**Instructions:**

- Enter the initial and final values you want to calculate the percentage change for.
- Click "Calculate Percentage Change" to see the result along with the formula used.
- Your calculation history will be displayed below the results.
- Click "Clear Results" to clear the current calculation and history.
- Click "Copy Results" to copy the current calculation result to the clipboard.

**Calculation History**

Percentage change word problems are a fundamental aspect of mathematics that are encountered in various aspects of our daily lives. These problems involve calculating the change in a quantity as a percentage of its original value or comparing two values with respect to their percentage change. Understanding the concept of percentage change and being able to solve related word problems is essential for making informed decisions in fields such as finance, economics, science, and everyday scenarios.

## Concept of Percentage Change

Percentage change is a measure of how much a quantity has changed in relation to its original value, expressed as a percentage. It is used to compare the relative increase or decrease in a value. The formula for calculating percentage change is as follows:

**Percentage Change (P%) = [(New Value – Old Value) / |Old Value|] * 100**

In this formula:

*New Value*is the updated or final value.*Old Value*is the original or initial value.*|Old Value|*represents the absolute value of the old value to ensure a positive result.

Percentage change can be positive or negative, depending on whether the value has increased or decreased. A positive percentage change indicates an increase, while a negative percentage change suggests a decrease.

## Formulae for Percentage Change

**Percentage Increase:**When a value increases, the formula to calculate the percentage increase is:**Percentage Increase = [(New Value – Old Value) / |Old Value|] * 100****Percentage Decrease:**When a value decreases, the formula to calculate the percentage decrease is:**Percentage Decrease = [(Old Value – New Value) / |Old Value|] * 100**

These formulae allow us to determine the magnitude of change in a value relative to its original state, which is crucial for various applications.

## Example Calculations

Let’s consider some practical examples to illustrate the application of percentage change in real-world scenarios.

### Example 1: Price Increase

Suppose you are interested in buying a smartphone that originally costs $500 but is now on sale for $600. To calculate the percentage increase in price, you can use the percentage change formula:

**Percentage Increase = [(New Price – Old Price) / |Old Price|] * 100**

**Percentage Increase = [($600 – $500) / $500] * 100 = 20%**

So, the price of the smartphone has increased by 20%.

### Example 2: Population Decrease

Imagine a city had a population of 100,000 people last year but now has 90,000 residents. To calculate the percentage decrease in population, you can use the percentage change formula for decrease:

**Percentage Decrease = [(Old Population – New Population) / |Old Population|] * 100**

**Percentage Decrease = [(100,000 – 90,000) / 100,000] * 100 = 10%**

The city’s population has decreased by 10%.

## Real-World Use Cases

Percentage change word problems and calculations are essential in numerous real-world scenarios:

### Finance and Investment

Percentage change is frequently used in finance to track the performance of investments, calculate returns, and assess the impact of market fluctuations. Investors rely on percentage change to make informed decisions about buying or selling assets.

### Economics

Economists use percentage change to analyze economic indicators such as inflation rates, unemployment rates, and GDP growth. These indicators provide insights into the health of an economy and help policymakers make informed decisions.

### Retail and Sales

In the retail industry, percentage change is used to analyze sales trends. Retailers can assess the effectiveness of marketing campaigns, price changes, and product launches by calculating the percentage change in sales revenue.

### Health and Medicine

Percentage change is used in medical research to analyze the effectiveness of treatments and interventions. It helps researchers understand the impact of a treatment on a particular condition or disease.

### Education

Educators use percentage change to evaluate student performance and assess improvements or declines in academic achievement. It is also used in grading and performance evaluation.

## Conclusion

Percentage change word problems and calculations are a fundamental mathematical tool that finds application in various aspects of our lives. Whether it’s analyzing financial investments, tracking economic trends, or making decisions in retail and healthcare, understanding percentage change is crucial. The concept allows us to compare values relative to their original state, providing valuable insights and informing decision-making processes.

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