# Even and Odd Numbers

In this article, we will learn about even and odd numbers, arithmetic rules for odd and even numbers, and examples.

### What are Even numbers?

• Numbers having 0, 2, 4, 6, or 8 at one’s place are called even numbers.
• Even numbers are divisible by 2 without any leftovers (remainders)
Examples: 6, 10, 22, 44, 96, 118, 792, etc.

### What are Odd numbers?

• Numbers having 1, 3, 5, 7, or 9 at one’s place are called odd numbers.
• Odd numbers have a leftover when divided into two equal groups.
Examples: 3, 11, 27, 71, 99, 111, 797, etc.

Regardless of how many digits a number has, you can identify if it is odd or even by looking at the last digit. For example, the numbers 8, 14, and 7,950 are even because their one’s place numbers are 8, 4, and 0.

Similarly, the numbers 63, 1,727, and 125 are odd because they have 3, 7, and 5 at their one’s place.

### Arithmetic Rules for Odd and Even Numbers:

1. The sum of two even numbers is always an even number.
Even + Even = Even
Example: 16 + 12 = 28
2. The sum of two odd numbers is always an even number.
Odd + Odd = Even
Example: 13 + 17 = 30
3. The sum of an odd number and an even number is an odd number.
Even + Odd = Odd
Example: 24 + 35 = 59
4. The difference of two even numbers is an even number.
Even – Even = Even
Example: 14 – 12 = 2
5. The difference of two odd numbers is an even number.
Odd – Odd = Even
Example: 17 – 5 = 12
6. The difference between an even number and an odd number is an odd number.
Even – Odd = Odd
Odd – Even = OddExamples: 30 – 13 = 17, 25 – 20 = 5
7. The product of two even numbers is always an even number.
Even x Even = Even
Example: 8 x 6 = 48
8. The product of an even number and an odd number is always an even number.
Even x Odd = Even
Example: 2 x 7 = 14
9. The product of two odd numbers is always an odd number.
Odd x Odd = Odd
Example: 9 x 3 = 27
10. An even number can be represented as 2n, where n is an integer.
Example: 2(4) = 8
11. When an even number is divided by 2, there is no remainder.
Example: 24 ÷ 2 = 12
12. An odd number can be represented as 2n + 1, where n is an integer.
Example: 2(2) + 1 = 5
13. When an odd number is divided by 2, it leaves a remainder of 1.
Example: 17 ÷ 2 = 8 remainder 1

These properties help us understand the characteristics and behavior of odd and even numbers.

## Solved Examples of Even and Odd Numbers

Example 1.
Is 15 + 31 even or odd?

Solution :
15 = odd number
31 = odd number

Rule : odd + odd = even

15 + 31 = 46, an even number

So, 15 + 31 is even.

Example 2 :
Is 16 + 110 even or odd?

Solution :
16 = even number
110 = even number

Rule : even + even = even

Moreover,
16 + 110 = 126, an even number

So, 16 + 110 is even.

Example 3 :
Is 9 + 88 even or odd?

Solution :
9 = odd number
88 = even number

Rule : odd + even = odd

Moreover,
9 + 88 = 97, an odd number

So, 9 + 88 is odd.

Example 4 :
Is 200 + 111 even or odd?

Solution :
200 = even number
111 = odd number

Rule : even + odd = odd

Moreover :
200 + 111 = 311, an odd number
So, 200 + 111 is odd.

Example 5 :
Is 100 x 52 even or odd?

Solution :
100 = even number
52 = even number

Rule : even x even = even

Moreover,
100 x 52 = 5200, an even number

So, 100 x 52 is even.

Example 6 :
Is 11 x 12 even or odd?
Solution :
11 = odd number
12 = even number

Rule : odd x even = even

Moreover,
11 x 12 = 132, an even number
So, 11 x 12 is even.

Example 7 :
Is 89 x 17 even or odd?
Solution :
89 = odd number
17 = odd number

Rule : odd x odd = odd
Moreover,
89 x 17 = 1513, an odd number.
So, 89 x 17 is odd.

Example 8:
Is 76 x 13 even or odd?

Solution :
76 = even number
13 = odd number

Rule : even x odd = even
Moreover,
76 x 13 = 988, an even number.
So, 76 x 13 is even.

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