Increase And Decrease Percentage Worksheet

Mastering Percentage Increase and Decrease: A Comprehensive Worksheet Guide

Understanding percentage increase and decrease is a fundamental skill in mathematics with wide-ranging applications in daily life, from calculating sale discounts to analyzing financial growth. This comprehensive guide provides a thorough understanding of percentage change, complete with worked examples, practice problems, and frequently asked questions. We'll move from basic concepts to more complex scenarios, equipping you with the tools to confidently tackle any percentage increase and decrease problem.

Introduction: What are Percentage Increases and Decreases?

A percentage increase or decrease shows the relative change in a value compared to its original value. It's expressed as a percentage, indicating the proportional increase or reduction. This concept is crucial for understanding various aspects of finance, statistics, and everyday situations. For example, understanding percentage change allows you to easily compare price changes, salary increases, population growth, or even the fluctuations in the stock market. This worksheet will guide you through the step-by-step process of calculating both percentage increases and decreases, providing you with the confidence to handle a wide array of problems. Mastering this concept is key to building a strong foundation in mathematical problem-solving.

Understanding the Formulae

The core of calculating percentage increases and decreases lies in understanding two fundamental formulae:

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

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

Notice the similarity; the only difference lies in the order of subtraction reflecting the increase or decrease. Always remember that the original value forms the denominator (the bottom part of the fraction). This ensures the percentage represents the change relative to the starting point.

Step-by-Step Guide: Calculating Percentage Increase

Let's break down the process with a practical example. Imagine a store is having a sale, and a shirt originally priced at $50 is now priced at $60. Let's calculate the percentage increase:

1. Identify the Original Value and the New Value:

   • Original Value = $50
   • New Value = $60

2. Find the Difference:

   • Difference = New Value - Original Value = $60 - $50 = $10

3. Calculate the Percentage Change:

   • Percentage Increase = [(Difference) / (Original Value)] x 100% = ($10 / $50) x 100% = 0.2 x 100% = 20%

Therefore, the price of the shirt increased by 20%.

Step-by-Step Guide: Calculating Percentage Decrease

Now, let's consider a scenario involving a percentage decrease. Suppose the same shirt is later discounted to $40. Let's calculate the percentage decrease:

1. Identify the Original Value and the New Value:

   • Original Value = $50
   • New Value = $40

2. Find the Difference:

   • Difference = Original Value - New Value = $50 - $40 = $10

3. Calculate the Percentage Change:

   • Percentage Decrease = [(Difference) / (Original Value)] x 100% = ($10 / $50) x 100% = 0.2 x 100% = 20%

The price of the shirt decreased by 20%.

Working with Different Units

The principles remain the same even when dealing with units other than currency. For example, let's say a population increased from 1000 to 1200.

1. Original Value: 1000
2. New Value: 1200
3. Difference: 1200 - 1000 = 200
4. Percentage Increase: (200 / 1000) * 100% = 20%

The population increased by 20%.

Advanced Scenarios: Finding the Original or New Value

Percentage increase and decrease problems can also ask you to find the original or new value given the percentage change and one of the values. These problems require slightly different approaches:

Finding the Original Value:

Let's say a price increased by 15% to reach $76. What was the original price?

1. Let 'x' represent the original value.
2. Set up an equation: x + 0.15x = 76 (This represents the original value plus 15% of the original value equals the new value)
3. Simplify: 1.15x = 76
4. Solve for x: x = 76 / 1.15 ≈ $66.09

Therefore, the original price was approximately $66.09.

Finding the New Value:

Suppose a quantity decreased by 20% from an original value of 800. What is the new value?

1. Calculate the decrease: 20% of 800 = (20/100) * 800 = 160
2. Subtract the decrease from the original value: 800 - 160 = 640

Therefore, the new value is 640. Alternatively, you could calculate this as 800 * (1 - 0.20) = 640.

Practice Worksheet: Percentage Increase and Decrease Problems

Now let's test your understanding with some practice problems:

1. A car's price increased from $20,000 to $22,500. What is the percentage increase?

2. A company's profit decreased from $500,000 to $400,000. What is the percentage decrease?

3. A student scored 80% on a test. If the test had 50 questions, how many questions did the student answer correctly? If the test were to have 100 questions, what would the student need to score to maintain the same percentage?

4. The population of a city increased by 10% to reach 132,000. What was the original population?

5. A store offers a 25% discount on a $120 item. What is the final price after the discount?

6. A house increased in value by 30% to $455,000. What was its original value?

7. A farmer’s harvest decreased by 15% this year compared to last year. If last year’s harvest was 15 tons, what was the harvest this year?

8. An investment grew by 8% in one year. If the initial investment was $10,000, what was the value of the investment after one year?

Answers:

1. 12.5%
2. 20%
3. 40 questions correctly; To maintain 80%, the student needs to answer 80 out of 100 questions correctly.
4. 120,000
5. $90
6. $350,000
7. 12.75 tons
8. $10,800

Frequently Asked Questions (FAQ)

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

A: Absolute change is the simple difference between the new and original values. Percentage change expresses this difference as a percentage of the original value, showing the relative change.

Q: Can a percentage decrease be greater than 100%?

A: No, a percentage decrease cannot be greater than 100%. A 100% decrease means the value has dropped to zero.

Q: How do I handle negative values when calculating percentage change?

A: The formulas still apply. Just be mindful of the signs when calculating the difference. A negative difference will result in a negative percentage change, indicating a decrease.

Q: What if the original value is zero?

A: You cannot calculate percentage change if the original value is zero as it results in division by zero which is undefined.

Q: Why is the original value used as the denominator in the formula?

A: The original value is used as the denominator because the percentage change is always calculated relative to the starting value. It allows for meaningful comparison of changes across different scales.

Conclusion:

Mastering percentage increase and decrease calculations is a crucial skill that extends far beyond the classroom. By understanding the underlying principles and practicing regularly, you’ll develop the confidence and expertise to confidently tackle various real-world problems involving percentage change. Remember the key formulas, break down problems systematically, and utilize the provided practice problems to reinforce your learning. With consistent practice, you will build a strong foundation in this essential mathematical concept.