Вариант 4. Выполните действия: а) 5 1/3 * 2 1/4 : 1 1/5 = ?, б) 2 2/5 : (3 2/5 - 1 11/15) = ?, в) 1 4/11 * 3 3/7 : 3 3/7 = ?, г) 1 8/9 : (3 1/6 - 1 3/4) = ?, д) 10 - 2 1/2 : 3 3/4 + (2 1/2 - 1 1/3) * 6 = ?

Решение:

а) \( 5\frac{1}{3} \cdot 2\frac{1}{4} : 1\frac{1}{5} \)

1. \( 5\frac{1}{3} = \frac{16}{3} \)
2. \( 2\frac{1}{4} = \frac{9}{4} \)
3. \( 1\frac{1}{5} = \frac{6}{5} \)
4. \( \frac{16}{3} \cdot \frac{9}{4} = \frac{16 \cdot 9}{3 \cdot 4} = \frac{4 \cdot 3}{1} = 12 \)
5. \( 12 : \frac{6}{5} = 12 \cdot \frac{5}{6} = \frac{12 \cdot 5}{6} = 2 \cdot 5 = 10 \)

б) \( 2\frac{2}{5} : (3\frac{2}{5} - 1\frac{11}{15}) \)

1. \( 2\frac{2}{5} = \frac{12}{5} \)
2. \( 3\frac{2}{5} = \frac{17}{5} \)
3. \( 1\frac{11}{15} = \frac{26}{15} \)
4. \( \frac{17}{5} - \frac{26}{15} = \frac{17 \cdot 3 - 26}{15} = \frac{51 - 26}{15} = \frac{25}{15} = \frac{5}{3} \)
5. \( \frac{12}{5} : \frac{5}{3} = \frac{12}{5} \cdot \frac{3}{5} = \frac{36}{25} = 1\frac{11}{25} \)

в) \( 1\frac{4}{11} \cdot 3\frac{3}{7} : 3\frac{3}{7} \)

1. \( 1\frac{4}{11} = \frac{15}{11} \)
2. \( 3\frac{3}{7} = \frac{24}{7} \)
3. \( \frac{15}{11} \cdot \frac{24}{7} : \frac{24}{7} = \frac{15}{11} \cdot \frac{24}{7} \cdot \frac{7}{24} = \frac{15}{11} \)

г) \( 1\frac{8}{9} : (3\frac{1}{6} - 1\frac{3}{4}) \)

1. \( 1\frac{8}{9} = \frac{17}{9} \)
2. \( 3\frac{1}{6} = \frac{19}{6} \)
3. \( 1\frac{3}{4} = \frac{7}{4} \)
4. \( \frac{19}{6} - \frac{7}{4} = \frac{19 \cdot 2 - 7 \cdot 3}{12} = \frac{38 - 21}{12} = \frac{17}{12} \)
5. \( \frac{17}{9} : \frac{17}{12} = \frac{17}{9} \cdot \frac{12}{17} = \frac{12}{9} = \frac{4}{3} = 1\frac{1}{3} \)

д) \( 10 - 2\frac{1}{2} : 3\frac{3}{4} + (2\frac{1}{2} - 1\frac{1}{3}) \cdot 6 \)

1. \( 2\frac{1}{2} = \frac{5}{2} \)
2. \( 3\frac{3}{4} = \frac{15}{4} \)
3. \( 1\frac{1}{3} = \frac{4}{3} \)
4. \( \frac{5}{2} : \frac{15}{4} = \frac{5}{2} \cdot \frac{4}{15} = \frac{5 \cdot 4}{2 \cdot 15} = \frac{20}{30} = \frac{2}{3} \)
5. \( 2\frac{1}{2} - 1\frac{1}{3} = \frac{5}{2} - \frac{4}{3} = \frac{15 - 8}{6} = \frac{7}{6} \)
6. \( \frac{7}{6} \cdot 6 = 7 \)
7. \( 10 - \frac{2}{3} + 7 = 17 - \frac{2}{3} = 16\frac{1}{3} \)

Ответ: а) \( 10 \); б) \( 1\frac{11}{25} \); в) \( \frac{15}{11} \); г) \( 1\frac{1}{3} \); д) \( 16\frac{1}{3} \)