N№5 5 10 6 + 9 : (3-1)-1 17 21 30 N№6 3-(2-1):+ 9 11 9 1 10 35 49 2

№5

1. $$\frac{5}{6} + \frac{10}{9} : (3 - 1\frac{17}{21}) - 1\frac{11}{30}$$
2. $$3 - 1\frac{17}{21} = \frac{3}{1} - \frac{38}{21} = \frac{3 \cdot 21}{1 \cdot 21} - \frac{38}{21} = \frac{63}{21} - \frac{38}{21} = \frac{63 - 38}{21} = \frac{25}{21}$$
3. $$\frac{10}{9} : \frac{25}{21} = \frac{10}{9} \cdot \frac{21}{25} = \frac{10 \cdot 21}{9 \cdot 25} = \frac{2 \cdot 7}{3 \cdot 5} = \frac{14}{15}$$
4. $$\frac{5}{6} + \frac{14}{15} = \frac{5 \cdot 5}{6 \cdot 5} + \frac{14 \cdot 2}{15 \cdot 2} = \frac{25}{30} + \frac{28}{30} = \frac{25 + 28}{30} = \frac{53}{30} = 1\frac{23}{30}$$
5. $$1\frac{23}{30} - 1\frac{11}{30} = \frac{53}{30} - \frac{41}{30} = \frac{53 - 41}{30} = \frac{12}{30} = \frac{6 \cdot 2}{6 \cdot 5} = \frac{2}{5}$$

Ответ: $$\frac{2}{5}$$

№6

1. $$3\frac{9}{10} - (2 - 1\frac{11}{35}) : \frac{9}{49} + \frac{1}{2}$$
2. $$2 - 1\frac{11}{35} = \frac{2}{1} - \frac{46}{35} = \frac{2 \cdot 35}{1 \cdot 35} - \frac{46}{35} = \frac{70}{35} - \frac{46}{35} = \frac{70 - 46}{35} = \frac{24}{35}$$
3. $$\frac{24}{35} : \frac{9}{49} = \frac{24}{35} \cdot \frac{49}{9} = \frac{24 \cdot 49}{35 \cdot 9} = \frac{8 \cdot 7}{5 \cdot 3} = \frac{56}{15} = 3\frac{11}{15}$$
4. $$3\frac{9}{10} - 3\frac{11}{15} = \frac{39}{10} - \frac{56}{15} = \frac{39 \cdot 3}{10 \cdot 3} - \frac{56 \cdot 2}{15 \cdot 2} = \frac{117}{30} - \frac{112}{30} = \frac{117 - 112}{30} = \frac{5}{30} = \frac{5}{5 \cdot 6} = \frac{1}{6}$$
5. $$\frac{1}{6} + \frac{1}{2} = \frac{1}{6} + \frac{1 \cdot 3}{2 \cdot 3} = \frac{1}{6} + \frac{3}{6} = \frac{1 + 3}{6} = \frac{4}{6} = \frac{2 \cdot 2}{2 \cdot 3} = \frac{2}{3}$$

Ответ: $$\frac{2}{3}$$