Two Operations, One Structure

Abstract Algebra · Axiom Academy

INTRO Two Operations, One Structure Discover how familiar number systems use both addition and multiplication together, connected by a powerful law The integers aren't just about addition OR multiplication—they have both operations working on the same set of numbers. Adjust the values and explore! These two operations aren't separate—they're connected by a fundamental relationship called the distributive law . Watch how multiplication distributes over addition! The distributive law isn't unique to integers. Explore different number systems and see that the same structure appears! Test your understanding! For each equation, determine whether the distributive law has been applied correctly. A ring is a set with two operations (usually called addition and multiplication) that satisfy certain axioms. The integers (ℤ), rationals (ℚ), and polynomials are all examples of rings.

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