Question

Multiplicative inverse of a negative rational number is-

• A. a positive rational number.
• B. a negative rational number.
• C. $0$
• D. $1$

Answer 1

The correct option is B

a negative rational number.

We know that the reciprocal or multiplicative inverse of the rational number $\frac{a}{b}$ is $\frac{c}{d}$ if $\frac{a}{b}\times \frac{c}{d}=1$.

Let $-\frac{a}{b}$ be a negative rational number whose reciprocal or multiplicative inverse is $\frac{c}{d}$.

Therefore as per the definition;

$\begin{array}{l} -\frac{a}{b}\times \frac{c}{d}=1\\ \Rightarrow \frac{c}{d}=-\frac{b}{a}\end{array}$

Thus multiplicative inverse of a negative rational number is a negative rational number.

Hence the correct option is (B).