1. **Problem:** Divide $\frac{3}{4}$ by $\frac{2}{5}$.\n\nStep 1: Write the problem as division of fractions: $\frac{3}{4} \div \frac{2}{5}$.\n\nStep 2: To divide by a fraction, multiply by its reciprocal: $\frac{3}{4} \times \frac{5}{2}$.\n\nStep 3: Multiply numerators and denominators: $\frac{3 \times 5}{4 \times 2} = \frac{15}{8}$.\n\nStep 4: The fraction $\frac{15}{8}$ is already in simplest form.\n\n**Answer:** $\frac{15}{8}$.\n\n2. **Problem:** Divide $\frac{7}{9}$ by $\frac{1}{3}$.\n\nStep 1: $\frac{7}{9} \div \frac{1}{3}$.\n\nStep 2: Multiply by reciprocal: $\frac{7}{9} \times \frac{3}{1}$.\n\nStep 3: Multiply numerators and denominators: $\frac{7 \times 3}{9 \times 1} = \frac{21}{9}$.\n\nStep 4: Simplify $\frac{21}{9} = \frac{7}{3}$.\n\n**Answer:** $\frac{7}{3}$.\n\n3. **Problem:** Divide $\frac{5}{8}$ by $\frac{10}{12}$.\n\nStep 1: $\frac{5}{8} \div \frac{10}{12}$.\n\nStep 2: Multiply by reciprocal: $\frac{5}{8} \times \frac{12}{10}$.\n\nStep 3: Multiply numerators and denominators: $\frac{5 \times 12}{8 \times 10} = \frac{60}{80}$.\n\nStep 4: Simplify by dividing numerator and denominator by 20: $\frac{60 \div 20}{80 \div 20} = \frac{3}{4}$.\n\n**Answer:** $\frac{3}{4}$.\n\n4. **Problem:** Divide $\frac{9}{10}$ by $\frac{3}{5}$.\n\nStep 1: $\frac{9}{10} \div \frac{3}{5}$.\n\nStep 2: Multiply by reciprocal: $\frac{9}{10} \times \frac{5}{3}$.\n\nStep 3: Multiply numerators and denominators: $\frac{9 \times 5}{10 \times 3} = \frac{45}{30}$.\n\nStep 4: Simplify $\frac{45}{30}$ by dividing numerator and denominator by 15: $\frac{3}{2}$.\n\n**Answer:** $\frac{3}{2}$.\n\n5. **Problem:** Divide $\frac{4}{7}$ by $\frac{2}{3}$.\n\nStep 1: $\frac{4}{7} \div \frac{2}{3}$.\n\nStep 2: Multiply by reciprocal: $\frac{4}{7} \times \frac{3}{2}$.\n\nStep 3: Multiply numerators and denominators: $\frac{4 \times 3}{7 \times 2} = \frac{12}{14}$.\n\nStep 4: Simplify $\frac{12}{14}$ by dividing numerator and denominator by 2: $\frac{6}{7}$.\n\n**Answer:** $\frac{6}{7}$.\n\n**Answer Key:**\n1: $\frac{15}{8}$; 2: $\frac{7}{3}$; 3: $\frac{3}{4}$; 4: $\frac{3}{2}$; 5: $\frac{6}{7}$.