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# Properties of Integers

Created by
@ProminentNavy

• R
• Q
• N
• Z (correct)
• ### Which property states that the order of integers in an operation does not change the result?

• Commutative Property (correct)
• Associative Property
• Closure
• Distributive Property
• ### What is the result of dividing one integer by another?

• Always an integer
• Always a fraction
• Not always an integer, but may be a fraction or a decimal (correct)
• Always a decimal
• ### What is the distance of an integer from zero?

<p>Absolute Value</p> Signup and view all the answers

### What is the integer with the same magnitude but opposite sign?

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

### What is the multiplicative inverse of an integer, except for zero?

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

### What is the result of adding or multiplying two integers?

<p>Always an integer</p> Signup and view all the answers

### What is the additive identity, which is neither positive nor negative?

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

## Study Notes

### Definition of Integers

• Integers are whole numbers, either positive, negative, or zero, without a fractional part.
• They are denoted by the symbol "Z" and include the set of numbers {..., -3, -2, -1, 0, 1, 2, 3, ...}.

### Properties of Integers

• Closure: The result of adding or multiplying two integers is always an integer.
• Commutative Property: The order of integers in an operation does not change the result. (e.g., a + b = b + a, a × b = b × a)
• Associative Property: The order in which integers are grouped in an operation does not change the result. (e.g., (a + b) + c = a + (b + c), (a × b) × c = a × (b × c))
• Distributive Property: Integers can be distributed across addition and subtraction operations. (e.g., a × (b + c) = a × b + a × c)

### Types of Integers

• Positive Integers: Integers greater than zero (e.g., 1, 2, 3, ...).
• Negative Integers: Integers less than zero (e.g., -1, -2, -3, ...).
• Zero: The additive identity, which is neither positive nor negative.

### Operations on Integers

• Addition: The result of adding two integers is always an integer.
• Subtraction: The result of subtracting one integer from another is always an integer.
• Multiplication: The result of multiplying two integers is always an integer.
• Division: The result of dividing one integer by another is not always an integer, but may be a fraction or a decimal.

### Important Concepts

• Absolute Value: The distance of an integer from zero, always a positive value.
• Opposite: The integer with the same magnitude but opposite sign.
• Reciprocal: The multiplicative inverse of an integer, except for zero.

### Definition and Properties of Integers

• Integers are whole numbers, either positive, negative, or zero, without a fractional part, denoted by the symbol "Z".
• The set of integers includes {..., -3, -2, -1, 0, 1, 2, 3,...}.
• Integers exhibit closure under addition and multiplication.

### Types of Integers

• Positive integers are integers greater than zero (e.g., 1, 2, 3,...).
• Negative integers are integers less than zero (e.g., -1, -2, -3,...).
• Zero is the additive identity, neither positive nor negative.

### Operations on Integers

• The result of adding two integers is always an integer.
• The result of subtracting one integer from another is always an integer.
• The result of multiplying two integers is always an integer.
• The result of dividing one integer by another is not always an integer, but may be a fraction or a decimal.

### Important Concepts

• The absolute value of an integer is its distance from zero, always a positive value.
• The opposite of an integer has the same magnitude but opposite sign.
• The reciprocal of an integer is its multiplicative inverse, except for zero.

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## Description

Learn about the definition and properties of integers, including closure, commutative property, and associative property. Test your understanding of whole numbers!

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