Understanding Percent Change

Introduction

• Percent change is a way to express changes in value in relative terms using percentages.
• "Percent" means "per 100", and "percent change" refers to "change per 100".

Basic Concept

• Percent change gives a relative measurement of the change compared to the original amount.
• Simple calculations involve starting with an amount (e.g., 100), noting the increase or decrease (e.g., 20), and expressing it as a percentage of the original amount.

Steps to Calculate Percent Change

1. Identify Absolute Change: Determine the difference between the new value and the original value.
2. Apply the Formula:
   • Percent Change = (Absolute Change / Original Amount) × 100

Visual Representation

• Fractions help visualize percent change. Convert changes into percentages using equivalent fractions.

Two Methods for Calculation

1. Diagram Method:

   • Illustrate original and changed amounts using diagrams to find the equivalent fraction in terms of percentage.

2. Arithmetic/Algebraic Method:

   • Use Algebra to solve: Convert the fraction (change/original) to percent by multiplying with 100.

Examples

• Doggie Day Care: Increase from 25 to 28 dogs represents a 12% increase.
• Discounted Shoes: Decrease in price from $65 to $50 represents a 23% decrease.

Calculations Without Absolute Change

• For problems without immediate absolute change, calculate difference (new value - original value) and use standard method.

Important Considerations

• Order in Subtraction: New value subtracts original for correct positive/negative outcome.
• Double-check Outcomes: Ensure answers make intuitive sense and align with the problem's context.

Special Cases and Considerations

• Doubling Amounts: Doubling any original amount results in a 100% increase.
• Halving Amounts: When an amount is halved, it results in a 50% decrease.

Further Intuition

• Beyond 100% Changes: Possible when end values substantially exceed the start values (e.g., increasing 1 to 3 is a 200% increase).

Practice and Application

• Engage actively with math problems to become proficient in applying percent change formulas.

Conclusion

• Percent change is a valuable tool for expressing relative changes, and understanding and applying it requires practice with diverse examples.

For more learning resources, visit Math Antics.