Operations & Order of Operations
The four operations, PEMDAS, and the commutative, associative, and distributive properties.
This page is a free outline of what the Operations & Order of Operations lesson covers — it is not the lesson itself. The interactive lesson, practice, quizzes, and AI Tutor are inside the app.
This lesson covers
- Associative Property The associative property says grouping doesn’t matter for addition or multiplication: (a + b) + c = a + (b + c). Handy for mental math — 17 + (8 + 2) = 27. Not for subtraction or division.
- Commutative Property The commutative property says order doesn’t matter for addition or multiplication: a + b = b + a and a × b = b × a. It doesn’t hold for subtraction or division.
- Distributive Property The distributive property says multiplying into parentheses multiplies every term inside: a(b + c) = ab + ac. So 3(x + 4) = 3x + 12 — the key move for clearing parentheses in algebra.
- Four Basic Operations The four basic operations are addition, subtraction, multiplication, and division — the building blocks of every calculation.
- Order of Operations (PEMDAS)
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Inside the app, Operations & Order of Operations comes with:
Read the explanation here for free — then practice it for real, with everything you need in one place.
24/7 AI Tutor — Ask anything and get a step-by-step explanation when you’re stuck — it teaches the concept, not just the answer. Every answer verified by three independent AIs.
- Practice sets — Open-book practice questions at your level, easiest-first — as many as you want, never scored.
- Quizzes — Scored quizzes on the whole lesson, so you know when you’re ready to move on.
- Skills Check — A concept-by-concept map of what you’ve mastered and what to focus on next.
- Worked examples — Tap the Brain Button on any example for alternative step-by-step explanations.
- Glossary — Plain-English definitions of every key term in the lesson.
- Formula sheet — The GED® & HiSET® formula sheets, on screen while you practice.
- Practice calculator — An on-screen calculator to build your calculator skills before test day.
- Math-fact flashcards — Quick drills for addition, multiplication, perfect squares, and square roots.
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