Question

Which of the following are rational numbers?
(i) $\frac{5}{-8}$

(ii) $\frac{-6}{11}$

(iii) $\frac{7}{15}$

(iv) $\frac{-8}{-12}$

(v) $6$

(vi) $-3$

(vii) $0$

(viii) $\frac{0}{1}$

(ix) $\frac{1}{0}$

(x) $\frac{0}{0}$

Answer 1

A rational number is in the form of $\frac{P}{Q}$, where $P$ and $Q$ are integers and $Q\ne 0$

i) $\frac{5}{-8}$ is a rational number because it is in the form of $\frac{P}{Q},$ where $P$ and $Q$ are integers and $Q\ne 0.$

ii) $\frac{-6}{11}$ is a rational number because it is in the form of $\frac{P}{Q}$, where $P$ and $Q$ are integers and $Q\ne 0.$

iii) $\frac{7}{15}$ is a rational number because it is in the form of $\frac{P}{Q}$, where $P$ and $Q$ are integers and $Q\ne 0.$

iv) $\frac{-8}{-12}$ is a rational number because it is in the form of $\frac{P}{Q}$, where $P$ and $Q$ are integers and $Q\ne 0.$

v) $6=\frac{6}{1}$ is a rational number because it is in the form of $\frac{P}{Q}$, where $P$ and $Q$ are integers and $Q\ne 0.$

vi) $-3=\frac{-3}{1}$ is a rational number because it is in the form of $\frac{P}{Q}$, where $P$ and $Q$ are integers and $Q\ne 0.$

vii) $0=\frac{0}{1}$ is a rational number because it is in the form of $\frac{P}{Q}$, where $P$ and $Q$ are integers and $Q\ne 0.$

viii) $\frac{0}{1}$ is a rational number because it is in the form of $\frac{P}{Q}$, where $P$ and $Q$ are integers and $Q\ne 0.$

ix) $\frac{1}{0}$ here, $Q=0$, so, it is not a rational number.

x) $\frac{0}{0}$ is not a rational number because, here, $Q=0.$