Find the product :

$\dfrac{6}{7} \times \dfrac{-21}{12}$

The product of two rational numbers $\dfrac{a}{b} \text{ and } \dfrac{c}{d}$ is given by $\dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{a \times c}{b \times d}$.

Multiplying,

$\dfrac{6}{7} \times \dfrac{-21}{12} = \dfrac{6 \times (-21)}{7 \times 12} \\[1em] = \dfrac{-126}{84} = \dfrac{-3}{2} \\[1em] = -1\dfrac{1}{2}$

Hence, $\mathbf{\dfrac{6}{7} \times \dfrac{-21}{12} = -1\dfrac{1}{2}}$.