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Rational Numbers

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Mathematics

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Complete the following table:

Numbers

Commutative for

 

Addition

Subtraction

Multiplication

Division

Rational numbers

Yes

   

...

Integers

 

No

   

Whole numbers

   

Yes

 

Natural numbers

     

No


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

1291 Views

Complete the following table:

Numbers

Commutative for

 

Addition

Subtraction

Multiplication

Division

Rational numbers

Yes

   

...

Integers

 

No

   

Whole numbers

   

Yes

 

Natural numbers

     

No


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

161 Views

Complete the following table:

Numbers

Associative for

 

Addition

Subtraction

Multiplication

Division

Rational numbers

     

No

Integers

   

Yes

 

Whole numbers

Yes

     

Natural numbers

 

No

 

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

1645 Views

Complete the following table:

Numbers

Associative for

 

Addition

Subtraction

Multiplication

Division

Rational numbers

     

No

Integers

   

Yes

 

Whole numbers

Yes

     

Natural numbers

 

No


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

216 Views

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

   
   


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

3110 Views