1. Calculate $\frac{2}{3} + \frac{4}{5}$: Find common denominator 15, so $\frac{2}{3} = \frac{10}{15}$ and $\frac{4}{5} = \frac{12}{15}$. Add: $\frac{10}{15} + \frac{12}{15} = \frac{22}{15} = 1 \frac{7}{15}$. 2. Calculate $4 \frac{2}{3} + 2 \frac{3}{4}$: Convert to improper fractions: $4 \frac{2}{3} = \frac{14}{3}$, $2 \frac{3}{4} = \frac{11}{4}$. Common denominator 12: $\frac{14}{3} = \frac{56}{12}$, $\frac{11}{4} = \frac{33}{12}$. Add: $\frac{56}{12} + \frac{33}{12} = \frac{89}{12} = 7 \frac{5}{12}$. 3. Calculate $50 \frac{3}{2} - 28 \frac{5}{6}$: Convert mixed numbers: $50 \frac{3}{2} = 50 + 1 \frac{1}{2} = 51 \frac{1}{2} = \frac{103}{2}$, $28 \frac{5}{6} = \frac{173}{6}$. Common denominator 6: $\frac{103}{2} = \frac{309}{6}$. Subtract: $\frac{309}{6} - \frac{173}{6} = \frac{136}{6} = 22 \frac{2}{3}$. 4. Calculate $6 \frac{1}{6} - \frac{3}{8}$: Convert $6 \frac{1}{6} = \frac{37}{6}$. Common denominator 24: $\frac{37}{6} = \frac{148}{24}$, $\frac{3}{8} = \frac{9}{24}$. Subtract: $\frac{148}{24} - \frac{9}{24} = \frac{139}{24} = 5 \frac{19}{24}$. 5. Calculate $4 \frac{9}{10} + 8 \frac{6}{15} + 14 \frac{7}{9}$: Convert to improper fractions: $4 \frac{9}{10} = \frac{49}{10}$, $8 \frac{6}{15} = \frac{126}{15}$, $14 \frac{7}{9} = \frac{133}{9}$. Common denominator 90: $\frac{49}{10} = \frac{441}{90}$, $\frac{126}{15} = \frac{756}{90}$, $\frac{133}{9} = \frac{1330}{90}$. Add: $441 + 756 + 1330 = 2527$, so $\frac{2527}{90} = 28 \frac{7}{90}$. 6. Calculate $4 \frac{2}{3} \times 2 \frac{3}{5}$: Convert to improper fractions: $\frac{14}{3} \times \frac{13}{5} = \frac{182}{15} = 12 \frac{2}{15}$. 7. Calculate $9 \times \frac{6}{5} \times 8 \frac{2}{4}$: Convert $8 \frac{2}{4} = 8 \frac{1}{2} = \frac{17}{2}$. Multiply: $9 \times \frac{6}{5} \times \frac{17}{2} = \frac{9 \times 6 \times 17}{5 \times 2} = \frac{918}{10} = 91 \frac{8}{10} = 91 \frac{4}{5}$. 8. Calculate $\frac{4}{5} \times \frac{8}{10} \times 5$: Simplify $\frac{8}{10} = \frac{4}{5}$. Multiply: $\frac{4}{5} \times \frac{4}{5} \times 5 = \frac{16}{25} \times 5 = \frac{80}{25} = 3 \frac{5}{25} = 3 \frac{1}{5}$. 9. Calculate $12 \times \frac{3}{4} \times \frac{5}{6}$: Multiply numerators and denominators: $\frac{12 \times 3 \times 5}{1 \times 4 \times 6} = \frac{180}{24} = 7 \frac{12}{24} = 7 \frac{1}{2}$. 10. Calculate $5 \frac{2}{3} \times 2 \frac{3}{4}$: Convert to improper fractions: $\frac{17}{3} \times \frac{11}{4} = \frac{187}{12} = 15 \frac{7}{12}$.