mathematics-statistics, algebra --- *This content is part of Dantes.io - Your Treasure Map to Knowledge* *Curated by humans at Dantes.io. Personal study use welcome; republishing this curation requires permission (team@dantes.io).* View this page online: https://dantes.io/subject/order-of-operations