Решите примеры на умножение и деление обыкновенных дробей.

Привет, ребята! Сейчас мы разберем, как решать примеры на умножение и деление обыкновенных дробей. Это не так сложно, как кажется! **Основные правила:** 1. **Умножение дробей:** Чтобы умножить две дроби, нужно умножить их числители (верхние числа) и знаменатели (нижние числа). \[\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}\] 2. **Деление дробей:** Чтобы разделить одну дробь на другую, нужно первую дробь умножить на перевернутую вторую дробь (то есть поменять местами числитель и знаменатель второй дроби). \[\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{a \times d}{b \times c}\] Теперь давайте разберем примеры из вашего задания: **Столбец 1** 1. \[\frac{2}{5} \times \frac{3}{4} = \frac{2 \times 3}{5 \times 4} = \frac{6}{20} = \frac{3}{10}\] 2. \[\frac{1}{7} \div \frac{2}{3} = \frac{1}{7} \times \frac{3}{2} = \frac{1 \times 3}{7 \times 2} = \frac{3}{14}\] 3. \[\frac{4}{5} \times \frac{6}{5} = \frac{4 \times 6}{5 \times 5} = \frac{24}{25}\] 4. \[\frac{1}{8} \div \frac{7}{9} = \frac{1}{8} \times \frac{9}{7} = \frac{1 \times 9}{8 \times 7} = \frac{9}{56}\] 5. \[\frac{2}{3} \times \frac{6}{7} = \frac{2 \times 6}{3 \times 7} = \frac{12}{21} = \frac{4}{7}\] 6. \[\frac{5}{6} \div \frac{4}{10} = \frac{5}{6} \times \frac{10}{4} = \frac{5 \times 10}{6 \times 4} = \frac{50}{24} = \frac{25}{12}\] 7. \[\frac{11}{14} \times \frac{7}{22} = \frac{11 \times 7}{14 \times 22} = \frac{77}{308} = \frac{1}{4}\] 8. \[\frac{4}{15} \div \frac{5}{8} = \frac{4}{15} \times \frac{8}{5} = \frac{4 \times 8}{15 \times 5} = \frac{32}{75}\] 9. \[\frac{3}{10} \times \frac{2}{6} = \frac{3 \times 2}{10 \times 6} = \frac{6}{60} = \frac{1}{10}\] 10. \[\frac{17}{33} \div \frac{11}{34} = \frac{17}{33} \times \frac{34}{11} = \frac{17 \times 34}{33 \times 11} = \frac{578}{363}\] 11. \[\frac{7}{30} \times \frac{6}{21} = \frac{7 \times 6}{30 \times 21} = \frac{42}{630} = \frac{1}{15}\] 12. \[\frac{4}{12} \div \frac{18}{20} = \frac{4}{12} \times \frac{20}{18} = \frac{4 \times 20}{12 \times 18} = \frac{80}{216} = \frac{10}{27}\] 13. \[\frac{21}{25} \times \frac{15}{42} = \frac{21 \times 15}{25 \times 42} = \frac{315}{1050} = \frac{3}{10}\] 14. \[\frac{14}{24} \div \frac{16}{21} = \frac{14}{24} \times \frac{21}{16} = \frac{14 \times 21}{24 \times 16} = \frac{294}{384} = \frac{49}{64}\] 15. \[\frac{50}{70} \times \frac{77}{150} = \frac{50 \times 77}{70 \times 150} = \frac{3850}{10500} = \frac{11}{30}\] 16. \[\frac{23}{45} \div \frac{9}{46} = \frac{23}{45} \times \frac{46}{9} = \frac{23 \times 46}{45 \times 9} = \frac{1058}{405}\] 17. \[\frac{30}{66} \times \frac{77}{90} = \frac{30 \times 77}{66 \times 90} = \frac{2310}{5940} = \frac{7}{18}\] 18. \[\frac{26}{32} \div \frac{12}{13} = \frac{26}{32} \times \frac{13}{12} = \frac{26 \times 13}{32 \times 12} = \frac{338}{384} = \frac{169}{192}\] 19. \[\frac{8}{19} \times \frac{38}{40} = \frac{8 \times 38}{19 \times 40} = \frac{304}{760} = \frac{4}{10} = \frac{2}{5}\] 20. \[\frac{16}{24} \div \frac{15}{25} = \frac{16}{24} \times \frac{25}{15} = \frac{16 \times 