Find the quotient:

$\dfrac{17}{8} \div \dfrac{51}{4}$

To divide one rational number by another, multiply the dividend by the reciprocal of the divisor.

Dividing,

$\dfrac{17}{8} \div \dfrac{51}{4} = \dfrac{17}{8} \times \dfrac{4}{51} \\[1em] = \dfrac{17 \times 4}{8 \times 51} \\[1em] = \dfrac{68}{408} \\[1em] = \dfrac{1}{6}$

Hence, $\mathbf{\dfrac{17}{8} \div \dfrac{51}{4} = \dfrac{1}{6}}$.