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A percentage is a number expressed as a fraction of 100. It is often denoted using the percent sign, "%". Percentages are used to express how large or small one quantity is relative to another quantity.
P% of X = (P/100) × X
Example: 20% of 150 = (20/100) × 150 = 30
X is what percent of Y? = (X/Y) × 100%
Example: 30 is what percent of 150? = (30/150) × 100% = 20%
Percentage change = ((New Value - Old Value) / |Old Value|) × 100%
Example: Change from 150 to 180 = ((180 - 150) / 150) × 100% = 20% increase
Example: Change from 150 to 120 = ((120 - 150) / 150) × 100% = -20% decrease
To find the original number after a percentage increase or decrease, use this formula: Original = Current / (1 + r), where r is the rate of change (positive for increase, negative for decrease).
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Percentage calculations are fundamental mathematical operations that express a portion of a whole as a fraction of 100. The term "percentage" literally means "per hundred," with the percentage symbol (%) representing this relationship. These calculations are ubiquitous in everyday life, from financial applications like discounts, interest rates, and taxes to statistical analysis, academic grading systems, and nutritional information. The versatility of percentages lies in their ability to standardize comparisons between different values and quantities, making them an essential tool for both simple daily calculations and complex professional analyses.
There are three primary types of percentage calculations, each addressing different scenarios. Finding the percentage of a number involves determining what portion of one value represents another (e.g., 15% of 80). Calculating the percentage change between two values measures the relative increase or decrease from an initial value to a final one, providing insights into growth or reduction rates. Finding what percentage one value is of another helps quantify the relative proportion between two quantities. These different applications highlight the flexibility of percentage calculations in addressing various mathematical questions across contexts.
While percentages appear straightforward, they can sometimes lead to misinterpretations in real-world applications. For instance, a common misconception involves consecutive percentage changes—a 50% increase followed by a 50% decrease does not return to the original value, but rather results in a 25% reduction. Similarly, when comparing percentage points versus percentage changes, confusion can arise; a shift from 10% to 15% represents a 5 percentage point increase but a 50% relative increase. Understanding these nuances is crucial for accurate financial planning, data analysis, and informed decision-making across personal and professional domains. Mastering percentage calculations empowers individuals to better interpret statistics, evaluate financial options, and make quantitative comparisons with confidence.