Integers: Definition and Properties

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7 Questions

What is the result of the sum of two integers?

Always an integer

What happens when you divide two integers?

The quotient is sometimes an integer, sometimes a decimal

What is the property that states that the order of integers in an operation does not change the result?

Commutative Property

Divisible by 2

Prime integer

What is the property that states that the multiplication of an integer over the sum of two integers is equal to the sum of their individual products?

Distributive Property

What is the result of the product of two integers?

Always an integer

Study Notes

Integers

Definition

• An integer is a whole number, either positive, negative, or zero, without a fractional part.
• Examples: ..., -3, -2, -1, 0, 1, 2, 3, ...

Properties

• Closure: The sum, difference, product, and quotient (except division by zero) of 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: The multiplication of an integer over the sum of two integers is equal to the sum of their individual products.

Operations

• Addition: The sum of two integers is always an integer.
• Subtraction: The difference of two integers is always an integer.
• Multiplication: The product of two integers is always an integer.
• Division: The quotient of two integers is not always an integer, but it can be expressed as an integer or a decimal.

Types of Integers

• Even Integers: divisible by 2, e.g., ..., -4, -2, 0, 2, 4, ...
• Odd Integers: not divisible by 2, e.g., ..., -3, -1, 1, 3, 5, ...
• Prime Integers: only divisible by 1 and themselves, e.g., 2, 3, 5, 7, ...

Integers

Definition and Examples

• An integer is a whole number with no fractional part, which can be positive, negative, or zero.
• Examples of integers include ..., -3, -2, -1, 0, 1, 2, 3, ...

Closure

• The sum of two integers is always an integer.
• The difference of two integers is always an integer.
• The product of two integers is always an integer.
• The quotient of two integers is an integer except for division by zero.

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

• The multiplication of an integer over the sum of two integers is equal to the sum of their individual products.

Operations with Integers

• The sum of two integers is always an integer.
• The difference of two integers is always an integer.
• The product of two integers is always an integer.
• The quotient of two integers is not always an integer, but it can be expressed as an integer or a decimal.

Even Integers

• Even integers are divisible by 2.
• Examples of even integers include ..., -4, -2, 0, 2, 4, ...

Odd Integers

• Odd integers are not divisible by 2.
• Examples of odd integers include ..., -3, -1, 1, 3, 5, ...

Prime Integers

• Prime integers are only divisible by 1 and themselves.
• Examples of prime integers include 2, 3, 5, 7, ...

Learn about integers, including their definition, examples, and properties such as closure, commutative property, and associative property.

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