Multiply `6/13` by the reciprocal of `(-7)/16.`

Options

A. `-96/91`
B. `-34/91`
C. `96/91`
D. `34/91`

Explanation

To solve the problem of multiplying \( \frac{6}{13} \) by the reciprocal of \( \frac{-7}{16} \), follow these steps:

### Step 1: Find the reciprocal of \( \frac{-7}{16} \)
The reciprocal of a fraction is obtained by swapping its numerator and denominator. Therefore, the reciprocal of \( \frac{-7}{16} \) is:
\[ \text{Reciprocal of } \frac{-7}{16} = \frac{16}{-7} = -\frac{16}{7} \]

### Step 2: Multiply \( \frac{6}{13} \) by \( -\frac{16}{7} \)
Now, we need to multiply \( \frac{6}{13} \) by \( -\frac{16}{7} \):
\[ \frac{6}{13} \times -\frac{16}{7} = \frac{6 \times -16}{13 \times 7} \]

### Step 3: Perform the multiplication
Calculate the numerator and the denominator:
- Numerator: \( 6 \times -16 = -96 \)
- Denominator: \( 13 \times 7 = 91 \)

Putting it together, we have:
\[ \frac{6}{13} \times -\frac{16}{7} = \frac{-96}{91} \]

### Final Answer
Thus, the final answer is:
\[ -\frac{96}{91} \]

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