Percent Of Increase Decrease Worksheet

Mastering Percentage Increase and Decrease: A Comprehensive Worksheet Guide

Understanding percentage increase and decrease is a fundamental skill in mathematics with widespread applications in various fields, from finance and economics to science and everyday life. This comprehensive guide will equip you with the knowledge and practice to confidently tackle percentage change problems. We'll break down the concepts, provide step-by-step solutions, and offer a variety of practice problems to solidify your understanding. This worksheet-style guide is perfect for students, professionals, or anyone looking to improve their mathematical prowess.

Introduction: Understanding Percentage Change

Percentage change refers to the relative change between an old value and a new value, expressed as a percentage. It can represent either an increase or a decrease. Mastering this concept requires understanding the core formula and how to apply it to diverse scenarios. We'll cover both percentage increase and percentage decrease calculations in detail, providing clear examples and practical applications. This article will serve as your ultimate resource for mastering percentage increase and decrease calculations, providing you with the tools and practice needed to excel.

Percentage Increase: A Step-by-Step Approach

Calculating percentage increase involves determining the extent to which a value has grown. The formula is straightforward, but understanding each component is crucial.

Formula: Percentage Increase = [(New Value - Old Value) / Old Value] x 100%

Let's break down each step with an example:

Example 1: A store initially priced a shirt at $25. After a price increase, the shirt now costs $30. What is the percentage increase?

Step 1: Identify the Old Value and New Value.

• Old Value = $25
• New Value = $30

Step 2: Calculate the Difference.

• Difference = New Value - Old Value = $30 - $25 = $5

Step 3: Divide the Difference by the Old Value.

• Difference / Old Value = $5 / $25 = 0.2

Step 4: Multiply by 100% to express the result as a percentage.

• 0.2 x 100% = 20%

Therefore, the percentage increase in the shirt's price is 20%.

Example 2 (More Complex): A company's annual revenue increased from $150,000 to $210,000. What's the percentage increase?

Following the same steps:

1. Old Value: $150,000
2. New Value: $210,000
3. Difference: $210,000 - $150,000 = $60,000
4. Division: $60,000 / $150,000 = 0.4
5. Percentage: 0.4 x 100% = 40%

The company's revenue increased by 40%.

Percentage Decrease: A Similar but Opposite Calculation

Calculating percentage decrease follows a similar structure to percentage increase, but the formula reflects the reduction in value.

Formula: Percentage Decrease = [(Old Value - New Value) / Old Value] x 100%

Example 3: A television originally priced at $500 is now on sale for $400. What is the percentage decrease?

Step 1: Identify the Old Value and New Value.

• Old Value = $500
• New Value = $400

Step 2: Calculate the Difference.

• Difference = Old Value - New Value = $500 - $400 = $100

Step 3: Divide the Difference by the Old Value.

• Difference / Old Value = $100 / $500 = 0.2

Step 4: Multiply by 100% to express the result as a percentage.

• 0.2 x 100% = 20%

Therefore, the percentage decrease in the television's price is 20%.

Example 4 (Real-world Application): A city's population decreased from 120,000 to 108,000. Calculate the percentage decrease.

1. Old Value: 120,000
2. New Value: 108,000
3. Difference: 120,000 - 108,000 = 12,000
4. Division: 12,000 / 120,000 = 0.1
5. Percentage: 0.1 x 100% = 10%

The city's population decreased by 10%.

Working Backwards: Finding the Original or New Value

Sometimes, you'll know the percentage change and either the original or new value, and need to find the missing value. This requires slightly rearranging the formulas.

Finding the Original Value (Knowing Percentage Increase and New Value):

Let's say the price of a product increased by 15% to reach a new price of $75. To find the original price:

1. Express the percentage as a decimal: 15% = 0.15
2. Add 1 to the decimal: 1 + 0.15 = 1.15 (This represents 100% + 15%)
3. Divide the new value by the result: $75 / 1.15 = $65.22 (approximately)

Therefore, the original price was approximately $65.22.

