Commutative Property

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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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