Решебник по математике 5 класс Виленкин ФГОС Часть 1, 2 Часть 2. Параграф 7. Инструменты для вычислений и измерений Задание 45

\[\boxed{\text{7.45.}}\]

\[\textbf{а)}\ \left( \frac{1}{2}\ :\frac{3}{4} - \frac{4}{9} \right)\ :\frac{3}{5} =\]

\[= \left( \frac{1}{2} \cdot \frac{4}{3} - \frac{4}{9} \right) \cdot \frac{5}{3} = \left( \frac{2}{3} - \frac{4}{9} \right) \cdot \frac{5}{3} =\]

\[= \left( \frac{4}{9} - \frac{4}{9} \right) \cdot \frac{5}{3} = 0\]

\[\textbf{б)}\ \frac{1}{2} \cdot \frac{8}{3} - \frac{4}{9}\ :\frac{3}{5} = \frac{4}{3} - \frac{4}{9} \cdot \frac{5}{3} =\]

\[= \frac{36}{27} - \frac{20}{27} = \frac{16}{27}\]

\[\textbf{в)}\ \frac{7}{5}\ :\left( \frac{9}{10} - \frac{2}{5} \cdot \frac{8}{9} \right) =\]

\[= \frac{7}{5}\ :\left( \frac{9}{10} - \frac{16}{45} \right) =\]

\[= \frac{7}{5}\ :\left( \frac{81}{90} - \frac{32}{90} \right) = \frac{7}{5}\ :\frac{49}{90} =\]

\[= \frac{7}{5} \cdot \frac{90}{49} = \frac{1 \cdot 18}{7} = \frac{17}{8} = 2\frac{1}{8}\]