By what number should `(-8)^(-1)` be multiplied to get `10^(-1)` ?

Options

A. (a) `frac(4)(5)`
B. (b) `frac(-5)(4)`
C. (c) `frac(-4)(5)`
D. (d) none of these

Answer

To solve the problem, we need to find the number \( x \) such that:

\[ (-8)^{-1} \times x = 10^{-1} \]

### Step 1: Calculate \((-8)^{-1}\)

The expression \((-8)^{-1}\) means the reciprocal of \(-8\):

\[ (-8)^{-1} = \frac{1}{-8} = -\frac{1}{8} \]

### Step 2: Calculate \(10^{-1}\)

The expression \(10^{-1}\) also means the reciprocal of \(10\):

\[ 10^{-1} = \frac{1}{10} \]

### Step 3: Set up the equation

Now we substitute the values we calculated into the equation:

\[ -\frac{1}{8} \times x = \frac{1}{10} \]

### Step 4: Solve for \(x\)

To find \(x\), we can multiply both sides of the equation by \(-8\):

\[ x = \frac{1}{10} \times (-8) \]

Calculating the right side:

\[ x = -\frac{8}{10} = -\frac{4}{5} \]

### Final Answer

Thus, the number that should be multiplied by \((-8)^{-1}\) to get \(10^{-1}\) is:

\[ \boxed{-\frac{4}{5}} \]

---