Whole Numbers

The whole numbers are the part of the number system in which it includes all the positive integers from 0 to infinity. In this article, we will discuss what are whole numbers, properties and the difference between the whole numbers and the natural numbers along with the examples.

Whole Numbers Definition

The whole numbers are the number without fractions and it is a collection of positive integers and zero. It is represented as “W” and the set of numbers are {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,……………}

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 operations are possible with the whole numbers.

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

Real Number System

Difference Between Whole Numbers and Natural Numbers

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 the whole number and natural numbers :

Natural and Whole Numbers on Number Line

Whole Numbers Properties

  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.

Can Whole Numbers be Negative?

The whole number can’t be negative!

As per 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 numbers contains all Natural Numbers, along with Zero. So yes, 0 (zero) is not only a whole number but the first whole number.

Whole Numbers Examples

Example 1:

Are 100, 227, 198, 4321 whole numbers?

Solution:

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

To learn more concepts like natural numbers, real numbers in a more engaging way, register at BYJU’S. Also, watch interesting videos on various maths topics by downloading BYJU’S– The Learning App from Google Play Store or the app store.

 

Practise This Question

All natural numbers are whole numbers.

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