Let's denote the original fraction as \( \frac{a}{b} \), where \( a \) is the numerator and \( b \) is the denominator.
If the numerator is increased by 25%, the new numerator becomes: \[ a + 0.25a = 1.25a \]
If the denominator is increased by 20%, the new denominator becomes: \[ b + 0.20b = 1.20b \]
Thus, the new fraction after these changes will be: \[ \frac{1.25a}{1.20b} \]
Now, let's express the new fraction in terms of the original fraction: \[ \frac{1.25a}{1.20b} = \frac{1.25}{1.20} \cdot \frac{a}{b} \]
Next, we can calculate \( \frac{1.25}{1.20} \): \[ \frac{1.25}{1.20} = \frac{125}{120} = \frac{25}{24} \]
This means: \[ \frac{1.25a}{1.20b} = \frac{25}{24} \cdot \frac{a}{b} \]
To find the percentage change in the fraction, we compare the new fraction with the original fraction: \[ \text{Percentage change} = \left( \frac{\text{new fraction} - \text{original fraction}}{\text{original fraction}} \right) \times 100% \]
Substituting in the values: \[ \text{Percentage change} = \left( \frac{\frac{25}{24} \cdot \frac{a}{b} - \frac{a}{b}}{\frac{a}{b}} \right) \times 100% \]
First, simplify the numerator: \[ \frac{25}{24} \cdot \frac{a}{b} - \frac{a}{b} = \left( \frac{25}{24} - 1 \right) \cdot \frac{a}{b} = \left( \frac{25}{24} - \frac{24}{24} \right) \cdot \frac{a}{b} = \frac{1}{24} \cdot \frac{a}{b} \]
The expression becomes: \[ \text{Percentage change} = \left( \frac{\frac{1}{24} \cdot \frac{a}{b}}{\frac{a}{b}} \right) \times 100% = \frac{1}{24} \times 100% = \frac{100}{24}% = \frac{25}{6}% \approx 4.17% \]
Thus, the change in the fraction, expressed as a percentage, is: \[ \boxed{\frac{25}{6}%} \quad \text{or approximately } 4.17% \]