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The expression you've provided is:

\[
\frac{\frac{9 \frac{1}{6} - 8 \frac{3}{4}}{15/2}}{}
\]

Let's break it down step by step:

### Step 1: Convert mixed numbers to improper fractions.
- \( 9 \frac{1}{6} = \frac{55}{6} \)
- \( 8 \frac{3}{4} = \frac{35}{4} \)

So the expression becomes:

\[
\frac{\frac{\frac{55}{6} - \frac{35}{4}}{\frac{15}{2}}}
\]

### Step 2: Find a common denominator to subtract the fractions \( \frac{55}{6} \) and \( \frac{35}{4} \).
The least common denominator of 6 and 4 is 12. Rewriting the fractions:

\[
\frac{55}{6} = \frac{110}{12}, \quad \frac{35}{4} = \frac{105}{12}
\]

Now subtract:

\[
\frac{110}{12} - \frac{105}{12} = \frac{5}{12}
\]

### Step 3: Divide by \( \frac{15}{2} \).
Dividing by a fraction is the same as multiplying by its reciprocal, so:

\[
\frac{\frac{5}{12}}{\frac{15}{2}} = \frac{5}{12} \times \frac{2}{15} = \frac{10}{180} = \frac{1}{18}
\]

### Final Answer:
The result of the expression is \( \frac{1}{18} \).

---

Would you like more details on any step or have any questions? 

Here are some related questions for practice:
1. How do you convert a mixed number to an improper fraction?
2. What is the least common denominator of 8 and 12?
3. How do you divide fractions, and why is it the same as multiplying by the reciprocal?
4. How do you simplify complex fractions like this one?
5. What is the result of dividing a number by 15/2?

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

Solve the expression (9 1/6 - 8 3/4) / (15/2).

Learn how to simplify the fractional expression (9 1/6 - 8 3/4) divided by 15/2 with a detailed step-by-step solution. This problem covers key concepts like converting mixed numbers to improper fractions, subtracting fractions, and dividing using the reciprocal method. Suitable for students in Grades 6-8.

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