Properties of Whole Numbers
2026-02-28 10:08 Diff
https://brightchamps.com/en-us/math/numbers/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 = 24


When we multiply 4 and 6, the product is 24, 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


The associative property refers to the grouping of three or more whole numbers in addition or multiplication without changing 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