25}{24 \times 15} = \frac{400}{360} = \frac{10}{9}\] 21. \[\frac{22}{30} \times \frac{10}{11} = \frac{22 \times 10}{30 \times 11} = \frac{220}{330} = \frac{2}{3}\] 22. \[\frac{10}{46} \div \frac{7}{11} = \frac{10}{46} \times \frac{7}{11} = \frac{10 \times 7}{46 \times 11} = \frac{70}{506} = \frac{35}{253}\] 23. \[\frac{14}{77} \times \frac{25}{23} = \frac{14 \times 25}{77 \times 23} = \frac{350}{1771}\] **Столбец 2** 1. \[\frac{4}{5} \times \frac{1}{2} = \frac{4 \times 1}{5 \times 2} = \frac{4}{10} = \frac{2}{5}\] 2. \[\frac{3}{7} \div \frac{6}{7} = \frac{3}{7} \times \frac{7}{6} = \frac{3 \times 7}{7 \times 6} = \frac{21}{42} = \frac{1}{2}\] 3. \[\frac{1}{2} \times \frac{3}{2} = \frac{1 \times 3}{2 \times 2} = \frac{3}{4}\] 4. \[\frac{5}{7} \div \frac{5}{7} = \frac{5}{7} \times \frac{7}{5} = \frac{5 \times 7}{7 \times 5} = \frac{35}{35} = 1\] 5. \[\frac{8}{11} \times \frac{16}{77} = \frac{8 \times 16}{11 \times 77} = \frac{128}{847}\] 6. \[\frac{5}{23} \div \frac{15}{46} = \frac{5}{23} \times \frac{46}{15} = \frac{5 \times 46}{23 \times 15} = \frac{230}{345} = \frac{2}{3}\] 7. \[\frac{14}{63} \times \frac{21}{28} = \frac{14 \times 21}{63 \times 28} = \frac{294}{1764} = \frac{1}{6}\] 8. \[\frac{18}{20} \div \frac{27}{40} = \frac{18}{20} \times \frac{40}{27} = \frac{18 \times 40}{20 \times 27} = \frac{720}{540} = \frac{4}{3}\] 9. \[\frac{63}{70} \times \frac{81}{270} = \frac{63 \times 81}{70 \times 270} = \frac{5103}{18900} = \frac{9}{35}\] 10. \[\frac{2}{33} \div \frac{24}{30} = \frac{2}{33} \times \frac{30}{24} = \frac{2 \times 30}{33 \times 24} = \frac{60}{792} = \frac{5}{66}\] 11. \[\frac{75}{150} \times \frac{5}{50} = \frac{75 \times 5}{150 \times 50} = \frac{375}{7500} = \frac{1}{20}\] 12. \[\frac{3}{20} \div \frac{17}{10} = \frac{3}{20} \times \frac{10}{17} = \frac{3 \times 10}{20 \times 17} = \frac{30}{340} = \frac{3}{34}\] 13. \[\frac{8}{11} \times \frac{4}{99} = \frac{8 \times 4}{11 \times 99} = \frac{32}{1089}\] 14. \[\frac{16}{24} \div \frac{7}{34} = \frac{16}{24} \times \frac{34}{7} = \frac{16 \times 34}{24 \times 7} = \frac{544}{168} = \frac{68}{21}\] 15. \[\frac{12}{26} \times \frac{8}{13} = \frac{12 \times 8}{26 \times 13} = \frac{96}{338} = \frac{48}{169}\] 16. \[\frac{9}{42} \div \frac{12}{21} = \frac{9}{42} \times \frac{21}{12} = \frac{9 \times 21}{42 \times 12} = \frac{189}{504} = \frac{3}{8}\] 17. \[\frac{17}{50} \times \frac{18}{51} = \frac{17 \times 18}{50 \times 51} = \frac{306}{2550} = \frac{17}{50}\] 18. \[\frac{3}{10} \div \frac{27}{30} = \frac{3}{10} \times \frac{30}{27} = \frac{3 \times 30}{10 \times 27} = \frac{90}{270} = \frac{1}{3}\] 19. \[\frac{4}{63} \times \frac{5}{30} = \frac{4 \times 5}{63 \times 30} = \frac{20}{1890} = \frac{2}{189}\] 20. \[\frac{13}{12} \div \frac{52}{20} = \frac{13}{12} \times \frac{20}{52} = \frac{13 \times 20}{12 \times 52} = \frac{260}{624} = \frac{5}{12}\] 21. \[\frac{7}{15} \times \frac{5}{2} = \frac{7 \times 5}{15 \times 2} = \frac{35}{30} = \frac{7}{6}\] 22. \[\frac{12}{15} \div \frac{20}{50} = \frac{12}{15} \times \frac{50}{20} = \frac{12 \times 50}{15 \times 