Commutative Property
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.
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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