Mathematics: Even and Odd Numbers

Even Numbers

• Even numbers are integers that are divisible by 2.
• They can be expressed as 2n, where n is an integer.
• Examples of even numbers include 0, 2, 4, 6, 8, 10, and so on.
• All even numbers end in 0, 2, 4, 6, or 8.
• Even numbers are closed under addition and subtraction. This means if you add or subtract two even numbers, the result is also an even number.
• Even numbers are not closed under multiplication. The product of two even numbers can be even or odd depending on the specific numbers involved.

Odd Numbers

• Odd numbers are integers that are not divisible by 2.
• They can be expressed as 2n + 1, where n is an integer.
• Examples of odd numbers include 1, 3, 5, 7, 9, and so on.
• All odd numbers end in 1, 3, 5, 7, or 9.
• Odd numbers are not closed under addition or subtraction. Adding or subtracting two odd numbers results in an even number, and adding or subtracting an odd number and an even number results in an odd number.
• Odd numbers are not closed under multiplication either. The product of two odd numbers is always odd.

Properties of Even and Odd Numbers

• The sum of two even numbers is always even.
• The sum of two odd numbers is always even.
• The sum of an even number and an odd number is always odd.
• The difference between two even numbers is always even.
• The difference between two odd numbers is always even.
• The difference between an even number and an odd number is always odd.
• The product of two even numbers is always even.
• The product of two odd numbers is always odd.
• The product of an even number and an odd number is always even.

This quiz explores the concepts of even and odd numbers, including their definitions, characteristics, and how they behave under various mathematical operations. Test your understanding of these fundamental integer classifications and their properties.