Properties of Mathematics: Commutative and Associative Properties

Properties of Mathematics

Commutative Property

• The commutative property states that the order of numbers or variables does not change the result of an operation.
• Applies to addition and multiplication:
  • a + b = b + a
  • a × b = b × a
• Examples:
  • 2 + 3 = 3 + 2 = 5
  • 4 × 5 = 5 × 4 = 20

Associative Property

• The associative property states that the order in which numbers or variables are grouped does not change the result of an operation.
• Applies to addition and multiplication:
  • (a + b) + c = a + (b + c)
  • (a × b) × c = a × (b × c)
• Examples:
  • (2 + 3) + 4 = 2 + (3 + 4) = 9
  • (3 × 4) × 2 = 3 × (4 × 2) = 24

Distributive Property

• The distributive property states that multiplication distributes over addition.
• a × (b + c) = a × b + a × c
• Examples:
  • 2 × (3 + 4) = 2 × 3 + 2 × 4 = 14
  • 5 × (2 + 1) = 5 × 2 + 5 × 1 = 15

Properties of Mathematics

Commutative Property

• The commutative property states that the order of numbers or variables does not change the result of an operation.
• Applies to addition: a + b = b + a
• Applies to multiplication: a × b = b × a
• Examples: 2 + 3 = 3 + 2 = 5, 4 × 5 = 5 × 4 = 20

Associative Property

• The associative property states that the order in which numbers or variables are grouped does not change the result of an operation.
• Applies to addition: (a + b) + c = a + (b + c)
• Applies to multiplication: (a × b) × c = a × (b × c)
• Examples: (2 + 3) + 4 = 2 + (3 + 4) = 9, (3 × 4) × 2 = 3 × (4 × 2) = 24

Distributive Property

• The distributive property states that multiplication distributes over addition.
• Formula: a × (b + c) = a × b + a × c
• Examples: 2 × (3 + 4) = 2 × 3 + 2 × 4 = 14, 5 × (2 + 1) = 5 × 2 + 5 × 1 = 15