20} = \frac{600}{300} = 2\] 23. \[\frac{13}{24} \times \frac{13}{48} = \frac{13 \times 13}{24 \times 48} = \frac{169}{1152}\] **Столбец 3** 1. \[\frac{5}{7} \times \frac{21}{15} = \frac{5 \times 21}{7 \times 15} = \frac{105}{105} = 1\] 2. \[\frac{4}{5} \div \frac{8}{20} = \frac{4}{5} \times \frac{20}{8} = \frac{4 \times 20}{5 \times 8} = \frac{80}{40} = 2\] 3. \[\frac{6}{7} \times \frac{3}{9} = \frac{6 \times 3}{7 \times 9} = \frac{18}{63} = \frac{2}{7}\] 4. \[\frac{40}{50} \div \frac{20}{5} = \frac{40}{50} \times \frac{5}{20} = \frac{40 \times 5}{50 \times 20} = \frac{200}{1000} = \frac{1}{5}\] 5. \[\frac{17}{20} \times \frac{10}{34} = \frac{17 \times 10}{20 \times 34} = \frac{170}{680} = \frac{1}{4}\] 6. \[\frac{14}{63} \div \frac{18}{28} = \frac{14}{63} \times \frac{28}{18} = \frac{14 \times 28}{63 \times 18} = \frac{392}{1134} = \frac{4}{13}\] 7. \[\frac{77}{25} \times \frac{11}{13} = \frac{77 \times 11}{25 \times 13} = \frac{847}{325}\] 8. \[\frac{81}{90} \div \frac{2}{3} = \frac{81}{90} \times \frac{3}{2} = \frac{81 \times 3}{90 \times 2} = \frac{243}{180} = \frac{9}{10}\] 9. \[\frac{42}{60} \times \frac{7}{12} = \frac{42 \times 7}{60 \times 12} = \frac{294}{720} = \frac{49}{120}\] 10. \[\frac{4}{3} \div \frac{12}{21} = \frac{4}{3} \times \frac{12}{21} = \frac{4 \times 21}{3 \times 12} = \frac{84}{36} = \frac{7}{3}\] 11. \[\frac{6}{3} \times \frac{5}{20} = \frac{6 \times 5}{3 \times 20} = \frac{30}{60} = \frac{1}{2}\] 12. \[\frac{10}{13} \div \frac{44}{11} = \frac{10}{13} \times \frac{11}{44} = \frac{10 \times 11}{13 \times 44} = \frac{110}{572} = \frac{5}{26}\] 13. \[\frac{13}{50} \times \frac{26}{12} = \frac{13 \times 26}{50 \times 12} = \frac{338}{600} = \frac{169}{300}\] 14. \[\frac{3}{9} \div \frac{1}{18} = \frac{3}{9} \times \frac{18}{1} = \frac{3 \times 18}{9 \times 1} = \frac{54}{9} = 6\] 15. \[\frac{25}{10} \times \frac{65}{90} = \frac{25 \times 65}{10 \times 90} = \frac{1625}{900} = \frac{65}{36}\] 16. \[\frac{4}{7} \div \frac{2}{21} = \frac{4}{7} \times \frac{21}{2} = \frac{4 \times 21}{7 \times 2} = \frac{84}{14} = 6\] 17. \[\frac{32}{54} \times \frac{13}{27} = \frac{32 \times 13}{54 \times 27} = \frac{416}{1458} = \frac{208}{729}\] 18. \[\frac{11}{99} \div \frac{9}{88} = \frac{11}{99} \times \frac{88}{9} = \frac{11 \times 88}{99 \times 9} = \frac{968}{891} = \frac{88}{81}\] 19. \[\frac{23}{15} \times \frac{92}{5} = \frac{23 \times 92}{15 \times 5} = \frac{2116}{75}\] 20. \[\frac{5}{15} \div \frac{25}{2} = \frac{5}{15} \times \frac{2}{25} = \frac{5 \times 2}{15 \times 25} = \frac{10}{375} = \frac{2}{75}\] 21. \[\frac{15}{7} \times \frac{40}{14} = \frac{15 \times 40}{7 \times 14} = \frac{600}{98} = \frac{300}{49}\] 22. \[\frac{15}{24} \div \frac{50}{3} = \frac{15}{24} \times \frac{3}{50} = \frac{15 \times 3}{24 \times 50} = \frac{45}{1200} = \frac{3}{80}\] 23. \[\frac{7}{24} \times \frac{14}{3} = \frac{7 \times 14}{24 \times 3} = \frac{98}{72} = \frac{49}{36}\] Надеюсь, теперь тебе все понятно. Помни, практика – ключ к успеху! Решай больше примеров, и ты станешь настоящим мастером в умножении и делении дробей. Удачи!