Lesson 1-6 Commutative and Associative Properties Designed by Skip Tyler, Varina High School

Commutative Property Commutative means that the order does not make any difference. a + b = b + aa b = b a Examples = = 3 2 The commutative property does not work for subtraction or division.

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.

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 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

Which property would justify the following statement? 8 + (2 + 6) = (8 + 2) Associative property of addition 2.Distributive property 3.Addition property of zero 4.Commutative property of addition

Evaluate: Rewrite the problem by grouping numbers that can be formed easily. (Associative property) This process may change the order in which the original problem was introduced. (Commutative property) ( ) + ( ) + ( ) (40) + (40) + (40) = 120 Commutative and Associative Properties Commutative and Associative properties are very helpful to solve problems using mental math strategies.

Evaluate: 4  7  25 Rewrite the problem by changing the order in which the original problem was introduced. (Commutative property) Group numbers that can be formed easily. (Associative property) 4  25  7 (4  25)  7 (100)  7 = 700 Commutative and Associative Properties Commutative and Associative properties are very helpful to solve problems using mental math strategies.

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