Контрольные задания > 1. (Устно.) Сложить: 1) \(\frac{3}{10} + \frac{4}{10}\); 2) \(\frac{5}{12} + \frac{1}{12}\); 3) \(\frac{7}{11} + \frac{4}{11}\); 4) \(\frac{7}{15} + \frac{8}{15}\); 5) \(\frac{5}{12} + \frac{4}{12}\); 6) \(\frac{7}{16} + \frac{5}{16}\); 2. Вычесть: 1) \(\frac{13}{20} - \frac{7}{20}\); 2) \(\frac{11}{14} - \frac{8}{14}\); 3) \(\frac{13}{25} - \frac{8}{25}\); 4) \(\frac{11}{24} - \frac{7}{24}\); 5) \(\frac{17}{36} - \frac{8}{36}\); 6) \(\frac{19}{27} - \frac{10}{27}\); 3. Найти сумму: 1) \(3 + \frac{1}{4}\); 2) \(5 + \frac{1}{2}\); 3) \(4 + 3\frac{1}{7}\); 4) \(5 + 2\frac{1}{3}\); 5) \(2\frac{1}{4} + 3\frac{1}{4}\); 6) \(4\frac{1}{7} + 2\frac{3}{7}\); 7) \(2\frac{3}{5} + 1\frac{2}{5}\); 8) \(6\frac{3}{4} + 2\frac{1}{4}\); 9) \(7\frac{3}{5} + 8\frac{4}{5}\); 4. Вычислить: 1) \(3 - \frac{3}{4}\); 2) \(5 - \frac{1}{2}\); 3) \(4 - \frac{2}{5}\); 4) \(7 - \frac{3}{5}\); 5) \(6 - 1\frac{3}{7}\); 6) \(7 - 2\frac{1}{4}\); 7) \(8\frac{3}{5} - 3\frac{1}{5}\); 8) \(3\frac{3}{5} - 1\frac{4}{5}\); 9) \(11\frac{4}{7} - 3\frac{5}{7}\); 10) \(13\frac{5}{9} - 3\frac{8}{9}\); 11) \(12\frac{3}{7} - 4\frac{4}{7}\); 12) \(23\frac{7}{8} - 5\frac{5}{8}\); 5. Найти значение числового выражения: 1) \(4\frac{5}{7} + 3\frac{2}{7} - \frac{6}{7}\); 2) \(6\frac{3}{11} + 1\frac{9}{11} - \frac{5}{11}\); 3) \(6\frac{3}{14} - 3\frac{2}{14} + 2\frac{5}{14}\); 4) \(9\frac{7}{12} - 1\frac{1}{12} + 3\frac{5}{12}\); 5) \(4\frac{5}{9} - 2\frac{7}{9} + 1\frac{8}{9}\); 6) \(3\frac{2}{7} - 1\frac{5}{7} + 3\frac{6}{7}\); 6. Выполнить действия: 1) \((\frac{3}{16} + \frac{5}{16}) - (3 + \frac{7}{16})\); 2) \((\frac{8}{15} - 2\frac{11}{15}) + (7 - 5\frac{4}{15})\);
Вопрос:

1. (Устно.) Сложить: 1) \(\frac{3}{10} + \frac{4}{10}\); 2) \(\frac{5}{12} + \frac{1}{12}\); 3) \(\frac{7}{11} + \frac{4}{11}\); 4) \(\frac{7}{15} + \frac{8}{15}\); 5) \(\frac{5}{12} + \frac{4}{12}\); 6) \(\frac{7}{16} + \frac{5}{16}\); 2. Вычесть: 1) \(\frac{13}{20} - \frac{7}{20}\); 2) \(\frac{11}{14} - \frac{8}{14}\); 3) \(\frac{13}{25} - \frac{8}{25}\); 4) \(\frac{11}{24} - \frac{7}{24}\); 5) \(\frac{17}{36} - \frac{8}{36}\); 6) \(\frac{19}{27} - \frac{10}{27}\); 3. Найти сумму: 1) \(3 + \frac{1}{4}\); 2) \(5 + \frac{1}{2}\); 3) \(4 + 3\frac{1}{7}\); 4) \(5 + 2\frac{1}{3}\); 5) \(2\frac{1}{4} + 3\frac{1}{4}\); 6) \(4\frac{1}{7} + 2\frac{3}{7}\); 7) \(2\frac{3}{5} + 1\frac{2}{5}\); 8) \(6\frac{3}{4} + 2\frac{1}{4}\); 9) \(7\frac{3}{5} + 8\frac{4}{5}\); 4. Вычислить: 1) \(3 - \frac{3}{4}\); 2) \(5 - \frac{1}{2}\); 3) \(4 - \frac{2}{5}\); 4) \(7 - \frac{3}{5}\); 5) \(6 - 1\frac{3}{7}\); 6) \(7 - 2\frac{1}{4}\); 7) \(8\frac{3}{5} - 3\frac{1}{5}\); 8) \(3\frac{3}{5} - 1\frac{4}{5}\); 9) \(11\frac{4}{7} - 3\frac{5}{7}\); 10) \(13\frac{5}{9} - 3\frac{8}{9}\); 11) \(12\frac{3}{7} - 4\frac{4}{7}\); 12) \(23\frac{7}{8} - 5\frac{5}{8}\); 5. Найти значение числового выражения: 1) \(4\frac{5}{7} + 3\frac{2}{7} - \frac{6}{7}\); 2) \(6\frac{3}{11} + 1\frac{9}{11} - \frac{5}{11}\); 3) \(6\frac{3}{14} - 3\frac{2}{14} + 2\frac{5}{14}\); 4) \(9\frac{7}{12} - 1\frac{1}{12} + 3\frac{5}{12}\); 5) \(4\frac{5}{9} - 2\frac{7}{9} + 1\frac{8}{9}\); 6) \(3\frac{2}{7} - 1\frac{5}{7} + 3\frac{6}{7}\); 6. Выполнить действия: 1) \((\frac{3}{16} + \frac{5}{16}) - (3 + \frac{7}{16})\); 2) \((\frac{8}{15} - 2\frac{11}{15}) + (7 - 5\frac{4}{15})\);

