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Properties of Addition and Multiplication in Math

Learn about the commutative and associative properties, as well as the properties of equality in mathematics with examples and explanations. Understand how changing the order or grouping of numbers does not change the result. Practice identifying and applying these properties to various equations.

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Properties of Addition and Multiplication in Math

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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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