Question

Write.
I.The rational number that does not have a reciprocal.
II.The rational numbers that are equal to their reciprocals.
III.The rational number that is equal to its negative.

Answer 1

Hint: In the given question we have to write the examples of the asked question which means we are asked to write rational number that does not have a reciprocal.it means those rational number which is not having its reciprocal, we have to write that one in the same way, three questions are to be asked to write but this is not means under a condition.

Complete step-by-step answer:
 In the given question we have to write a rational number but under some interesting condition. Let us write three rational numbers one after another.
In the first part, we had asked hat write a rational number that does not have a reciprocal rational numbers are those numbers which can be written in the form of \[\dfrac{p}{q}\] where \[q \ne 0\]
So the rational number which does not have reciprocal is zero
This is because zero is a rational number where zero is treated as \[\dfrac{0}{1}\] (rational number)
But if we reciprocal it
We get \[\dfrac{1}{0}\] which is not defined
Therefore zero is the rational number that does not have a reciprocal.
In the second part, We have to write rational numbers that are equal to its reciprocal.
So \[1\] and \[ - 1\] are the rational numbers which are equal to its reciprocal
If we reciprocal \[\dfrac{1}{1}\], we get \[\dfrac{1}{1}\]
And if we reciprocal \[\dfrac{{ - 1}}{1}\], we get \[\dfrac{1}{{ - 1}}\] which means \[ - 1\] so \[1\] and \[ - 1\] are the rational numbers which are equal to their reciprocals.
In the third part, we had to write the rational number that is equal to its negative
So, zero is the rational number that is equal to its negative.
So if we take negative of zero, we get zero itself which means \[-{\text{ }}\left( 0 \right){\text{ }} = {\text{ }}0\]
Therefore zero is the rational number equal to its negative.

Note: If we take reciprocal of \[\dfrac{{ - 4}}{3}\] where \[\dfrac{4}{3}\] is a rational number, therefore reciprocal of \[\dfrac{{ - 4}}{3}\] is \[\left( {\dfrac{{ - 3}}{4}} \right)\]
Which ultimately becomes \[\left( {\dfrac{{ - 3}}{4}} \right)\] because negative cannot be there in the denominator. So we keep the negative sign out and simply do the reciprocal of the rational number.