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 \[10\times 0\] = 0Here 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.