Lesson 53: Percent Increase & Decrease

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• Lesson Description
• Learning Objectives
• Topics Covered
• Key Terms
• Lesson Examples
• Practice Problems
• Tips & Common Mistakes
• Summary
• Challenge Problems
• Unit Navigation

Lesson Description

This lesson teaches how to calculate percent increase and decrease, interpret changes, and apply these concepts in real-world situations like prices, salaries, population, and discounts.

Learning Objectives

• Calculate percent increase and percent decrease.
• Apply percent change to real-world contexts.
• Interpret and solve problems involving increases and decreases in quantities.

Topics Covered

• Percent increase formula: (new − original) ÷ original × 100%
• Percent decrease formula: (original − new) ÷ original × 100%
• Application to real-world scenarios

Key Terms

• Percent Change: The amount of increase or decrease expressed as a percent of the original value.
• Increase: When a quantity grows larger; calculated as a positive percent change.
• Decrease: When a quantity gets smaller; calculated as a negative percent change.

Lesson Examples

Example 1: Percent Increase

1. An item price increases from $50 to $60. Find the percent increase.
2. Calculate: (60 − 50) ÷ 50 × 100 = 10 ÷ 50 × 100 = 20%.
3. Answer: 20% increase.

Example 2: Percent Decrease

1. A population decreases from 1200 to 1080. Find the percent decrease.
2. Calculate: (1200 − 1080) ÷ 1200 × 100 = 120 ÷ 1200 × 100 = 10%.
3. Answer: 10% decrease.

Practice Problems

1. The price of a book drops from $40 to $32. Find the percent decrease.
2. A store increases a $75 item by 15%. What is the new price?
3. A city's population grows from 25,000 to 26,250. Calculate the percent increase.
4. A stock decreases from $120 to $102. Find the percent decrease.

Tips & Common Mistakes

• Always use the original value as the base for percent change calculations.
• Remember that increase and decrease are directional; a decrease is subtracted from the original.
• Convert the fraction to a percentage by multiplying by 100.

Summary

Percent increase and decrease help describe changes in quantities. Accurate calculation and correct base selection are essential for solving practical problems in finance, population studies, and everyday life.

Challenge Problems

1. An item costs $200 and is increased by 12%, then later decreased by 10%. What is the final price?
2. A population grows by 5% annually. If it is currently 20,000, what will it be next year?
3. A salary is increased by 8% and then decreased by 5%. Calculate the net percent change.