Percent Increase And Decrease Worksheet

Mastering Percent Increase and Decrease: A Comprehensive Worksheet Guide

Understanding percent increase and decrease is a fundamental skill in mathematics with widespread applications in everyday life, from calculating sale discounts to analyzing financial growth. This comprehensive guide provides a detailed explanation of percent increase and decrease, accompanied by various worksheet examples and problem-solving strategies to solidify your understanding. We'll cover the core concepts, delve into practical applications, and address common challenges, ensuring you're well-equipped to tackle any percent increase or decrease problem.

What are Percent Increase and Decrease?

Percent increase and decrease refer to the relative change in a value expressed as a percentage. A percent increase indicates an upward change, while a percent decrease signifies a downward change. These calculations are vital in various fields, including finance, statistics, and even everyday shopping.

Understanding the Formulas

The core formulas are surprisingly straightforward:

• Percent Increase: [(New Value - Original Value) / Original Value] x 100%

• Percent Decrease: [(Original Value - New Value) / Original Value] x 100%

Notice that the denominator is always the original value. This is crucial for accurate calculations. The result will be a percentage representing the relative change.

Step-by-Step Guide to Solving Percent Increase and Decrease Problems

Let's break down the process into manageable steps:

1. Identify the Original Value and the New Value: Clearly distinguish between the starting value (original) and the value after the increase or decrease (new).

2. Find the Difference: Subtract the original value from the new value (for increase) or the new value from the original value (for decrease). This gives you the absolute change.

3. Divide by the Original Value: Divide the absolute change (from step 2) by the original value.

4. Multiply by 100%: Multiply the result from step 3 by 100 to express the change as a percentage.

Worksheet Examples: Percent Increase

Let's work through some examples using the percent increase formula.

Example 1:

A shirt originally cost $25. After a price increase, it now costs $30. What is the percentage increase?

1. Original Value: $25
2. New Value: $30
3. Difference: $30 - $25 = $5
4. Division: $5 / $25 = 0.2
5. Percentage: 0.2 x 100% = 20%

Therefore, the price increased by 20%.

Example 2:

A company's profit was $100,000 last year. This year, their profit increased to $125,000. What is the percentage increase in profit?

1. Original Value: $100,000
2. New Value: $125,000
3. Difference: $125,000 - $100,000 = $25,000
4. Division: $25,000 / $100,000 = 0.25
5. Percentage: 0.25 x 100% = 25%

The company's profit increased by 25%.

Worksheet Examples: Percent Decrease

Now let's tackle some examples using the percent decrease formula.

Example 1:

A pair of shoes was originally priced at $80. They are now on sale for $60. What is the percentage decrease?

1. Original Value: $80
2. New Value: $60
3. Difference: $80 - $60 = $20
4. Division: $20 / $80 = 0.25
5. Percentage: 0.25 x 100% = 25%

The shoes are discounted by 25%.

Example 2:

The population of a town decreased from 5,000 to 4,500. What is the percentage decrease in population?

1. Original Value: 5,000
2. New Value: 4,500
3. Difference: 5,000 - 4,500 = 500
4. Division: 500 / 5,000 = 0.1
5. Percentage: 0.1 x 100% = 10%

The town's population decreased by 10%.

Advanced Problems and Applications

Let's explore more complex scenarios:

Finding the New Value after a Percent Increase/Decrease:

Sometimes, you'll know the original value and the percentage change, and you need to find the new value. In this case, you can modify the formulas:

• New Value (Increase): Original Value x (1 + Percentage Increase/100)

• New Value (Decrease): Original Value x (1 - Percentage Decrease/100)

Example:

A house is worth $200,000. Its value increases by 15% over the next year. What is its new value?

New Value = $200,000 x (1 + 15/100) = $200,000 x 1.15 = $230,000

Successive Percentage Changes:

When dealing with multiple percentage changes, it's crucial to understand that they don't simply add up. Each percentage change is calculated based on the previous value.

Example:

A product costs $50. Its price increases by 10%, then decreases by 10%. What is the final price?

1. 10% Increase: $50 x (1 + 10/100) = $55
2. 10% Decrease (from $55): $55 x (1 - 10/100) = $49.50

Notice the final price is not $50, illustrating the importance of sequential calculations.

Real-World Applications

Percent increase and decrease are crucial in various real-world situations:

• Finance: Calculating interest earned on savings accounts, investment returns, loan repayments, and inflation rates.
• Sales and Marketing: Determining discounts, markups, and profit margins.
• Science: Analyzing growth rates in populations, measuring changes in physical quantities, and interpreting experimental data.
• Economics: Studying economic growth, inflation, and unemployment rates.

Frequently Asked Questions (FAQ)

Q: What if the percentage increase or decrease is negative?

A: A negative percentage increase would indicate a decrease, and a negative percentage decrease would indicate an increase. This is simply a matter of interpreting the sign of the result correctly.

Q: Can I use a calculator for these problems?

A: Absolutely! Calculators are extremely helpful, especially for more complex problems involving multiple percentage changes or large numbers.

Q: How do I handle percentage changes with decimal values?

A: Follow the same steps as outlined above. Ensure you maintain accuracy throughout the calculations.

Conclusion

Mastering percent increase and decrease is a valuable skill with wide-ranging applications. By understanding the fundamental formulas, following a systematic approach, and practicing with various examples, you can confidently tackle a variety of problems related to percentage changes. Remember to pay attention to the original value and the order of operations when dealing with successive changes. With consistent practice, you’ll develop a strong understanding of this crucial mathematical concept. This comprehensive guide, along with diligent practice using the included worksheet examples, will enable you to build proficiency and solve any percent increase or decrease problem you may encounter. Remember to break down complex problems into smaller, manageable steps, and don't hesitate to utilize a calculator for efficiency. This ensures accuracy and aids in building a solid foundational knowledge of this important mathematical skill.