If `13lekle21, 9leple19, 2ltmlt6 and k, p, and m` are integers, what is the largest possible value of `(k-p)/(m)`?

Answer

To solve the problem, we need to find the largest possible value of \((k - p) / m\) given the constraints on \(k\), \(p\), and \(m\):

1. **Identify the ranges for \(k\), \(p\), and \(m\)**:
- \(k\) is an integer such that \(13 \leq k \leq 21\).
- \(p\) is an integer such that \(9 \leq p \leq 19\).
- \(m\) is an integer such that \(2 < m < 6\).

2. **Determine the maximum value of \(k\)**:
- The maximum value of \(k\) is \(21\).

3. **Determine the minimum value of \(p\)**:
- The minimum value of \(p\) is \(9\).

4. **Determine the minimum value of \(m\)**:
- Since \(m\) must be greater than \(2\) and less than \(6\), the smallest integer value for \(m\) is \(3\).

5. **Substitute the values into the expression**:
\[ \frac{k - p}{m} = \frac{21 - 9}{3} \]

6. **Calculate the expression**:
- First, calculate \(21 - 9\):
\[ 21 - 9 = 12 \]
- Now divide by \(m\):
\[ \frac{12}{3} = 4 \]

7. **Conclusion**:
- The largest possible value of \((k - p) / m\) is \(4\).