Решебник по математике 6 класс Виленкин ФГОС Часть 1, 2 Часть 2. Задачи на повторение 28

\[\boxed{\mathbf{П.\ 28}}\]

\[10\frac{1}{5}\ :\frac{17}{15} = \frac{51}{5} \cdot \frac{15}{17} = 3 \cdot 3 = 9\]

\[9 - 2\frac{4}{9} + 3\frac{7}{9} = 6\frac{5}{9} + 3\frac{7}{9} =\]

\[= 9\frac{12}{9} = 10\frac{3}{9} = 10\frac{1}{3}\]

\[\frac{20}{31} \cdot 10\frac{1}{3} = \frac{20}{31} \cdot \frac{31}{3} = \frac{20}{3} = 6\frac{2}{3}\]

\[6\frac{2}{3} - 2\frac{5}{6} = 6\frac{4}{6} - 2\frac{5}{6} =\]

\[= 5\frac{10}{6} - 2\frac{5}{6} = 3\frac{5}{6}\]

\[1\frac{5}{9}\ :2\frac{1}{3} = \frac{14}{9}\ :\frac{7}{3} = \frac{14}{9} \cdot \frac{3}{7} = \frac{2}{3}\]

\[2\frac{1}{15} - \frac{2}{3} + 1\frac{2}{5} =\]

\[= 1\frac{16}{15} - \frac{10}{15} + 1\frac{6}{15} = 2\frac{12}{15} = 2\frac{4}{5}\]

\[2\frac{4}{5} \cdot 2\frac{6}{7} = \frac{14}{5} \cdot \frac{20}{7} = 2 \cdot 4 = 8\]

\[\textbf{в)}\ 25,48 \cdot 3\frac{1}{4} - \left( 3,75 - 2\frac{1}{6} \right)\ :\frac{1}{6} =\]

\[= 82,81 - 9,5 = 73,31\]

\[3,75 - 2\frac{1}{6} = 3\frac{3}{4} - 2\frac{1}{6} =\]

\[= 3\frac{9}{12} - 2\frac{2}{12} = 1\frac{7}{12}\]

\[1\frac{7}{12}\ :\frac{1}{6} = \frac{19}{12} \cdot 6 = \frac{19}{2} = 9,5\]

\[25,48 \cdot 3\frac{1}{4} = 25\frac{48}{100} \cdot \frac{13}{4} =\]

\[= 25\frac{12}{25} \cdot \frac{13}{4} = \frac{637 \cdot 13}{100} =\]

\[= \frac{8281}{100} = 82,81\]

\[= 8,2 + 7,28 = 15,48\]

\[\frac{15}{16}\ :\frac{375}{1000} = \frac{15}{16}\ :\frac{3}{8} = \frac{15}{16} \cdot \frac{8}{3} =\]

\[= \frac{5}{2} = 2,5\]

\[1,872\ :\frac{9}{35} = 1\frac{872}{1000} \cdot \frac{35}{9} =\]

\[= 1\frac{109}{125} \cdot \frac{35}{9} = \frac{234 \cdot 35}{125 \cdot 9} =\]

\[= \frac{26 \cdot 7}{25} = \frac{182}{25} = 7,28\]

\[1,5 \cdot 3\frac{4}{5} = \frac{3}{2} \cdot \frac{19}{5} = \frac{57}{10} = 5,7\]