# Whole Numbers

**What are whole numbers?**

Whole numbers are the set of numbers that include zero and all the positive numbers that we count with, like 0, 1, 2, 3, 4, 5, etc. What this set doesn’t include are negative numbers and numbers that are expressed as fractions or decimals. In other words, whole numbers include zero and all positive integers. The set of whole numbers goes on forever.

**A Little More About Terminology**

The term “whole number” is sometimes used interchangeably with “natural number,” although the set of natural numbers (or counting numbers) does not include zero. There is some debate about whether or not zero is a whole number, but for the purpose of this tutorial, we will consider it one.

Distinguishing Whole Numbers, Integers, Fractions, and Decimals

Challenge: Look at the following numbers and decide which ones are whole numbers.

-3, -1, 0, 1, 3, 1/3, 0.333

Answer:

-3 and -1 are negative numbers, so they are not whole numbers.

0, 1, and 3 are all whole numbers.

1/3 is not a whole number because it’s a fraction.

0.333 is not a whole number because it’s a decimal.

**Even and Odd Numbers**

All whole numbers except for zero can be described as either even or odd. A number is called “even” if it can be divided by 2 with no remainder. Since 4 ÷ 2 = 2, the number 4 is an even number. In fact, all numbers that end in 0, 2, 4, 6, and 8 are even numbers.

Odd numbers, on the other hand, are not divisible by 2. If we try to divide 5 by 2, for example, we get a quotient of 2 with a remainder of 1. All numbers that end in odd numbers (1, 3, 5, 7, and 9) are odd numbers.

Challenge: Look at the following numbers and decide which ones are odd and which ones are even.

12, 24, 33, 49, 50, 62, 75, 88, 91, 100

Answer: By looking at the last digit of each number, we can determine that 12, 24, 50, 62, 88 and 100 are even, while 33, 49, 75, and 91 are odd.

**Basic Operations With Even And Odd Whole Numbers**

It’s helpful to remember a few rules for the way odd and even numbers work together in equations.

Addition rule 1: Even + Even = Even (Example: 2 + 6 = 8)

Addition rule 2: Even + Odd = Odd (Example: 2 + 5 = 7)

Addition rule 3: Odd + Odd = Even (Example: 3 + 5 = 8)

**The subtraction rules mirror the addition rules.**

Subtraction rule 1: Even – Even = Even (Example: 8 – 6 = 2)

Subtraction rule 2: Even – Odd = Odd (Example: 8 – 5 = 3)

Subtraction rule 3: Odd – Odd = Even (Example: 7 – 5 = 2)

**The multiplication rules are a little different.**

(Note that there are no division rules for odd and even numbers.)

Multiplication rule 1: Even x Even = Even (Example: 2 x 4 = 8)

Multiplication rule 2: Even x Odd = Even (Example: 2 x 3 = 6)

Multiplication rule 3: Odd x Odd = Odd (Example: 3 x 5 = 15)