Решебник по алгебре 7 класс Мерзляк Задание 4

\[\boxed{\text{4\ (4).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ \frac{7}{12} \cdot \frac{40}{21} = \frac{1 \cdot 10}{3 \cdot 3} = \frac{10}{9}\]

\[2)\ \frac{17}{72} \cdot \frac{2}{3} = \frac{17 \cdot 2}{72 \cdot 3} = \frac{17 \cdot 1}{36 \cdot 3} =\]

\[= \frac{17}{108}\]

\[3)\ 18\frac{5}{12} - \frac{10}{9} = 18\frac{5}{12} - 1\frac{1}{9} =\]

\[= 17 + \left( \frac{5^{\backslash 3}}{12} - \frac{1^{\backslash 4}}{9} \right) =\]

\[= 17 + \left( \frac{15 - 4}{36} \right) = 17 + \frac{11}{36} =\]

\[= 17\frac{11}{36}\]

\[4)\ 17\frac{11}{36} - \frac{107}{108} =\]

\[= 17 + \left( \frac{11^{\backslash 3}}{36} - \frac{17}{108} \right) =\]

\[= 17 + \frac{33 - 17}{108} = 17 + \frac{16}{108} =\]

\[= 17\frac{4}{27}\]

\[Ответ:17\frac{4}{27}.\]

\[1)\ 5\frac{1}{8}\ :1\frac{9}{32} = \frac{41}{8}\ :\frac{41}{32} =\]

\[= \frac{41 \cdot 32}{8 \cdot 41} = 4\]

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

\[3)\ 2\frac{3}{4} \cdot \frac{5}{11} = \frac{11}{4} \cdot \frac{5}{11} = \frac{5}{4} = 1\frac{1}{4}\]

\[Ответ:1\frac{1}{4}.\]

\[1) - 1,42 + 3,22 = 1,8\]

\[2)\ 1,8\ :( - 0,4) = - 18\ :4 =\]

\[= - \frac{18}{4} = - 4\frac{1}{2} = - 4,5\ \]

\[3) - 6 \cdot ( - 0,7) = 4,2\]

\[4) - 4,5 + 4,2 = - 0,3\]

\[Ответ:\ - 0,3.\]

\[1) - \frac{7^{\backslash 2}}{18} + \frac{11^{\backslash 3}}{12} = \frac{- 14 + 33}{36} =\]

\[= \frac{19}{36}\]

\[2)\ \frac{19}{36}\ :\left( - \frac{19}{48} \right) = - \frac{19 \cdot 48}{36 \cdot 19} =\]

\[= - \frac{4}{3} = - 1\frac{1}{3}\]

\[Ответ:\ - 1\frac{1}{3}.\]

\[1) - 3\frac{1^{\backslash 5}}{12} - 2\frac{1^{\backslash 4}}{15} =\]

\[= - 3\frac{5}{60} - 2\frac{4}{60} = - 5\frac{9}{60} =\]

\[= - 5\frac{3}{20}\]

\[2) - 5\frac{3}{20}\ :\left( - 5\frac{3}{20} \right) = 1\]

\[Ответ:1.\]