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Questions and Answers
What is the result of adding two integers with different signs?
Which property states that the order of integers in an operation does not change the result?
What is the result of subtracting an integer?
What is the definition of prime integers?
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What is the result of multiplying two integers with different signs?
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When is the quotient of two integers an integer?
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Study Notes
Integers
Definition
- Integers are whole numbers, either positive, negative, or zero, without a fractional part.
- Examples: ..., -3, -2, -1, 0, 1, 2, 3, ...
Properties
- Closure: The result of adding, subtracting, or multiplying two integers is always an integer.
- Commutative Property: The order of integers in an operation does not change the result.
- Associative Property: The order in which integers are grouped in an operation does not change the result.
- Distributive Property: Integers can be distributed over addition and subtraction.
Operations
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Addition:
- The sum of two integers with the same sign is an integer with that sign.
- The sum of two integers with different signs is an integer with the sign of the integer with the larger absolute value.
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Subtraction:
- Subtracting an integer is equivalent to adding its additive inverse.
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Multiplication:
- The product of two integers with the same sign is a positive integer.
- The product of two integers with different signs is a negative integer.
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Division:
- The quotient of two integers is an integer if and only if the dividend is divisible by the divisor.
Types of Integers
- Even Integers: Integers that are exactly divisible by 2.
- Odd Integers: Integers that are not exactly divisible by 2.
- Prime Integers: Integers greater than 1 that have exactly two distinct factors: 1 and themselves.
- Composite Integers: Integers greater than 1 that have more than two distinct factors.
What are Integers?
- Whole numbers, either positive, negative, or zero, without a fractional part
- Examples: ..., -3, -2, -1, 0, 1, 2, 3, ...
Properties of Integers
Closure
- The result of adding, subtracting, or multiplying two integers is always an integer
Commutative Property
- The order of integers in an operation does not change the result
Associative Property
- The order in which integers are grouped in an operation does not change the result
Distributive Property
- Integers can be distributed over addition and subtraction
Operations on Integers
Addition
- The sum of two integers with the same sign is an integer with that sign
- The sum of two integers with different signs is an integer with the sign of the integer with the larger absolute value
Subtraction
- Subtracting an integer is equivalent to adding its additive inverse
Multiplication
- The product of two integers with the same sign is a positive integer
- The product of two integers with different signs is a negative integer
Division
- The quotient of two integers is an integer if and only if the dividend is divisible by the divisor
Types of Integers
Even Integers
- Integers that are exactly divisible by 2
Odd Integers
- Integers that are not exactly divisible by 2
Prime Integers
- Integers greater than 1 that have exactly two distinct factors: 1 and themselves
Composite Integers
- Integers greater than 1 that have more than two distinct factors
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Description
Learn about the properties of integers, including closure, commutative property, and associative property. Understand the definition and examples of integers.
