## The Lesson

An odd number is a whole number that cannot be divided exactly by 2.## Dictionary Definition

The Oxford English Dictionary defines an even number as a number "having one left over as remainder when divided by two. Opposed to even."## Examples of Odd Numbers

Some examples of odd numbers are given below:## Odd Numbers on a Number Line

The image below shows the odd numbers on the number line.## How to Check if a Number Is an Odd Number

A number is odd if it cannot be divided exactly by 2. If it is divided by 2, the answer will not be a whole number. There will be a remainder of 1.## Question

Is 25 an odd number?## Step-by-Step:

# 1

Divide the number by 2.

25 ÷ 2 = 12.5 = 12 r 1

# 2

Check if the answer from

**Step 1**is a whole number. If it is not, and there is a remainder of 1, the original number is odd. Else it is even. In our example, 12.5 is not a whole number.## Answer:

25 is an odd number.## A Formula to Generate Odd Numbers

The formula below generates odd numbers:If

**k**takes a whole number (1, 2, 3...), then

**n**will always be odd.

k = 0 ∴ n = 2k + 1 = 2 × 0 + 1 = 1

k = 1 ∴ n = 2k + 1 = 2 × 1 + 1 = 3

k = 2 ∴ n = 2k + 1 = 2 × 2 + 1 = 5

k = 3 ∴ n = 2k + 1 = 2 × 3 + 1 = 7

k = 4 ∴ n = 2k + 1 = 2 × 4 + 1 = 9