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Last updated on May 26th, 2025

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Whole Numbers

Professor Greenline Explaining Math Concepts

A Whole number is any natural number along with zero. It does not contain fractions, decimals, or negative numbers, and this type of number begins at 0 and continues to infinity. In this topic, we are going to learn about whole numbers in detail.

Whole Numbers for Canadian Students
Professor Greenline from BrightChamps

What are Whole Numbers?

In our daily lives, we keep count of various things,  such as age, quantities, and items. The counting numbers in mathematics are referred to as natural numbers. Zero, along with natural numbers, is included in the collection of whole numbers. For instance, 0, 2, 77, and 9999 are some examples of whole numbers, and the set of whole numbers goes up to infinity. The capital letter ‘W’ is used to represent whole numbers. 

Professor Greenline from BrightChamps

Difference between Whole Numbers and Natural Numbers

Understanding the differences between whole and natural numbers helps us easily distinguish between numbers and solve calculations efficiently. 
 

Whole Numbers

Natural Numbers

The collection of whole numbers, denoted as W, consists of {0, 1, 2, 3, 4,...} and extends infinitely.

The set of natural numbers, represented as N, includes { 1, 2, 3, 4,...}  and continues infinitely.
 

Zero (0) is the smallest whole number.

1 is the smallest natural number. 

Every natural number is a whole number. Except for 0, all whole numbers are natural numbers.

 

Professor Greenline from BrightChamps

Representing Whole Numbers on Number Line

Whole numbers can be represented visually using a number line. It is a horizontal line that includes all positive integers and zero, arranged in order. The starting point of the number line is zero, and it consists of whole numbers and the natural numbers, as seen below:  
 

Professor Greenline from BrightChamps

Properties of Whole Numbers

Whole numbers are a fundamental aspect of mathematics, consisting of natural numbers along with zero. Understanding the key properties of whole numbers helps in solving complex mathematical problems more easily and strengthens the foundation of arithmetic knowledge. The properties of whole numbers include: 

 

  • Closure property: When we add or multiply two whole numbers, the result is always a whole number. This means whole numbers are closed under addition and multiplication because these operations always give whole numbers. This property can be represented as follows:

x + y = W, or 
x × y = W
W is a whole number. 
For example, 2 + 3 = 5, which is a whole number.
2 × 4 = 8, which is a whole number.

 

 

  • Commutative property: When we switch the order of two whole numbers in addition or multiplication, the result remains the same. Irrespective of the ordering of the whole numbers, the sum and product remain the same. The commutative property of addition is: x + y = y + x

The commutative property of multiplication is: x × y = y × x
 For instance, 3 + 1 = 1 + 3 = 4
4 × 3 = 3 × 4 = 12

 

 

  • Additive identity: If we add a whole number with zero the result is always the same whole number, i.e., x + 0 = x

For example, 8 + 0 = 8 

 

 

  • Multiplicative identity: If we multiply a whole number by 1 the result is always the same whole number. It is represented as: x × 1 = x

For instance, 4 × 1 = 4

 

 

  • Associative property: If the grouping of three whole numbers is changed in addition or multiplication, the result stays the same. This is represented as: x + (y + z) = (x + y) + z (associative property of addition).

x × (y × z) = (x × y) × z (associative property of multiplication).
For instance, 1 + (5 + 2) = 1 + 7 = 8 
(1 + 5) + 2 = 6 + 2 = 8

Likewise, 1 × (5 × 2) = 1 × 10 = 10
(1 × 5) × 2 = 5 × 2 = 10

 

 

  • Distributive property: The multiplication of a whole number is distributed over the sum or difference of the whole numbers. It is represented as: x × (y + z) = (x × y) + (x × z).

For example, take a look at this: 
2 × (3 + 6) = 2 × 9 = 18
(2 × 3) + (2 × 6) = 6 + 12 = 18
Thus, 2 × (3 + 6) = (2 × 3) + (2 × 6)

 

 

  • Multiplication by zero: If we multiply a whole number by zero, the result is always zero, i.e., a × 0 = 0

For instance, 14 × 0 = 0

 

 

  • Division by zero: Any whole number cannot be divided by zero. This is expressed as: 

a/0 is undefined. 
 

Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them on Whole Numbers

Whole numbers are a set of numbers, including 0 and all natural numbers and they do not have fractional or decimal parts. Students often make errors, when they work with whole numbers which lead to incorrect calculations and conclusions. Here are some common mistakes and solutions to help avoid these errors: 

Mistake 1

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Assuming that Natural Numbers are Whole Numbers 

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Students often get confused about whole numbers and natural numbers. Therefore, kids should clearly understand the differences between these two types of numbers to avoid confusion. Natural numbers begin at 1, whereas whole numbers start from 0 and include all positive integers. 

