This worksheet provides a comprehensive guide to understanding and solving problems involving increasing and decreasing percentages. Mastering these concepts is crucial for various applications, from everyday budgeting to advanced financial analysis. This guide will break down the process step-by-step, providing examples and exercises to solidify your understanding.
Understanding Percentage Increases and Decreases
Before diving into calculations, let's clarify the core concepts:
-
Percentage Increase: This refers to the amount by which a value increases, expressed as a percentage of the original value. For example, a price increasing from $100 to $120 represents a 20% increase.
-
Percentage Decrease: This is the amount by which a value decreases, also expressed as a percentage of the original value. A price dropping from $100 to $80 represents a 20% decrease.
Calculating Percentage Increase
The formula for calculating a percentage increase is straightforward:
[(New Value - Original Value) / Original Value] x 100%
Example:
A store initially priced a shirt at $50. The price increased to $60. What is the percentage increase?
- Find the difference: $60 - $50 = $10
- Divide the difference by the original value: $10 / $50 = 0.2
- Multiply by 100%: 0.2 x 100% = 20%
Therefore, the price increased by 20%.
Calculating Percentage Decrease
The formula for calculating a percentage decrease is similar:
[(Original Value - New Value) / Original Value] x 100%
Example:
A pair of shoes originally cost $150. They are now on sale for $120. What is the percentage decrease?
- Find the difference: $150 - $120 = $30
- Divide the difference by the original value: $30 / $150 = 0.2
- Multiply by 100%: 0.2 x 100% = 20%
Therefore, the price decreased by 20%.
Finding the New Value After a Percentage Change
Often, you'll need to calculate the new value after a percentage increase or decrease. This can be done using the following formulas:
- Percentage Increase: New Value = Original Value x (1 + Percentage Increase/100)
- Percentage Decrease: New Value = Original Value x (1 - Percentage Decrease/100)
Examples:
-
Increase: A house valued at $200,000 appreciates by 15%. What is its new value? New Value = $200,000 x (1 + 15/100) = $230,000
-
Decrease: A car priced at $30,000 is discounted by 10%. What is its new price? New Value = $30,000 x (1 - 10/100) = $27,000
Worksheet Exercises
Now let's test your understanding with some exercises:
Instructions: Solve the following problems, showing your work.
-
A bicycle originally cost $250. The price increased by 8%. What is the new price?
-
A video game that cost $60 is now on sale for $48. What is the percentage decrease?
-
A company's profits increased from $50,000 to $65,000. What is the percentage increase?
-
A population of 1200 decreased by 15%. What is the new population?
-
An investment of $1000 grew by 25%. What is the final value of the investment?
Solutions (Hide until you've attempted the exercises)
(Answers will be provided here separated from the questions to allow for independent problem-solving.)
-
$270
-
20%
-
30%
-
1020
-
$1250
This worksheet provides a foundational understanding of increasing and decreasing percentages. Further exploration into compound interest and more complex percentage calculations can build upon this knowledge. Remember to practice consistently to master these important mathematical concepts!
