In these lessons, we learn what the commutative property means and how to use it in arithmetic operations.

**Related Pages**

Identity Property Of Addition, Multiplication

More Lessons for Arithmetic

Math Worksheets

The basic Number Properties (or laws) that apply to arithmetic operations are Commutative Property, Associative Property, Identity Property and Distributive Property.

The following diagrams show the Commutative Property of Addition and Multiplication. Scroll down the page for more examples and solutions.

An operation is commutative if a change in the order of the numbers does not change the results. This means the numbers can be swapped.

Numbers can be added in any order.

For example:

4 + 5 = 5 + 4

x + y = y + x

Numbers can be multiplied in any order.

For example:

5 × 3 = 3 × 5

a × b = b × a

Numbers that are subtracted are NOT commutative.

For example:

4 – 5 ≠ 5 – 4

x – y ≠ y –x

Numbers that are divided are NOT commutative.

For example:

4 ÷ 5 ≠ 5 ÷ 4

x ÷ y ≠ y ÷ x

The following videos explain more about the commutative property of addition and multiplication.

The following table summarizes which number properties are applicable to the different operations:

Number Properties | × | ÷ | + | – |

Commutative | Yes | No | Yes | No |

Associative | Yes | No | Yes | No |

Distributive | Yes | No | No | No |

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