| Task $\underline{98666}$ Topics | $[$ Ordinary fractions $]$ [Equations in integers $]$ |
| :---: | :---: |

Find all irreducible fractions that double after increasing both the numerator and the denominator by 10.
Let $2{ }^{a} / b=a+10 / b+10$. Then $2 a(b+10)=b(a+10), a(b+20)=10 b$. From this, it is clear that $a$ is a divisor of 10 (by the condition that $b$ and $a$ have no common divisors). For $a=1$ and $a=10$, integer values are not obtained; for $a=2$ we get $b=5$, and for $a=5 b=20$. The latter case is not suitable - the fraction is reducible.

## Answer

$2 / 5$.