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Commutative Property

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More Lessons for Arithmetic
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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.

Commutative Property

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.

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


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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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