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:

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

Verify that: ${\left(x÷y\right)}^{-1}=x^{-1}÷Y^{-1}$ by taking $x=\frac{-5}{11}, y=\frac{7}{3}$

Verify that: $\left|x+y\right|\le \left|x\right|+\left|y\right|$ by taking $x=\frac{2}{3}, y=\frac{-3}{5}$

Find the reciprocal of:

$\frac{2}{-5}\times \frac{3}{-7}$

Find the reciprocal of:

$\frac{-4}{3}\times \frac{-5}{-8}$