Problem 2. Does there exist a fraction equal to $\frac{7}{13}$, the difference between the denominator and the numerator of which is 24?
Answer: Yes, it exists, $\frac{28}{52}$.

Solution. Since $\frac{7}{13}$ is an irreducible fraction, any fraction equal to it has the form $\frac{7 x}{13 x}$, where $x$ is some natural number. In this case, the difference between the denominator and the numerator of such a fraction will be equal to $6 x$. We have $6 x=24$, hence $x=4$. This is the only fraction that fits the condition of the problem.

## Criteria

4 p. A correct example is provided, or it is proven that such a fraction exists.