To solve the expression \( 3 \frac{6}{7} \div 6 \frac{3}{4} \), we first convert both mixed numbers into improper fractions and then perform the division.

### Step 1: Convert mixed numbers to improper fractions
- \( 3 \frac{6}{7} = \frac{27}{7} \)
- \( 6 \frac{3}{4} = \frac{27}{4} \)

### Step 2: Perform the division
Dividing by a fraction is the same as multiplying by its reciprocal:
\[
\frac{27}{7} \div \frac{27}{4} = \frac{27}{7} \times \frac{4}{27}
\]

### Step 3: Multiply the fractions
\[
\frac{27}{7} \times \frac{4}{27} = \frac{27 \times 4}{7 \times 27} = \frac{108}{189}
\]
The \( 27 \)'s cancel out, leaving:
\[
= \frac{4}{7}
\]

### Final Answer:
\[
3 \frac{6}{7} \div 6 \frac{3}{4} = \frac{4}{7}
\]

Would you like more details on this process or any further clarification?

Here are 5 related questions:
1. How do you multiply two fractions?
2. What is the reciprocal of a fraction and how is it used in division?
3. Can you explain why dividing by a fraction is equivalent to multiplying by its reciprocal?
4. How do you convert improper fractions back into mixed numbers?
5. How do you simplify fractions?

**Tip:** Always simplify fractions after performing operations to get the final reduced form.

Explore how to divide mixed numbers like 3 6/7 by 6 3/4. This guide converts mixed numbers into improper fractions and demonstrates division using reciprocal multiplication. Suitable for Grades 6-8 with step-by-step explanations.

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