1.6 The Commutative and Associative Properties

ObjectiveThe student will be able to:

recognize and use the commutative and associative properties and the properties of

equality.

Indicators: NS4Designed by Skip Tyler, Varina High SchoolEdited by Eddie Judd, Crestwood Middle School

Commutative PropertyCommutative means that the order

does not make any difference.a + b = b + a a • b = b • a

Examples

4 + 5 = 5 + 4

2 • 3 = 3 • 2

The commutative property does not work for subtraction or division.

Associative PropertyAssociative means that the grouping

does not make any difference.(a + b) + c = a + (b + c) (ab) c = a (bc)

Examples

(1 + 2) + 3 = 1 + (2 + 3)

(2 • 3) • 4 = 2 • (3 • 4)

The associative property does not work for subtraction or division.

Name the property

1) 5a + (6 + 2a) = 5a + (2a + 6)

commutative (switching order)

2) 5a + (2a + 6) = (5a + 2a) + 6

associative (switching groups)

3) 2(3 + a) = 6 + 2a

distributive

Which property would justify rewriting the following expression without parentheses?

3(2x + 5y)1. Associative property of

multiplication2. Distributive property3. Addition property of

zero4. Commutative property

of multiplicationAnswer Now

Which property would justify the following statement?

8x + 4 = 4 + 8x1. Associative property of

addition

2. Distributive property

3. Addition property of zero

4. Commutative property of addition

Answer Now

Which property would justify the following statement?

8 + (2 + 6) = (8 + 2) + 6 1. Associative property of

addition

2. Distributive property

3. Addition property of zero

4. Commutative property of addition

Answer Now

Assignment• Pg 36 25-43 all