1028. a) $$(\frac{2}{15}+1\frac{7}{12})\cdot \frac{30}{103}-2:2\frac{1}{4}\cdot \frac{9}{32}+2\frac{1}{3};$$ б) $$(7\frac{1}{2}\cdot 2\frac{2}{3}-12\frac{1}{4}:\frac{7}{9}):6+3\frac{1}{8}+5\frac{2}{7}$$

a) Вычислим значение выражения: $$(\frac{2}{15}+1\frac{7}{12})\cdot \frac{30}{103}-2:2\frac{1}{4}\cdot \frac{9}{32}+2\frac{1}{3}$$

1. $$\frac{2}{15}+1\frac{7}{12} = \frac{2}{15} + \frac{19}{12} = \frac{2 \cdot 4}{15 \cdot 4} + \frac{19 \cdot 5}{12 \cdot 5} = \frac{8}{60} + \frac{95}{60} = \frac{8+95}{60} = \frac{103}{60}$$
2. $$\frac{103}{60} \cdot \frac{30}{103} = \frac{103 \cdot 30}{60 \cdot 103} = \frac{30}{60} = \frac{1}{2}$$
3. $$2:2\frac{1}{4} = 2 : \frac{9}{4} = 2 \cdot \frac{4}{9} = \frac{2 \cdot 4}{9} = \frac{8}{9}$$
4. $$\frac{8}{9} \cdot \frac{9}{32} = \frac{8 \cdot 9}{9 \cdot 32} = \frac{8}{32} = \frac{1}{4}$$
5. $$\frac{1}{2} - \frac{1}{4} = \frac{1 \cdot 2}{2 \cdot 2} - \frac{1}{4} = \frac{2}{4} - \frac{1}{4} = \frac{2-1}{4} = \frac{1}{4}$$
6. $$2\frac{1}{3} = \frac{7}{3}$$
7. $$\frac{1}{4} + \frac{7}{3} = \frac{1 \cdot 3}{4 \cdot 3} + \frac{7 \cdot 4}{3 \cdot 4} = \frac{3}{12} + \frac{28}{12} = \frac{3+28}{12} = \frac{31}{12} = 2\frac{7}{12}$$

Ответ: $$2\frac{7}{12}$$

б) Вычислим значение выражения: $$(7\frac{1}{2}\cdot 2\frac{2}{3}-12\frac{1}{4}:\frac{7}{9}):6+3\frac{1}{8}+5\frac{2}{7}$$

1. $$7\frac{1}{2} \cdot 2\frac{2}{3} = \frac{15}{2} \cdot \frac{8}{3} = \frac{15 \cdot 8}{2 \cdot 3} = \frac{120}{6} = 20$$
2. $$12\frac{1}{4} : \frac{7}{9} = \frac{49}{4} : \frac{7}{9} = \frac{49}{4} \cdot \frac{9}{7} = \frac{49 \cdot 9}{4 \cdot 7} = \frac{7 \cdot 9}{4} = \frac{63}{4} = 15\frac{3}{4}$$
3. $$20 - 15\frac{3}{4} = 19\frac{4}{4} - 15\frac{3}{4} = (19 - 15) + (\frac{4}{4} - \frac{3}{4}) = 4 + \frac{1}{4} = 4\frac{1}{4} = \frac{17}{4}$$
4. $$\frac{17}{4} : 6 = \frac{17}{4} : \frac{6}{1} = \frac{17}{4} \cdot \frac{1}{6} = \frac{17 \cdot 1}{4 \cdot 6} = \frac{17}{24}$$
5. $$3\frac{1}{8} = \frac{25}{8}$$
6. $$\frac{17}{24} + \frac{25}{8} = \frac{17}{24} + \frac{25 \cdot 3}{8 \cdot 3} = \frac{17}{24} + \frac{75}{24} = \frac{17+75}{24} = \frac{92}{24} = \frac{23}{6} = 3\frac{5}{6}$$
7. $$5\frac{2}{7} = \frac{37}{7}$$
8. $$3\frac{5}{6} + 5\frac{2}{7} = \frac{23}{6} + \frac{37}{7} = \frac{23 \cdot 7}{6 \cdot 7} + \frac{37 \cdot 6}{7 \cdot 6} = \frac{161}{42} + \frac{222}{42} = \frac{161+222}{42} = \frac{383}{42} = 9\frac{5}{42}$$

Ответ: $$9\frac{5}{42}$$