Express `-5/8` as a rational number with numerator:
15

Answer

To express \(-\frac{5}{8}\) as a rational number with a numerator of 15, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the relationship between the original numerator and the desired numerator**:
We start with \(-\frac{5}{8}\) and want to change the numerator to 15.

2. **Determine the multiplication factor**:
To find out what we need to multiply \(-5\) by to get \(15\), we can set up the equation:
\[ -5 \times x = 15 \]
Solving for \(x\), we find:
\[ x = \frac{15}{-5} = -3 \]

3. **Multiply both the numerator and denominator by the same factor**:
To maintain the equality of the rational number, we multiply both the numerator and the denominator by \(-3\):
\[ -\frac{5 \times (-3)}{8 \times (-3)} = \frac{15}{-24} \]

4. **Simplify the expression**:
The expression \(\frac{15}{-24}\) can also be written as:
\[ -\frac{15}{24} \]
This is the final form of the rational number with a numerator of 15.

### Final Answer:
\[ -\frac{15}{24} \]