Задание 3. Вариант 1. Выполните действия: а) \(\frac{13}{18} + \frac{7}{12}\); б) \(\frac{7}{9} - \frac{5}{12}\); в) \(4 \frac{1}{6} + 1 \frac{5}{12}\); г) \(\frac{8}{15} - \frac{4}{21} - \frac{1}{7}\)

**Решение:** * **а) \(\frac{13}{18} + \frac{7}{12}\):** НОК(18, 12) = 36. \(\frac{13}{18} = \frac{13 \times 2}{18 \times 2} = \frac{26}{36}\). \(\frac{7}{12} = \frac{7 \times 3}{12 \times 3} = \frac{21}{36}\). \(\frac{26}{36} + \frac{21}{36} = \frac{47}{36} = 1 \frac{11}{36}\) * **б) \(\frac{7}{9} - \frac{5}{12}\):** НОК(9, 12) = 36. \(\frac{7}{9} = \frac{7 \times 4}{9 \times 4} = \frac{28}{36}\). \(\frac{5}{12} = \frac{5 \times 3}{12 \times 3} = \frac{15}{36}\). \(\frac{28}{36} - \frac{15}{36} = \frac{13}{36}\) * **в) \(4 \frac{1}{6} + 1 \frac{5}{12}\):** \(4 \frac{1}{6} = 4 \frac{2}{12}\). \(4 \frac{2}{12} + 1 \frac{5}{12} = 5 \frac{7}{12}\) * **г) \(\frac{8}{15} - \frac{4}{21} - \frac{1}{7}\):** НОК(15, 21, 7) = 105. \(\frac{8}{15} = \frac{8 \times 7}{15 \times 7} = \frac{56}{105}\). \(\frac{4}{21} = \frac{4 \times 5}{21 \times 5} = \frac{20}{105}\). \(\frac{1}{7} = \frac{1 \times 15}{7 \times 15} = \frac{15}{105}\). \(\frac{56}{105} - \frac{20}{105} - \frac{15}{105} = \frac{21}{105} = \frac{1}{5}\) **Ответ:** а) \(1 \frac{11}{36}\); б) \(\frac{13}{36}\); в) \(5 \frac{7}{12}\); г) \(\frac{1}{5}\)