Associative Property & Identity Property

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

Associative Property

An operation is associative if a change in grouping does not change the results. This means the parenthesis (or brackets) can be moved.

Numbers that are added can be grouped in any order.

For example:	(4 + 5) + 6 = 5 + (4 + 6)
	(x + y) + z = x + (y + z)

Numbers that are multiplied can be grouped in any order.

For example:	(4 × 5) × 6 = 5 × (4 × 6)
	(x × y) × z = x × (y × z)

Numbers that are subtracted are NOT associative.

For example:	(4 – 5) – 6 ≠ 5 – (4 – 6)
	(x – y) – z ≠ x – (y – z)

Numbers that are divided are NOT associative.

For example:	(4 ÷ 5) ÷ 6 ≠ 5 ÷ (4 ÷ 6)
	(x ÷ y ) ÷ z ≠ y ÷ ( x ÷ z)

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

The following video explains: What is the associative property? Why does it have the name it does? How can you recognize it when you see it? How can you distinguish it from other situations that look very similar?