Commutative Property

Commutative Property

The property of an operation that allows the order of the terms to be changed without changing the result.

This property simplifies calculations.
It is especially useful in simplifying mental math.


Addition and multiplication of whole numbers are commutative operations :

  • 9 + 3 = 3 + 9
  • 9 × 3 = 3 × 9

\(\forall x,y\in \mathbb{R} : x+y = y+x\).

  • The operation of multiplication on the set of real numbers also is a commutative operation :

\(\forall x,y\in \mathbb{R} : x×y = y×x\).

  • The composition of translations of the plane is a commutative operation.
  • The addition of functions defined in \(\mathbb{R}\) is a commutative operation.
  • The subtraction of integers is a noncommutative operation.

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