Understanding Even and Odd Numbers

Study Notes

Definitions

Even Numbers
- Integers that are divisible by 2 without a remainder.
- Can be expressed in the form: ( n = 2k ), where ( k ) is an integer.
- Examples: -4, -2, 0, 2, 4, 6, etc.
- Characteristics:
  - The last digit is 0, 2, 4, 6, or 8.
  - The sum of two even numbers is always even.
  - The product of two even numbers is always even.
Odd Numbers
- Integers that are not divisible by 2, leaving a remainder of 1 when divided by 2.
- Can be expressed in the form: ( n = 2k + 1 ), where ( k ) is an integer.
- Examples: -3, -1, 1, 3, 5, 7, etc.
- Characteristics:
  - The last digit is 1, 3, 5, 7, or 9.
  - The sum of two odd numbers is always even.
  - The product of two odd numbers is always odd.

Even Numbers

Defined as integers divisible by 2 with no remainder.
Can be mathematically represented as ( n = 2k ) where ( k ) is an integer.
Examples include negative, zero, and positive values: -4, -2, 0, 2, 4, 6.
Last digit of even numbers will always be one of: 0, 2, 4, 6, or 8.
When two even numbers are added, the result is always even.
The product of two even numbers also results in an even number.

Odd Numbers

Defined as integers that are not divisible by 2, resulting in a remainder of 1.
Can be mathematically expressed as ( n = 2k + 1 ) where ( k ) is an integer.
Examples include negative, positive integers, and excludes zero: -3, -1, 1, 3, 5, 7.
Last digit of odd numbers will always be one of: 1, 3, 5, 7, or 9.
Summing two odd numbers always yields an even number.
The product of two odd numbers will always be odd.

Description

Test your knowledge on the definitions and characteristics of even and odd numbers. This quiz will cover integer properties and provide examples to enhance your understanding. Perfect for students looking to reinforce their math fundamentals.