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The problem involves finding the average rate of change of the water level during a dry spell. The water level fell by \( 2 \frac{1}{2} \) inches over a period of \( 2 \frac{6}{7} \) weeks. To find the average rate of change, we need to simplify the complex fraction:

\[
\frac{-2 \frac{1}{2}}{2 \frac{6}{7}}
\]

### Step 1: Convert Mixed Numbers to Improper Fractions
- \( 2 \frac{1}{2} \) becomes \( \frac{5}{2} \) (since \( 2 \times 2 + 1 = 5 \)).
- \( 2 \frac{6}{7} \) becomes \( \frac{20}{7} \) (since \( 2 \times 7 + 6 = 20 \)).

So the fraction now becomes:

\[
\frac{-\frac{5}{2}}{\frac{20}{7}} = - \frac{5}{2} \times \frac{7}{20}
\]

### Step 2: Multiply the Fractions
Now, multiply \( \frac{-5}{2} \times \frac{7}{20} \):

\[
\frac{-5 \times 7}{2 \times 20} = \frac{-35}{40}
\]

### Step 3: Simplify the Fraction
To simplify \( \frac{-35}{40} \), find the greatest common divisor (GCD) of 35 and 40, which is 5. Divide both the numerator and denominator by 5:

\[
\frac{-35 \div 5}{40 \div 5} = \frac{-7}{8}
\]

### Final Answer:
The water level changed by \( \frac{-7}{8} \) inches per week.

Would you like more details or have any questions? Here are five related questions for further practice:

1. How do you convert mixed numbers into improper fractions?
2. What is the rule for dividing fractions?
3. How can you identify the greatest common divisor (GCD) to simplify fractions?
4. What does a negative rate of change signify in this context?
5. Can you explain why simplifying fractions is important in real-world problems?

**Tip:** Always remember to check if fractions can be simplified before finalizing your answer to avoid extra steps in the solution.

The water level of a lake fell by 2 1/2 in. during a 2 6/7-week-long dry spell. Simplify the complex fraction to find the average rate at which the water level changed every week.

Learn how to simplify fractions to find the average rate at which the water level of a lake changed during a dry spell. This problem involves converting mixed numbers to improper fractions and multiplying fractions. Suitable for Grades 6-8.

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