4. If the numerator of a fraction is reduced by $8\%$, and the denominator is increased by $8\%$, the new fraction will be 2 less than the original fraction. Determine the value of the original fraction.
4. Let the given fraction be $\frac{x}{y}$.

If the numerator $x$ is reduced by $8\%$, the numerator of the new fraction will be $0.92 x$.

If the denominator $y$ is increased by $8\%$, the denominator of the new fraction will be $1.08 y$.

The new fraction is of the form $\frac{0.92 x}{1.08 y}$.

Further, $\frac{0.92 x}{1.08 y}=\frac{92 x}{108 y}=\frac{23 x}{27 y}$.

We need to solve the equation $\frac{x}{y}-\frac{0.92 x}{1.08 y}=2$

$\frac{x}{y} \cdot\left(1-\frac{23}{27}\right)=2$

$\frac{x}{y} \cdot \frac{4}{27}=2$

$\frac{x}{y}=2: \frac{4}{27}$

$\frac{x}{y}=2 \cdot \frac{27}{4}$

$\frac{x}{y}=\frac{27}{2}$

Note: The equation $\frac{x}{y} \cdot \frac{4}{27}=2$ can also be solved in other ways, for example, after dividing by 4, we get $\frac{x}{y} \cdot \frac{1}{27}=\frac{2}{4}$, or $\frac{x}{y} \cdot \frac{1}{27}=\frac{1}{2}$, and by multiplying by 27 we get $\frac{x}{y}=\frac{27}{2}$. This method of solving also scores 3 points.