Professor Greenline from BrightChamps

Real-life Applications of Whole Numbers

In our daily lives, we count objects and items like fruits, vehicles, people, and ages using
whole numbers. Whole numbers are vital in various fields to indicate and represent counts. The real-life applications of whole numbers are countless.

 

  • Whole numbers are used in the fields of banking and finance to indicate deposit interest rates and withdrawal amounts of customers. It makes the transactions easy to understand and it reduces confusion.

 

  • In engineering and construction, whole numbers are used to represent the measured distance, area, volume, and time. For example, the distance between two cities might be 30 km, which is represented using whole numbers.

 

  • Manufacturers and producers use whole numbers to keep track of the number of products available in stock or currently being produced.

 

  • Whole numbers are used in demographic studies to represent the total population of a city or country. For example, the population of a country is recorded in a census.
     
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Solved Examples on Whole Numbers

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

Identify the whole numbers among the following numbers: (-2, 0, 4,1/7, 6)

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 0, 4, and 6 are the whole numbers.

Explanation

In the given list of numbers:
-2 is a negative number, so it is not a whole number.
0 is a whole number because whole numbers start from 0 and include all
positive integers.
4 is a positive integer, and all positive integers are whole numbers, hence 4 is a
whole number.
1/7 is a fraction, and whole numbers cannot be fractions, so 1/7 is not a whole
number.
6 is a positive integer, therefore 6 is a whole number.
The whole numbers in the list are 0, 4, and 6.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 2

Identify the whole numbers among the following numbers: (1, -4, 9, 1/2, 0)

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1, 9, and 0 are the whole numbers.

Explanation

In the given list, 1 is a positive integer, so it is a whole number.
-4 is a negative number, so it is not a whole number.
9 is a positive integer, therefore it is a whole number.
1/2 is a fraction, hence it is not a whole number.
0 is a whole number because it is part of the set of whole numbers.
The whole numbers in the list are 1, 9, and 0.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 3

Identify the whole numbers among the following numbers: (1, -4, 9, 1/2, 0)

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

1, 9, and 0 are the whole numbers. 

Explanation

In the given list, 1 is a positive integer, so it is a whole number.
-4 is a negative number, so it is not a whole number.
9 is a positive integer, therefore it is a whole number.
1/2 is a fraction, hence it is not a whole number.
0 is a whole number because it is part of the set of whole numbers.
The whole numbers in the list are 1, 9, and 0.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 4

Identify the whole numbers among the following numbers: (-6, 6, 0.5, 17, 12)

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

6, 17, and 12 are the whole numbers.

Explanation

Here, -6 is a negative number, so it is not a whole number.
6 is a positive integer, therefore it is a whole number.
0.5 is a decimal number, hence it is not a whole number.
17 and 12 are positive integers, so they are whole numbers.
The whole numbers in the list are 6, 17, and 12.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 5

Identify the whole numbers among the following numbers: (3, -8, 9, 0, -4)

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

3, 9, and 0 are the whole numbers.

Explanation

In the given list of numbers, 3 is a positive integer, so it is a whole number.
-8 is a negative number, hence it is not a whole number.
9 is a positive integer, therefore it is a whole number.
0 is a whole number.
-4 is a negative number, so it is not a whole number.
The whole numbers in the list are 3, 9, and 0.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 6

Identify the whole numbers among the following numbers: (2, 0, -18, 5, 1/5)

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

2, 0, and 5 are the whole numbers. 

Explanation

In the given list of numbers, 2 is a positive integer, so it is a whole number.
0 is a whole number.
-18 is a negative number, therefore it is not a whole number.
5 is a positive integer, hence it is a whole number.
1/5 is a fraction, so it is not a whole number.
The whole numbers in the list are 2, 0, and 5.

Max from BrightChamps Praising Clear Math Explanations
Ray Thinking Deeply About Math Problems

FAQs on Whole Numbers

1.Define whole numbers.

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2.Is -2 a whole number?

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3.Differentiate natural numbers and whole numbers.

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4.What is the smallest whole number?

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5.How can children in Canada use numbers in everyday life to understand Whole Numbers?

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6.What are some fun ways kids in Canada can practice Whole Numbers with numbers?

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7.What role do numbers and Whole Numbers play in helping children in Canada develop problem-solving skills?

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8.How can families in Canada create number-rich environments to improve Whole Numbers skills?

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

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Max, the Girl Character from BrightChamps

Fun Fact

: She loves to read number jokes and games.

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