Calculate percentages, percentage changes, differences, and increases with step-by-step solutions. Perfect for homework, business calculations, and everyday percentage problems.
Percentage calculations are fundamental mathematical operations used in countless real-world applications from calculating discounts and tips to analyzing data and financial planning. A percentage represents a fraction of 100 and is denoted by the % symbol.
Understanding percentages is crucial for making informed decisions in business, education, and everyday life. Whether you're calculating a price reduction, determining test scores, or analyzing statistical data, percentage calculations provide clear, standardized comparisons.
Where: Part = portion of the whole, Whole = total amount
Example: 15% of 200 = (15 ÷ 100) × 200 = 30
| Application | Example | Calculation Type | Formula Used |
|---|---|---|---|
| Shopping Discount | 20% off $50 item | Basic % | $50 × 0.20 = $10 discount |
| Tip Calculation | 15% tip on $80 bill | Basic % | $80 × 0.15 = $12 tip |
| Sales Tax | 8.5% tax on $100 | Basic % | $100 × 0.085 = $8.50 tax |
| Test Score | 18 out of 25 questions | Basic % | (18 ÷ 25) × 100 = 72% |
| Price Increase | $100 to $120 | % Change | ((120-100) ÷ 100) × 100 = 20% |
| Weight Loss | 200 lbs to 180 lbs | % Change | ((200-180) ÷ 200) × 100 = 10% |
| Comparing Prices | $100 vs $120 | % Difference | |120-100| ÷ ((120+100)÷2) × 100 = 18.18% |
Percentage Change: Shows how much something has increased or decreased relative to its original value. It has direction (positive for increase, negative for decrease) and uses the original value as the base.
Percentage Difference: Compares two values without considering which is the "original" value. It's always positive and uses the average of both values as the base.
Converting Percentages: To convert a percentage to a decimal, divide by 100. To convert a decimal to a percentage, multiply by 100.
Mental Math Shortcuts: 10% of a number is that number with the decimal moved one place left. 1% is moving it two places left. Use these to calculate other percentages quickly.
Percentage of a Percentage: When calculating compound percentages (like a 20% discount followed by 10% tax), apply each percentage separately, not together.
Avoid Common Mistakes: A 50% increase followed by a 50% decrease does not return to the original value. The final value will be 25% less than the original.