922. Find the fraction with the smallest possible denominator that lies between $\frac{7}{25}$ and $\frac{8}{25}$. List all solutions.
$\triangle$ Let the required fraction be $\frac{a}{b}$, where $a$ and $b$ are natural numbers. Then

$$
\frac{7}{25}<\frac{a}{b}<\frac{8}{25}
$$

Now let's consider several cases depending on $b$.

1) The cases $b=1$ and $b=2$ should be discarded, as the fraction $\frac{a}{b}$ would be too large in these cases.
2) Let $b=3$. Then $a=1$. Does the inequality

$$
\frac{7}{25}<\frac{1}{3}<\frac{8}{25} ?
$$

hold? No, because it reduces to the incorrect inequality $21<25<24$.

3) Let $b=4$. Then $a=1$. But the inequality

$$
\frac{7}{25}<\frac{1}{4}<\frac{8}{25}
$$

also does not hold (check it).

4) Let $b=5$. In this case, $a=2$. But the inequality

$$
\frac{7}{25}<\frac{2}{5}<\frac{8}{25}
$$

is also false.

5) Let $b=6$. Then the value $a=1$ is too small, and for $a=2$ we get the fraction $\frac{2}{6}=\frac{1}{3}$, which we have already considered.
6) Let $b=7$. Here we need to take $a=2$. Let's check the corresponding inequality:

$$
\frac{7}{25}<\frac{2}{7}<\frac{8}{25}, \quad 49<50<56 .
$$

Since the last inequality is true, the fraction $\frac{2}{7}$ satisfies the requirement of the problem.

Answer: $\frac{2}{7}$