Commutative and Associative Properties Commutative Property Commutative means

Commutative and Associative Properties

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.

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) 5 a + (6 + 2 a) = 5 a + (2 a + 6) commutative (switching order) 2) 5 a + (2 a + 6) = (5 a + 2 a) + 6 associative (switching groups) 3) 2(3 + a) = 6 + 2 a distributive

Which property would justify rewriting the following expression without parentheses? 3(2 x + 5 y) 1. Associative property of multiplication 2. Distributive property 3. Addition property of zero 4. Commutative property of multiplication 1 2 3 4 5 6 7 8 9 10 11 12 21 22 23 24 25 26 27 28 29 30 31 32 13 14 15 16 17 18 19 20

Which property would justify the following statement? 8 x + 4 = 4 + 8 x 1. Associative property of addition 2. Distributive property 3. Addition property of zero 4. Commutative property of addition 1 2 3 4 5 6 7 8 9 10 11 12 21 22 23 24 25 26 27 28 29 30 31 32 13 14 15 16 17 18 19 20

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 1 2 3 4 5 6 7 8 9 10 11 12 21 22 23 24 25 26 27 28 29 30 31 32 13 14 15 16 17 18 19 20

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