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МатематикаВопрос:
26. Найди значение суммы или разности.
Ответ:
Решение:
Выполняем сложение и вычитание дробей, приводя их к общему знаменателю.
Раздел А
| \(\frac{1}{3} + \frac{1}{6}\) | = \(\frac{2}{6} + \frac{1}{6} = \frac{3}{6}\) | = \(\frac{1}{2}\) |
| \(\frac{1}{2} + \frac{1}{3}\) | = \(\frac{3}{6} + \frac{2}{6} = \frac{5}{6}\) | |
| \(\frac{3}{5} - \frac{1}{10}\) | = \(\frac{6}{10} - \frac{1}{10} = \frac{5}{10}\) | = \(\frac{1}{2}\) |
| \(\frac{1}{12} + \frac{5}{6}\) | = \(\frac{1}{12} + \frac{10}{12} = \frac{11}{12}\) | |
| \(\frac{1}{3} + \frac{1}{4}\) | = \(\frac{4}{12} + \frac{3}{12} = \frac{7}{12}\) | |
| \(\frac{1}{3} + \frac{2}{5}\) | = \(\frac{5}{15} + \frac{6}{15} = \frac{11}{15}\) | |
| \(\frac{1}{2} - \frac{1}{4}\) | = \(\frac{2}{4} - \frac{1}{4} = \frac{1}{4}\) | |
| \(\frac{8}{7} - 1\) | = \(\frac{8}{7} - \frac{7}{7} = \frac{1}{7}\) | |
| \(\frac{1}{4} - \frac{1}{5}\) | = \(\frac{5}{20} - \frac{4}{20} = \frac{1}{20}\) | |
| \(\frac{1}{2} + \frac{3}{7}\) | = \(\frac{7}{14} + \frac{6}{14} = \frac{13}{14}\) | |
| \(\frac{3}{4} - \frac{1}{8}\) | = \(\frac{6}{8} - \frac{1}{8} = \frac{5}{8}\) | |
| \(\frac{1}{5} + \frac{1}{6}\) | = \(\frac{6}{30} + \frac{5}{30} = \frac{11}{30}\) | |
| \(\frac{4}{15} + \frac{2}{5}\) | = \(\frac{4}{15} + \frac{6}{15} = \frac{10}{15}\) | = \(\frac{2}{3}\) |
| \(\frac{7}{10} - \frac{1}{2}\) | = \(\frac{7}{10} - \frac{5}{10} = \frac{2}{10}\) | = \(\frac{1}{5}\) |
| \(\frac{1}{3} - \frac{1}{4}\) | = \(\frac{4}{12} - \frac{3}{12} = \frac{1}{12}\) |
Раздел Б
| \(\frac{1}{3} - \frac{1}{6}\) | = \(\frac{2}{6} - \frac{1}{6} = \frac{1}{6}\) | |
| \(\frac{3}{20} + \frac{3}{4}\) | = \(\frac{3}{20} + \frac{15}{20} = \frac{18}{20}\) | = \(\frac{9}{10}\) |
| \(\frac{7}{9} - \frac{2}{3}\) | = \(\frac{7}{9} - \frac{6}{9} = \frac{1}{9}\) | |
| \(\frac{1}{4} + \frac{1}{5}\) | = \(\frac{5}{20} + \frac{4}{20} = \frac{9}{20}\) | |
| \(\frac{2}{5} + \frac{4}{15}\) | = \(\frac{6}{15} + \frac{4}{15} = \frac{10}{15}\) | = \(\frac{2}{3}\) |
| \(\frac{1}{3} + \frac{1}{4}\) | = \(\frac{4}{12} + \frac{3}{12} = \frac{7}{12}\) | |
| \(\frac{2}{3} - \frac{2}{5}\) | = \(\frac{10}{15} - \frac{6}{15} = \frac{4}{15}\) | |
