Percent Increase and Decrease

In this lesson, we will learn how to calculate percent increase and percent decrease. These concepts are essential for understanding how quantities change in relation to their original values.

Percent Increase

To find the percent increase, use the formula:

$$ext{Percent Increase} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100\%$$

Percent Decrease

To find the percent decrease, use the formula:

$$\text{Percent Decrease} = \frac{\text{Original Value} - \text{New Value}}{\text{Original Value}} \times 100\%$$

Worked Example

Example: A shirt originally costs $40. If the price is reduced to $30, what is the percent decrease?

1. Identify the original value and the new value:

   • Original Value = $40
   • New Value = $30

2. Apply the percent decrease formula:

   $$\text{Percent Decrease} = \frac{40 - 30}{40} \times 100\%$$

3. Simplify the numerator:

   $$\text{Percent Decrease} = \frac{10}{40} \times 100\%$$

4. Divide:

   $$\text{Percent Decrease} = 0.25 \times 100\%$$

5. Calculate the final result:

   $$\text{Percent Decrease} = 25\%$$

Thus, the percent decrease from $40 to $30 is 25%.

Key Questions

• If a car's value drops from $20,000 to $15,000, what is the percent decrease?
• A stock increases from $50 to $75. What is the percent increase?
• How do you find the original value if the new value is $80 after a 20% increase?
• If a product costs $60 and is on sale for $45, what is the percent decrease?

Keywords

• Percent Increase
• Percent Decrease
• Calculation
• Original Value
• New Value