By what rational number should $\dfrac{-9}{35}$ be multiplied to get $\dfrac{3}{5}$ ?

Let the required number be x. Then,

$\dfrac{-9}{35} \times x = \dfrac{3}{5} \\[1em] \Rightarrow x = \dfrac{3}{5} \div \dfrac{-9}{35} \\[1em] = \dfrac{3}{5} \times \dfrac{35}{-9} \quad \left[\text{Reciprocal of } \dfrac{-9}{35} \text{ is } \dfrac{35}{-9}\right] \\[1em] = \dfrac{3}{5} \times \dfrac{-35}{9} \quad \left[\because \dfrac{35}{-9} = \dfrac{35 \times (-1)}{-9 \times (-1)} = \dfrac{-35}{9}\right] \\[1em] = \dfrac{1}{1} \times \dfrac{-7}{3} \quad \text{[Dividing 3 and 9 by 3, 35 and 5 by 5]} \\[1em] = \dfrac{1 \times (-7)}{1 \times 3} \\[1em] = \dfrac{-7}{3}$

Hence, the required number is $\dfrac{-7}{3}$.