Integers: Definition and Properties
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Questions and Answers

Which of the following is a property of adding integers?

  • Closure Property of Division
  • Associative Property of Addition (correct)
  • Commutative Property of Multiplication
  • Distributive Property of Subtraction
  • What is the result of multiplying any integer by -1?

  • The result is always an even integer
  • The result is the additive inverse (correct)
  • The result is always zero
  • The result is always an odd integer
  • Which of the following is an example of a prime integer?

  • 6
  • 15
  • 4
  • 11 (correct)
  • What is the result of dividing 12 by 3?

    <p>4 with a remainder of 0</p> Signup and view all the answers

    What is the term for integers that are divisible by 2?

    <p>Even integers</p> Signup and view all the answers

    A temperature of -5°C can be represented by which type of integer?

    <p>Negative integer</p> Signup and view all the answers

    Study Notes

    Integers

    Definition

    • A set of whole numbers, including:
      • Positive integers (1, 2, 3, ...)
      • Negative integers (-1, -2, -3, ...)
      • Zero (0)

    Properties

    • Closure: The result of adding, subtracting, multiplying, or dividing integers is always an integer.
    • Commutative Property: The order of integers does not change the result of addition or multiplication.
    • Associative Property: The order in which integers are added or multiplied does not change the result.
    • Distributive Property: Multiplication distributes over addition.

    Types of Integers

    • Even integers: Divisible by 2 (..., -4, -2, 0, 2, 4, ...)
    • Odd integers: Not divisible by 2 (..., -3, -1, 1, 3, ...)
    • Prime integers: Only divisible by 1 and themselves (2, 3, 5, 7, 11, ...)

    Operations on Integers

    • Addition: Combine two or more integers to get a sum.
    • Subtraction: Find the difference between two integers.
    • Multiplication: Combine two or more integers to get a product.
    • Division: Divide one integer by another, resulting in a quotient and possibly a remainder.

    Real-World Applications

    • Counting and measuring quantities
    • Representing temperatures (e.g., -5°C, 0°C, 5°C)
    • Financial transactions (e.g., +$10, -$5, $0)

    Integers

    Definition

    • Integers are a set of whole numbers including positive integers, negative integers, and zero.

    Properties

    • Integers are closed under addition, subtraction, multiplication, and division.
    • The commutative property applies to integers in addition and multiplication.
    • The associative property applies to integers in addition and multiplication.
    • The distributive property applies to integers, where multiplication distributes over addition.

    Types of Integers

    Even Integers

    • Even integers are divisible by 2, such as ..., -4, -2, 0, 2, 4, ...

    Odd Integers

    • Odd integers are not divisible by 2, such as ..., -3, -1, 1, 3, ...

    Prime Integers

    • Prime integers are only divisible by 1 and themselves, such as 2, 3, 5, 7, 11, ...

    Operations on Integers

    Addition

    • Addition combines two or more integers to get a sum.

    Subtraction

    • Subtraction finds the difference between two integers.

    Multiplication

    • Multiplication combines two or more integers to get a product.

    Division

    • Division divides one integer by another, resulting in a quotient and possibly a remainder.

    Real-World Applications

    • Integers are used for counting and measuring quantities.
    • Integers represent temperatures, such as -5°C, 0°C, and 5°C.
    • Integers are used in financial transactions, such as +$10, -$5, and $0.

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    Quiz Team

    Description

    Learn about integers, including their definition, properties, and rules. Discover the closure, commutative, and associative properties of integers.

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