Вариант 3. 1. Выполните действия: а) 2 1/7 : 4 1/6 - 2 1/3 = ?, б) 6 1/5 - 4 1/3 : 1 1/3 = ?, в) 7 2/3 - 5 4/5 : 2 4/5 = ?, г) 5 4/19 * 3 4/7 + 15/19 : 7/25 - 1 2/3 = ?, д) 2 3/11 * 7/9 + 6 8/11 : 1 1/7 - 1 1/8 = ?

Решение:

а) \( 2\frac{1}{7} : 4\frac{1}{6} - 2\frac{1}{3} \)

1. \( 2\frac{1}{7} = \frac{15}{7} \)
2. \( 4\frac{1}{6} = \frac{25}{6} \)
3. \( 2\frac{1}{3} = \frac{7}{3} \)
4. \( \frac{15}{7} : \frac{25}{6} = \frac{15}{7} \cdot \frac{6}{25} = \frac{3 \cdot 5}{7} \cdot \frac{6}{5 \cdot 5} = \frac{3 \cdot 6}{7 \cdot 5} = \frac{18}{35} \)
5. \( \frac{18}{35} - \frac{7}{3} = \frac{18 \cdot 3 - 7 \cdot 35}{105} = \frac{54 - 245}{105} = -\frac{191}{105} = -1\frac{86}{105} \)

б) \( 6\frac{1}{5} - 4\frac{1}{3} : 1\frac{1}{3} \)

1. \( 6\frac{1}{5} = \frac{31}{5} \)
2. \( 4\frac{1}{3} = \frac{13}{3} \)
3. \( 1\frac{1}{3} = \frac{4}{3} \)
4. \( \frac{13}{3} : \frac{4}{3} = \frac{13}{3} \cdot \frac{3}{4} = \frac{13}{4} \)
5. \( \frac{31}{5} - \frac{13}{4} = \frac{31 \cdot 4 - 13 \cdot 5}{20} = \frac{124 - 65}{20} = \frac{59}{20} = 2\frac{19}{20} \)

в) \( 7\frac{2}{3} - 5\frac{4}{5} : 2\frac{4}{5} \)

1. \( 7\frac{2}{3} = \frac{23}{3} \)
2. \( 5\frac{4}{5} = \frac{29}{5} \)
3. \( 2\frac{4}{5} = \frac{14}{5} \)
4. \( \frac{29}{5} : \frac{14}{5} = \frac{29}{5} \cdot \frac{5}{14} = \frac{29}{14} \)
5. \( \frac{23}{3} - \frac{29}{14} = \frac{23 \cdot 14 - 29 \cdot 3}{42} = \frac{322 - 87}{42} = \frac{235}{42} = 5\frac{25}{42} \)

г) \( 5\frac{4}{19} \cdot 3\frac{4}{7} + \frac{15}{19} : \frac{7}{25} - 1\frac{2}{3} \)

1. \( 5\frac{4}{19} = \frac{99}{19} \)
2. \( 3\frac{4}{7} = \frac{25}{7} \)
3. \( 1\frac{2}{3} = \frac{5}{3} \)
4. \( \frac{99}{19} \cdot \frac{25}{7} = \frac{99 \cdot 25}{19 \cdot 7} = \frac{2475}{133} \)
5. \( \frac{15}{19} : \frac{7}{25} = \frac{15}{19} \cdot \frac{25}{7} = \frac{375}{133} \)
6. \( \frac{2475}{133} + \frac{375}{133} - \frac{5}{3} = \frac{2850}{133} - \frac{5}{3} = \frac{2850 \cdot 3 - 5 \cdot 133}{399} = \frac{8550 - 665}{399} = \frac{7885}{399} \)

д) \( 2\frac{3}{11} \cdot \frac{7}{9} + 6\frac{8}{11} : 1\frac{1}{7} - 1\frac{1}{8} \)

1. \( 2\frac{3}{11} = \frac{25}{11} \)
2. \( 6\frac{8}{11} = \frac{74}{11} \)
3. \( 1\frac{1}{7} = \frac{8}{7} \)
4. \( 1\frac{1}{8} = \frac{9}{8} \)
5. \( \frac{25}{11} \cdot \frac{7}{9} = \frac{175}{99} \)
6. \( \frac{74}{11} : \frac{8}{7} = \frac{74}{11} \cdot \frac{7}{8} = \frac{37 \cdot 7}{11 \cdot 4} = \frac{259}{44} \)
7. \( \frac{175}{99} + \frac{259}{44} - \frac{9}{8} = \frac{175 \cdot 44 + 259 \cdot 99 - 9 \cdot 99 \cdot 44 / 8}{396} = \frac{7700 + 25641 - 4356}{396} = \frac{28985}{396} \)

Ответ: а) \( -1\frac{86}{105} \); б) \( 2\frac{19}{20} \); в) \( 5\frac{25}{42} \); г) \( \frac{7885}{399} \); д) \( \frac{28985}{396} \)