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Rational Numbers

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Question
CBSEENMA8001933
Wired Faculty App

Fill in the blanks in the following table:

Numbers

Closed under
 

Addition

Subtraction

Multiplication

Division

Rational numbers

Yes

Yes

  

No

Integers

  

Yes

  

No

Whole numbers

...

  

Yes

  

Natural numbers

  

No

    
   

Solution

Using the closure property over addition, subtraction, multiplication and division for rational numbers, integers, whole-numbers and natural numbers, we have:

Numbers

Closed under
 

Addition

Subtraction

Multiplication

Division

Rational numbers

Yes

Yes

Yes

No

Integers

Yes

Yes

Yes

No

Whole numbers

Yes

No

Yes

No

Natural numbers

Yes

No

Yes

No

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Question
CBSEENMA8001934
Wired Faculty App

Complete the following table:

Numbers

Commutative for
 

Addition

Subtraction

Multiplication

Division

Rational numbers

Yes

    

...

Integers

  

No

    

Whole numbers

    

Yes

  

Natural numbers

      

No

Solution

Numbers

Commutative for
 

Addition

Subtraction

Multiplication

Division

Rational numbers

Yes

No

Yes

No

Integers

Yes

No

Yes

No

Whole numbers

Yes

No

Yes

No

Natural numbers

Yes

No

Yes

No

Question
CBSEENMA8001935
Wired Faculty App

Complete the following table:

Numbers

Associative for
 

Addition

Subtraction

Multiplication

Division

Rational numbers

      

No

Integers

    

Yes

  

Whole numbers

Yes

      

Natural numbers

  

No

  

Solution

Numbers

Associative for
 

Addition

Subtraction

Multiplication

Division

Rational numbers

Yes

No

Yes

No

Integers

Yes

No

Yes

No

Whole numbers

Yes

No

Yes

No

Natural numbers

Yes

No

Yes

No

Question
CBSEENMA8001936
Wired Faculty App

If a property holds for rational numbers, will it also hold for integers? For whole Numbers? Which will? Which will not?

Solution

(i) Any property which is true for rational numbers, is also true for integers except for any integers ‘a’ and ‘b’ (a ÷ b) is not necessarily an integer.

(ii) All properties which are true for rational numbers, are also true for whole numbers also except:

(a) For ‘a’ and ‘b’ being whole numbers, (a – b) may not be a whole number.

(b) For ‘a’ and ‘b’ being whole numbers (b ? 0), a ÷ b may not be whole number.

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