(3) Work these out mentally. \( \begin{array}{lll}\text { a } \frac{1}{2} \div \frac{2}{3} & \text { b } \frac{1}{4} \div \frac{3}{5} & \text { c } \frac{3}{7} \div \frac{1}{2} \\ \text { d } \frac{5}{9} \div \frac{6}{7} & \text { e } \frac{2}{5} \div \frac{5}{9} & \text { f } \frac{1}{10} \div \frac{3}{7} \\ 4 & \text { Work these out mentally. Write each answer as a mixed number. } \\ \begin{array}{lll}\text { a } \frac{1}{2} \div \frac{1}{3} & \text { b } \frac{3}{5} \div \frac{4}{7} & \text { c } \frac{1}{3} \div \frac{2}{7} \\ \text { d } \frac{7}{9} \div \frac{1}{2} & \text { e } \frac{5}{6} \div \frac{2}{11} & \text { f } \frac{4}{7} \div \frac{3}{13} \\ \text { 5. Work these out mentally. Cancel each answer to its simplest form. } \\ \begin{array}{lll}\text { a } \frac{5}{8} \div \frac{1}{2} & \text { b } \frac{4}{13} \div \frac{3}{13} & \text { c } \frac{5}{8} \div \frac{5}{12} \\ \text { d } \frac{1}{3} \div \frac{5}{9} & \text { e } \frac{1}{4} \div \frac{1}{12} & \text { f } \frac{7}{9} \div \frac{1}{6}\end{array}\end{array}\end{array}> \)

Let's solve each division problem step by step. When dividing fractions, we multiply by the reciprocal of the divisor. ### Part 1: 1. **a** \( \frac{1}{2} \div \frac{2}{3} \) - Reciprocal of \( \frac{2}{3} \) is \( \frac{3}{2} \). - Calculation: \( \frac{1}{2} \times \frac{3}{2} = \frac{3}{4} \). 2. **b** \( \frac{1}{4} \div \frac{3}{5} \) - Reciprocal of \( \frac{3}{5} \) is \( \frac{5}{3} \). - Calculation: \( \frac{1}{4} \times \frac{5}{3} = \frac{5}{12} \). 3. **c** \( \frac{3}{7} \div \frac{1}{2} \) - Reciprocal of \( \frac{1}{2} \) is \( 2 \). - Calculation: \( \frac{3}{7} \times 2 = \frac{6}{7} \). 4. **d** \( \frac{5}{9} \div \frac{6}{7} \) - Reciprocal of \( \frac{6}{7} \) is \( \frac{7}{6} \). - Calculation: \( \frac{5}{9} \times \frac{7}{6} = \frac{35}{54} \). 5. **e** \( \frac{2}{5} \div \frac{5}{9} \) - Reciprocal of \( \frac{5}{9} \) is \( \frac{9}{5} \). - Calculation: \( \frac{2}{5} \times \frac{9}{5} = \frac{18}{25} \). 6. **f** \( \frac{1}{10} \div \frac{3}{7} \) - Reciprocal of \( \frac{3}{7} \) is \( \frac{7}{3} \). - Calculation: \( \frac{1}{10} \times \frac{7}{3} = \frac{7}{30} \). ### Part 2: 1. **a** \( \frac{1}{2} \div \frac{1}{3} \) - Reciprocal of \( \frac{1}{3} \) is \( 3 \). - Calculation: \( \frac{1}{2} \times 3 = \frac{3}{2} = 1 \frac{1}{2} \). 2. **b** \( \frac{3}{5} \div \frac{4}{7} \) - Reciprocal of \( \frac{4}{7} \) is \( \frac{7}{4} \). - Calculation: \( \frac{3}{5} \times \frac{7}{4} = \frac{21}{20} = 1 \frac{1}{20} \). 3. **c** \( \frac{1}{3} \div \frac{2}{7} \) - Reciprocal of \( \frac{2}{7} \) is \( \frac{7}{2} \). - Calculation: \( \frac{1}{3} \times \frac{7}{2} = \frac{7}{6} = 1 \frac{1}{6} \). 4. **d** \( \frac{7}{9} \div \frac{1}{2} \) - Reciprocal of \( \frac{1}{2} \) is \( 2 \). - Calculation: \( \frac{7}{9} \times 2 = \frac{14}{9} = 1 \frac{5}{9} \). 5. **e** \( \frac{5}{6} \div \frac{2}{11} \) - Reciprocal of \( \frac{2}{11} \) is \( \frac{11}{2} \). - Calculation: \( \frac{5}{6} \times \frac{11}{2} = \frac{55}{12} = 4 \frac{7}{12} \). 6. **f** \( \frac{4}{7} \div \frac{3}{13} \) - Reciprocal of \( \frac{3}{13} \) is \( \frac{13}{3} \). - Calculation: \( \frac{4}{7} \times \frac{13}{3} = \frac{52}{21} = 2 \frac{10}{21} \). ### Part 3: 1. **a** \( \frac{5}{8} \div \frac{1}{2} \) - Reciprocal of \( \frac{1}{2} \) is \( 2 \). - Calculation: \( \frac{5}{8} \times 2 = \frac{10}{8} = \frac{5}{4} = 1 \frac{1}{4} \). 2. **b** \( \frac{4}{13} \div \frac{3}{13} \) - Reciprocal of \( \frac{3}{13} \) is \( \frac{13}{3} \). - Calculation: \( \frac{4}{13} \times \frac{13}{3} = \frac{4}{3} = 1 \frac{1}{3} \). 3. **c** \( \frac{5}{8} \div \frac{5}{12} \) - Reciprocal of \( \frac{5}{12} \) is \( \frac{12}{5} \). - Calculation: \( \frac{5}{8} \times \frac{12}{5} = \frac{12}{8} = \frac{3}{2} = 1 \frac{1}{2} \). 4. **d** \( \frac{1}{3} \div \frac{5}{9} \) - Reciprocal of \( \frac{5}{9} \) is \( \frac{9}{5} \). - Calculation: \( \frac{1}{3} \times \frac{9}{5} = \frac{9}{15} = \frac{3}{5} \). 5. **e** \( \frac{1}{4} \div \frac{1}{12} \) - Reciprocal of \( \frac{1}{12} \) is \( 12 \). - Calculation: \( \frac{1}{4} \times 12 = 3 \). 6. **f** \( \frac{7}{9} \div \frac{1}{6} \)