Question

The reciprocal of a negative rational number is
A. negative
B. positive
C. cannot be determined
D. none

Answer 1

Hint: Given a negative rational number, we have to find out the reciprocal and say what type of number it is. The reciprocal of a number is also called its multiplicative inverse. The product of a number and its reciprocal is 1. The reciprocal of a fraction is found by flipping its numerator and denominator.

Complete step-by-step answer:
Rational number: A number that can be expressed as fraction p/q of two integers, a numerator p and a non zero denominator q.
The decimal expansion of a rational number always either terminates after a finite number of digits or begins to repeat the same finite sequence of digits over and over. Moreover, any repeating or terminating decimal represents a rational number.
A real number that is not rational is called an irrational number.

If \[\dfrac{a}{b}\] is a rational number then multiplicative inverse of this number is \[\dfrac{b}{a}\]
If \[\dfrac{-a}{b}\]is a negative rational number then the reciprocal is \[\dfrac{-b}{a}\].
From the above we can say that the reciprocal of a negative rational number is negative.
Example: Considering the number as \[\dfrac{-2}{3}\]then the reciprocal of the number is \[\dfrac{-3}{2}\].
Now considering one more example, taking the number as \[-3\]then the reciprocal is \[\dfrac{-1}{3}\]
Hence we can say that the reciprocal of a negative rational number is negative.

Note: Reciprocal of a number is just writing the multiplicative inverse. From the above examples we can clearly state that reciprocal of a negative rational number is negative.
For checking, the product of a number and its reciprocal is 1