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Last updated on July 5th, 2025

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Properties of Whole Numbers

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There are different types of properties of whole numbers that help us perform operations on them. These properties describe the characteristics of operations. In this article, we will be learning about the properties of whole numbers when we add, subtract, multiply, and divide.

Properties of Whole Numbers for Filipino Students
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What are Whole Numbers?


The set of whole numbers consists of all the natural numbers, including zero. Whole numbers are a subset of real numbers, which include only positive integers and zero. Whole numbers do not include negative numbers, fractions, or decimals. Whole numbers are represented by W. Whole numbers begin with zero and continue with 1, 2, 3, 4, and so on. Since whole numbers start from 0, zero is the smallest whole number. Arithmetic operations like addition, subtraction, multiplication, and division can be performed on whole numbers.
 

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Difference between Whole Numbers and Natural Numbers

Parameters Whole Numbers Natural Numbers
Definition Whole numbers are natural numbers, including zero Natural numbers are a set of positive integers starting from 1 and continuing
Representation The set of whole numbers is represented by W The set of natural numbers is represented by N
Examples Whole numbers are 0, 1, 2, and so on. Natural numbers are 1, 2, 3, and so on.

 

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What are the Properties of Whole Numbers

The basic arithmetic operations are applicable on whole numbers, resulting in five main properties: closure property, commutative property, associative property, and distributive property.

 


Closure Property

The Closure property of numbers states that when you add or multiply any two whole numbers, the result will always be a whole number.

For example, 4 + 6 = 10
When we add 4 and 6, the sum is 10, which is also a whole number. 

The closure property is not applicable to the subtraction and division of whole numbers.

 

 


Commutative Property of Addition and Multiplication

The commutative property says that the sum and product of whole numbers will not change even if you change the order of the numbers. 

For example, consider that ‘a’  and ‘b’ are two whole numbers. According to this property 

a + b = b + a 
a × b = b × a

 Example: Consider a = 13 and b = 2
13 + 2 = 2 + 13
13 × 2 = 2 × 13

 


 
Associative Property of Addition and Multiplication

Associative property means addition or multiplication of three or more whole numbers. The order of the number doesn't change the result.

For example, consider a, b, c are three whole numbers. According to the associative property:
a + (b + c) = (a + b)+ c 
a × (b × c) = (a × b)  × c 
  
Example: For Addition
4 + (3 + 5) = (4 + 3) + 5
4 + 8 = 7 + 5
12 = 12

For Multiplication
2 × (3 × 4) = (2 × 3) × 4
2 × 12 = 6 × 4 
24 = 24 

 

 

Distributive Property of Multiplication Over Addition

It states that when you multiply a number by a sum, it is the same as multiplying that same number by each part of the sum separately. It can be written as :
a ×(b + c) = (a × b)  + (a × c)

For example, a=3, b=4, c=5
3 × (4 + 5) = (3 × 4)  + (3 × 5)
3 × 9 = 12 + 15
27 = 27

 

 

Identity Property

  • Additive Identity: 
    The property states that when you add 0 to any whole number, the answer will be the whole number itself. 
    For example, consider ‘a’ as a whole number 
    a + 0 = a
     
  • Multiplicative Identity:
    This property states that when we multiply a whole number by 1 then it results in the whole number itself. 
    For example, consider ‘b’ as a whole number
    1 × b = b
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Common Mistakes and How to Avoid Them in Properties of Whole Numbers

Students may often make mistakes like mixing up the properties of whole numbers and get confused. Here are some common mistakes that students make and how to avoid them.

Mistake 1

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Getting Confused with Whole numbers and natural numbers 

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Students think that whole numbers also start from 1, like natural numbers, because those two are very similar. So, students should remember that whole numbers include 0, and natural numbers start with 1. For example, 0 is a whole number but not a natural number.
 

Mistake 2

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 Using the closure property with subtraction and division

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Students assume that subtraction and division are closed under the closure property. The closure property says that adding or multiplying two numbers, the answer is always a whole number; it doesn't work for subtraction and division. Thus, students should learn the properties clearly so that they may know whole numbers are closed only under addition and multiplication. For example, 7/2 is 3.5, which is not a whole number.

Mistake 3

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Ignoring zero in multiplication and division

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Students may assume that (0 x a = a), instead of (0 x a = 0). To avoid this error, students should memorize that 0 multiplied by any whole number gives zero itself, and dividing by 0 is undefined.

Mistake 4

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:Mistakenly thinking that the distributive property works on division

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Students think that the distributive property works on division also, but that's not true; it only works on multiplication over addition. So, students should practice the properties properly to know that distributive property only works for addition and multiplication of whole numbers, not for division.

Mistake 5

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Using exponents incorrectly

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Students may think 23 = 2 × 3 instead of 2 × 2 × 2, so students should remember that exponents mean repeated multiplication, not multiplying with an exponent.
 

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Real Life Applications of Properties of Whole Numbers

Here are some real-life examples where we use properties of whole numbers 

 

Closure property is used in Banking Transactions 

This states that when we add or multiply two whole numbers, the result is always a whole number. This is used in the banking sector. When depositing and withdrawing money from any account, these transactions involve whole numbers. So, banks use this property to keep track of deposits and withdrawals.
 

Shopping and Budgeting

During shopping, we use the commutative property of addition and multiplication to simplify the calculations. For example, a person purchasing two items costs ₹10 and ₹20 each. To find the total bill, the person uses the commutative property. The total bill will be ₹30.
 

Shopping Discounts 

In this particular application, we use the distributive property, which states that multiplication distributes over addition. This is commonly used for calculating discounts that a particular store is providing. For example, if a store offers a 20% discount on ₹50 and ₹30 items, you can first add the prices  (₹50 +  ₹30) and find 20% of ₹80. This makes it easier to find the total discount. 
 

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Solved examples of Properties of Whole Numbers

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Problem 1

Verify whether the product of 3 and 5 follows the closure property of whole numbers or not.

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3 × 5 = 15
Since 15 is a whole number, it follows the closure property.
 

Explanation

Here, the closure property states that the product of any two whole numbers will be a whole number. Since 3 and 5 both are whole numbers, the result 15 is also a whole number. The property is satisfied.

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Problem 2

verify that 27 + 3 = 3 + 27

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27 + 3 = 30
                 3 + 27 = 30 
 

Explanation

The Commutative property states that changing the order of the numbers doesn't affect the sum. 
 

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Problem 3

What is 15 × 0?

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15 × 0 = 0 

Explanation

Any whole number multiplied by zero is zero. 
 

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Problem 4

If a person deposits ₹2000 in a bank, and he already has ₹500, how much money is in his account now?

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2000 + 500 = ₹2500

Explanation

 The sum of two numbers will always be a whole number.

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Problem 5

A carpenter needs 30 wooden planks for a table. If he has 4 planks, how many more does he need?

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30 – 4 = 26
 

Explanation

He needs 30 planks. He had 4 planks with him, so to know how many he needed, subtract 4 from 30. He needs 26 more.
 

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FAQs on Properties of Whole Numbers

1.Can whole numbers be negative?

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2.What is the smallest whole number?

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3. Can a whole number be a fraction or decimal?

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4.Is every whole number also a natural number?

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5.Why is zero not used in division?

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6.How can children in Philippines use numbers in everyday life to understand Properties of Whole Numbers?

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7.What are some fun ways kids in Philippines can practice Properties of Whole Numbers with numbers?

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8.What role do numbers and Properties of Whole Numbers play in helping children in Philippines develop problem-solving skills?

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9.How can families in Philippines create number-rich environments to improve Properties of 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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Fun Fact

: She loves to read number jokes and games.

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