Addition and Subtraction Basics

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Questions and Answers

What is the result of the operation $3 + 7$?

  • $11$
  • $10$ (correct)
  • $12$
  • $9$

Which property states that the order of addition does not affect the sum?

  • Commutative Property (correct)
  • Identity Property
  • Associative Property
  • Distributive Property

Which statement about subtraction is true?

  • Subtraction is associative.
  • The result of subtraction depends on the order of operations. (correct)
  • Subtraction can yield a larger result than its terms.
  • Subtraction is commutative.

What is the identity property of subtraction?

<p>a - 0 = a (A)</p> Signup and view all the answers

If $10 - (2 - 3)$ is calculated, what is the result?

<p>$11$ (D)</p> Signup and view all the answers

Which of the following describes how the result of addition compares to its operands?

<p>The result is always larger or equal to both operands. (D)</p> Signup and view all the answers

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Study Notes

Addition

  • Definition: Combining two or more numbers to get a total.
  • Notation: Represented by the symbol +.
  • Properties:
    • Commutative Property: a + b = b + a (order does not matter).
    • Associative Property: (a + b) + c = a + (b + c) (grouping does not matter).
    • Identity Property: a + 0 = a (adding zero does not change the number).
  • Example:
    • 3 + 5 = 8
    • 2 + (4 + 6) = 2 + 10 = 12

Subtraction

  • Definition: Taking one number away from another.
  • Notation: Represented by the symbol -.
  • Properties:
    • Not Commutative: a - b ≠ b - a (order matters).
    • Not Associative: (a - b) - c ≠ a - (b - c) (grouping matters).
    • Identity Property: a - 0 = a (subtracting zero does not change the number).
  • Example:
    • 8 - 3 = 5
    • 10 - (4 - 2) = 10 - 2 = 8

Key Differences

  • Operation:
    • Addition combines values.
    • Subtraction removes values.
  • Result:
    • Addition results in a larger or equal number.
    • Subtraction results in a smaller or equal number.

Addition

  • Definition: The process of combining two or more numbers to yield a total.
  • Symbol: Represented by the + sign.
  • Commutative Property: The order of numbers does not affect the sum; e.g., a + b = b + a.
  • Associative Property: The way numbers are grouped does not change the sum; e.g., (a + b) + c = a + (b + c).
  • Identity Property: Adding zero to a number leaves it unchanged; e.g., a + 0 = a.
  • Examples:
    • Simple addition: 3 + 5 = 8.
    • Grouping example: 2 + (4 + 6) simplifies to 2 + 10 = 12.

Subtraction

  • Definition: The process of taking one number away from another.
  • Symbol: Represented by the - sign.
  • Non-Commutative: The order of numbers matters; a - b ≠ b - a.
  • Non-Associative: The way numbers are grouped affects the result; (a - b) - c ≠ a - (b - c).
  • Identity Property: Subtracting zero from a number does not change it; e.g., a - 0 = a.
  • Examples:
    • Simple subtraction: 8 - 3 = 5.
    • Grouping example: 10 - (4 - 2) simplifies to 10 - 2 = 8.

Key Differences

  • Operation Nature:
    • Addition is a process of combining values.
    • Subtraction is a process of removing values.
  • Result Implications:
    • Addition generally yields a larger or equal result.
    • Subtraction results in a smaller or equal outcome.

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