Commutative Property

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

The commutative property states that the order of numbers in addition or multiplication does not change the result.

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

 

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Commutative Property

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.

• Commutative property of Addition

• Commutative property of Multiplication

Summary of Number Properties

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

Importance of the Commutative Property:
The commutative property is fundamental in:

• Simplifying calculations: It allows you to rearrange numbers to make mental math easier (e.g., 17+8+3 can be 17+3+8=20+8=28).
• Algebra: It allows you to reorder terms in expressions (e.g., 3+x is the same as x+3; 5y is the same as y5).

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