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Commutative Property Definition

Definition: The Commutative property states that order does not matter. Multiplication and addition are commutative.
Examples of the Commutative Property for Addition
  • 4 + 2 = 2 + 4
  • 5 + 3 + 2 = 5 + 2 + 3
  • b + a = a + b (Yes, algebraic expressions are also commutative for addition)
Examples of the Commutative Property for Multiplication
  • 4 • 2 = 2 • 4
  • 5 • 3 • 2 = 5 • 2 • 3
  • a • b = b • a(Yes, algebraic expressions are also commutative for multiplication)


Non Examples of the Commutative Property

Subtraction (Not Commutative)

Subtraction is probably an example that you know, intuitively, is not commutative .
  • 4 − 2 2 − 4
  • 4 −3 3 − 4
  • a − b b − a
In addition, division, compositions of functions and matrix multiplication are two well known examples that are not commutative..

Division (Not Commutative)

Division is probably an example that you know, intuitively, is not commutative .
  • 4 ÷ 2 2 ÷ 4
  • 4 ÷ 3 3 ÷ 4
  • a ÷ b b ÷ a
In addition, division, compositions of functions and matrix multiplication are two well known examples that are not commutative..