55. When Tanya introduced Svetlana to her problem (see problem 54), Svetlana decided to find another interesting property of the fraction $\frac{2}{5}$. She discovered that if 2 is added to the numerator of this fraction, and the denominator is multiplied by 2, then after simplification, the original fraction is obtained again. Svetlana thought that, as in the previous case, such a fraction is unique. Is she right?

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55. No, not correct, there are as many such fractions as you like. Let's determine their form. Let the original fraction be $\frac{a}{b}$, then $\frac{a+2}{2 b}=\frac{a}{b}$, from which $a=2$. With the numerator equal to 2 and any odd denominator, the fraction will be irreducible. Therefore, the sought fractions have the form $\frac{2}{2 n+1}$. Such fractions are: $\frac{2}{3}, \frac{2}{5}, \frac{2}{7}, \frac{2}{9}$, etc.