Answer
a) rational; integer
b) rational; neither
c) rational; natural number; integer
d) irrational
e) rational; neither
f) rational; natural number; integer
Work Step by Step
a) -5 is an integer because it can be expressed as a fraction $\frac{-5}{1}$. It is not a natural number because it is negative, but it is an integer.
b) $\frac{-25}{6}$ is rational because it is expressed as a fraction. It is neither a natural number nor an integer.
c) $\sqrt 25$ is equal to 5, and therefore it is rational because it can be expressed as a fraction $\frac{5}{1}$. It is also a natural number and an integer.
d) Since $\pi$ is irrational, $3\pi$ is also irrational. $\pi$ cannot be expressed as a fraction and it does not terminate, so it is irrational.
e) $\frac{24}{16}$ is rational because it is expressed as a fraction. It is neither a natural number nor an integer.
f) $10^{20}$ is an integer because it can be expressed as a fraction $\frac{10^{20}}{1}$. It is a natural number and it is an integer.
