Chapter 1 - Introduction to Algebraic Expressions - 1.7 Multiplication and Division of Real Numbers - 1.7 Exercise Set - Page 58: 48

$\dfrac{3}{35}$

The product of two numbers with opposite signs is negative while the product of two numbers with the same sign is positive. Multiplying the numbers from left-to-right, then the given expression, $ -\dfrac{1}{2}\cdot\dfrac{3}{5}\cdot\left(-\dfrac{2}{7}\right) $, simplifies to \begin{array}{l}\require{cancel} -\dfrac{3}{10}\cdot\left(-\dfrac{2}{7}\right) \\\\= \dfrac{6}{70} \\\\= \dfrac{\cancel{2}\cdot3}{\cancel{2}\cdot35} \\\\= \dfrac{3}{35} .\end{array}