1. Найдите сумму: 1) 12 3/8 + 8 1/6; 3) 9 8/21 + 4 11/14; 2) 3 13/15 + 6 7/10; 4) 8 5/9 + 7 3/4 + 12 7/12.

Задание 1: Найдите сумму 1) $12\frac{3}{8} + 8\frac{1}{6} = 12\frac{9}{24} + 8\frac{4}{24} = 20\frac{13}{24}$ 2) $3\frac{13}{15} + 6\frac{7}{10} = 3\frac{26}{30} + 6\frac{21}{30} = 9\frac{47}{30} = 10\frac{17}{30}$ 3) $9\frac{8}{21} + 4\frac{11}{14} = 9\frac{16}{42} + 4\frac{33}{42} = 13\frac{49}{42} = 14\frac{7}{42} = 14\frac{1}{6}$ 4) $8\frac{5}{9} + 7\frac{3}{4} + 12\frac{7}{12} = 8\frac{20}{36} + 7\frac{27}{36} + 12\frac{21}{36} = 27\frac{68}{36} = 28\frac{32}{36} = 28\frac{8}{9}$ Задание 2: Вычислите 1) $1 - \frac{7}{15} = \frac{15}{15} - \frac{7}{15} = \frac{8}{15}$ 2) $3 - \frac{9}{23} = 2\frac{23}{23} - \frac{9}{23} = 2\frac{14}{23}$ 3) $4 - 1\frac{2}{3} = 3\frac{3}{3} - 1\frac{2}{3} = 2\frac{1}{3}$ 4) $10 - 5\frac{4}{11} = 9\frac{11}{11} - 5\frac{4}{11} = 4\frac{7}{11}$ Задание 3: Найдите разность 1) $7\frac{5}{6} - 3\frac{2}{3} = 7\frac{5}{6} - 3\frac{4}{6} = 4\frac{1}{6}$ 2) $8\frac{5}{12} - 6\frac{7}{20} = 8\frac{25}{60} - 6\frac{21}{60} = 2\frac{4}{60} = 2\frac{1}{15}$ 3) $11\frac{11}{12} - 5\frac{7}{9} = 11\frac{33}{36} - 5\frac{28}{36} = 6\frac{5}{36}$ 4) $9\frac{17}{24} - 8\frac{11}{36} = 9\frac{51}{72} - 8\frac{22}{72} = 1\frac{29}{72}$ Задание 4: Выполните вычитание 1) $3\frac{1}{16} - \frac{1}{8} = 3\frac{1}{16} - \frac{2}{16} = 2\frac{17}{16} - \frac{2}{16} = 2\frac{15}{16}$ 2) $7\frac{9}{20} - 5\frac{17}{30} = 7\frac{27}{60} - 5\frac{34}{60} = 6\frac{87}{60} - 5\frac{34}{60} = 1\frac{53}{60}$ 3) $4\frac{2}{7} - 1\frac{4}{9} = 4\frac{18}{63} - 1\frac{28}{63} = 3\frac{81}{63} - 1\frac{28}{63} = 2\frac{53}{63}$ 4) $8\frac{5}{36} - 1\frac{43}{108} = 8\frac{15}{108} - 1\frac{43}{108} = 7\frac{123}{108} - 1\frac{43}{108} = 6\frac{80}{108} = 6\frac{20}{27}$ 5) $9\frac{7}{9} - 4\frac{5}{6} = 9\frac{14}{18} - 4\frac{15}{18} = 8\frac{32}{18} - 4\frac{15}{18} = 4\frac{17}{18}$ 6) $6\frac{7}{32} - 2\frac{11}{48} = 6\frac{21}{96} - 2\frac{22}{96} = 5\frac{117}{96} - 2\frac{22}{96} = 3\frac{95}{96}$ Задание 5: Решите уравнение 1) $10\frac{5}{8} - x = 7\frac{3}{5} \Rightarrow x = 10\frac{5}{8} - 7\frac{3}{5} = 10\frac{25}{40} - 7\frac{24}{40} = 3\frac{1}{40}$ 2) $(x - 2\frac{7}{8}) + 3\frac{5}{6} = 4\frac{2}{3} \Rightarrow x - 2\frac{7}{8} = 4\frac{2}{3} - 3\frac{5}{6} = 4\frac{4}{6} - 3\frac{5}{6} = 3\frac{10}{6} - 3\frac{5}{6} = \frac{5}{6} \Rightarrow x = \frac{5}{6} + 2\frac{7}{8} = \frac{20}{24} + 2\frac{21}{24} = 2\frac{41}{24} = 3\frac{17}{24}$ Задание 6: Выполните действия 1) $6\frac{7}{8} - 3\frac{1}{3} + 5\frac{5}{16} = 6\frac{21}{24} - 3\frac{8}{24} + 5\frac{5}{16} = 3\frac{13}{24} + 5\frac{5}{16} = 3\frac{26}{48} + 5\frac{15}{48} = 8\frac{41}{48}$ 2) $5\frac{9}{14} - 2\frac{3}{7} + 6,7 = 5\frac{9}{14} - 2\frac{6}{14} + 6\frac{7}{10} = 3\frac{3}{14} + 6\frac{7}{10} = 3\frac{15}{70} + 6\frac{49}{70} = 9\frac{64}{70} = 9\frac{32}{35}$ 3) $(15\frac{5}{6} - 9\frac{25}{27}) - 2\frac{17}{18} = (15\frac{45}{54} - 9\frac{50}{54}) - 2\frac{17}{18} = (14\frac{99}{54} - 9\frac{50}{54}) - 2\frac{17}{18} = 5\frac{49}{54} - 2\frac{17}{18} = 5\frac{49}{54} - 2\frac{51}{54} = 4\frac{103}{54} - 2\frac{51}{54} = 2\frac{52}{54} = 2\frac{26}{27}$ 4) $(18 - 10\frac{5}{9}) - (6\frac{1}{8} - 3\frac{2}{3}) = (7\frac{4}{9}) - (6\frac{3}{24} - 3\frac{16}{24}) = 7\frac{4}{9} - (5\frac{27}{24} - 3\frac{16}{24}) = 7\frac{4}{9} - 2\frac{11}{24} = 7\frac{32}{72} - 2\frac{33}{72} = 6\frac{104}{72} - 2\frac{33}{72} = 4\frac{71}{72}$ Задание 7: Скорость по течению = $20\frac{1}{2} + 1\frac{7}{8} = 20\frac{4}{8} + 1\frac{7}{8} = 21\frac{11}{8} = 22\frac{3}{8}$ км/ч Скорость против течения = $20\frac{1}{2} - 1\frac{7}{8} = 20\frac{4}{8} - 1\frac{7}{8} = 19\frac{12}{8} - 1\frac{7}{8} = 18\frac{5}{8}$ км/ч Задание 8: Первый рабочий делает $\frac{1}{12}$ задания в час, второй — $\frac{1}{8}$ задания в час. Первый сделал $5 \times \frac{1}{12} = \frac{5}{12}$ задания. Второй сделал $3 \times \frac{1}{8} = \frac{3}{8}$ задания. Вместе они сделали: $\frac{5}{12} + \frac{3}{8} = \frac{10}{24} + \frac{9}{24} = \frac{19}{24}$ задания. Осталось выполнить: $1 - \frac{19}{24} = \frac{5}{24}$ части задания.