7.5. Comparing the fractions $\frac{111110}{111111}, \frac{222221}{222223}, \frac{333331}{333334}$, arrange them in ascending order.
# Solution

Consider the numbers

$$
\begin{aligned}
& 1-x=\frac{1}{111111}, 1-y=\frac{2}{222223}, \quad 1-z=\frac{3}{333334}, \text { and their reciprocals } \\
& \frac{1}{1-x}=111111, \frac{1}{1-y}=111111+\frac{1}{2}, \frac{1}{1-z}=111111+\frac{1}{3} \\
& \text { We see that } \frac{1}{1-x}1-z>1-y. \text{ Therefore, } x<z<y.
\end{aligned}
$$