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Properties whole Numbers - Closure

Whole numbers are numbers starting from 0

Eg: 0, 1, 2, 3, 4, ….

Operation

 

Closed or not

Addition

3 + 5 = 8

8 is a whole number

Also,

2 + 0 = 2

2 is a whole number

So, whole numbers are closed under addition

So, if we add any two numbers,

we get a whole number

So, it is closed

Subtraction

3 – 5 = –2

But, –2 is not a whole number

So, whole number are not closed under subtraction

 

So, if we subtract any two numbers,

we do not get a whole number

So, it is not closed

Multiplication

 

3 × 5 = 15

15 is a whole number

Also,

2 × 0 = 0

0 is a whole number

So, whole numbers are closed under multiplication

So, if we multiply any two numbers,

we get a whole number

So, it is closed

Division

 

3 ÷ 5 = 3/5

But, 3/5 is not a whole number

So, whole number are not closed under division

So, if we divide any two numbers,

we do not get a whole number

So, it is not closed

 

Hence,

Whole numbers are closed under Addition and Multiplication

but not under Subtraction and Division

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Transcript

Properties whole Numbers - Closure Whole numbers are numbers starting from 0 Eg: 0, 1, 2, 3, 4, …. 3 + 5 = 8 8 is a whole number Also, 2 + 0 = 2 2 is a whole number So, whole numbers are closed under addition So, if we add any two numbers, we get a whole number So, it is closed 3 – 5 = –2 But, –2 is not a whole number So, whole number are not closed under subtraction So, if we subtract any two numbers, we do not get a whole number So, it is not closed 3 × 5 = 15 15 is a whole number Also, 2 × 0 = 0 0 is a whole number So, whole numbers are closed under multiplication So, if we multiply any two numbers, we get a whole number So, it is closed 3 ÷ 5 = 3/5 But, 3/5 is not a whole number So, whole number are not closed under division So, if we divide any two numbers, we do not get a whole number So, it is not closed Hence, Whole numbers are closed under Addition and Multiplication but not under Subtraction and Division

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.