If $\left|x\right|=0$, then $x$ has no reciprocal. 

If $x<y$ then $x^{-1} < y^{-1}$

The negative of a negative rational number is a positive rational number.

Product of two rational numbers can never be an integer.

Product of two integers is never a fraction.

If $x$ and $y$ are two rational numbers such that $x>y,$ then $x-y$ is always a positive rational number.

For $x=\frac{3}{4}$ and $y=\frac{-9}{8}$, insert a rational number between:

${\left(x+y\right)}^{-1} and x^{-1}+y^{-1}$

For $x=\frac{3}{4}$ and $y=\frac{-9}{8}$, insert a rational number between:

${\left(x-y\right)}^{-1} and x^{-1}-y^{-1}$