Question

The reciprocal of a negative rational number is

• A. a positive rational number
• B. a negative rational number
• C. can be either a positive or a negative rational number
• D. cannot be determined

Answer 1

The correct option is B

a negative rational number

Reciprocal of a rational number $\frac{a}{b}$ is $\frac{b}{a}$.
The sign of the number doesn't change while taking the reciprocal.
For example, reciprocal of $\frac{2}{5}$ is $\frac{5}{2}$
and reciprocal of $\frac{-1}{6}$ is $\frac{-6}{1}$.
Hence, while taking the reciprocal, numerator and denominator are interchanged, but the sign of the rational number remains the same.
Hence the answer.