Let the base of the number system be $q$. Then the numerator can be transformed as follows:

$$\begin{gathered} 1010000-101111=\left(q^{6}+q^{4}\right)-\left(q^{5}+q^{3}+q^{2}+q+1\right)=\left(q^{3}+q+1\right)\left(q^{3}-q^{2}-1\right)= \\ =1011(1000-101) \end{gathered}$$

Similarly for the denominator:

$$\begin{gathered} 1011011-100100=\left(q^{6}+q^{4}+q^{3}+q+1\right)-\left(q^{5}+q^{2}\right)=\left(q^{3}+q+1\right)\left(q^{3}+1-q^{2}\right)= \\ =1011(1001-100) . \end{gathered}$$

Therefore, in any number system, the fraction can be simplified by the number in the form of 1011.