Whole Numbers

In this article, we will learn about whole numbers. How are whole numbers different from natural numbers? We will also try and understand various properties of whole numbers.

What are Whole Numbers?

A set of Whole Numbers is a collection of positive numbers and zero.  The whole numbers set is represented as {0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ,……………}. Whole Numbers are the combination of zero and positive integers.

These numbers are positive including zero and do not include fractional or decimal parts (3/4, 2.2 and 5.3 are not whole numbers). Addition, Subtraction, Multiplication and Division activities are possible among the whole numbers.

If again you have doubt, What is a whole number in math? A more comprehensive understanding of the whole numbers can be obtained from the following chart:

Number System

Difference Between Whole Numbers & Natural Numbers

Whole Numbers Natural Numbers
Whole Numbers: {0, 1, 2, 3, 4, 5, 6,…..} Natural Numbers: {1, 2, 3, 4, 5, 6,……}
Counting starts from 0 Counting starts from 1
All whole numbers are not natural numbers All Natural numbers are whole numbers

Below figure will help us to understand the difference between whole numbers and natural numbers :

Whole and Natural Numbers on Number Line

Can Whole Numbers be Negative?

Whole number can’t be negative!

As per Whole Numbers definition: { 0,1,2,3,4,5,6,7,……till positive infinity} are whole numbers. There is no place for negative numbers.

Is 0 a whole number?

The set of Whole Numbers contains of all Natural Numbers, along with Zero. So yes, 0 (zero) is not only a whole number but the first whole number.

Properties of Whole Numbers

  1. Closure Property: They can be closed under addition and multiplication, i.e., if x and y are two whole numbers then x*y or x+y is also a whole number.
  2. Commutative Property of Addition and Multiplication: The sum and product of two whole numbers will be the same whatever the order they are added or multiplied in, i.e., if x and y are two whole numbers x+y=y+x and x*y=y*x
  3. Additive identity: When a whole number is added to 0, its value remains unchanged, i.e., if x is a whole number then x+0=0+x=x
  4. Multiplicative identity: When a whole number is multiplied by 1, its value remains unchanged, i.e., if x is a whole number then x*1=1*x=x
  5. Associative Property: When whole numbers are being added or multiplied as a set, they can be grouped in any order, and the result will be the same, i.e. if x, y and z are whole numbers then x+(y+z)=(x+y)+z and x*(y*z)=(x*y)*z
  6. Distributive Property: If x,y and z are three whole numbers, the distributive property of multiplication over addition is x*(y+z)=(x*y)+(x*z), similarly the distributive property of multiplication over subtraction is x*(y-z)=(x*y)-(x*z)
  7. Multiplication by zero: When a whole number is multiplied to 0, the result is always 0, i.e., x*0=0*x=0
  8. Division by zero: Division of a whole number by o is not defined, i.e., if x is a whole number then x/0 is not defined.

Whole Numbers Examples

Example 1: Are 100, 227, 198, 4321 whole numbers?

Solutions: Yes. 100, 227, 198, 4321 are all whole numbers.

Example 2: Solve 10 x (5 + 10) using the distributive property.

Solution: The whole numbers have following distributive properties: x*(y+z) = (x*y)+(x*z)

10 x (5 + 10) = (10 x 5) + (10 x 10)

= 50 + 100

= 150

This implies 10 x (5 + 10) = 150


Practise This Question

The set of natural numbers along with ____ form collection of whole numbers.