23. Вычислите А) \( \left(2\frac{1}{4}+\frac{3}{3}\right) : \left(8\frac{5}{1}-1\frac{2}{5}\right) \cdot 1,2 \) Б) \( \left(12,75-6\frac{11}{12}+14,8-7\frac{2}{15}\right) : \left(10\frac{2}{3}-3\frac{11}{12}\right) \) В) \( \left(5,07-\frac{1}{20}-23,4:\frac{13}{50}\right) \cdot \frac{1}{4}+0,074 \cdot \frac{1}{2} \) Г) \( \left(3\frac{2}{3}+1\frac{3}{4}\right) : \left(6\frac{7}{12}-2\frac{1}{4}\right) \cdot 0,8 \) Д) \( \left(11,25-3\frac{5}{12}+4,3-7\frac{19}{30}\right) : \left(7\frac{1}{2}-5\frac{5}{6}\right) \) E) \( \left(3,04:\frac{1}{30}-16,03:\frac{7}{20}\right) \cdot \frac{1}{5}+0,072 \cdot \frac{1}{3} \) Ё) \( \left(5\frac{3}{5}-1\frac{1}{3}\right) : \left(7\frac{7}{12}-2\frac{1}{4}\right) \cdot 1,25 \) Ж) \( \left(9,5-3\frac{3}{5}+5,5-6\frac{13}{15}\right) \cdot \left(2\frac{5}{12}+1\frac{1}{3}\right) \)

23. Вычислите

А) \( \left(2\frac{1}{4}+1\right) : \left(8\frac{5}{1}-1\frac{2}{5}\right) \cdot 1,2 = \left(3\frac{1}{4}\right) : \left(8\frac{25}{5}-1\frac{2}{5}\right) \cdot 1,2 = \frac{13}{4} : \left(7\frac{23}{5}\right) \cdot 1,2 = \frac{13}{4} : \frac{38}{5} \cdot 1,2 = \frac{13}{4} \cdot \frac{5}{38} \cdot \frac{6}{5} = \frac{13 \cdot 5 \cdot 6}{4 \cdot 38 \cdot 5} = \frac{13 \cdot 6}{4 \cdot 38} = \frac{13 \cdot 3}{2 \cdot 38} = \frac{39}{76} \approx 0,513 \)

Б) \( \left(12,75-6\frac{11}{12}+14,8-7\frac{2}{15}\right) : \left(10\frac{2}{3}-3\frac{11}{12}\right) = \left(\frac{51}{4}-\frac{83}{12}+\frac{74}{5}-\frac{107}{15}\right) : \left(\frac{40}{3}-\frac{47}{12}\right) = \left(\frac{153-83}{12}+\frac{222-107}{15}\right) : \left(\frac{160-47}{12}\right) = \left(\frac{70}{12}+\frac{115}{15}\right) : \frac{113}{12} = \left(\frac{35}{6}+\frac{23}{3}\right) : \frac{113}{12} = \left(\frac{35+46}{6}\right) : \frac{113}{12} = \frac{81}{6} : \frac{113}{12} = \frac{27}{2} \cdot \frac{12}{113} = \frac{27 \cdot 6}{113} = \frac{162}{113} \approx 1,434 \)

В) \( \left(5,07-\frac{1}{20}-23,4:\frac{13}{50}\right) \cdot \frac{1}{4}+0,074 \cdot \frac{1}{2} = \left(5,07-0,05-23,4\cdot\frac{50}{13}\right) \cdot \frac{1}{4}+0,037 = \left(5,02-90\right) \cdot \frac{1}{4}+0,037 = -84,98 \cdot \frac{1}{4}+0,037 = -21,245+0,037 = -21,208 \)

Г) \( \left(3\frac{2}{3}+1\frac{3}{4}\right) : \left(6\frac{7}{12}-2\frac{1}{4}\right) \cdot 0,8 = \left(\frac{11}{3}+\frac{7}{4}\right) : \left(\frac{79}{12}-\frac{9}{4}\right) \cdot 0,8 = \left(\frac{44+21}{12}\right) : \left(\frac{79-27}{12}\right) \cdot 0,8 = \frac{65}{12} : \frac{52}{12} \cdot 0,8 = \frac{65}{52} \cdot 0,8 = \frac{5}{4} \cdot 0,8 = 1,25 \cdot 0,8 = 1 \)

Д) \( \left(11,25-3\frac{5}{12}+4,3-7\frac{19}{30}\right) : \left(7\frac{1}{2}-5\frac{5}{6}\right) = \left(\frac{45}{4}-\frac{41}{12}+\frac{43}{10}-\frac{229}{30}\right) : \left(\frac{15}{2}-\frac{29}{6}\right) = \left(\frac{135-41}{12}+\frac{129-229}{30}\right) : \left(\frac{45-29}{6}\right) = \left(\frac{94}{12}-\frac{100}{30}\right) : \frac{16}{6} = \left(\frac{47}{6}-\frac{10}{3}\right) : \frac{8}{3} = \left(\frac{47-20}{6}\right) : \frac{8}{3} = \frac{27}{6} : \frac{8}{3} = \frac{9}{2} \cdot \frac{3}{8} = \frac{27}{16} \approx 1,688 \)

E) \( \left(3,04:\frac{1}{30}-16,03:\frac{7}{20}\right) \cdot \frac{1}{5}+0,072 \cdot \frac{1}{3} = \left(3,04 \cdot 30 - 16,03 \cdot \frac{20}{7}\right) \cdot \frac{1}{5}+0,024 = \left(91,2 - \frac{320,6}{7}\right) \cdot \frac{1}{5}+0,024 \approx \left(91,2 - 45,8\right) \cdot \frac{1}{5}+0,024 = 45,4 \cdot \frac{1}{5}+0,024 = 9,08+0,024 = 9,104 \)

Ё) \( \left(5\frac{3}{5}-1\frac{1}{3}\right) : \left(7\frac{7}{12}-2\frac{1}{4}\right) \cdot 1,25 = \left(\frac{28}{5}-\frac{4}{3}\right) : \left(\frac{91}{12}-\frac{9}{4}\right) \cdot 1,25 = \left(\frac{84-20}{15}\right) : \left(\frac{91-27}{12}\right) \cdot 1,25 = \frac{64}{15} : \frac{64}{12} \cdot 1,25 = \frac{64}{15} \cdot \frac{12}{64} \cdot 1,25 = \frac{12}{15} \cdot 1,25 = \frac{4}{5} \cdot \frac{5}{4} = 1 \)

Ж) \( \left(9,5-3\frac{3}{5}+5,5-6\frac{13}{15}\right) \cdot \left(2\frac{5}{12}+1\frac{1}{3}\right) = \left(\frac{19}{2}-\frac{18}{5}+\frac{11}{2}-\frac{103}{15}\right) \cdot \left(\frac{29}{12}+\frac{4}{3}\right) = \left(\frac{19+11}{2}-\frac{54+103}{15}\right) \cdot \left(\frac{29+16}{12}\right) = \left(\frac{30}{2}-\frac{157}{15}\right) \cdot \frac{45}{12} = \left(15-\frac{157}{15}\right) \cdot \frac{15}{4} = \left(\frac{225-157}{15}\right) \cdot \frac{15}{4} = \frac{68}{15} \cdot \frac{15}{4} = \frac{68}{4} = 17 \)