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Rational Numbers
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 |
|
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 |
|
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 |
If a property holds for rational numbers, will it also hold for integers? For whole Numbers? Which will? Which will not?
(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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Mock Test Series
Mock Test Series