Question

find the reciprocal of \\(\frac{-1}{13}\\).

select the correct choice below and, if necessary, fill in the answer box within your choice.

\\(\bigcirc\\) a. the reciprocal of \\(\frac{-1}{13}\\) is \\(\square\\).
\\(\bigcirc\\) b. the reciprocal does not exist.

Explanation:

Step1: Recall the definition of reciprocal

The reciprocal of a number \( \frac{a}{b} \) (where \( a
eq0 \) and \( b
eq0 \)) is \( \frac{b}{a} \), because the product of a number and its reciprocal is 1.

Step2: Apply the definition to \( \frac{-1}{13} \)

For the number \( \frac{-1}{13} \), we swap the numerator and the denominator. So the reciprocal of \( \frac{-1}{13} \) is \( \frac{13}{-1} \), which simplifies to \( - 13 \). Also, we can check that \( \frac{-1}{13}\times(-13)=1 \), which satisfies the property of reciprocal.

Answer:

A. The reciprocal of \( \frac{-1}{13} \) is \( -13 \).