Understanding the Properties of Addition of Whole Numbers

Whole numbers are the set of natural numbers along with 0. They start from 0 and go on (0, 1, 2, 3, 4, ...). These numbers are used for counting and basic calculations. The addition of whole numbers is a fundamental concept in mathematics that helps us combine quantities. Understanding the properties of addition, such as closure, commutativity, associativity, and identity, is an essential skill that makes calculations easy and error-free. In this guide, you’ll learn each property with clear explanations and easy examples.

Table of Contents

• Properties of Addition of Whole Numbers
• Solved Examples on Properties of Addition of Whole Numbers
• Practice Questions on Properties of Addition of Whole Numbers

Properties of Addition of Whole Numbers

Closure property: 

The sum of any two whole numbers is a whole number. Whole numbers are closed under addition.

Consider the numbers 10 and 24.

10 + 24 = 34; 34 is a whole number.

Commutative property: 

Two whole numbers can be added in any order. If p and q are two whole numbers

then,

p + q = q + p

Consider the numbers 87 and 45.

87 + 45 = 132

45 + 87 = 132

Therefore, 87 + 45 = 45 + 87 = 132.

Associative property: 

The sum of any three whole numbers remains the same if it is grouped and added

in any order.

Consider the whole numbers p, q, and r.

p + (q + r) = (p + q) + r

Consider the numbers 120, 42, and 58.

120 + (42 + 58) = 120 + 100 = 220

(120 + 42) + 58 = 162 + 58 = 220

Therefore, 120 + (42 + 58) = (120 + 42) + 58 = 220.

Identity Property:

If 0 is added to any whole number, the sum is the number itself. Consider the whole number p.

p + 0 = 0 + p = p

Hence, 0 is called the additive identity.

Consider the numbers 76 and 0.

76 + 0 = 0 + 76 = 76

Solved Examples on Properties of Addition of Whole Numbers

Example 1: Find the sum using the associative property: 786 + 214 + 675
Solution: (786 + 214) + 675 = 1000 + 675 = 1675
786 + (214 + 675) = 786 + 889 = 1675
(786 + 214) + 675 = 786 + (214 + 675) = 1675

Example 2: Verify the commutative property for the following: 1526 + 2435
Solution: 1526 + 2435 = 3961

2435 + 1526 = 3961

1526 + 2435 = 2435 + 1526

Example 3: Verify the closure property for the following: 75 + 15
Solution: 75 + 15 = 90. 90 is also a whole number
∴ the closure property is verified for the addition of whole numbers.

Practice Questions on Properties of Addition of Whole Numbers

1. Solve using the associative property: (5 + 8) + 12 

2. Complete the following and identify the property. 189453 + 0 = ___.

3. Complete the following and identify the property: (361 + ___ ) + 199 = 361 + (177 + ___ )

4. Fill in the blank using the commutative property: h15 + ___ = 22 + 15