Properties of Mathematics: Commutative and Associative Properties
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Questions and Answers

What is the commutative property of addition and multiplication?

  • The result of an operation is always a negative number.
  • The order of numbers or variables does not change the result of an operation. (correct)
  • The order of numbers or variables changes the result of an operation.
  • The result of an operation is always zero.

    • What is an example of the associative property of multiplication?

  • (2 + 3) × 4
  • (3 × 4) × 2 (correct)
  • (3 × 4) × (2 × 4)
  • (2 × 3) × 4

    • What is the formula for the distributive property?

  • a × (b × c) = (a × b) × c
  • a × (b - c) = a × b - a × c
  • a × (b / c) = a × b / a × c
  • a × (b + c) = a × b + a × c (correct)

    • What is an example of the commutative property of addition?

    <p>2 + 3 = 3 + 2</p> Signup and view all the answers

    What is an example of the associative property of addition?

    <p>(2 + 3) + 4 = 2 + (3 + 4)</p> Signup and view all the answers

    Study Notes

    Properties of Mathematics

    Commutative Property

    • The commutative property states that the order of numbers or variables does not change the result of an operation.
    • Applies to addition and multiplication:
      • a + b = b + a
      • a × b = b × a
    • Examples:
      • 2 + 3 = 3 + 2 = 5
      • 4 × 5 = 5 × 4 = 20

    Associative Property

    • The associative property states that the order in which numbers or variables are grouped does not change the result of an operation.
    • Applies to addition and multiplication:
      • (a + b) + c = a + (b + c)
      • (a × b) × c = a × (b × c)
    • Examples:
      • (2 + 3) + 4 = 2 + (3 + 4) = 9
      • (3 × 4) × 2 = 3 × (4 × 2) = 24

    Distributive Property

    • The distributive property states that multiplication distributes over addition.
    • a × (b + c) = a × b + a × c
    • Examples:
      • 2 × (3 + 4) = 2 × 3 + 2 × 4 = 14
      • 5 × (2 + 1) = 5 × 2 + 5 × 1 = 15

    Properties of Mathematics

    Commutative Property

    • The commutative property states that the order of numbers or variables does not change the result of an operation.
    • Applies to addition: a + b = b + a
    • Applies to multiplication: a × b = b × a
    • Examples: 2 + 3 = 3 + 2 = 5, 4 × 5 = 5 × 4 = 20

    Associative Property

    • The associative property states that the order in which numbers or variables are grouped does not change the result of an operation.
    • Applies to addition: (a + b) + c = a + (b + c)
    • Applies to multiplication: (a × b) × c = a × (b × c)
    • Examples: (2 + 3) + 4 = 2 + (3 + 4) = 9, (3 × 4) × 2 = 3 × (4 × 2) = 24

    Distributive Property

    • The distributive property states that multiplication distributes over addition.
    • Formula: a × (b + c) = a × b + a × c
    • Examples: 2 × (3 + 4) = 2 × 3 + 2 × 4 = 14, 5 × (2 + 1) = 5 × 2 + 5 × 1 = 15

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    Description

    Learn about the commutative and associative properties of mathematics, including how they apply to addition and multiplication operations.

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