Whole Numbers – Properties of Whole Numbers – Part 1

Table of Contents

• Closure Property
• Closure Property of Addition
• Closure Property of Subtraction
• Closure Property of Multiplication
• Closure Property of Division
• Summary
• What’s Next?

In our previous segment, we learnt how to multiply whole numbers using the number line. We will now learn the properties of whole numbers, starting with the Closure property in this segment.

What is Closure property?

When a set is closed for some mathematical operation, it is said to be showing Closure property. In simple words, this means, if a set of numbers are added, subtracted, multiplied or divided, resulting in the same set of numbers, they are said to be closed under that mathematical operation.

For example, if two whole numbers are added, subtracted, multiplied or divided and the resultant number is also a whole number, then whole numbers show closure property of that particular operation.

Let us now understand this in detail

Closure property – Addition

Let us look at these examples: 4 + 5 = 9

22 + 33 = 55

In the above mathematical expressions, 4 and 5, 22 and 33 are whole numbers. And their addition respectively gives 9 and 55, which are also whole numbers. This means that whole numbers are closed under addition.

Closure property – Subtraction

Let us now check if this property holds true for the subtraction of whole numbers.

Here are two whole numbers: 35 and 20. 35 – 20 = 15.

Here the result is a whole number.

But what about 20 – 35? The answer to this is -15.

This is a negative number, that is a number less than 0. This means it is not a whole number.

This means that subtraction of whole numbers does not always give a whole number. Thus, whole numbers are not closed under subtraction.

Closure property – Multiplication

When two whole numbers are multiplied, the product is also a whole number. For example:

\[2\times 5\] = 10 \[10\times 0\] = 0

Here all the numbers are whole numbers. Thus, we can say that whole numbers are closed under multiplication.

Closure property – Division

Let us now divide two whole numbers and see if they are closed under division

\[6\div 3\] = 2, which is a whole number. \[6\div 5\] = 1.2, which is not a whole number.

This means that the division of two whole numbers does not always give a whole number. We can therefore conclude that whole numbers are not closed under division.

Summary

Operations	Closure Property of Whole Numbers
Addition	✔

Subtraction	?
Multiplication	✔
Division	?

What’s next?

In our next segment of Class 6 Maths, we will learn about the Commutative property of whole numbers.