Find ten rational numbers between $-\dfrac{2}{5}$ and $\dfrac{1}{7}$.

Writing the given numbers with same denominator 35 (L.C.M. of 5 and 7), we get:

$-\dfrac{2}{5} = -\dfrac{14}{35} \\[0.5em] \dfrac{1}{7} = \dfrac{5}{35}$

$\text{As } -14 \lt -13 \lt -12 \lt -11 \lt -10 \lt -9 \lt -8 \lt -7 \lt 0 \lt 1 \lt 2 \lt 5, \\[0.7em] -\dfrac{14}{35} \lt -\dfrac{13}{35} \lt -\dfrac{12}{35} \lt -\dfrac{11}{35} \lt -\dfrac{10}{35} \lt -\dfrac{9}{35} \lt -\dfrac{8}{35} \lt -\dfrac{7}{35} \lt 0 \lt \dfrac{1}{35} \lt \dfrac{2}{35} \lt \dfrac{5}{35} \\[0.7em] \Rightarrow -\dfrac{2}{5} \lt -\dfrac{13}{35} \lt -\dfrac{12}{35} \lt -\dfrac{11}{35} \lt -\dfrac{2}{7} \lt -\dfrac{9}{35} \lt -\dfrac{8}{35} \lt -\dfrac{1}{5} \lt 0 \lt \dfrac{1}{35} \lt \dfrac{2}{35} \lt \dfrac{5}{35}$

Therefore, ten rational numbers between $-\dfrac{2}{5}$ and $\dfrac{1}{7}$ are:

$\bold{-\dfrac{13}{35}}, \bold{-\dfrac{12}{35}}, \bold{-\dfrac{11}{35}}, \bold{-\dfrac{2}{7}}, \bold{-\dfrac{9}{35}}, \\[0.5em] \bold{-\dfrac{8}{35}}, \bold{-\dfrac{1}{5}}, 0, \bold{\dfrac{1}{35}}, \bold{\dfrac{2}{35}}$