Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 509

\[\boxed{\mathbf{509}.}\]

\[1)\ \left( 0,645\ :0,3 - 1\frac{107}{180} \right) \bullet\]

\[\cdot \left( 4\ :6,25 - 1\ :5 + \frac{1}{7} \bullet 1,96 \right) =\]

\[= \left( \frac{645}{1000}\ :\frac{3}{10} - \frac{180 + 107}{180} \right) \bullet\]

\[\cdot \left( 4\ :\frac{625}{100} - \frac{1}{5} + \frac{1}{7} \bullet \frac{196}{100} \right) =\]

\[= \left( \frac{129}{200} \bullet \frac{10}{3} - \frac{287}{180} \right) \bullet\]

\[\cdot \left( \frac{4 \bullet 100}{625} - \frac{1}{5} + \frac{28}{100} \right) =\]

\[= \left( \frac{43}{20} - \frac{287}{180} \right) \bullet \left( \frac{16}{25} - \frac{1}{5} + \frac{7}{25} \right) =\]

\[= \left( \frac{387}{180} - \frac{287}{180} \right) \bullet \left( \frac{23}{25} - \frac{5}{25} \right) =\]

\[= \frac{100}{180} \bullet \frac{18}{25} = \frac{5}{9} \bullet \frac{18}{25} = \frac{2}{5} = 0,4;\]

\[2)\ \left( \frac{1}{2} - 0,375 \right)\ :0,125 +\]

\[+ \left( \frac{5}{6} - \frac{7}{12} \right)\ :(0,358 - 0,108) =\]

\[= \left( \frac{1}{2} - \frac{375}{1000} \right)\ :\frac{125}{1000} +\]

\[+ \left( \frac{10}{12} - \frac{7}{12} \right)\ :\left( \frac{358}{1000} - \frac{108}{1000} \right) =\]

\[= \left( \frac{1}{2} - \frac{3}{8} \right) \bullet \frac{1000}{125} + \frac{3}{12}\ :\frac{250}{1000} =\]

\[= \left( \frac{4}{8} - \frac{3}{8} \right) \bullet 8 + \frac{3}{12}\ :\frac{1}{4} =\]

\[= \frac{1}{8} \bullet 8 + \frac{3}{12} \bullet 4 =\]

\[= 1 + \frac{3}{3} = 1 + 1 = 2.\]