### Решение заданий:
**1)** $[(\frac{15}{28} - \frac{11}{36}) \cdot \frac{21}{29} + 6 \frac{6}{7} : \frac{16}{21}] : 16 \frac{1}{2}$
1. $\frac{15}{28} - \frac{11}{36} = \frac{135 - 77}{252} = \frac{58}{252} = \frac{29}{126}$
2. $\frac{29}{126} \cdot \frac{21}{29} = \frac{1}{6}$
3. $6 \frac{6}{7} : \frac{16}{21} = \frac{48}{7} \cdot \frac{21}{16} = 3 \cdot 3 = 9$
4. $\frac{1}{6} + 9 = 9 \frac{1}{6} = \frac{55}{6}$
5. $\frac{55}{6} : 16 \frac{1}{2} = \frac{55}{6} : \frac{33}{2} = \frac{55}{6} \cdot \frac{2}{33} = \frac{5}{3} \cdot \frac{1}{3} = \frac{5}{9}$
**Ответ: 5/9**
**2)** $[(4 \frac{5}{7} - 1 \frac{11}{14}) \cdot 4 \frac{2}{3} + (3 \frac{2}{9} - 1 \frac{5}{6}) \cdot \frac{18}{25}] : 2 \frac{3}{4}$
1. $4 \frac{5}{7} - 1 \frac{11}{14} = 4 \frac{10}{14} - 1 \frac{11}{14} = 3 \frac{24}{14} - 1 \frac{11}{14} = 2 \frac{13}{14} = \frac{41}{14}$
2. $\frac{41}{14} \cdot \frac{14}{3} = \frac{41}{3} = 13 \frac{2}{3}$
3. $3 \frac{2}{9} - 1 \frac{5}{6} = 3 \frac{4}{18} - 1 \frac{15}{18} = 2 \frac{22}{18} - 1 \frac{15}{18} = 1 \frac{7}{18} = \frac{25}{18}$
4. $\frac{25}{18} \cdot \frac{18}{25} = 1$
5. $13 \frac{2}{3} + 1 = 14 \frac{2}{3} = \frac{44}{3}$
6. $\frac{44}{3} : 2 \frac{3}{4} = \frac{44}{3} : \frac{11}{4} = \frac{44}{3} \cdot \frac{4}{11} = 4 \cdot \frac{4}{3} = \frac{16}{3} = 5 \frac{1}{3}$
**Ответ: 5 1/3**
**3)** $1 \frac{9}{40} \cdot [7 \frac{5}{7} : 3 \frac{3}{5} - (\frac{53}{56} - \frac{29}{35}) : \frac{33}{40}]$
1. $7 \frac{5}{7} : 3 \frac{3}{5} = \frac{54}{7} : \frac{18}{5} = \frac{54}{7} \cdot \frac{5}{18} = \frac{3 \cdot 5}{7} = \frac{15}{7}$
2. $\frac{53}{56} - \frac{29}{35} = \frac{265 - 232}{280} = \frac{33}{280}$
3. $\frac{33}{280} : \frac{33}{40} = \frac{33}{280} \cdot \frac{40}{33} = \frac{40}{280} = \frac{1}{7}$
4. $\frac{15}{7} - \frac{1}{7} = \frac{14}{7} = 2$
5. $1 \frac{9}{40} \cdot 2 = \frac{49}{40} \cdot 2 = \frac{49}{20} = 2 \frac{9}{20}$
**Ответ: 2 9/20**
**4)** $[(5 \frac{5}{9} - \frac{7}{18}) : 35 + (\frac{40}{63} - \frac{8}{21}) : 20 + (\frac{83}{90} - \frac{41}{50}) : 2] \cdot 35$
1. $5 \frac{5}{9} - \frac{7}{18} = 5 \frac{10}{18} - \frac{7}{18} = 5 \frac{3}{18} = 5 \frac{1}{6} = \frac{31}{6}$
2. $\frac{31}{6} : 35 = \frac{31}{210}$
3. $\frac{40}{63} - \frac{8}{21} = \frac{40}{63} - \frac{24}{63} = \frac{16}{63}$
4. $\frac{16}{63} : 20 = \frac{16}{63 \cdot 20} = \frac{4}{63 \cdot 5} = \frac{4}{315}$
5. $\frac{83}{90} - \frac{41}{50} = \frac{415 - 369}{450} = \frac{46}{450} = \frac{23}{225}$
6. $\frac{23}{225} : 2 = \frac{23}{450}$
7. $(\frac{31}{210} + \frac{4}{315} + \frac{23}{450}) \cdot 35 = \frac{31}{6} + \frac{4}{9} + \frac{23}{12,85} \approx \text{ (расчет упростим)} \rightarrow \frac{31 \cdot 15 + 4 \cdot 10 + 23 \cdot \frac{7}{3}}{315} \cdot 35 = \frac{465 + 40 + 53,6}{315} \cdot 35 = \frac{558,6}{9} = 62,06$
*Прим: В 4-м пункте дроби после сложения с 35 дают итоговый результат, арифметически наиболее верно представить ответ как сумму произведений: (31/6)*35/35 + (4/63)*35/20 + (23/225)*35/2 = 31/6 + 1/9 + 23/12.85 = 5.166 + 0.111 + 0.051 = 5.328.*
