Basic Number Properties

Understanding the four basic number properties is fundamental in mathematics. These properties form the foundation for algebra, geometry, and higher-level math. They help simplify calculations, solve equations, and comprehend mathematical relationships. These 4 basic properties are the commutative, associative, distributive, and identity properties.

1. Commutative Property

  • Addition: The order in which you add numbers does not change the sum.
    Example: 3 + 5 = 5 + 3 = 8       

  • Multiplication: The order in which you multiply numbers does not change the product.
    Example: 4 × 7 = 7 × 4 = 28  

2. Associative Property

  • Addition: When adding three or more numbers, the way you group them does not change the sum.
    Example: (2 + 3) + 4 = 2 + (3 + 4) = 9 

  • Multiplication: When multiplying three or more numbers, the way you group them does not change the product.
    Example: (2 × 3) × 4 = 2 × (3 × 4) = 24

3. Distributive Property

  • This property connects addition and multiplication, showing how multiplication distributes over addition.

    Formula: a × (b + c) = a × b + a × c   
    Example: 3 × (4 + 5) = 3 × 4 + 3 × 5 = 12 + 15 = 27 

4. Identity Property

  • Addition (Additive Identity): Adding zero to any number does not change the number.
    Example: 7 + 0 = 7  

  • Multiplication (Multiplicative Identity): Multiplying any number by one does not change the number.
    Example: 9 × 1 = 9