$\dfrac{-1}{4} \times \left[\dfrac{2}{5} + \left(\dfrac{-5}{6}\right)\right]$ = ?

1. $\left[\dfrac{-1}{4} \times \dfrac{2}{5}\right] + \left[\dfrac{-1}{4} \times \left(\dfrac{-5}{6}\right)\right]$

2. $\left[\dfrac{-1}{4} \times \dfrac{2}{5}\right] - \left(\dfrac{-5}{6}\right)$

3. $\dfrac{2}{5} + \left(\dfrac{-1}{4}\right) \times \left(\dfrac{-5}{6}\right)$

4. $\left[\dfrac{2}{5} + \left(\dfrac{-5}{6}\right)\right] - \dfrac{1}{4}$

By the distributive law of multiplication over addition, for any three rational numbers $\dfrac{a}{b}, \dfrac{c}{d} \text{ and } \dfrac{e}{f}$, we have

$\dfrac{a}{b} \times \left(\dfrac{c}{d} + \dfrac{e}{f}\right) = \left(\dfrac{a}{b} \times \dfrac{c}{d}\right) + \left(\dfrac{a}{b} \times \dfrac{e}{f}\right)$

So, $\dfrac{-1}{4}$ has to be multiplied by each of the two rational numbers inside the bracket separately.

Expanding the given expression by this law,

$\dfrac{-1}{4} \times \left[\dfrac{2}{5} + \left(\dfrac{-5}{6}\right)\right] = \left[\dfrac{-1}{4} \times \dfrac{2}{5}\right] + \left[\dfrac{-1}{4} \times \left(\dfrac{-5}{6}\right)\right]$

Hence, Option 1 is the correct option.