Evens and Odds

An even number is any word that is divisible by 2: numbers that are within the set {…-6, -4, -2, 0, 2, 4, 6,…}. Remember, though, that an even number is divisible by 2 and not have any remainder. Keep in mind also that 0 is an even number. Consecutive even numbers are all located 2 units apart. For example, if x is an even number, then the next consecutive even number would be represented as X + 2.

Odd numbers, on the other hand, are numbers within the set {…-5, -3, -1, 1, 3, 5,…}.

The following charts demonstrate the properties of odd and even numbers. To check the property of a number, you can simply substitute the appropriate numbers.

Properties of odd and even numbers with Addition

Property

Example

Even + Even = Even

2 + 8 = 10

Odd + Odd = Even

3 + 9 = 12

Odd + Even = Odd

3 + 8 = 11

Properties of odd and even numbers with Multiplication

Property

Example

Even x Even = Even

4 x 6 = 24

Even x Odd = Even

4 x 5 = 20

Odd x Odd = Odd

3 x 9 = 27

Consider the following example:

If R is an odd integer, what are the next two consecutive odd integers?

A) T and V

B) R and R+1

C) R+1 and R+2

D) R+2 and R+4

E) R+1 and R+3

Note: the correct answer is (D)

Here’s another example:

If x is an odd integer and y is an even integer, tell whether each expression is odd or even.

A. x2 23

B. xy

C. y2

D. x + y

E. 2x + y

Note (A) is odd. (B) is even. (C) is even. (D) is odd, and (E) is even.