What are Percentages?
A percentage is a number expressed as a fraction of 100. It is often denoted using the percent sign, "%". For example, 25% means 25 per 100, or 25/100, or 0.25.
Common Percentage Calculations
- Finding the percentage: (X ÷ Y) × 100 = P%
- Finding the value of a percentage: (P% ÷ 100) × Y = X
- Percentage increase: [(New - Original) ÷ Original] × 100
- Percentage decrease: [(Original - New) ÷ Original] × 100
- Increasing by a percentage: Original + (Original × P% ÷ 100)
- Decreasing by a percentage: Original - (Original × P% ÷ 100)
Real-World Applications
- Shopping: Calculate discounts and sales prices
- Finance: Determine interest rates, taxes, and tips
- Business: Analyze profit margins and growth rates
- Education: Calculate grades and test scores
- Statistics: Express probabilities and distributions
Tip: When calculating percentage change, remember that an increase from 100 to 150 is a 50% increase, but a decrease from 150 to 100 is a 33.33% decrease. The percentage change depends on the direction and the reference value.