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Understanding Number Properties: Distributive, Commutative, and Associative Properties

This unit explores fundamental number properties, focusing on the Distributive Property and its applications. The Distributive Property states that for any real numbers a, b, and c, a(b + c) = ab + ac. Additionally, we cover the Commutative and Associative Properties of both addition and multiplication. These foundational concepts allow for the manipulation of mathematical expressions, helping students simplify and evaluate numbers effectively. Each property is illustrated with examples to enhance understanding.

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Understanding Number Properties: Distributive, Commutative, and Associative Properties

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Presentation Transcript

  1. Unit 3 Number Properties

  2. The Distributive Property • If a, b, and c, are real numbers then a(b + c) = ab x ac

  3. Number Properties • Four Properties of Arithmetic: • The commutative Property of Addition • The Associative Property of Addition • The Commutative Property of Multiplication • The Associative Property of Multiplication.

  4. The Commutative Property Of Addition Of Multiplication If a and b are real numbers then; a x b = b x a • If a and b are real numbers, then; a + b = b + a

  5. The Associative Property Of Addition Of Multiplication If a, b, and c are real numbers then; (a x b)x c = a x (b x c) • If a, b, and c are real numbers, then; (a + b) + c = a + (b + c)

  6. The Associative Property Of Addition Of Multiplication If a, b, and c are real numbers then; (a x b)x c = a x (b x c) • If a, b, and c are real numbers, then; (a + b) + c = a + (b + c)

  7. State the number property • 3(4 + 5) = 3 x 4 + 3 x 5 ___________________ • 6(8 + 2) = (8 + 2)6 ___________________ • 3 + (6 + 8) = (6 + 8) + 3 ___________________ • 5(3 x 2) = (5 x 3)2 ___________________ • 3 + (6 + 8) = (3 + 6) + 8 ___________________ • 5(3 x 2) = (3 x 2)5 ___________________ • 4 + (2 + (-1)) = 4 + ((-1) + 2) _______________ • 7(8 – 2) = 7 x 8 – 7 x ___________________

  8. State the number property • 3(4 + 5) = 3 x 4 + 3 x 5 Distributive • 6(8 + 2) = (8 + 2)6 Commutative (mul) • 3 + (6 + 8) = (6 + 8) + 3 Commutative (add) • 5(3 x 2) = (5 x 3)2 Associative (mul) • 3 + (6 + 8) = (3 + 6) + 8 Associative (add) • 5(3 x 2) = (3 x 2)5 Commutative (mul) • 4 + (2 + (-1)) = 4 + ((-1) + 2) Commutative (add) • 7(8 – 2) = 7 x 8 – 7 x Distributive

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