Смотреть решения всех заданий с листа

Ответ:

Задание 1. Сложить (устно)

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

Задание 2. Вычесть

  1. \(\frac{13}{20} - \frac{7}{20} = \frac{13-7}{20} = \frac{6}{20} = \frac{3}{10}\)
  2. \(\frac{11}{14} - \frac{8}{14} = \frac{11-8}{14} = \frac{3}{14}\)
  3. \(\frac{13}{25} - \frac{8}{25} = \frac{13-8}{25} = \frac{5}{25} = \frac{1}{5}\)
  4. \(\frac{11}{24} - \frac{7}{24} = \frac{11-7}{24} = \frac{4}{24} = \frac{1}{6}\)
  5. \(\frac{17}{36} - \frac{8}{36} = \frac{17-8}{36} = \frac{9}{36} = \frac{1}{4}\)
  6. \(\frac{19}{27} - \frac{10}{27} = \frac{19-10}{27} = \frac{9}{27} = \frac{1}{3}\)

Задание 3. Найти сумму

  1. \(3 + \frac{1}{4} = 3\frac{1}{4}\)
  2. \(5 + \frac{1}{2} = 5\frac{1}{2}\)
  3. \(4 + 3\frac{1}{7} = 7\frac{1}{7}\)
  4. \(5 + 2\frac{1}{3} = 7\frac{1}{3}\)
  5. \(2\frac{1}{4} + 3\frac{1}{4} = (2+3) + (\frac{1}{4} + \frac{1}{4}) = 5 + \frac{2}{4} = 5 + \frac{1}{2} = 5\frac{1}{2}\)
  6. \(4\frac{1}{7} + 2\frac{3}{7} = (4+2) + (\frac{1}{7} + \frac{3}{7}) = 6 + \frac{4}{7} = 6\frac{4}{7}\)
  7. \(2\frac{3}{5} + 1\frac{2}{5} = (2+1) + (\frac{3}{5} + \frac{2}{5}) = 3 + \frac{5}{5} = 3 + 1 = 4\)
  8. \(6\frac{3}{4} + 2\frac{1}{4} = (6+2) + (\frac{3}{4} + \frac{1}{4}) = 8 + \frac{4}{4} = 8 + 1 = 9\)
  9. \(7\frac{3}{5} + 8\frac{4}{5} = (7+8) + (\frac{3}{5} + \frac{4}{5}) = 15 + \frac{7}{5} = 15 + 1\frac{2}{5} = 16\frac{2}{5}\)

