This worksheet provides a comprehensive guide to understanding and calculating percentage increases and decreases. Mastering these skills is crucial for various applications, from everyday budgeting and shopping to more complex financial analyses. We'll cover the fundamentals, offer practical examples, and provide you with exercises to solidify your understanding.
Understanding Percentage Change
Before diving into calculations, let's define what we mean by percentage increase and decrease. A percentage increase represents the growth of a value over time, while a percentage decrease shows the reduction in a value. Both are expressed as a percentage of the original value.
Key Formulas:
- Percentage Increase:
[(New Value - Original Value) / Original Value] x 100% - Percentage Decrease:
[(Original Value - New Value) / Original Value] x 100%
Notice that the only difference between the two formulas lies in the order of subtraction in the numerator. This reflects the increase or decrease in value.
Practical Examples:
Let's illustrate these formulas with real-world examples.
Example 1: Percentage Increase
Imagine a shirt originally priced at $20 is now selling for $25. To calculate the percentage increase:
- Find the difference: $25 (New Value) - $20 (Original Value) = $5
- Divide by the original value: $5 / $20 = 0.25
- Multiply by 100%: 0.25 x 100% = 25%
Therefore, the price of the shirt increased by 25%.
Example 2: Percentage Decrease
A pair of shoes initially priced at $80 is now on sale for $60. Let's calculate the percentage decrease:
- Find the difference: $80 (Original Value) - $60 (New Value) = $20
- Divide by the original value: $20 / $80 = 0.25
- Multiply by 100%: 0.25 x 100% = 25%
The price of the shoes decreased by 25%.
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. Here's how to approach these scenarios:
Scenario 1: Finding the Original Value
Let's say a product increased in price by 15% to reach a new price of $34.50. To find the original price:
- Convert the percentage to a decimal: 15% = 0.15
- Add 1 to the decimal: 1 + 0.15 = 1.15 (This represents 100% + 15%)
- Divide the new value by the result: $34.50 / 1.15 = $30
The original price was $30.
Scenario 2: Finding the New Value
If a product decreased in price by 20% from an original price of $50, the new price would be calculated as:
- Convert percentage to a decimal: 20% = 0.20
- Subtract the decimal from 1: 1 - 0.20 = 0.80 (This represents 100% - 20%)
- Multiply the original value by the result: $50 x 0.80 = $40
The new price is $40.
Worksheet Exercises:
Now it's your turn! Try solving these problems:
- A car originally cost $25,000 and is now worth $22,000. What is the percentage decrease in value?
- A company's profits increased from $50,000 to $65,000. What is the percentage increase?
- A dress is on sale for $45 after a 25% discount. What was the original price?
- A house increased in value by 10% to reach a value of $330,000. What was the original value?
Remember to show your work! Use the formulas and techniques explained above. Good luck!
Conclusion:
Understanding percentage increases and decreases is a fundamental skill with broad applications. By mastering the formulas and practicing with various examples, you can confidently tackle percentage problems in any context. This worksheet provides a solid foundation for further exploration of related mathematical concepts.
