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 |
|||
Complete the following table:
Numbers |
Commutative for |
|||
Addition |
Subtraction |
Multiplication |
Division |
|
Rational numbers |
Yes |
... |
||
Integers |
No |
|||
Whole numbers |
Yes |
|||
Natural numbers |
No |
Complete the following table:
Numbers |
Associative for |
|||
Addition |
Subtraction |
Multiplication |
Division |
|
Rational numbers |
No |
|||
Integers |
Yes |
|||
Whole numbers |
Yes |
|||
Natural numbers |
No |
If a property holds for rational numbers, will it also hold for integers? For whole Numbers? Which will? Which will not?
Mention the rational numbers that are equal to their reciprocals.
The rational numbers 1 and (–1) are equal to their reciprocals respectively.