To solve \( \left( 2 \frac{3}{4} \times 1 \frac{1}{5} \right) \div \frac{3}{8} \), let's break down each step.

### Step 1: Convert Mixed Numbers to Improper Fractions
1. **Convert \(2 \frac{3}{4}\):**
   \[
   2 \frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4}
   \]
2. **Convert \(1 \frac{1}{5}\):**
   \[
   1 \frac{1}{5} = \frac{1 \times 5 + 1}{5} = \frac{5 + 1}{5} = \frac{6}{5}
   \]

So, the expression becomes:
\[
\left( \frac{11}{4} \times \frac{6}{5} \right) \div \frac{3}{8}
\]

### Step 2: Multiply Fractions
Multiply \( \frac{11}{4} \) and \( \frac{6}{5} \):
\[
\frac{11}{4} \times \frac{6}{5} = \frac{11 \times 6}{4 \times 5} = \frac{66}{20}
\]

### Step 3: Simplify \( \frac{66}{20} \)
Divide the numerator and denominator by their greatest common divisor, 2:
\[
\frac{66}{20} = \frac{33}{10} = 3 \frac{3}{10}
\]

### Step 4: Divide by \( \frac{3}{8} \)
Now, divide \( \frac{33}{10} \) by \( \frac{3}{8} \):
\[
\frac{33}{10} \div \frac{3}{8} = \frac{33}{10} \times \frac{8}{3} = \frac{33 \times 8}{10 \times 3} = \frac{264}{30}
\]

### Step 5: Simplify \( \frac{264}{30} \)
Divide both numerator and denominator by their greatest common divisor, 6:
\[
\frac{264}{30} = \frac{44}{5} = 8 \frac{4}{5}
\]

### Final Answer:
\[
8 \frac{4}{5}
\]

Would you like more details, or do you have any questions?

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Here are some related questions for further practice:
1. What is \( (3 \frac{1}{2} \times 2 \frac{1}{3}) \div \frac{5}{6} \)?
2. How do you simplify \( \frac{15}{9} \div \frac{3}{7} \)?
3. Calculate \( (1 \frac{4}{5} \times 2 \frac{1}{6}) \div 1 \frac{1}{2} \).
4. What is the product of \( \frac{7}{8} \) and \( 2 \frac{2}{3} \)?
5. How can you convert \( 4 \frac{3}{5} \) into an improper fraction?

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

Explore the detailed solution to (2 3/4 x 1 1/5) divided by 3/8, covering converting mixed numbers to improper fractions, multiplication and division of fractions, and simplification techniques. Ideal for students in Grades 5-7.

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