Find 10 rational numbers between $\dfrac{-3}{4} \text{ and } \dfrac{5}{6}$.

The given rational numbers have different denominators, so first write them with a common denominator.

$[\text{ LCM of } 4 \text{ and } 6 = 12] \\[1em] \Rightarrow \dfrac{-3}{4} = \dfrac{-3 \times 3}{4 \times 3} = \dfrac{-9}{12} \\[1em] \Rightarrow \dfrac{5}{6} = \dfrac{5 \times 2}{6 \times 2} = \dfrac{10}{12}$

We note that -8, -7, -6, …, 8, 9 are the integers between -9 and 10

i.e. -9 < -8 < -7 < -6 < -5 < -4 < -3 < -2 < -1 < 0 < 1 < … < 9 < 10

Choosing any ten of these integers as numerators over the common denominator 12, we get the required rational numbers.

Hence, ten rational numbers between $\mathbf{\dfrac{-3}{4} \text{ and } \dfrac{5}{6}}$ are

$\mathbf{\dfrac{-8}{12}, \dfrac{-7}{12}, \dfrac{-6}{12}, \dfrac{-5}{12}, \dfrac{-4}{12}, \dfrac{-3}{12}, \dfrac{-2}{12}, \dfrac{-1}{12}, \dfrac{0}{12} \text{ and } \dfrac{1}{12}}$.