Percentage Comparison

What Percentage Is One Number of Another?

To find what percentage one number A is of another number B (where B ≠ 0): Percentage = (A / B) · 100%.

Example: A sports club is attended by 9 students from a class of 36. What percentage attends? (9/36) × 100% = 25%.

Percentage Increase and Decrease

To find by what percentage A exceeds B: Excess % = ((A − B) / B) · 100%. If A > B, positive (increase). If A < B, negative (decrease).

Example: Price rose from $40 to $50: ((50−40)/40) × 100% = 25% increase. If it fell from $50 to $40: ((40−50)/50) × 100% = −20% decrease.

Important Asymmetry

A 25% increase followed by a 25% decrease does not return to the original value. If X increases by 25%: X × 1.25 = 1.25X. Then decreasing by 25%: 1.25X × 0.75 = 0.9375X, which is 93.75% of the original. The percentages are applied to different base values, so they are not inverse operations.