Every rational number is

1. a natural number
2. an integer
3. a real number
4. a whole number

Between two rational numbers

1. there is no rational number
2. there is exactly one rational number
3. there are infinitely many rational numbers
4. there are only rational numbers and no irrational numbers.

The product of any two irrational numbers is

1. always an irrational number
2. always a rational number
3. always an integer
4. sometimes rational, sometimes irrational

The division of two irrational numbers is

1. a rational number
2. an irrational number
3. either a rational number or an irrational number
4. neither rational number nor irrational number