Closure Property of Whole Numbers With Examples

The Closure Property is one of the fundamental properties of whole numbers and applies to basic arithmetic operations such as addition and multiplication. The property states that when you perform an operation on any two whole numbers, the result is always a whole number.

Closure Property of Whole Numbers

1. Addition: The sum of any two whole numbers is always a whole number.
   • Example: 3+5=8
     • Here, both 3 and 5 are whole numbers, and their sum, 8, is also a whole number.
2. Multiplication: The product of any two whole numbers is always a whole number.
   • Example: 4×6=24
     • Here, both 4 and 6 are whole numbers, and their product, 24, is also a whole number.

Detailed Examples

1. Addition Example:
   • Let’s take two whole numbers:
   • 7 and 9.
   • 7+9=16
   • 7 is a whole number.
   • 9 is a whole number.
   • Their sum, 16, is also a whole number.
   • This demonstrates the Closure Property under addition for whole numbers.

1. Multiplication Example:
   • Let’s take two whole numbers:
   • 5 and 3. 5×3=15
     • 5 is a whole number.
     • 3 is a whole number.
     • Their product, 15, is also a whole number.
     • This demonstrates the Closure Property under multiplication for whole numbers.

Important Points

• Whole Numbers: Whole numbers include all non-negative integers (0, 1, 2, 3, …). They do not include fractions, decimals, or negative numbers.
• Closure under Addition: For any whole numbers a and b, a + b is always a whole number.
• Closure under Multiplication: For any whole numbers a and b, a × b is always a whole number.
• Non-closure Operations:
  • Subtraction: Whole numbers are not closed under subtraction because subtracting a larger number from a smaller number does not result in a whole number. For example, 3−5=−2, and -2 is not a whole number.
  • Division: Whole numbers are not closed under division because dividing one whole number by another does not always result in a whole number. For example, 4÷3=4/3​, which is not a whole number.

Summary

The Closure Property of Whole Numbers ensures that when you add or multiply any two whole numbers, the result will always be another whole number. This property is essential because it guarantees that the set of whole numbers is consistent and predictable when performing these operations.