#### Answer

(a) rational, integer, natural number
(b) rational, integer
(c) rational, integer, natural number
(d) irrational
(e) rational
(f) rational, integer

#### Work Step by Step

(a) 16 is rational, since it can be expressed as a ratio of integers (16/1). It is an integer and a natural number.
(b) $-16$ is rational, since it can be expressed as a ratio of integers (-16/1). It is an integer, but not a natural number (because it is negative).
(c) $\sqrt{16}=4$ is rational, since it can be expressed as a ratio of integers (4/1). It is an integer and a natural number.
(d) $\sqrt{2}$ is irrational because it can't be expressed as a ratio of integers (does not simplify).
(e) $\displaystyle \frac{8}{3}$ is rational, since it is a ratio of integers. However, it is not a natural number or an integer.
(f) $\displaystyle -\frac{8}{2}=-4$ is rational, since it is a ratio of integers. It is an integer, but not a natural number (negative).