Even numbers are numbers that can be divided evenly by 2 and end in 0, 2, 4, 6, or 8, while odd numbers cannot be divided evenly by 2 and end in 1, 3, 5, 7, or 9. The rules for adding, subtracting and multiplying even and odd numbers always result in a whole number that is either even or odd, but dividing numbers can result in a fraction which is neither even nor odd.

1. Even and Odd Numbers
Even numbers are numbers that can be divided evenly by 2. Even numbers can be
shown as a set like this:
{ … -4, -2, 0, 2, 4, … }
Odd numbers are numbers that cannot be divided evenly by 2.
Odd numbers can be shown as a set like this:
{ … -5, -3, -1, 1, 3, 5, … }
Zero is considered an even number.
Is It Even or Odd?
To tell whether a number is even or odd, look at the number in the ones place. That
single number will tell you whether the entire number is odd or even.
 An even number ends in 0, 2, 4, 6, or 8.
 An odd number ends in 1, 3, 5, 7, or 9.
Consider the number 3,842,917. It ends in 7, an odd number.
Therefore, 3,842,917 is an odd number. Likewise, 8,322 is an
even number because it ends in 2.
Adding Even and Odd Numbers
 even + even = even
4 + 2 = 6
 even + odd = odd
4 + 3 = 7
 odd + odd = even

2. 5 + 3 = 8
Subtracting Even and Odd Numbers
 even - even = even
4 - 2 = 2
 even - odd = odd
4 - 3 = 1
 odd - odd = even
5 - 3 = 2
Multiplying Even and Odd Numbers
 even x even = even
4 x 2 = 8
 even x odd = even
4 x 3 = 12
 odd x odd = odd
5 x 3 = 15
Division, or The Fraction Problem
As you can see, there are rules that tell what happens when you add, subtract, or
multiplyeven and odd numbers. In any of these operations, you will always get a
particular kind of whole number.
But when you divide numbers, something tricky can happen—you might be left
with a fraction. Fractions are not even numbers or odd numbers, because they are
not whole numbers. They are only parts of numbers, and can be written in different
ways.

3. For example, you can't say that the fraction 1/3 is odd because the denominator is an
odd number. You could just as well write that same fraction as 2/6, in which the
denominator is an even number.
The terms “even number” and “odd number” are only used for whole numbers and
their opposites (additive inverses).