1. The Concept of 'Per Cent'
The word percent originates from the Latin per centum, meaning "by the hundred." Whenever you see a percentage, treat it as a fraction with a denominator of 100. For instance, 15% is simply 15 / 100 = 0.15.
2. Three Core Percentage Formulas
Formula 1: Finding P% of Number X
Result = (P / 100) × X
Example: To calculate a 15% tip on a $60 dinner bill: (15 / 100) × 60 = 0.15 × 60 = $9.00.
Formula 2: Finding What Percentage X is of Y
Percentage = (X / Y) × 100%
Example: If a student scores 42 out of 50 on an algebra midterm: (42 / 50) × 100% = 0.84 × 100% = 84%.
Formula 3: Percentage Increase or Decrease
Percentage Change = ((New Value − Old Value) / Old Value) × 100%
Example: A stock rises from $80 to $100: ((100 − 80) / 80) × 100% = (20 / 80) × 100% = +25%.
3. Reverse Percentage (Finding the Original Price)
If an item is on sale for $72 after a 20% discount, what was the original sticker price? Since the sale price represents 80% (100% − 20%) of the original:
Original Price = Sale Price / (1 − Discount Rate) = 72 / 0.80 = $90.00.