Whole Numbers: Definition and Difference Between Whole Numbers and Natural Numbers

Glide to success with Doorsteptutor material for NDA Mathematics: fully solved questions with step-by-step explanation- practice your way to success.

The whole numbers are the part of the number system in which it includes all the positive integers from 0 to infinity. These numbers exist in the number line; hence they are all real numbers. All the whole numbers are real numbers but not all the real numbers are whole numbers. Natural numbers along with β€˜0’ are called whole numbers. The examples are: 0,11,25,36, etc.

  • Whole Numbers and Natural Numbers

  • Natural Numbers

  • Difference between natural and whole numbers

  • Real numbers

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 β€œW” 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 are not whole numbers). Addition, Subtraction, Multiplication and Division operations are possible with the whole numbers.

Whole Numbers Definition

Whole Numbers Definition

Loading Image β€’β€’β€’

Whole Numbers Properties

The properties of whole numbers are based on arithmetic operations such as addition, subtraction, division and multiplication. Two whole numbers if added or multiplied will give a whole number itself. Subtraction of two whole numbers may not result in whole numbers, i.e. it can be an integer too. Also, division of two whole numbers results in getting a fraction in some cases. Now let us see some more properties here;

Closure Property

They can be closed under addition and multiplication, i.e., if and are two whole numbers then is also a whole number.

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

Additive Identity

When a whole number is added to 0, its value remains unchanged, i.e., if x is a whole number then

Multiplicative Identity

When a whole number is multiplied by 1, its value remains unchanged, i.e., if x is a whole number then

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 and

Distributive Property

If x,y and z are three whole numbers, the distributive property of multiplication over addition is similarly, the distributive property of multiplication over subtraction is

Multiplication by Zero

When a whole number is multiplied to 0, the result is always 0, i.e.,

Division by Zero

Division of a whole number by o is not defined, i.e., if x is a whole number then is not defined.

Difference between Whole Numbers and Natural Numbers

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:

Whole Numbers and Natural Numbers

Whole Numbers and Natural Numbers

Loading Image β€’β€’β€’

Can Whole Numbers be Negative?

The whole number can’t be negative!

As per definition: {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 whole numbers?

Solution: Yes. are all whole numbers.

Example 2: Solve using the distributive property.

Solution: The whole numbers have following distributive properties:

This implies

Example 3: Solve using the Associative properties.

Solution:

The whole numbers have following Associative properties:

Comparing value,

Put the value of x, y, and z

Put the value of x, y, and z

This is implying

Frequently Asked Questions on Whole Numbers

Define Whole Numbers

The numbers are defined as the positive numbers including zero. The whole number does not contain any decimal or fractional part. It means that it represents the whole thing without pieces. The set of whole numbers is mathematically represented as:

Can Whole Numbers be Negative?

No, the whole numbers cannot be negative. The whole numbers start from and so on. All the natural numbers are considered as whole numbers, but all the whole numbers are not natural numbers. Thus, the negative numbers are not considered as whole numbers.

What Are the Properties of Whole Numbers?

The properties of whole numbers are:Whole numbers are closed under addition and multiplicationThe addition and multiplication of two numbers is commutativeThe addition and multiplication of whole numbers is associativeIt obeys the distributive property of multiplication over additionThe additive identity of whole numbers is 0The multiplicative identity of whole numbers is 1