16 16 21 2 27 2) 중·4·유 + (4+1). + 큵ㆍ4 57 3 45 1 6)+(23-15- 4 +ㅎ 8 15 7 a) )(5-42- 5 5 6) 24+ 16 10 39 2 3 1- 35 = . 9 58 2 4 1- 5 1

Решение:

а)

\[\frac{1}{4} \cdot 4 \frac{3}{4} \cdot \frac{16}{57} + (4 \frac{3}{4} + 1 \frac{2}{3}) \cdot \frac{16}{21} + \frac{2}{27} \cdot 4 \frac{1}{2} = \] \[= \frac{1}{4} \cdot \frac{19}{4} \cdot \frac{16}{57} + (\frac{19}{4} + \frac{5}{3}) \cdot \frac{16}{21} + \frac{2}{27} \cdot \frac{9}{2} = \] \[= \frac{1 \cdot 19 \cdot 16}{4 \cdot 4 \cdot 57} + (\frac{19 \cdot 3 + 5 \cdot 4}{12}) \cdot \frac{16}{21} + \frac{2 \cdot 9}{27 \cdot 2} = \] \[= \frac{1 \cdot 1 \cdot 4}{1 \cdot 1 \cdot 3} + \frac{57 + 20}{12} \cdot \frac{16}{21} + \frac{1 \cdot 1}{3 \cdot 1} = \] \[= \frac{4}{3} + \frac{77}{12} \cdot \frac{16}{21} + \frac{1}{3} = \frac{4}{3} + \frac{77 \cdot 16}{12 \cdot 21} + \frac{1}{3} = \frac{4}{3} + \frac{11 \cdot 4}{3 \cdot 3} + \frac{1}{3} = \frac{4}{3} + \frac{44}{9} + \frac{1}{3} = \frac{4 \cdot 3 + 44 + 1 \cdot 3}{9} = \frac{12 + 44 + 3}{9} = \frac{59}{9} = 6 \frac{5}{9}\]

б)

\[(\frac{4}{5} + \frac{1}{6}) \cdot (23 \frac{2}{3} - 15 \frac{5}{9}) \cdot \frac{45}{58} - \frac{1}{2} = \] \[(\frac{4 \cdot 6 + 1 \cdot 5}{30}) \cdot (\frac{23 \cdot 3 + 2}{3} - \frac{15 \cdot 9 + 5}{9}) \cdot \frac{45}{58} - \frac{1}{2} = \] \[(\frac{24 + 5}{30}) \cdot (\frac{69 + 2}{3} - \frac{135 + 5}{9}) \cdot \frac{45}{58} - \frac{1}{2} = \frac{29}{30} \cdot (\frac{71}{3} - \frac{140}{9}) \cdot \frac{45}{58} - \frac{1}{2} = \] \[\frac{29}{30} \cdot (\frac{71 \cdot 3 - 140}{9}) \cdot \frac{45}{58} - \frac{1}{2} = \frac{29}{30} \cdot (\frac{213 - 140}{9}) \cdot \frac{45}{58} - \frac{1}{2} = \frac{29}{30} \cdot \frac{73}{9} \cdot \frac{45}{58} - \frac{1}{2} = \frac{29 \cdot 73 \cdot 45}{30 \cdot 9 \cdot 58} - \frac{1}{2} = \frac{1 \cdot 73 \cdot 1}{2 \cdot 1 \cdot 2} - \frac{1}{2} = \frac{73}{4} - \frac{1}{2} = \frac{73 - 1 \cdot 2}{4} = \frac{73 - 2}{4} = \frac{71}{4} = 17 \frac{3}{4}\]

а)

\[(5 \frac{8}{15} - 4 \frac{7}{10}) \cdot 2 \frac{2}{3} - \frac{5}{9} = \] \[(\frac{5 \cdot 15 + 8}{15} - \frac{4 \cdot 10 + 7}{10}) \cdot \frac{2 \cdot 3 + 2}{3} - \frac{5}{9} = (\frac{75 + 8}{15} - \frac{40 + 7}{10}) \cdot \frac{6 + 2}{3} - \frac{5}{9} = \] \[(\frac{83}{15} - \frac{47}{10}) \cdot \frac{8}{3} - \frac{5}{9} = (\frac{83 \cdot 2 - 47 \cdot 3}{30}) \cdot \frac{8}{3} - \frac{5}{9} = (\frac{166 - 141}{30}) \cdot \frac{8}{3} - \frac{5}{9} = \frac{25}{30} \cdot \frac{8}{3} - \frac{5}{9} = \frac{5}{6} \cdot \frac{8}{3} - \frac{5}{9} = \frac{5 \cdot 8}{6 \cdot 3} - \frac{5}{9} = \frac{5 \cdot 4}{3 \cdot 3} - \frac{5}{9} = \frac{20}{9} - \frac{5}{9} = \frac{20 - 5}{9} = \frac{15}{9} = \frac{5}{3} = 1 \frac{2}{3}\]

б)

\[(\frac{5}{24} + \frac{5}{16}) \cdot (1 \frac{2}{3} - \frac{3}{5}) \cdot 1 \frac{4}{5} = \] \[(\frac{5 \cdot 2 + 5 \cdot 3}{48}) \cdot (\frac{1 \cdot 3 + 2}{3} - \frac{3}{5}) \cdot \frac{1 \cdot 5 + 4}{5} = (\frac{10 + 15}{48}) \cdot (\frac{3 + 2}{3} - \frac{3}{5}) \cdot \frac{5 + 4}{5} = \frac{25}{48} \cdot (\frac{5}{3} - \frac{3}{5}) \cdot \frac{9}{5} = \] \[\frac{25}{48} \cdot (\frac{5 \cdot 5 - 3 \cdot 3}{15}) \cdot \frac{9}{5} = \frac{25}{48} \cdot (\frac{25 - 9}{15}) \cdot \frac{9}{5} = \frac{25}{48} \cdot \frac{16}{15} \cdot \frac{9}{5} = \frac{25 \cdot 16 \cdot 9}{48 \cdot 15 \cdot 5} = \frac{5 \cdot 4 \cdot 3}{4 \cdot 3 \cdot 1} = \frac{5}{1} = 5\]

Ответ: а) \(6 \frac{5}{9}\), б) \(17 \frac{3}{4}\), a) \(1 \frac{2}{3}\), б) \(5\)

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