Intermediate Algebra (6th Edition)

$-\frac{23}{5}$, $-\frac{5}{23}$
We are given that the opposite of a number $a$ is $\frac{23}{5}$. We know that the opposite of number $a$ is equal to $-a$. Therefore, if $-a=\frac{23}{5}$, $a=-\frac{23}{5}$. We know that the reciprocal of a nonzero number $a$ is $\frac{1}{a}$, where $a\times\frac{1}{a}=1$. Therefore, if $a=-\frac{23}{5}$, then $\frac{1}{a}=-\frac{5}{23}$. $-\frac{23}{5}\times-\frac{5}{23}=1$