https://file.aiquickdraw.com/mathbot/file/1725928781384zf5hh7e0.jpg

The problem presented in the image asks for the quotient of \( 2 \div \frac{3}{7} \), using the number line and model for assistance. Let's walk through the solution.

### Step-by-step Process:
1. **Understand the division**: 
   - The problem is asking how many times \( \frac{3}{7} \) fits into 2.

2. **Interpret the number line**:
   - The number line represents whole numbers from 0 to 3, with fractional divisions.
   - Each section between 0 and 1, and so on, can be divided into seventh parts because we're dealing with a fraction with denominator 7.
   - \( \frac{3}{7} \) is approximately a little less than half of 1.

3. **Perform the division**:
   - To divide \( 2 \) by \( \frac{3}{7} \), we multiply 2 by the reciprocal of \( \frac{3}{7} \), which is \( \frac{7}{3} \).
   \[
   2 \div \frac{3}{7} = 2 \times \frac{7}{3} = \frac{14}{3}
   \]
   - Converting \( \frac{14}{3} \) to a mixed number, we get:
   \[
   \frac{14}{3} = 4 \frac{2}{3}
   \]
   So, the answer is \( 4 \frac{2}{3} \).

4. **Select the correct answer**:
   - From the options given in the image, the correct answer is \( 4 \frac{2}{3} \).

This division represents that \( \frac{3}{7} \) fits into 2 approximately 4 and \( \frac{2}{3} \) times.

Do you want further details or have any questions?

### Relative Questions:
1. How do you multiply by the reciprocal in fraction division?
2. How can you use the number line to represent division?
3. What is the importance of converting improper fractions to mixed numbers?
4. How would you divide a whole number by a different fraction?
5. Why is it important to understand reciprocal operations in fraction division?

**Tip**: When dividing by a fraction, always remember to multiply by its reciprocal (flip the numerator and denominator).

Find the quotient 2 ÷ 3/7 using the model provided.

Learn how to solve the fraction division problem 2 ÷ 3/7 using a number line and reciprocal method. This example demonstrates the division of whole numbers by fractions and is suitable for Grades 6-7 students.

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