If the numerator of a fraction is increased by 10% and denominator is…

Concept

When a numerator is scaled by a factor and a denominator is scaled by a factor, the value of the fraction is multiplied by (numerator factor) / (denominator factor). A percent rise of p% multiplies a quantity by (1 + p/100); a percent fall of q% multiplies it by (1 - q/100). Percentage changes on the top and bottom do NOT simply add or cancel — they combine multiplicatively.

Application

1. Let the original fraction be a/b.

2. The numerator rises by 10%, so it becomes 1.1a; the denominator falls by 10%, so it becomes 0.9b.

3. New value = (1.1a) / (0.9b) = (1.1 / 0.9) × (a/b) = (11/9) × (a/b). So the fraction is multiplied by 11/9.

4. Increase factor = 11/9 - 1 = 2/9.

5. As a percent: (2/9) × 100 = 22.22%, i.e. about 22.2%.

Cross-check

Pick concrete numbers: a = 10, b = 10, so the fraction is 1. New fraction = 11 / 9 = 1.2222. The rise from 1 to 1.2222 is 0.2222, or 22.22% — matching the algebra.

Answer: 22.2% (approximately).