Properties of Odd Numbers With Examples
Properties of Odd Numbers With Examples
Properties of Odd Numbers
Odd Numbers: An odd number is an integer which is not divisible by 2. When divided by 2, it leaves a remainder of 1.
Examples of odd numbers are 1, 3, 5, 7, 9, 11, and so on.
Properties of Odd Numbers:
- Odd + Odd = Even
- Example: 3+5=8
- Explanation: Adding two odd numbers always results in an even number. This happens because the extra “1” from each odd number sums up to form a multiple of 2, which is even.
- Odd – Odd = Even
- Example: 9−5=4
- Explanation: Subtracting one odd number from another always results in an even number. This is similar to addition because the difference of the two extra “1”s results in a multiple of 2.
- Odd × Odd = Odd
- Example: 3×5=15
- Explanation: Multiplying two odd numbers always results in an odd number. The product does not have a factor of 2, hence it remains odd.
- Odd × Even = Even
- Example: 3×4=12
- Explanation: Multiplying an odd number by an even number always results in an even number. This is because the even number has at least one factor of 2, making the product divisible by 2.
- Odd ± Even = Odd
- Example: 5+4=9 and 7−2=5
- Explanation: Adding or subtracting an even number from an odd number always results in an odd number. This is because the even number does not affect the “oddness” of the other number.
- Consecutive Odd Numbers
- Example: 3 and 5, 11 and 13
- Explanation: Consecutive odd numbers are always 2 units apart. This is because there is always one even number between two odd numbers.
Visual Representations:
- Adding Odd Numbers:
- Shows how adding two odd numbers results in an even number.
- Multiplying Odd Numbers:
- Demonstrates that the product of two odd numbers is still odd.
- Odd and Even Interaction:
- Illustrates that the sum or difference of an odd and an even number is always odd.
These properties of odd numbers help in understanding their behavior in various arithmetic operations and their relationship with even numbers.