(5) \( \frac{5}{6} \div 2 \frac{2}{3}= \)

To solve \( \frac{5}{6} \div 2 \frac{2}{3} \), first convert the mixed number \( 2 \frac{2}{3} \) into an improper fraction. This gives you \( 2 \times 3 + 2 = 8/3 \). Now, the division of fractions can be turned into a multiplication by taking the reciprocal: \( \frac{5}{6} \div \frac{8}{3} \) becomes \( \frac{5}{6} \times \frac{3}{8} \). When you multiply, you get: \( \frac{5 \times 3}{6 \times 8} = \frac{15}{48} \). Now simplify \( \frac{15}{48} \). Both 15 and 48 can be divided by 3: \( \frac{15 \div 3}{48 \div 3} = \frac{5}{16} \). So, \( \frac{5}{6} \div 2 \frac{2}{3} = \frac{5}{16} \). And there you have it—easy as pie!