# 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
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 multiply** even 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.

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).

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