Percent Of Increase Decrease Worksheet

Mastering Percentage Increase and Decrease: A Comprehensive Worksheet Guide

Understanding percentage increase and decrease is a fundamental skill applicable across various fields, from finance and business to science and everyday life. This comprehensive guide provides a detailed explanation of percentage change calculations, along with numerous practice problems to solidify your understanding. We'll cover everything from the basic formulas to more complex scenarios, equipping you with the tools to confidently tackle any percentage increase or decrease worksheet.

Introduction: Understanding Percentage Change

Percentage change refers to the extent to which a value has increased or decreased over a period. It's expressed as a percentage, providing a standardized way to compare changes regardless of the original value's magnitude. This is crucial in analyzing trends, comparing data sets, and making informed decisions. This worksheet guide will walk you through the methods for calculating percentage increase and decrease, offering a variety of examples and practice problems to help you master this essential skill. The concepts covered are applicable to various scenarios including calculating profit margins, understanding price fluctuations, analyzing growth rates, and more. By the end of this guide, you'll be comfortable calculating percentage change and interpreting the results within different contexts.

Formula for Percentage Increase

The formula for calculating percentage increase is straightforward:

Percentage Increase = [(New Value - Original Value) / Original Value] x 100%

Let's break it down:

New Value: The value after the increase.
Original Value: The initial value before the increase.

Example 1:

Suppose the price of a product increased from $50 to $60. What is the percentage increase?

New Value: $60
Original Value: $50

Percentage Increase = [($60 - $50) / $50] x 100% = (10 / 50) x 100% = 20%

Therefore, the price increased by 20%.

Formula for Percentage Decrease

The formula for calculating percentage decrease is very similar:

Percentage Decrease = [(Original Value - New Value) / Original Value] x 100%

The only difference is that we subtract the new value from the original value.

Example 2:

A shop reduced the price of a dress from $100 to $80. What is the percentage decrease?

Original Value: $100
New Value: $80

Percentage Decrease = [($100 - $80) / $100] x 100% = (20 / 100) x 100% = 20%

The price decreased by 20%.

Working with Percentage Increase and Decrease Problems: A Step-by-Step Approach

Solving percentage increase and decrease problems often involves multiple steps. Here's a systematic approach:

Identify the Original Value and the New Value: Clearly distinguish between the starting value and the value after the change.
Determine the Type of Change: Is it an increase or a decrease? This will dictate which formula to use.
Apply the Appropriate Formula: Substitute the values into the correct formula (percentage increase or decrease).
Calculate the Percentage Change: Perform the calculation carefully, ensuring you follow the order of operations (PEMDAS/BODMAS).
Interpret the Result: State your answer clearly, indicating whether it's a percentage increase or decrease.

Practice Problems: Percentage Increase

Problem 1: A company's revenue increased from $1 million to $1.2 million. Calculate the percentage increase.

Problem 2: The number of students enrolled in a course increased from 50 to 65. What is the percentage increase?

Problem 3: A stock price rose from $25 to $30. Find the percentage increase.

Problem 4: The population of a city grew from 10,000 to 12,500. What is the percentage increase?

Problem 5: A farmer's wheat yield increased from 500 bushels to 600 bushels. Calculate the percentage increase.

Practice Problems: Percentage Decrease

Problem 6: A store discounted an item from $50 to $40. Calculate the percentage decrease.

Problem 7: The number of employees in a company decreased from 100 to 80. Find the percentage decrease.

Problem 8: A car's value depreciated from $20,000 to $15,000. What is the percentage decrease?

Problem 9: The weight of a person decreased from 180 pounds to 162 pounds. Calculate the percentage decrease.

Problem 10: The number of visitors to a website dropped from 5,000 to 4,000. What is the percentage decrease?

Advanced Scenarios: Finding the Original or New Value

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

Finding the Original Value (given percentage increase and new value):

Original Value = New Value / (1 + Percentage Increase/100)

Finding the Original Value (given percentage decrease and new value):

Original Value = New Value / (1 - Percentage Decrease/100)

Finding the New Value (given percentage increase and original value):

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

Finding the New Value (given percentage decrease and original value):

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

Practice Problems: Finding Missing Values

Problem 11: The price of a bicycle increased by 15%, resulting in a new price of $230. What was the original price?

Problem 12: After a 20% discount, a TV costs $600. What was the original price?

Problem 13: A company's profits increased by 25%. If the original profit was $50,000, what is the new profit?

Problem 14: A student's score decreased by 10% resulting in a final score of 81. What was the original score?

Problem 15: A town's population decreased by 5% to 9,500 people. What was the original population?

Understanding Successive Percentage Changes

When dealing with multiple percentage changes, the changes are not simply additive. You must calculate each change sequentially.

Example 3: A price increases by 10% and then decreases by 10%. Is the final price the same as the original price?

No. Let's say the original price is $100.

10% increase: $100 x 1.10 = $110
10% decrease: $110 x 0.90 = $99

The final price is $99, not $100. This is because the 10% decrease is calculated on the increased price of $110, not the original price.

Real-World Applications of Percentage Increase and Decrease

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

Finance: Calculating interest rates, returns on investments, inflation rates, and loan repayments.
Business: Analyzing sales growth, profit margins, market share changes, and cost reductions.
Science: Measuring changes in quantities like population, temperature, or chemical concentrations.
Everyday Life: Calculating discounts, sales tax, tips, and changes in personal finances.

Frequently Asked Questions (FAQ)

Q1: What is the difference between absolute change and percentage change?

Absolute change: The actual difference between the new and original values (New Value - Original Value).
Percentage change: The relative change expressed as a percentage of the original value. Percentage change provides a standardized way to compare changes across different scales.

Q2: Can I use a calculator for percentage increase and decrease calculations?

Yes, calculators greatly simplify the process, especially with more complex problems or large numbers. However, understanding the underlying formulas is crucial for interpreting the results and solving problems where you need to find missing values.

Q3: What if the new value is zero?

If the new value is zero, the percentage decrease is 100%. The formula will still work correctly in this instance.

Q4: How do I handle negative percentage changes?

Negative percentage changes represent a decrease. The formula for percentage decrease will yield a negative value, indicating a reduction. For example, a -15% change signifies a 15% decrease.

Conclusion: Mastering Percentage Calculations

Understanding and applying percentage increase and decrease calculations is a vital skill with broad applicability. Through consistent practice and a firm grasp of the formulas, you can confidently tackle various problems involving percentage change. Remember to always identify the original and new values, choose the appropriate formula, and carefully perform the calculations. By mastering these concepts, you'll gain valuable insights into data analysis and problem-solving in various contexts, improving decision-making in your personal and professional life. Remember to review the practice problems and formulas regularly to reinforce your understanding and build confidence in your ability to handle any percentage increase or decrease worksheet.