Mastering Percentages: Formulas and Real-World Math
A percentage (from the Latin per centum, meaning "by a hundred") is a number expressed as a fraction of 100. Understanding how to manually calculate percentages is a critical life skill for shopping, calculating tips, analyzing exam marks, and managing corporate profit margins.
Formula 1: What is X% of Y?
To find a specific percentage of a number, convert the percentage to a decimal by dividing by 100, then multiply by the number.
Example: What is 25% of 80?
(25 ÷ 100) × 80 = 0.25 × 80 = 20.
Formula 2: X is what percent of Y? (Exam Marks)
This is the most common formula used by students to calculate their exam grades. Divide the part by the whole, then multiply by 100.
Example: If you scored 45 marks out of 60, what is your percentage?
(45 ÷ 60) × 100 = 0.75 × 100 = 75%.
Percentage Increase and Decrease
To find how much a number has grown or shrunk (e.g., inflation or store discounts):
Formula: ((New Value - Old Value) ÷ Old Value) × 100.
If a ₹500 shirt is discounted to ₹400, the percentage decrease is ((400 - 500) ÷ 500) × 100 = (-100 ÷ 500) × 100 = -20%.