Whole Numbers Quiz

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Questions and Answers

What defines the set of whole numbers?

  • Fractions and decimals
  • Negative integers only
  • Only positive integers
  • Non-negative integers including zero (correct)

Which property confirms that adding two whole numbers results in another whole number?

  • Associative property of multiplication
  • Closure under addition (correct)
  • Commutative property of subtraction
  • Distributive property

What is the additive identity element of whole numbers?

  • 1
  • 0 (correct)
  • -1
  • None of the above

Which statement is true about the set of integers?

<p>Integers consist of positive and negative whole numbers, including zero (A)</p> Signup and view all the answers

What is the result of adding an integer and its additive inverse?

<p>Zero (B)</p> Signup and view all the answers

What is the role of the number 1 in the context of integers?

<p>It is the multiplicative identity element (A)</p> Signup and view all the answers

Which property is satisfied by integers regarding multiplication over addition?

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

Which of the following examples is NOT a whole number?

<p>-3 (C)</p> Signup and view all the answers

Why are whole numbers and integers considered closed under addition?

<p>Their sums always produce numbers within their sets (A)</p> Signup and view all the answers

What does the set of integers include?

<p>All negative and positive whole numbers, including zero (B)</p> Signup and view all the answers

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Study Notes

Whole Numbers

  • Whole numbers are non-negative integers, including zero.
  • Represented by the letter "W" and defined as: W = {0, 1, 2, 3, 4, 5, …}
  • Example values include 0, 49, 67, 52.

Natural Numbers

  • Also known as "counting numbers," starting from 1 to infinity.
  • Represented by the letter "N" and defined as: N = {1, 2, 3, 4, 5, …}
  • Example values include 35, 59, 110.

Integers

  • Comprise both whole numbers and negative natural numbers.
  • Represented by the symbol "Z" and defined as: Z = {… -3, -2, -1, 0, 1, 2, 3 …}
  • Example values include -52, 0, -1, 16, 82.

Rational Numbers

  • Defined as numbers that can be expressed as a fraction p/q, where p and q are integers and q ≠ 0.
  • Represented by the letter "Q."
  • Example fractions include 7/1, 10/2, 1/1, and 0/1.

Properties of Rational Numbers

  • Closed under addition, subtraction, multiplication, and division.
  • Satisfy commutative and associative properties for addition and multiplication.
  • Follow the distributive property for addition and subtraction.

Properties of Whole Numbers

  • Closed under addition and multiplication.
  • Zero serves as the additive identity; one is the multiplicative identity.
  • Complies with commutative and associative properties for addition and multiplication.
  • Adheres to the distributive property of multiplication over addition and vice versa.

Properties of Integers

  • Closed under addition, subtraction, and multiplication.
  • Zero acts as the additive identity; one is the multiplicative identity.
  • Follows commutative and associative properties across addition, subtraction, and multiplication.
  • Satisfies the distributive property relative to addition and subtraction.
  • Each integer 'a' has an additive inverse '-a' so that a + (-a) = 0.

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