П.28 Найдите значение выражения: a) \frac{20}{31} \cdot (10\frac{1}{5}:1\frac{2}{15}-2\frac{4}{9}+3\frac{7}{9})-2\frac{5}{6}; б) (2\frac{1}{15}-1\frac{5}{9}:2\frac{1}{3}+1\frac{2}{5}) \cdot 2\frac{6}{7}-3\frac{1}{7}; в) 25,48 \cdot 3\frac{1}{4}-(3,75 -2\frac{1}{6}) : \frac{1}{6}; г) \frac{15}{16}: 0,375 +1,872 : \frac{9}{25} +1,5 \cdot 3\frac{4}{5}.

• a) \frac{20}{31} \cdot (10\frac{1}{5}:1\frac{2}{15}-2\frac{4}{9}+3\frac{7}{9})-2\frac{5}{6}

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1. \(10\frac{1}{5}:1\frac{2}{15} = \frac{51}{5}:\frac{17}{15} = \frac{51}{5} \cdot \frac{15}{17} = \frac{3 \cdot 3}{1} = 9\)
2. \(-2\frac{4}{9}+3\frac{7}{9} = -\frac{22}{9} + \frac{34}{9} = \frac{12}{9} = \frac{4}{3}\)
3. \(9 + \frac{4}{3} = \frac{27}{3} + \frac{4}{3} = \frac{31}{3}\)
4. \(\frac{20}{31} \cdot \frac{31}{3} = \frac{20}{3}\)
5. \(\frac{20}{3} - 2\frac{5}{6} = \frac{20}{3} - \frac{17}{6} = \frac{40}{6} - \frac{17}{6} = \frac{23}{6} = 3\frac{5}{6}\)

\[\frac{20}{31} \cdot (10\frac{1}{5}:1\frac{2}{15}-2\frac{4}{9}+3\frac{7}{9})-2\frac{5}{6} = \frac{23}{6} - 2\frac{5}{6} = \frac{23}{6} - \frac{17}{6} = \frac{6}{6} = 1\]

• б) (2\frac{1}{15}-1\frac{5}{9}:2\frac{1}{3}+1\frac{2}{5}) \cdot 2\frac{6}{7}-3\frac{1}{7}

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1. \(1\frac{5}{9}:2\frac{1}{3} = \frac{14}{9} : \frac{7}{3} = \frac{14}{9} \cdot \frac{3}{7} = \frac{2}{3}\)
2. \(2\frac{1}{15}-\frac{2}{3}+1\frac{2}{5} = \frac{31}{15} - \frac{10}{15} + \frac{21}{15} = \frac{42}{15} = \frac{14}{5}\)
3. \(\frac{14}{5} \cdot 2\frac{6}{7} = \frac{14}{5} \cdot \frac{20}{7} = \frac{2 \cdot 4}{1} = 8\)
4. \(8 - 3\frac{1}{7} = 8 - \frac{22}{7} = \frac{56}{7} - \frac{22}{7} = \frac{34}{7} = 4\frac{6}{7}\)

\[(2\frac{1}{15}-1\frac{5}{9}:2\frac{1}{3}+1\frac{2}{5}) \cdot 2\frac{6}{7}-3\frac{1}{7} = 4\frac{6}{7}\]

• в) 25,48 \cdot 3\frac{1}{4}-(3,75 -2\frac{1}{6}) : \frac{1}{6}

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1. \(25,48 \cdot 3\frac{1}{4} = 25,48 \cdot 3,25 = 82,81\)
2. \(3,75 - 2\frac{1}{6} = 3,75 - 2,1666... = 1,58333...\)
3. \(1,58333... : \frac{1}{6} = 1,58333... \cdot 6 = 9,5\)
4. \(82,81 - 9,5 = 73,31\)

\[25,48 \cdot 3\frac{1}{4}-(3,75 -2\frac{1}{6}) : \frac{1}{6} = 73,31\]

• г) \frac{15}{16}: 0,375 +1,872 : \frac{9}{25} +1,5 \cdot 3\frac{4}{5}.

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1. \(\frac{15}{16} : 0,375 = \frac{15}{16} : \frac{3}{8} = \frac{15}{16} \cdot \frac{8}{3} = \frac{5}{2} = 2,5\)
2. \(1,872 : \frac{9}{25} = 1,872 : 0,36 = 5,2\)
3. \(1,5 \cdot 3\frac{4}{5} = 1,5 \cdot \frac{19}{5} = 1,5 \cdot 3,8 = 5,7\)
4. \(2,5 + 5,2 + 5,7 = 13,4\)

\[\frac{15}{16}: 0,375 +1,872 : \frac{9}{25} +1,5 \cdot 3\frac{4}{5} = 13,4\]