Задание 4. Вычислить

  1. \(3 - \frac{3}{4} = 2\frac{4}{4} - \frac{3}{4} = 2\frac{4-3}{4} = 2\frac{1}{4}\)
  2. \(5 - \frac{1}{2} = 4\frac{2}{2} - \frac{1}{2} = 4\frac{2-1}{2} = 4\frac{1}{2}\)
  3. \(4 - \frac{2}{5} = 3\frac{5}{5} - \frac{2}{5} = 3\frac{5-2}{5} = 3\frac{3}{5}\)
  4. \(7 - \frac{3}{5} = 6\frac{5}{5} - \frac{3}{5} = 6\frac{5-3}{5} = 6\frac{2}{5}\)
  5. \(6 - 1\frac{3}{7} = 5\frac{7}{7} - 1\frac{3}{7} = (5-1)\frac{7-3}{7} = 4\frac{4}{7}\)
  6. \(7 - 2\frac{1}{4} = 6\frac{4}{4} - 2\frac{1}{4} = (6-2)\frac{4-1}{4} = 4\frac{3}{4}\)
  7. \(8\frac{3}{5} - 3\frac{1}{5} = (8-3)\frac{3-1}{5} = 5\frac{2}{5}\)
  8. \(3\frac{3}{5} - 1\frac{4}{5} = 2\frac{8}{5} - 1\frac{4}{5} = (2-1)\frac{8-4}{5} = 1\frac{4}{5}\)
  9. \(11\frac{4}{7} - 3\frac{5}{7} = 10\frac{11}{7} - 3\frac{5}{7} = (10-3)\frac{11-5}{7} = 7\frac{6}{7}\)
  10. \(13\frac{5}{9} - 3\frac{8}{9} = 12\frac{14}{9} - 3\frac{8}{9} = (12-3)\frac{14-8}{9} = 9\frac{6}{9} = 9\frac{2}{3}\)
  11. \(12\frac{3}{7} - 4\frac{4}{7} = 11\frac{10}{7} - 4\frac{4}{7} = (11-4)\frac{10-4}{7} = 7\frac{6}{7}\)
  12. \(23\frac{7}{8} - 5\frac{5}{8} = (23-5)\frac{7-5}{8} = 18\frac{2}{8} = 18\frac{1}{4}\)

Задание 5. Найти значение числового выражения

  1. \(4\frac{5}{7} + 3\frac{2}{7} - \frac{6}{7} = (4+3) + (\frac{5}{7} + \frac{2}{7}) - \frac{6}{7} = 7 + \frac{7}{7} - \frac{6}{7} = 7 + 1 - \frac{6}{7} = 8 - \frac{6}{7} = 7\frac{7}{7} - \frac{6}{7} = 7\frac{1}{7}\)
  2. \(6\frac{3}{11} + 1\frac{9}{11} - \frac{5}{11} = (6+1) + (\frac{3}{11} + \frac{9}{11}) - \frac{5}{11} = 7 + \frac{12}{11} - \frac{5}{11} = 7 + 1\frac{1}{11} - \frac{5}{11} = 8\frac{1}{11} - \frac{5}{11} = 7\frac{12}{11} - \frac{5}{11} = 7\frac{7}{11}\)
  3. \(6\frac{3}{14} - 3\frac{2}{14} + 2\frac{5}{14} = (6-3+2) + (\frac{3}{14} - \frac{2}{14} + \frac{5}{14}) = 5 + \frac{3-2+5}{14} = 5 + \frac{6}{14} = 5 + \frac{3}{7} = 5\frac{3}{7}\)
  4. \(9\frac{7}{12} - 1\frac{1}{12} + 3\frac{5}{12} = (9-1+3) + (\frac{7}{12} - \frac{1}{12} + \frac{5}{12}) = 11 + \frac{7-1+5}{12} = 11 + \frac{11}{12} = 11\frac{11}{12}\)
  5. \(4\frac{5}{9} - 2\frac{7}{9} + 1\frac{8}{9} = (4-2+1) + (\frac{5}{9} - \frac{7}{9} + \frac{8}{9}) = 3 + \frac{5-7+8}{9} = 3 + \frac{6}{9} = 3 + \frac{2}{3} = 3\frac{2}{3}\)
  6. \(3\frac{2}{7} - 1\frac{5}{7} + 3\frac{6}{7} = (3-1+3) + (\frac{2}{7} - \frac{5}{7} + \frac{6}{7}) = 5 + \frac{2-5+6}{7} = 5 + \frac{3}{7} = 5\frac{3}{7}\)

Задание 6. Выполнить действия

  1. \((\frac{3}{16} + \frac{5}{16}) - (3 + \frac{7}{16}) = \frac{8}{16} - (3 + \frac{7}{16}) = \frac{1}{2} - 3 - \frac{7}{16} = \frac{8}{16} - 3 - \frac{7}{16} = -3 + \frac{8-7}{16} = -3 + \frac{1}{16} = -2\frac{15}{16}\)
  2. \((\frac{8}{15} - 2\frac{11}{15}) + (7 - 5\frac{4}{15}) = (\frac{8}{15} - \frac{41}{15}) + (\frac{105}{15} - \frac{79}{15}) = (\frac{8-41}{15}) + (\frac{105-79}{15}) = \frac{-33}{15} + \frac{26}{15} = \frac{-33+26}{15} = \frac{-7}{15} = -\frac{7}{15}\)

Ответ: смотри решение выше

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