Let the rational number be[tex]\frac{x}{y}[/tex].
If we divide this rational number by a factor k, then it becomes [tex]\frac{x}{ky}[/tex].
We need to find 'k'.
Now, twice the opposite of the given rational number is [tex]\frac{-2x}{y}[/tex]
By the given information,
[tex]\frac{x}{ky} =\frac{-2x}{y}[/tex]
xy = -2kxy
-2k = 1
[tex]k = -\frac{1}{2}[/tex]
Hence, we should divide the given rational number by [tex]-\frac{1}{2}[/tex].
