Контрольные задания
Вопрос:

The user wants me to analyze the provided image and return the information in a JSON format.

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Ответ:

Задание 110.

  1. \(5\frac{2}{7} \cdot 3 \frac{10}{4} = \frac{37}{7} \cdot \frac{40}{4} = \frac{37}{7} \cdot 10 = \frac{370}{7} = 52\frac{6}{7}\)
  2. \(5\frac{2}{5} \cdot 3 \frac{4}{11} = \frac{27}{5} \cdot \frac{37}{11} = \frac{999}{55} = 18\frac{9}{55}\)

Задание 111.

  1. \(2\frac{2}{3} \cdot 1\frac{7}{11} = \frac{8}{3} \cdot \frac{18}{11} = \frac{8 \cdot 6}{11} = \frac{48}{11} = 4\frac{4}{11}\)
  2. \(2\frac{5}{9} \cdot 1\frac{7}{17} = \frac{23}{9} \cdot \frac{24}{17} = \frac{23 \cdot 8}{3 \cdot 17} = \frac{184}{51} = 3\frac{31}{51}\)

Задание 110. (Продолжение)

  1. \(5\frac{6}{13} \cdot 1\frac{10}{21} = \frac{71}{13} \cdot \frac{31}{21} = \frac{2201}{273} = 8\frac{5}{273}\)
  2. \(7\frac{7}{10} \cdot \frac{4}{9} = \frac{77}{10} \cdot \frac{4}{9} = \frac{77 \cdot 2}{5 \cdot 9} = \frac{154}{45} = 3\frac{19}{45}\)
  3. \(4\frac{11}{20} \cdot \frac{3}{10} = \frac{81}{20} \cdot \frac{3}{10} = \frac{243}{200} = 1\frac{43}{200}\)
  4. \(3\frac{7}{10} \cdot 2\frac{5}{8} = \frac{37}{10} \cdot \frac{21}{8} = \frac{777}{80} = 9\frac{57}{80}\)

Задание 111. (Продолжение)

  1. \(1\frac{6}{17} \cdot \frac{8}{9} = \frac{23}{17} \cdot \frac{8}{9} = \frac{184}{153} = 1\frac{31}{153}\)
  2. \(5\frac{8}{9} \cdot \frac{3}{11} = \frac{53}{9} \cdot \frac{3}{11} = \frac{53}{3 \cdot 11} = \frac{53}{33} = 1\frac{20}{33}\)
  3. \(8\frac{5}{21} \cdot \frac{3}{10} = \frac{173}{21} \cdot \frac{3}{10} = \frac{173}{7 \cdot 10} = \frac{173}{70} = 2\frac{33}{70}\)
  4. \(5\frac{9}{13} \cdot \frac{7}{15} = \frac{74}{13} \cdot \frac{7}{15} = \frac{518}{195} = 2\frac{128}{195}\)

Задание 112.

  1. \(3\frac{2}{5} \cdot 1\frac{3}{7} = \frac{17}{5} \cdot \frac{10}{7} = \frac{17 \cdot 2}{7} = \frac{34}{7} = 4\frac{6}{7}\)
  2. \(3\frac{4}{9} \cdot 2\frac{1}{5} = \frac{31}{9} \cdot \frac{11}{5} = \frac{341}{45} = 7\frac{26}{45}\)
  3. \(1\frac{4}{7} \cdot \frac{5}{6} = \frac{11}{7} \cdot \frac{5}{6} = \frac{55}{42} = 1\frac{13}{42}\)
  4. \(4\frac{5}{13} \cdot \frac{3}{8} = \frac{57}{13} \cdot \frac{3}{8} = \frac{171}{104} = 1\frac{67}{104}\)
  5. \(5\frac{7}{10} \cdot \frac{7}{9} = \frac{57}{10} \cdot \frac{7}{9} = \frac{19 \cdot 7}{10 \cdot 3} = \frac{133}{30} = 4\frac{13}{30}\)
  6. \(6\frac{1}{11} \cdot \frac{4}{7} = \frac{67}{11} \cdot \frac{4}{7} = \frac{268}{77} = 3\frac{37}{77}\)
  7. \(7\frac{8}{13} \cdot \frac{5}{9} = \frac{99}{13} \cdot \frac{5}{9} = \frac{11 \cdot 5}{13} = \frac{55}{13} = 4\frac{3}{13}\)
  8. \(1\frac{4}{14} \cdot \frac{2}{9} = \frac{18}{14} \cdot \frac{2}{9} = \frac{9}{7} \cdot \frac{2}{9} = \frac{2}{7}\)
  9. \(4\frac{2}{9} \cdot \frac{5}{7} = \frac{38}{9} \cdot \frac{5}{7} = \frac{190}{63} = 3\frac{1}{63}\)
  10. \(1\frac{1}{3} \cdot \frac{5}{11} = \frac{4}{3} \cdot \frac{5}{11} = \frac{20}{33}\)
  11. \(1\frac{2}{5} \cdot \frac{7}{13} = \frac{7}{5} \cdot \frac{7}{13} = \frac{49}{65}\)
  12. \(3\frac{1}{3} \cdot \frac{5}{14} = \frac{10}{3} \cdot \frac{5}{14} = \frac{5}{3} \cdot \frac{5}{7} = \frac{25}{21} = 1\frac{4}{21}\)
  13. \(1\frac{1}{5} \cdot \frac{14}{15} = \frac{6}{5} \cdot \frac{14}{15} = \frac{2}{5} \cdot \frac{14}{5} = \frac{28}{25} = 1\frac{3}{25}\)
  14. \(1\frac{1}{16} \cdot \frac{7}{17} = \frac{17}{16} \cdot \frac{7}{17} = \frac{7}{16}\)
  15. \(1\frac{3}{7} \cdot \frac{1}{4} = \frac{10}{7} \cdot \frac{1}{4} = \frac{5}{7} \cdot \frac{1}{2} = \frac{5}{14}\)
  16. \(4\frac{1}{3} \cdot \frac{3}{13} = \frac{13}{3} \cdot \frac{3}{13} = 1\)

Задание 113.

