Question

The reciprocal of a positive rational number is always negative. If true, then enter 1 and if false, then enter 0.

Answer 1

Hint: Before solving this question, one must be familiar with the term rational number, irrational number and reciprocal. Here is a definition for rational number, irrational number and reciprocal.

Rational and irrational numbers are the complex form of representation of numbers in Mathematics. A number which is written in the form of a ratio of two integers is a rational number whereas an irrational number has endless non-repeating digits. The example of an irrational is \[\pi =3.141\]
and that of a rational number is \[\dfrac{1}{2}\] .

RATIONAL NUMBER: Rational numbers are represented in p/q form where q is not equal to zero, in other words, the denominator, i.e. q, should not be zero.

IRRATIONAL NUMBER: Irrational numbers are the numbers that cannot be represented as a simple fraction. It is a contradiction of rational numbers but is a type of real numbers.

RECIPROCAL: The reciprocal is also called the "Multiplicative Inverse". A reciprocal, or multiplicative inverse, is simply one of a pair of numbers that, when multiplied together is equal to 1.

Now, let us solve the question.

Complete step-by-step answer:
Now, as we know what are ‘rational numbers’, ‘irrational numbers’, and ‘reciprocal’ we are in a condition to solve the question.
So, the reciprocal of a positive number is never a negative number.
Let us take some examples:-
Say, \[\dfrac{5}{9}\] . So, the reciprocal of \[\dfrac{5}{9}\] would be \[\dfrac{9}{5}\] , which is also positive.
Let us take another example, say, \[\dfrac{17}{4}\] . So, the reciprocal of \[\dfrac{17}{4}\] would be \[\dfrac{17}{4}\] , which is positive.
Let us take one last example, say \[\dfrac{36}{7}\] . So, the reciprocal of \[\dfrac{36}{7}\] would be \[\dfrac{7}{36}\] , which is again positive.
So, we can conclude that the reciprocal of a positive rational number can never be negative.
Therefore, the answer is 0.

Note: Always try to remember the definition of Rational number, Irrational number, Integer, Whole number, complex number etc.