Выполните действия с дробями и смешанными числами

№1. Выполните действия: а) $20\frac{17}{37} + 14\frac{12}{37} + 31\frac{8}{37} = (20+14+31) + (\frac{17}{37} + \frac{12}{37} + \frac{8}{37}) = 65 + \frac{17+12+8}{37} = 65 + \frac{37}{37} = 65 + 1 = 66$ б) $6\frac{100}{107} + 9\frac{106}{107} = (6+9) + (\frac{100}{107} + \frac{106}{107}) = 15 + \frac{206}{107} = 15 + 1\frac{99}{107} = 16\frac{99}{107}$ в) $12\frac{19}{32} - 4\frac{3}{32} = (12-4) + (\frac{19}{32} - \frac{3}{32}) = 8 + \frac{19-3}{32} = 8 + \frac{16}{32} = 8 + \frac{1}{2} = 8\frac{1}{2}$ г) $150 - \frac{149}{150} = 149 + 1 - \frac{149}{150} = 149 + \frac{150}{150} - \frac{149}{150} = 149 + \frac{1}{150} = 149\frac{1}{150}$ д) $17\frac{2}{13} - 16\frac{5}{13} = 16\frac{15}{13} - 16\frac{5}{13} = (16-16) + (\frac{15}{13} - \frac{5}{13}) = 0 + \frac{10}{13} = \frac{10}{13}$ №2. Выполните действия: а) $30\frac{16}{43} + 42\frac{19}{43} + 9\frac{8}{43} = (30+42+9) + (\frac{16}{43} + \frac{19}{43} + \frac{8}{43}) = 81 + \frac{16+19+8}{43} = 81 + \frac{43}{43} = 81 + 1 = 82$ б) $4\frac{112}{113} + 7\frac{101}{113} = (4+7) + (\frac{112}{113} + \frac{101}{113}) = 11 + \frac{213}{113} = 11 + 1\frac{100}{113} = 12\frac{100}{113}$ в) $21\frac{29}{48} - 4\frac{5}{48} = (21-4) + (\frac{29}{48} - \frac{5}{48}) = 17 + \frac{24}{48} = 17 + \frac{1}{2} = 17\frac{1}{2}$ г) $180 - \frac{179}{180} = 179 + 1 - \frac{179}{180} = 179 + \frac{180}{180} - \frac{179}{180} = 179 + \frac{1}{180} = 179\frac{1}{180}$ д) $23\frac{4}{19} - 22\frac{7}{19} = 22\frac{23}{19} - 22\frac{7}{19} = (22-22) + (\frac{23}{19} - \frac{7}{19}) = 0 + \frac{16}{19} = \frac{16}{19}$ №3. Выполните действия: а) $12\frac{7}{20} + 7\frac{3}{20} - 4 = (12+7-4) + (\frac{7}{20} + \frac{3}{20}) = 15 + \frac{10}{20} = 15 + \frac{1}{2} = 15\frac{1}{2}$ б) $71\frac{8}{13} + 8\frac{12}{13} + \frac{9}{13} = 71\frac{8}{13} + (8 + \frac{12}{13} + \frac{9}{13}) = 71\frac{8}{13} + 8 + \frac{21}{13} = 71\frac{8}{13} + 8 + 1\frac{8}{13} = (71+8+1) + (\frac{8}{13} + \frac{8}{13}) = 80 + \frac{16}{13} = 80 + 1\frac{3}{13} = 81\frac{3}{13}$ в) $11\frac{21}{28} - 9\frac{12}{28} + \frac{1}{28} = (11-9) + (\frac{21}{28} - \frac{12}{28} + \frac{1}{28}) = 2 + \frac{21-12+1}{28} = 2 + \frac{10}{28} = 2 + \frac{5}{14} = 2\frac{5}{14}$ г) $24 - 8\frac{7}{11} - 4\frac{9}{11} = 24 - (8\frac{7}{11} + 4\frac{9}{11}) = 24 - ((8+4) + (\frac{7}{11} + \frac{9}{11})) = 24 - (12 + \frac{16}{11}) = 24 - (12 + 1\frac{5}{11}) = 24 - 13\frac{5}{11} = 23\frac{11}{11} - 13\frac{5}{11} = (23-13) + (\frac{11}{11} - \frac{5}{11}) = 10 + \frac{6}{11} = 10\frac{6}{11}$ д) $(10-6\frac{15}{28}) + (2\frac{15}{28}-1\frac{17}{28})$ Первая скобка: $10 - 6\frac{15}{28} = 9\frac{28}{28} - 6\frac{15}{28} = (9-6) + (\frac{28}{28} - \frac{15}{28}) = 3 + \frac{13}{28} = 3\frac{13}{28}$ Вторая скобка: $2\frac{15}{28} - 1\frac{17}{28} = 1\frac{43}{28} - 1\frac{17}{28} = (1-1) + (\frac{43}{28} - \frac{17}{28}) = 0 + \frac{26}{28} = \frac{13}{14}$ Складываем результаты: $3\frac{13}{28} + \frac{13}{14} = 3\frac{13}{28} + \frac{26}{28} = 3 + \frac{13+26}{28} = 3 + \frac{39}{28} = 3 + 1\frac{11}{28} = 4\frac{11}{28}$ е) $5\frac{16}{24} - (2\frac{15}{24}-1\frac{17}{24}) + 17\frac{5}{24}$ Сначала посчитаем то, что в скобках: $2\frac{15}{24} - 1\frac{17}{24} = 1\frac{39}{24} - 1\frac{17}{24} = (1-1) + (\frac{39}{24} - \frac{17}{24}) = 0 + \frac{22}{24} = \frac{11}{12}$ Теперь подставляем в выражение: $5\frac{16}{24} - \frac{11}{12} + 17\frac{5}{24} = 5\frac{2}{3} - \frac{11}{12} + 17\frac{5}{24}$ Приведем все дроби к общему знаменателю 24: $5\frac{16}{24} - \frac{22}{24} + 17\frac{5}{24} = (5+17) + (\frac{16}{24} - \frac{22}{24} + \frac{5}{24}) = 22 + \frac{16-22+5}{24} = 22 + \frac{-6+5}{24} = 22 + \frac{-1}{24} = 21 + 1 - \frac{1}{24} = 21 + \frac{24}{24} - \frac{1}{24} = 21 + \frac{23}{24} = 21\frac{23}{24}$ **Ответы:** **№1:** **а) 66** **б) $16\frac{99}{107}$** **в) $8\frac{1}{2}$** **г) $149\frac{1}{150}$** **д) $\frac{10}{13}$** **№2:** **а) 82** **б) $12\frac{100}{113}$** **в) $17\frac{1}{2}$** **г) $179\frac{1}{180}$** **д) $\frac{16}{19}$** **№3:** **а) $15\frac{1}{2}$** **б) $81\frac{3}{13}$** **в) $2\frac{5}{14}$** **г) $10\frac{6}{11}$** **д) $4\frac{11}{28}$** **е) $21\frac{23}{24}$**