Percentage Triad

Three rearrangements of part, whole, and rate — plus percent change for growth and decline.

Name	Formula	Note
P% of X	`result = (P / 100) × X` Tips, discounts, tax — percent of a known amount.	Tips, discounts, tax — percent of a known amount.
X is what % of Y	`result = (X / Y) × 100` Part over whole, scaled per hundred. Y ≠ 0.	Part over whole, scaled per hundred. Y ≠ 0.
Percent change	`Δ% = ((B − A) / A) × 100` Relative change from old A to new B. A ≠ 0.	Relative change from old A to new B. A ≠ 0.
Find the whole	`X = result / (P / 100)` Rearrange “P% of X” when the part and rate are known.	Rearrange “P% of X” when the part and rate are known.
Find the rate	`P = (X / Y) × 100` Same as “is what %” — rate from part and whole.	Same as “is what %” — rate from part and whole.
Compound caution	`100 → −50% → +50% = 75` Percents apply to the current base, not the original.	Percents apply to the current base, not the original.

Open a calculator and put these formulas to work.