About Percentage Calculations
Percentages are a fundamental mathematical concept used to express proportions, changes, and comparisons. The word "percent" comes from the Latin "per centum," meaning "by the hundred." A percentage is simply a fraction with a denominator of 100.
Common Percentage Calculations
What is B% of A?
This is the most basic percentage calculation. To find what a certain percentage of a number is, multiply the number by the percentage and divide by 100. For example, 25% of 200 = (25 × 200) ÷ 100 = 50.
What percentage of A is B?
To find what percentage one number is of another, divide the part by the whole and multiply by 100. For example, to find what percentage 50 is of 200: (50 ÷ 200) × 100 = 25%.
Increase by a Percentage
To increase a number by a percentage, calculate the percentage amount and add it to the original number. A shortcut is to multiply the number by (1 + percentage/100). For example, increasing 100 by 20% = 100 × (1 + 20/100) = 100 × 1.20 = 120.
Decrease by a Percentage
Similar to increases, but subtract instead. The shortcut formula is: number × (1 - percentage/100). For example, decreasing 100 by 20% = 100 × (1 - 20/100) = 100 × 0.80 = 80.
Percentage Change
To calculate the percentage change between two values, use: ((New Value - Old Value) ÷ Old Value) × 100. A positive result indicates an increase, while a negative result indicates a decrease. For example, the percentage change from 50 to 75 is ((75 - 50) ÷ 50) × 100 = 50% increase.
Reverse Percentage (Finding the Whole)
If you know that a number represents a certain percentage of an unknown whole, you can find the whole by dividing the known number by the percentage and multiplying by 100. For example, if 30 is 15% of a number, the whole number is (30 ÷ 15) × 100 = 200.
Real-World Applications
- Finance: Interest rates, discounts, profit margins, tax calculations
- Statistics: Data analysis, probability, survey results
- Shopping: Sale prices, tips, discounts
- Education: Grades, test scores, grade point averages
- Business: Growth rates, market share, performance metrics
- Health: Body mass index, nutrient daily values, medication dosages
Tips for Working with Percentages
- Remember that percentage means "out of 100" - 50% is literally 50/100 or 0.5
- Converting between decimals, fractions, and percentages helps verify calculations
- Percentage increases and decreases are not symmetric (increasing by 50% then decreasing by 50% doesn't return to the original)
- When comparing multiple percentage changes, use percentage points to avoid ambiguity
- Double-check your reference point - "percent of" vs "percent change" can give very different results
Common Percentage Equivalents
- 10% = 0.1 = 1/10
- 25% = 0.25 = 1/4
- 33.33% = 0.3333... = 1/3
- 50% = 0.5 = 1/2
- 75% = 0.75 = 3/4
- 100% = 1.0 = 1/1