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Let's go through the problems one by one from your worksheet.

### Problems 11–14: Division of Fractions
1. **Problem 11**: \( \frac{5}{8} \div \frac{1}{7} \)
   - To divide fractions, multiply the first fraction by the reciprocal of the second.
   - \( \frac{5}{8} \times \frac{7}{1} = \frac{35}{8} \)
   - So, the answer is \( \frac{35}{8} \), or \( 4 \frac{3}{8} \) in mixed number form.

2. **Problem 12**: \( \frac{1}{7} \div \frac{5}{8} \)
   - Reciprocal of \( \frac{5}{8} \) is \( \frac{8}{5} \).
   - \( \frac{1}{7} \times \frac{8}{5} = \frac{8}{35} \)
   - So, the answer is \( \frac{8}{35} \).

3. **Problem 13**: \( \frac{3}{5} \div \frac{3}{4} \)
   - Reciprocal of \( \frac{3}{4} \) is \( \frac{4}{3} \).
   - \( \frac{3}{5} \times \frac{4}{3} = \frac{12}{15} \)
   - Simplify \( \frac{12}{15} \) by dividing both the numerator and denominator by 3: \( \frac{4}{5} \).
   - So, the answer is \( \frac{4}{5} \).

4. **Problem 14**: \( \frac{3}{4} \div \frac{3}{5} \)
   - Reciprocal of \( \frac{3}{5} \) is \( \frac{5}{3} \).
   - \( \frac{3}{4} \times \frac{5}{3} = \frac{15}{12} \)
   - Simplify \( \frac{15}{12} \) by dividing by 3: \( \frac{5}{4} \), or \( 1 \frac{1}{4} \) in mixed number form.

### Problem 15: Water Level in Mirror Lake
- The initial water level is 8 feet below sea level (negative value), and after the storm, the water rises by 5 feet.

   a. **Addition and subtraction expressions**:
   - **Addition expression**: \( -8 + 5 \)
   - **Subtraction expression**: \( -8 - (-5) \) (subtracting a negative number is like adding).

   b. **Model on a number line**:
   - Starting at -8 on the number line.
   - Adding 5 brings you to -3, representing the new water level.

   c. **Evaluate expressions**:
   - The water level after the storm is \( -8 + 5 = -3 \). So, the water level is 3 feet below sea level after the storm.

### Problem 16: Estimate and Find the Quotient
- The division problem is \( 4,872 \div 12 \).
   - **Estimate**: You could round \( 4,872 \) to \( 4,800 \), and \( 4,800 \div 12 = 400 \).
   - **Exact quotient**: \( 4,872 \div 12 = 406 \).

Would you like further details or explanations on any part of this? Here are some related questions:

1. How do you multiply and divide fractions in general?
2. What is the importance of understanding negative numbers in real-world situations?
3. How would you graph negative values on a number line?
4. What happens when you subtract negative numbers from another negative?
5. Can you estimate other division problems using rounding techniques?

**Tip**: When dividing fractions, remember that dividing by a fraction is the same as multiplying by its reciprocal.

For problems 11-14, divide the fractions. Problem 15: In Mirror Lake, the water level is 8 feet below sea level. After a storm, the water level rises 5 feet. Write addition and subtraction expressions, model the expressions on a number line, and determine the water level after the storm. Problem 16: Estimate and then find the quotient of 4,872 ÷ 12.

Solve problems involving division of fractions, understanding negative numbers on a number line, and estimating long division with large numbers. Suitable for students in grades 6-7.

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