The given expression is:

\[
\frac{\frac{x}{8} - \frac{p}{16}}{p}
\]

Let's simplify it step by step.

### Step 1: Simplify the numerator
The numerator is \(\frac{x}{8} - \frac{p}{16}\).

To simplify this, find a common denominator. The least common denominator (LCD) of 8 and 16 is 16.

\[
\frac{x}{8} = \frac{2x}{16}
\]

So, the numerator becomes:

\[
\frac{2x}{16} - \frac{p}{16} = \frac{2x - p}{16}
\]

### Step 2: Substitute the simplified numerator back into the expression
Now substitute \(\frac{2x - p}{16}\) for the numerator in the original expression:

\[
\frac{\frac{2x - p}{16}}{p}
\]

### Step 3: Simplify the entire expression
This can be written as:

\[
\frac{2x - p}{16p}
\]

This is the simplified form of the expression.

### Final Answer:
\[
\frac{2x - p}{16p}
\]

Would you like more details or have any questions?

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Here are 5 related questions to expand your understanding:

1. How would the expression change if the denominator was a different variable, say \(q\), instead of \(p\)?
2. What is the result if \(x = 0\) in the final expression?
3. How would you approach simplifying if the numerator included an additional term, e.g., \(\frac{x}{8} - \frac{p}{16} + \frac{q}{24}\)?
4. Can you factor the expression further if \(x\) and \(p\) have common factors?
5. What happens to the expression if \(p = 0\)? Is the expression defined?

**Tip:** When simplifying complex fractions, always look for common denominators in the numerator before dividing by the denominator.

Learn how to simplify the fractional expression (x/8 - p/16) / p step-by-step with detailed explanations. This problem covers key concepts in fractional expressions and simplification. Suitable for students in Grades 7-9.

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