| \(\frac{1}{5} - \frac{1}{6}\) | = \(\frac{6}{30} - \frac{5}{30} = \frac{1}{30}\) | |
| \(\frac{1}{2} + \frac{1}{4}\) | = \(\frac{2}{4} + \frac{1}{4} = \frac{3}{4}\) | |
| \(\frac{7}{6} - 1\) | = \(\frac{7}{6} - \frac{6}{6} = \frac{1}{6}\) | |
| \(\frac{1}{2} + \frac{2}{7}\) | = \(\frac{7}{14} + \frac{4}{14} = \frac{11}{14}\) | |
| \(\frac{1}{2} - \frac{1}{3}\) | = \(\frac{3}{6} - \frac{2}{6} = \frac{1}{6}\) | |
| \(\frac{3}{4} + \frac{1}{8}\) | = \(\frac{6}{8} + \frac{1}{8} = \frac{7}{8}\) | |
| \(\frac{5}{6} - \frac{7}{12}\) | = \(\frac{10}{12} - \frac{7}{12} = \frac{3}{12}\) | = \(\frac{1}{4}\) |
| \(\frac{2}{5} + \frac{3}{10}\) | = \(\frac{4}{10} + \frac{3}{10} = \frac{7}{10}\) |
Раздел В
| \(\frac{11}{20} - \frac{5}{12}\) | = \(\frac{33}{60} - \frac{25}{60} = \frac{8}{60}\) | = \(\frac{2}{15}\) |
| \(\frac{8}{9} + \frac{7}{54}\) | = \(\frac{48}{54} + \frac{7}{54} = \frac{55}{54}\) | = \(1\frac{1}{54}\) |
| \(\frac{5}{6} - \frac{17}{21}\) | = \(\frac{35}{42} - \frac{34}{42} = \frac{1}{42}\) | |
| \(\frac{3}{16} + \frac{1}{24}\) | = \(\frac{9}{48} + \frac{2}{48} = \frac{11}{48}\) | |
| \(\frac{5}{6} - \frac{22}{27}\) | = \(\frac{45}{54} - \frac{44}{54} = \frac{1}{54}\) | |
| \(\frac{7}{25} - \frac{4}{15}\) | = \(\frac{21}{75} - \frac{20}{75} = \frac{1}{75}\) | |
| \(\frac{3}{10} + \frac{1}{6}\) | = \(\frac{9}{30} + \frac{5}{30} = \frac{14}{30}\) | = \(\frac{7}{15}\) |
| \(\frac{2}{5} - \frac{11}{30}\) | = \(\frac{12}{30} - \frac{11}{30} = \frac{1}{30}\) | |
| \(\frac{3}{8} + \frac{7}{20}\) | = \(\frac{15}{40} + \frac{14}{40} = \frac{29}{40}\) | |
| \(\frac{1}{6} - \frac{1}{7}\) | = \(\frac{7}{42} - \frac{6}{42} = \frac{1}{42}\) | |
| \(\frac{5}{9} + \frac{7}{15}\) | = \(\frac{25}{45} + \frac{21}{45} = \frac{46}{45}\) | = \(1\frac{1}{45}\) |
| \(\frac{3}{8} - \frac{19}{56}\) | = \(\frac{21}{56} - \frac{19}{56} = \frac{2}{56}\) | = \(\frac{1}{28}\) |
| \(\frac{19}{45} - \frac{7}{18}\) | = \(\frac{38}{90} - \frac{35}{90} = \frac{3}{90}\) | = \(\frac{1}{30}\) |
| \(\frac{1}{4} - \frac{1}{8}\) | = \(\frac{2}{8} - \frac{1}{8} = \frac{1}{8}\) | |
| \(\frac{11}{14} + \frac{8}{21}\) | = \(\frac{33}{42} + \frac{16}{42} = \frac{49}{42}\) | = \(\frac{7}{6}\) = \(1\frac{1}{6}\) |
Ответ: см. решения в таблицах.
