Express `-5/8` as a rational number with numerator:
10

Answer

To express \(-\frac{5}{8}\) as a rational number with a numerator of \(10\), we can follow these steps:

### Step 1: Identify the current fraction
We start with the fraction \(-\frac{5}{8}\). Here, the numerator is \(-5\) and the denominator is \(8\).

### Step 2: Determine the factor to change the numerator
We want to change the numerator from \(-5\) to \(10\). To do this, we need to find a factor that will convert \(-5\) to \(10\). Since \(5 \times 2 = 10\), we can multiply the numerator by \(-2\) (to keep the sign consistent).

### Step 3: Maintain the value of the fraction
To maintain the value of the fraction while changing the numerator, we must also multiply the denominator by the same factor. Therefore, we will multiply the denominator by \(-2\) as well.

### Step 4: Perform the multiplication
Now we can perform the multiplication:
- New numerator: \(-5 \times -2 = 10\)
- New denominator: \(8 \times -2 = -16\)

### Step 5: Write the new fraction
Putting it all together, we have:
\[ \frac{10}{-16} \]

### Step 6: Simplify the fraction (if needed)
The fraction \(\frac{10}{-16}\) can be simplified by dividing both the numerator and the denominator by \(2\):
\[ \frac{10 \div 2}{-16 \div 2} = \frac{5}{-8} \]
However, we can also leave it as \(\frac{10}{-16}\) since it is already in the required form.

### Final Answer
Thus, \(-\frac{5}{8}\) expressed as a rational number with a numerator of \(10\) is:
\[ \frac{10}{-16} \]