What is 3 and 3 4ths divided by 5 6ths?

To divide (3 \frac{3}{4}) by (5 \frac{1}{6}), first convert both mixed numbers to improper fractions. (3 \frac{3}{4}) becomes (\frac{15}{4}) and (5 \frac{1}{6}) becomes (\frac{31}{6}). Then, divide by multiplying by the reciprocal:

[ \frac{15}{4} \div \frac{31}{6} = \frac{15}{4} \times \frac{6}{31} = \frac{90}{124} = \frac{45}{62}. ]

So, (3 \frac{3}{4} \div 5 \frac{1}{6} = \frac{45}{62}).