Question

The reciprocal of a positive rational number is positive. Choose the correct option.
A . True
B . False
C . Cannot be determined
D. None

Answer 1

Hint: The reciprocal of the positive number is always a positive number. The number can be real number, rational number, whole number or of any type.

Complete step-by-step answer:
In the question, we have to check whether the reciprocal of a positive rational number is positive or not. So, here we can take an example of the rational number that is positive. It can also be noted that the rational number will be of the form \[\dfrac{p}{q}\] where p and q are integers and \[q\ne 0\].
So, we have \[\dfrac{1}{2}\]as a positive rational number. The reciprocal of this rational number is \[\dfrac{2}{1}\]which is also a rational number. Now take another example \[\dfrac{-1}{-3}\]which is also a positive rational number because \[\dfrac{-1}{-3}=\dfrac{1}{3}\]and the reciprocal of this rational number is \[\dfrac{3}{1}\]which is again a positive rational number. So, we can say the reciprocal of a positive rational number is positive. Hence the statement that reciprocal of a positive rational number is positive is true. So, the correct answer is option A.

Note: It can be noted that the reciprocal of the rational number is also a rational number. The positive rational number can also be found from two negative numbers in the fractional form. The negatives get cancelled and will become positive, so care has to be taken for this condition too. Also, note that \[\sqrt{3}\]is not a rational number but \[\sqrt{9}\]is a rational number because \[\sqrt{9}=3\].