Chapter 1 - Introduction to Algebraic Expressions - 1.7 Multiplication and Division of Real Numbers - 1.7 Exercise Set - Page 58: 91

$-\dfrac{10}{51}$

To find the reciprocal of a number, interchange the numerator and the denominator. Hence, the reciprocal of the expression, $ \dfrac{51}{-10} $, is \begin{array}{l}\require{cancel} \dfrac{-10}{51} \\\\= -\dfrac{10}{51} .\end{array}