Real Numbers Algebra

A comprehensive tool demonstrating fundamental algebraic laws for real numbers including commutative, associative, identity, and inverse laws for both addition and multiplication, as well as the distributive law.

Real Numbers Algebra

Fundamental Laws

This tool demonstrates the key algebraic properties of real numbers:

Addition Laws

  • Commutative Law: a + b = b + a
  • Associative Law: (a + b) + c = a + (b + c)
  • Identity Law: a + 0 = 0 + a
  • Inverse Law: a + (-a) = (-a) + a = 0

Multiplication Laws

  • Commutative Law: a × b = b × a
  • Associative Law: a(bc) = (ab)c
  • Identity Law: a × 1 = 1 × a
  • Inverse Law: a × (1/a) = (1/a) × a = 1 (where a ≠ 0)

Mixed Operations

  • Distributive Law: a(b + c) = ab + ac
Calculator

Inputs

Results

Commutative Addition (a + b = b + a)--
Associative Addition ((a + b) + c = a + (b + c))--
Identity Addition (a + 0 = 0 + a)--
Inverse Addition (a + (-a) = 0)--
Commutative Multiplication (a × b = b × a)--
Associative Multiplication (a(bc) = (ab)c)--
Identity Multiplication (a × 1 = a)--
Distributive Law (a(b + c) = ab + ac)--