What Is Percentage?
A percentage expresses a number as a fraction of 100, and percent problems come in a few recurring forms. The most common ask either what amount corresponds to a given percentage of a number, what percentage one number is of another, or how a value changed as a percentage.
Each form is the same relationship read differently. Since "percent" means "per hundred," X% of Y is (X/100)·Y, and the question "X is what percent of Y?" is simply (X/Y)·100. Percentage change compares a new value with an original value as a ratio scaled to 100.
Formula
X% of Y = (X / 100) × Y
X as a percentage of Y = (X / Y) × 100%
Percentage change = ((new − original) / |original|) × 100%
Examples: 20% of 50 = 10; 10 is 25% of 40.
Applications
- Computing discounts, tips, taxes, and interest amounts
- Finding what share one quantity is of a larger total
- Measuring growth or decline in business and finance data
- Comparing test scores and survey responses as percentages
- Converting ratios and proportions into comparable percentages
Sources
- Aufmann, R. N., & Lockwood, J. (2014). Prealgebra (7th ed.). Cengage Learning.
- Miller, C. D., Heeren, V. E., Hornsby, J., & Heeren, C. (2011). Mathematical Ideas (12th ed.). Pearson.