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).
