Whole Numbers: Definition, Properties, Examples and pictures

Whole Numbers: Definition, Properties, and Examples

Whole Numbers Symbol : W

 

Numbers System: We use numbers to count things. There are various kinds of numbers in a number system, such as; natural numbers, whole numbers, real numbers, odd and even numbers, etc.
Whole numbers and natural number are real numbers that do not contain fractions, decimals, or negative values .We make use of numbers in our everyday life for telling the cost of items, telling time, counting objects, representing or exchanging money, measuring the temperature, etc.

Whole Numbers Definition

Whole Numbers are the set of natural numbers and 0. The set of whole numbers is written as W= {0,1,2,3,…}.

Properties of Whole Numbers

The basic operations on whole numbers are addition, subtraction, multiplication, and division, which further leads to four main properties of whole numbers that are listed below:

 

Closure Property	When two whole numbers W1 and W2 are added or multiplied, the result (W1+W2) or W1.W2 will always be a whole number.
	Example: 2+3=5 OR 3+2=5 (whole number), 2×3=6 OR 3×2=6 (whole number)
	The closure property is not true in the subtraction of whole numbers.
	Example: Subtraction 5–3= 2 (whole number), 3–5= –2 (not a whole number )
Commutative Property	The sum or the product of two whole numbers  remain the same even after interchanging the order of the numbers.
	Let W1 and W2 be two whole numbers, according to the commutative property W1+W2=W2+W1 or W1.W2=W2.W1
	Example: Sum, 8+3=11 and 3+8=11.
	Product, 8×3=24 and 3×8=24
	This property does not hold good for subtraction or division.
	Example: Subtraction 5–3= 2 (whole number), 3–5= –2 (not a whole number )
	Division, 8/4=2 and 4/8=1/2 which is not a whole number.
Associative Property	The sum or product of three whole numbers remains unchanged by grouping the numbers in any order.
	Let W1,W2 and W3 be three whole numbers, according to the associative property (W1+W2)+W3=W1+(W2+W3) or W1×(W2×W3)=(W1×W2)×W3
	Example: When we add three numbers, Let 3,4,5 we get the same sum:
	3+(4+5) = 12 or (3+4)+5=12
	Similarly, when we multiply any three numbers 3,4,5, we get the same product no matter how the numbers are grouped:
	3×(4×5)=60, (3×4)×5=60, (5x3)x4=60
	The associative property is not true for subtraction and division.
Distributive Property	This property states that the multiplication of a whole number is distributed over the sum of the whole numbers.
	Suppose W1 and W2 are multiplied with the whole number W3 and the products are added, then W3 can be multiplied with the sum of W1 and W2 to get the same answer. This situation can be represented as: W3×(W1+W2)=(W1×W3)+(W3×W2).
	Example: W1=2,W2=4 and W3=6 : 6×(2+4)=36 and (6×2)+(6×4)=36
	The distributive property is true for subtraction as well.
	Example: W1=2,W2=4 and W3=6 : 6×(4-2)=12 and (6×4)-(6×2)=12

 

 

Special Properties of Whole Numbers

There are some special properties of whole numbers other than the main properties discussed in the above section,

Additive identity	When a whole number is added to 0, its value itself whole number i.e., if W1 is a whole number, then W1+0 =0+W1 =W1
	Example: 8+0=8=0+8.4+0=4=0+4.
	The number 0 is called the additive identity for the whole number.
Multiplicative identity	Any whole number multiplied by 1 gives the same value of the whole number, i.e., if W1 is a whole number, then W1×1=W1=1×W1
	Example: 8×1=1×8=8.
	The number 1 is called the multiplicative identity for the whole number.
Multiplication by zero	Any whole number multiplied by 0 always gives 0, i.e., W1×0=0=0×W1
	Example: 8×0=0×8=0.
Division by zero	Division of a whole number by 0 is not defined, i.e., if W1 is a whole number, then W1x0 is not defined.

 

FAQs on Whole Numbers

Following are some common questions which candidates may have in their mind regarding Whole Numbers:

Q1. Define whole numbers, or what are whole numbers?
Ans: Whole numbers in Math is the set of positive integers and 0. In other words, it is a set of natural numbers, including 0.Decimals, fractions, negative integers are not part of whole numbers.

Q2. What are the four properties of whole numbers?
Ans: The four properties of whole numbers are:
1. Closure property.
2. Associative property.
3. Commutative property.
4. Distributive property

Q3. What is the use of whole numbers?
Ans: These are numbers that we are the most used to working with, including zero. We see whole numbers on nutrition labels or signs on the highway telling us how many miles are to the next city. 

Q4. What is the smallest whole number?
Ans: Zero is the smallest whole number.

Q5. Which numbers are not whole numbers?
Ans: A negative integer, fractions, part of rational numbers and decimals do not belong to whole numbers.

Q6. Which is the largest whole number?
Ans: There is no largest whole number. Every whole number has an immediate successor or a number that comes after. So the whole numbers are infinite to count, and thus, there is nothing such largest whole number.

 

Whole Numbers on Number Line

 All the integers starting from 0 represent the Whole numbers .Whole numbers on the number line.

 

Refer to the following Reference Books for Maths

 

1.      Mathematics by Chand Publishing

2.      NCERT Textbooks  

3.      Quantitative Aptitude for competitive examinations by RS Aggarwal

4.      For Entrance Exam by ES Ramasamy