Example

Percentage Decrease Calculation

Percentage decrease is a way of expressing the reduction of a value as a percentage of its original amount. The formula used to calculate percentage decrease is:

\[ \text{Percentage Decrease} = \frac{\text{Original Value} - \text{New Value}}{\text{Original Value}} \times 100 \]

The general approach to calculating percentage decrease includes:

• Identifying the original and new values.
• Subtracting the new value from the original value to find the decrease.
• Dividing the decrease by the original value.
• Multiplying the result by 100 to convert it into a percentage.

Example 1: Basic Percentage Decrease

If the original price of a product is $100 and the new price is $80, the percentage decrease is calculated as:

• Step 1: Subtract the new value from the original value: \( 100 - 80 = 20 \) (decrease).
• Step 2: Divide the decrease by the original value: \( \frac{20}{100} = 0.2 \).
• Step 3: Multiply by 100 to get the percentage decrease: \( 0.2 \times 100 = 20\% \).

Example 2: Percentage Decrease in Sales Price

If a product originally costs $250 and is now on sale for $150, the percentage decrease is calculated as:

• Step 1: Subtract the new value from the original value: \( 250 - 150 = 100 \) (decrease).
• Step 2: Divide the decrease by the original value: \( \frac{100}{250} = 0.4 \).
• Step 3: Multiply by 100 to get the percentage decrease: \( 0.4 \times 100 = 40\% \).

Real-life Applications of Percentage Decrease

Percentage decrease is widely used in various fields, such as:

• Calculating the discount or sale price of products.
• Determining the reduction in costs over time.
• Understanding price reductions in sales or promotional offers.
• Analyzing data in scientific or financial reports where values decrease over time.

Common Operations with Percentage Decrease

Percentage Decrease Formula: \( \frac{\text{Original Value} - \text{New Value}}{\text{Original Value}} \times 100 \)

Real-life Example: A store is offering a 20% discount on a $150 product. To find the new price, subtract 20% of $150 from the original price: \( 150 - (150 \times 0.20) = 150 - 30 = 120 \).

Modifying Percentage Decrease Calculations: If the equation involves a sale, multiple price reductions, or complex discounts, applying percentage decrease in stages may be required.