How Percentages Work: Core Mathematical Formulas
The word "percent" derives from the Latin per centum, meaning "by the hundred." A percentage is simply a ratio or fraction whose denominator is 100.
1. Calculating the Percentage of a Value
To find \(P\%\) of a number \(V\), divide the percentage by 100 and multiply by the total:
$$\text{Result} = \frac{P}{100} \times V$$
2. Finding the Proportion Ratio
To determine what percentage a part \(A\) represents of a whole \(B\), divide \(A\) by \(B\) and multiply by 100:
$$\text{Percentage} = \left(\frac{A}{B}\right) \times 100\%$$
3. Percentage Change (Increase or Decrease)
To measure how much a metric grew or dropped from an initial value \(V_1\) to a new value \(V_2\):
$$\Delta\% = \left(\frac{V_2 - V_1}{V_1}\right) \times 100\%$$
If the result is positive, it represents a percentage increase; if negative, it represents a percentage decrease (discount or contraction).