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Integer Operations Quiz
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Integer Operations Quiz

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Questions and Answers

What is the result of 5 + (-2)?

  • 7
  • 3
  • -3 (correct)
  • -7
  • What is the result of (-3) × 4?

  • -12 (correct)
  • 12
  • -3
  • 3
  • What is the result of (-2) ÷ (-4)?

  • -2
  • -0.5
  • 2
  • 0.5 (correct)
  • What is the result of 8 - (-3)?

    <p>11</p> Signup and view all the answers

    What is the correct order of operations for the expression 2 × 3 + 12 - 8?

    <p>Parentheses, Exponents, Multiplication and Division, Addition and Subtraction</p> Signup and view all the answers

    What is the result of 9 - 4 + (-2)?

    <p>3</p> Signup and view all the answers

    What is the result of a + (-a) in integer properties?

    <p>0</p> Signup and view all the answers

    Which property states that the order of integers does not change the result?

    <p>Commutative property</p> Signup and view all the answers

    Which property is demonstrated by the equation (a × b) × c = a × (b × c)?

    <p>Associative property</p> Signup and view all the answers

    What is the multiplicative identity in integer properties?

    <p>1</p> Signup and view all the answers

    Which property is demonstrated by the equation a × (b + c) = a × b + a × c?

    <p>Distributive property</p> Signup and view all the answers

    What is the additive inverse of an integer a in integer properties?

    <p>-a</p> Signup and view all the answers

    Study Notes

    Integer Operations

    Addition of Integers

    • Rules:
      • Same signs: Add the numbers and keep the same sign
      • Different signs: Subtract the smaller number from the larger number and keep the sign of the larger number
    • Examples:
      • 2 + 3 = 5 (same signs)
      • 2 + (-3) = -1 (different signs)
      • (-2) + 3 = 1 (different signs)

    Subtraction of Integers

    • Rules:
      • Subtracting a positive number is the same as adding a negative number
      • Subtracting a negative number is the same as adding a positive number
    • Examples:
      • 4 - 2 = 2 (subtracting a positive number)
      • 4 - (-2) = 6 (subtracting a negative number)
      • (-4) - 2 = -6 (subtracting a positive number)

    Multiplication of Integers

    • Rules:
      • Same signs: Multiply the numbers and the result is positive
      • Different signs: Multiply the numbers and the result is negative
    • Examples:
      • 2 × 3 = 6 (same signs)
      • 2 × (-3) = -6 (different signs)
      • (-2) × 3 = -6 (different signs)

    Division of Integers

    • Rules:
      • Same signs: Divide the numbers and the result is positive
      • Different signs: Divide the numbers and the result is negative
    • Examples:
      • 6 ÷ 2 = 3 (same signs)
      • 6 ÷ (-2) = -3 (different signs)
      • (-6) ÷ 2 = -3 (different signs)

    Order of Operations

    • When performing multiple operations, follow the order:
      1. Parentheses (if present)
      2. Exponents (if present)
      3. Multiplication and Division (from left to right)
      4. Addition and Subtraction (from left to right)

    Integer Operations

    Addition of Integers

    • Same signs: Add numbers and keep the same sign
    • Different signs: Subtract the smaller number from the larger number and keep the sign of the larger number
    • Addition is commutative: 2 + 3 = 3 + 2
    • Addition is associative: (2 + 3) + 4 = 2 + (3 + 4)

    Subtraction of Integers

    • Subtracting a positive number is the same as adding a negative number
    • Subtracting a negative number is the same as adding a positive number
    • Subtraction is not commutative: 2 - 3 ≠ 3 - 2

    Multiplication of Integers

    • Same signs: Multiply numbers and the result is positive
    • Different signs: Multiply numbers and the result is negative
    • Multiplication is commutative: 2 × 3 = 3 × 2
    • Multiplication is associative: (2 × 3) × 4 = 2 × (3 × 4)

    Division of Integers

    • Same signs: Divide numbers and the result is positive
    • Different signs: Divide numbers and the result is negative
    • Division is not commutative: 6 ÷ 2 ≠ 2 ÷ 6
    • Division by zero is undefined

    Order of Operations

    • Follow the order: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)
    • Evaluate expressions from top to bottom and left to right
    • Use parentheses to group numbers and operations when necessary

    Integer Properties

    Commutative Property

    • The order of integers does not affect the result of addition and multiplication.
    • Addition: a + b = b + a
    • Multiplication: a × b = b × a

    Associative Property

    • The order of grouping integers does not change the result of addition and multiplication.
    • Addition: (a + b) + c = a + (b + c)
    • Multiplication: (a × b) × c = a × (b × c)

    Distributive Property

    • Multiplication distributes over addition.
    • a × (b + c) = a × b + a × c

    Identity Properties

    Additive Identity

    • 0 is the additive identity, as it does not change the result when added to an integer.
    • a + 0 = a

    Multiplicative Identity

    • 1 is the multiplicative identity, as it does not change the result when multiplied by an integer.
    • a × 1 = a

    Inverse Properties

    Additive Inverse

    • The additive inverse of an integer is the integer that, when added, results in 0.
    • The additive inverse of a is -a, since a + (-a) = 0

    Multiplicative Inverse

    • The multiplicative inverse of an integer is the integer that, when multiplied, results in 1.
    • The multiplicative inverse of a (if it exists) is 1/a, since a × (1/a) = 1

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    Description

    Test your understanding of adding and subtracting integers with same and different signs.

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