Основное свойство дроби: Если числитель и знаменатель дроби умножить или разделить на одно и то же число, не равное нулю, то величина дроби не изменится.

  1. \( \frac{4}{12}=\frac{9}{?} \) — неверно
  2. \( \frac{9}{18}=\frac{12}{15}=\frac{8}{?} \) — неверно
  3. \( \frac{10}{20}=\frac{15}{?} \) — неверно
  4. \( \frac{16}{24}=\frac{20}{?} \) — неверно
  5. \( \frac{14}{28}=\frac{21}{?} \) — неверно
  6. \( \frac{4}{36}=\frac{9}{?} \) — неверно
  7. \( \frac{30}{40}=\frac{32}{?} \) — неверно
  8. \( \frac{24}{60}=\frac{50}{?} \) — неверно
  9. \( \frac{55}{100}=\frac{16}{?} \) — неверно

Задание 114.

  1. A 5; Б 4; В 1; Г 2.
  2. A 5; Б 2; В 1; Г 6.
  3. A 5; Б 3; В 2; Г 1.
  4. A 4; Б 3; В 1; Г 6.

Задание 116.

  1. \( \frac{7}{12} \)
  2. \( \frac{2}{15} \)
  3. \( \frac{9}{10} \)
  4. \( \frac{28}{45} \)
  5. \( \frac{4}{21} \)
  6. \( \frac{6}{11} \)
  7. \( \frac{3}{8} \)
  8. \( \frac{30}{49} \)
  9. \( \frac{66}{77} = \frac{6}{7} \)
  10. \( \frac{27}{75} = \frac{9}{25} \)
  11. \( \frac{1}{15} \)
  12. \( \frac{5}{13} \)
  13. \( \frac{4}{9} \)
  14. \( \frac{1}{15} \)
  15. \( \frac{1}{35} \)
  16. \( \frac{7}{22} = \frac{7}{22} \)
  17. \( \frac{1}{5} \)
  18. \( \frac{7}{24} \)
  19. \( \frac{15}{16} \)
  20. \( \frac{5}{24} \)
  21. \( \frac{2}{13} \)
  22. \( \frac{39}{340} \)
  23. \( \frac{14}{9} \)
  24. \( \frac{160}{567} \)
  25. \( \frac{4}{33} \)

Задание 117.

  1. \( \frac{1}{3} \)
  2. \( \frac{1}{3} \)
  3. \( \frac{1}{5} \)
  4. \( \frac{1}{2} \)
  5. \( \frac{1}{5} \)
  6. \( \frac{1}{7} \)
  7. \( \frac{1}{2} \)
  8. \( \frac{1}{4} \)
  9. \( \frac{1}{5} \)
  10. \( \frac{1}{3} \)
  11. \( \frac{1}{4} \)
  12. \( \frac{1}{5} \)
  13. \( \frac{1}{7} \)
  14. \( \frac{1}{3} \)
  15. \( \frac{1}{6} \)
  16. \( \frac{3}{5} \)
  17. \( \frac{1}{4} \)
  18. \( \frac{1}{3} \)
  19. \( \frac{9}{10} \)
  20. \( \frac{1}{4} \)
  21. \( \frac{1}{7} \)
  22. \( \frac{2}{3} \)
  23. \( \frac{1}{5} \)
  24. \( \frac{3}{4} \)
  25. \( \frac{5}{6} \)
  26. \( \frac{1}{3} \)
  27. \( \frac{7}{24} \)
  28. \( \frac{4}{5} \)
  29. \( \frac{3}{4} \)
  30. \( \frac{1}{3} \)
  31. \( \frac{1}{4} \)
  32. \( \frac{1}{3} \)
  33. \( \frac{1}{4} \)
  34. \( \frac{1}{5} \)
  35. \( \frac{1}{6} \)
  36. \( \frac{7}{24} \)
  37. \( \frac{3}{5} \)
  38. \( \frac{1}{4} \)

Задание 118.

  1. \( \frac{1}{3} \)
  2. \( \frac{2}{3} \)
  3. \( \frac{3}{7} \)
  4. \( \frac{1}{2} \)
  5. \( \frac{2}{3} \)
  6. \( \frac{1}{2} \)
  7. \( \frac{2}{3} \)
  8. \( \frac{1}{2} \)
  9. \( \frac{1}{3} \)
  10. \( \frac{1}{3} \)
  11. \( \frac{3}{5} \)
  12. \( \frac{12}{5} = 2\frac{2}{5} \)
  13. \( \frac{13}{7} = 1\frac{6}{7} \)
  1. \( \frac{1}{3} \)
  2. \( \frac{2}{3} \)
  3. \( \frac{1}{3} \)
  4. \( \frac{28}{3} = 9\frac{1}{3} \)
  5. \( \frac{1}{3} \)
  6. \( \frac{3}{5} \)
  7. \( \frac{1}{3} \)
  8. \( \frac{2}{3} \)
  9. \( \frac{5}{3} = 1\frac{2}{3} \)
  10. \( \frac{1}{3} \)
  11. \( \frac{1}{5} \)
  12. \( \frac{3}{3} = 1 \)
  13. \( \frac{4}{3} = 1\frac{1}{3} \)
  14. \( \frac{1}{3} \)
  15. \( \frac{1}{5} \)
  16. \( \frac{4}{3} = 1\frac{1}{3} \)
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