2. The difference between two fractions is $\frac{1}{5}$. The numerator of the first fraction is three times larger than the numerator of the second fraction, and the denominator of the first fraction is twice as large as the denominator of the second fraction. Determine these fractions.
Solution. If the second fraction is $\frac{a}{b}$, then the first fraction is $\frac{3 a}{2 b}$. According to the condition, we have $\frac{3 a}{2 b}-\frac{a}{b}=\frac{1}{5}$, so $\frac{a}{b}=\frac{2}{5}$. The first fraction is $\frac{6}{10}$.