Question

What is the multiplicative inverse of a negative rational number?
A) A positive rational number
B) A negative rational number
C) $0$
D) $1$

Answer 1

Hint: In this question, we have been asked the multiplicative inverse of a negative rational number. First, read about what is a multiplicative inverse. Using its properties, find out the multiplicative inverse of a general negative rational number and then choose the best or the closest option.

Complete step-by-step solution:
We have to find the multiplicative inverse of a negative rational number. But let us first know about multiplication inverse.
What is multiplicative inverse?
Multiplication inverse is just another name for ‘reciprocal’. For any number $k$, multiplicative inverse or reciprocal can be simply stated as $\dfrac{1}{k}$. For example: multiplicative inverse of certain natural numbers like $6$ is $\dfrac{1}{6}$, $568$ is $\dfrac{1}{{568}}$, etc. However, it should be kept in mind that $0$ has no multiplicative inverse. This is because if we find its reciprocal, we will get $\dfrac{1}{0}$. This is equal to infinity $\left( \infty \right)$. Hence, $0$ has no multiplicative inverse.
A very important property of multiplication inverse is that when a number is multiplied with its reciprocal or multiplicative inverse, we get $1$. Using this property only, we find multiplicative inverses of numbers.
Now, moving towards the question, when any negative number is multiplied with a positive number, our final result is a negative number. But here, we know that the product should be 1. So, the multiplicative inverse of a negative number will be a negative number only.

Hence, our answer is option B) A negative rational number.

Note: We have to know that, Rational numbers are those numbers which can be expressed in the form $\dfrac{p}{q}$, where $q \ne 0$.
Example: $\dfrac{1}{3},\dfrac{9}{8}$ are certain examples of rational numbers. These numbers can be located on the number line.