Chapter 1 - Introduction to Algebraic Expressions - 1.7 Multiplication and Division of Real Numbers - 1.7 Exercise Set - Page 58: 115

$1$

The given expression, $ -\dfrac{5}{9}\div\left( -\dfrac{5}{9} \right) $, simplifies to \begin{array}{l}\require{cancel} -\dfrac{5}{9}\cdot\left( -\dfrac{9}{5} \right) \\\\= \dfrac{-5(-9)}{9(5)} \\\\= \dfrac{45}{45} \\\\= 1 .\end{array}