Odd Numbers

Odd numbers are integers that are not divisible by 2. In other words, when an odd number is divided by 2, there is always a remainder of 1. The set of odd numbers includes the numbers 1, 3, 5, 7, 9, and so on.

Properties of Odd Numbers:

• Every odd number can be represented in the form 2n + 1, where n is an integer.
• The sum of two odd numbers is always an even number.
• The difference between two odd numbers is always an even number.
• Multiplying two odd numbers always results in another odd number.

Identifying Odd Numbers:

To determine if a number is odd, divide it by 2. If there is a remainder of 1, the number is odd. For example, when 11 is divided by 2, the quotient is 5 with a remainder of 1, so 11 is an odd number.

Practice Problems:

1. Determine whether the following numbers are odd or even: 16, 25, 37, 42, 53.
2. Find the sum of the first 5 odd numbers.
3. If x is an odd number, what can you say about the value of 2x?

Answers:

1. 16 is even, 25 is odd, 37 is odd, 42 is even, 53 is odd.
2. The first 5 odd numbers are 1, 3, 5, 7, 9. Their sum is 25.
3. 2x is always even, because multiplying any number by 2 results in an even number.

Now that you understand the concept of odd numbers, try solving more problems and practice identifying odd numbers in different sets of integers.