Finding the Original Value (Knowing Percentage Decrease and New Value):

If a product's price decreased by 20% to $60, the original price can be calculated:

1. Express the percentage as a decimal: 20% = 0.20
2. Subtract the decimal from 1: 1 - 0.20 = 0.80 (This represents 100% - 20%)
3. Divide the new value by the result: $60 / 0.80 = $75

Therefore, the original price was $75.

Finding the New Value (Knowing Percentage Increase and Original Value):

If a company's profits increased by 25% from an original profit of $100,000:

1. Express the percentage as a decimal: 25% = 0.25
2. Multiply the original value by (1 + decimal): $100,000 x (1 + 0.25) = $125,000

Therefore, the new profit is $125,000.

Finding the New Value (Knowing Percentage Decrease and Original Value):

If the population of a town decreased by 10% from 5000:

1. Express the percentage as a decimal: 10% = 0.10
2. Multiply the original value by (1 - decimal): 5000 x (1 - 0.10) = 4500

Therefore, the new population is 4500.

Practical Applications and Real-World Examples

Percentage increase and decrease are used extensively in various real-world scenarios:

• Finance: Calculating interest earned on savings accounts, determining loan repayments, analyzing stock market fluctuations, and tracking inflation rates.
• Business: Assessing sales growth or decline, analyzing profit margins, and evaluating the effectiveness of marketing campaigns.
• Science: Measuring changes in physical quantities (e.g., temperature, volume, mass), analyzing experimental data, and presenting scientific findings.
• Everyday Life: Calculating discounts on purchases, determining tips in restaurants, and understanding changes in utility bills.

Practice Problems: Testing Your Skills

Here are some practice problems to reinforce your understanding:

1. A bicycle originally cost $200 and is now sold for $250. What is the percentage increase?
2. A house that cost $300,000 five years ago is now worth $270,000. What is the percentage decrease in value?
3. A student scored 70% on their first exam and 84% on their second exam. What is the percentage increase in their score?
4. A company's profits decreased by 15% to $85,000. What were the original profits?
5. The price of a laptop increased by 20% to $1200. What was the original price?
6. A town's population decreased by 5% to 4750 people. What was the original population?
7. A dress is on sale for $45 after a 25% discount. What was the original price?
8. A car's value depreciated by 12% in one year. If its current value is $17,600, what was its value last year?

Solutions to Practice Problems

1. Percentage increase = [(250 - 200) / 200] x 100% = 25%
2. Percentage decrease = [(300,000 - 270,000) / 300,000] x 100% = 10%
3. Percentage increase = [(84 - 70) / 70] x 100% = 20%
4. Original profits = $85,000 / (1 - 0.15) = $100,000
5. Original price = $1200 / (1 + 0.20) = $1000
6. Original population = 4750 / (1 - 0.05) = 5000
7. Original price = $45 / (1 - 0.25) = $60
8. Last year's value = $17,600 / (1 - 0.12) = $20,000

Frequently Asked Questions (FAQ)

• Q: What if the new value is less than the old value? A: This indicates a percentage decrease. Use the formula for percentage decrease.
• Q: Can the percentage increase or decrease be more than 100%? A: Yes, absolutely. This happens when the new value is more than double (increase) or less than half (decrease) of the old value.
• Q: How do I handle negative values? A: The formulas still apply. Just ensure you correctly substitute the values, keeping track of the signs.
• Q: Are there any shortcuts or tricks for these calculations? A: While the formulas are fundamental, practice will help you perform these calculations more quickly and efficiently. Understanding the underlying concepts will also help you spot errors more easily.
• Q: What if I have to deal with very large or very small numbers? A: Using a calculator will be essential for accuracy and efficiency with large or complex calculations.

Conclusion: Mastering Percentage Change

Understanding percentage increase and decrease is a valuable skill applicable across numerous disciplines. By mastering the formulas, practicing with examples, and understanding the various applications, you can confidently tackle any percentage change problem. Remember to always carefully identify the old and new values and correctly apply the appropriate formula. Continue practicing, and you'll become proficient in these essential mathematical calculations. This guide served as a strong foundation; now, it’s your turn to build upon it and become a percentage change expert!