Objective The student will be able to:

1
ObjectiveThe student will be able to

• recognize and use the commutative and
  associative properties and the properties of
  equality.

2
Commutative Property

• Commutative 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.

3
Associative Property

• Associative 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.

4
Name the property1) 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

5
Which property would justify rewriting the
following expression without parentheses? 3(2x
5y)

1. Associative property of multiplication
2. Distributive property
3. Addition property of zero
4. Commutative property of multiplication

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6
Which property would justify the following
statement? 8x 4 4 8x

1. Associative property of addition
2. Distributive property
3. Addition property of zero
4. Commutative property of addition

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7
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

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