 ((4,000 - 5,000) / ((4,000 + 5,000) / 2)) x 100 

Let's solve this expression step by step:

### Expression:
\[
\left(\frac{{4,000 - 5,000}}{{\left(\frac{{4,000 + 5,000}}{2}\right)}}\right) \times 100
\]

### Step 1: Calculate \( 4,000 - 5,000 \)
\[
4,000 - 5,000 = -1,000
\]

### Step 2: Calculate \( 4,000 + 5,000 \)
\[
4,000 + 5,000 = 9,000
\]

### Step 3: Calculate the average \(\frac{9,000}{2}\)
\[
\frac{9,000}{2} = 4,500
\]

### Step 4: Divide the result from Step 1 by the result from Step 3
\[
\frac{-1,000}{4,500} \approx -0.2222
\]

### Step 5: Multiply by 100 to get the final result
\[
-0.2222 \times 100 = -22.22
\]

So, the final result is approximately:
\[
\boxed{-22.22}
\]

Would you like more details or have any questions?

Here are 8 related questions:

1. How would the result change if the values of 4,000 and 5,000 were closer in value?
2. What does the negative result represent in this calculation?
3. How would you interpret this result in a financial context?
4. Can you apply this calculation to measure percentage change in other fields, like economics?
5. What happens if you reverse the subtraction order, making it \(5,000 - 4,000\)?
6. How does this formula relate to the concept of relative percentage error?
7. Why is it important to use the average of the two numbers in the denominator?
8. Can this formula be applied to data that is not numerical, such as percentages or ratios?

**Tip:** When dealing with negative results in percentage calculations, consider the context to understand whether it indicates a decrease or loss.

Explore how to calculate percentage change and interpret negative results in mathematical calculations. This analysis covers arithmetic operations, percentage change formulas, and the interpretation of negative values in mathematical contexts. Suitable for Grades 9-12.

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