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.
The following videos explain more about the commutative property of addition and multiplication.
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.
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.
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 |
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 |
Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.
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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