2. Умножение и деление обыкновенных дробей 5 21 9 7 15 24 4 8 20 5 10 2 6 3 28 7 9 30 40 20 3 50 5 4 17 10 5 20 34 2

Ответ:

• \[\frac{5}{7} \times \frac{21}{15} \div \frac{9}{24} = \frac{5}{7} \times \frac{21}{15} \times \frac{24}{9} = \frac{5 \times 21 \times 24}{7 \times 15 \times 9} = \frac{5 \times 3 \times 7 \times 8 \times 3}{7 \times 3 \times 5 \times 3 \times 3} = \frac{8}{3} = 2\frac{2}{3}\]
• \[\frac{4}{5} \div \frac{8}{10} \div \frac{2}{20} = \frac{4}{5} \times \frac{10}{8} \times \frac{20}{2} = \frac{4 \times 10 \times 20}{5 \times 8 \times 2} = \frac{4 \times 2 \times 5 \times 4 \times 5}{5 \times 4 \times 2 \times 2} = 20\]
• \[\frac{6}{7} \times \frac{3}{9} \div \frac{28}{30} = \frac{6}{7} \times \frac{3}{9} \times \frac{30}{28} = \frac{6 \times 3 \times 30}{7 \times 9 \times 28} = \frac{2 \times 3 \times 3 \times 10}{7 \times 3 \times 3 \times 4 \times 7} = \frac{2 \times 10}{7 \times 4 \times 7} = \frac{20}{196} = \frac{5}{49}\]
• \[\frac{40}{50} \div \frac{20}{5} \times \frac{3}{4} = \frac{4}{5} \times \frac{5}{20} \times \frac{3}{4} = \frac{4 \times 5 \times 3}{5 \times 20 \times 4} = \frac{4 \times 5 \times 3}{5 \times 4 \times 5 \times 4} = \frac{3}{20}\]
• \[\frac{17}{20} \div \frac{10}{34} \div \frac{5}{2} = \frac{17}{20} \times \frac{34}{10} \times \frac{2}{5} = \frac{17 \times 34 \times 2}{20 \times 10 \times 5} = \frac{17 \times 17 \times 2 \times 2}{4 \times 5 \times 2 \times 5 \times 5} = \frac{17 \times 17}{5 \times 5 \times 5} = \frac{289}{125} = 2\frac{39}{125}\]

Ответ: