Which number is the additive inverse of the reciprocal of `- (5)/(8)` ?

Options

A. `8 (5)/(8)`
B. `1 (3)/(5)`
C. `2 (2)/(5)`
D. `(5)/(8)`

Answer

To find the additive inverse of the reciprocal of \(-\frac{5}{8}\), we can follow these steps:

### Step 1: Find the reciprocal of \(-\frac{5}{8}\).
The reciprocal of a fraction is obtained by flipping the numerator and the denominator. Therefore, the reciprocal of \(-\frac{5}{8}\) is:

\[ \text{Reciprocal} = -\frac{8}{5} \]

### Step 2: Define the additive inverse.
The additive inverse of a number \(x\) is the number \(y\) such that:

\[ x + y = 0 \]

This means that \(y\) is the opposite of \(x\).

### Step 3: Find the additive inverse of \(-\frac{8}{5}\).
Let \(x = -\frac{8}{5}\). To find the additive inverse \(y\), we set up the equation:

\[ -\frac{8}{5} + y = 0 \]

### Step 4: Solve for \(y\).
To isolate \(y\), we can add \(\frac{8}{5}\) to both sides of the equation:

\[ y = \frac{8}{5} \]

### Conclusion:
The additive inverse of the reciprocal of \(-\frac{5}{8}\) is:

\[ \frac{8}{5} \]