8) 4 1/4 : 1 1/6 =

Convert mixed numbers to improper fractions: $$4 \frac{1}{4} = \frac{17}{4}$$ and $$1 \frac{1}{6} = \frac{7}{6}$$. To divide by a fraction, multiply by its reciprocal: $$\frac{17}{4} \div \frac{7}{6} = \frac{17}{4} \times \frac{6}{7}$$. Multiply the fractions: $$\frac{17 \times 6}{4 \times 7} = \frac{102}{28}$$. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 2: $$\frac{102 \div 2}{28 \div 2} = \frac{51}{14}$$. Convert back to a mixed number: $$\frac{51}{14} = 3 \frac{9}{14}$$.