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Properties of Equality and Commutative & Associative Properties

This lesson covers the commutative and associative properties of addition and multiplication, as well as the properties of equality. Students will learn how to recognize and use these properties through examples and practice problems.

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Properties of Equality and Commutative & Associative Properties

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  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) • Associative property of multiplication • Distributive property • Addition property of zero • Commutative property of multiplication

  6. Which property would justify the following statement? 8x + 4 = 4 + 8x • Associative property of addition • Distributive property • Addition property of zero • Commutative property of addition

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

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