Страница 6 номер 1.1.12, ГДЗ по алгебре за 7, 8 и 9 класс к задачнику Ткачевой
Найти значение числового выражения: 1) \(-\frac{2}{3} \cdot \left(1\frac{1}{2} - \frac{2}{5}\right)\); 2) \(\frac{5}{6} : \left(-1\frac{2}{3} + \frac{1}{4}\right)\); 3) \(-5\frac{1}{3} - 1\frac{1}{3} \cdot 0{,}5\); 4) \(-2\frac{3}{4} + 1\frac{1}{4} \cdot 0{,}4\); 5) \(\frac{16 - 2\frac{1}{3}}{-4}\); 6) \(\frac{5}{4\frac{1}{7} - 15}\); 7) \(-3\frac{1}{6} - 2\frac{5}{8} : 2\frac{1}{4}\); 8) \(-2\frac{2}{5} + 3\frac{1}{15} : 2\frac{1}{11}\).
1) \[\begin{aligned} &-\frac{2}{3} \cdot \left(1\frac{1}{2} - \frac{2}{5}\right) = -\frac{2}{3} \cdot \left(\frac{15}{10} - \frac{4}{10}\right) = {} \\ &= -\frac{2}{3} \cdot \frac{11}{10} = -\frac{22}{30} = -\frac{11}{15}. \end{aligned}\]
2) \[\begin{aligned} &\frac{5}{6} : \left(-1\frac{2}{3} + \frac{1}{4}\right) = \frac{5}{6} : \left(-\frac{20}{12} + \frac{3}{12}\right) = {} \\ &= \frac{5}{6} : \left(-\frac{17}{12}\right) = \frac{5}{6} \cdot \left(-\frac{12}{17}\right) = -\frac{10}{17}. \end{aligned}\]
3) \[\begin{aligned} &-5\frac{1}{3} - 1\frac{1}{3} \cdot 0{,}5 = -\frac{16}{3} - \frac{4}{3} \cdot \frac{1}{2} = {} \\ &= -\frac{16}{3} - \frac{2}{3} = -\frac{18}{3} = -6. \end{aligned}\]
4) \[\begin{aligned} &-2\frac{3}{4} + 1\frac{1}{4} \cdot 0{,}4 = -\frac{11}{4} + \frac{5}{4} \cdot \frac{2}{5} = {} \\ &= -\frac{11}{4} + \frac{2}{4} = -\frac{9}{4} = -2\frac{1}{4}. \end{aligned}\]
5) \[\begin{aligned} &\frac{16 - 2\frac{1}{3}}{-4} = \left(16 - 2\frac{1}{3}\right) : (-4) = 13\frac{2}{3} : (-4) = {} \\ &= -\frac{41}{3} \cdot \frac{1}{4} = -\frac{41}{12} = -3\frac{5}{12}. \end{aligned}\]
6) \[\begin{aligned} &\frac{5}{4\frac{1}{7} - 15} = 5 : \left(4\frac{1}{7} - 15\right) = 5 : \left(\frac{29}{7} - \frac{105}{7}\right) = {} \\ &= 5 : \left(-\frac{76}{7}\right) = 5 \cdot \left(-\frac{7}{76}\right) = -\frac{35}{76}. \end{aligned}\]
7) \[\begin{aligned} &-3\frac{1}{6} - 2\frac{5}{8} : 2\frac{1}{4} = -\frac{19}{6} - \frac{21}{8} \cdot \frac{4}{9} = {} \\ &= -\frac{19}{6} - \frac{7}{6} = -\frac{26}{6} = -\frac{13}{3} = -4\frac{1}{3}. \end{aligned}\]
8) \[\begin{aligned} &-2\frac{2}{5} + 3\frac{1}{15} : 2\frac{1}{11} = -\frac{12}{5} + \frac{46}{15} \cdot \frac{11}{23} = {} \\ &= -\frac{12}{5} + \frac{22}{15} = -\frac{36}{15} + \frac{22}{15} = -\frac{14}{15}. \end{aligned}\]
Ответ: 1) \(-\frac{11}{15}\); 2) \(-\frac{10}{17}\); 3) \(-6\); 4) \(-2\frac{1}{4}\); 5) \(-3\frac{5}{12}\); 6) \(-\frac{35}{76}\); 7) \(-4\frac{1}{3}\); 8) \(-\frac{14}{15}\).
Найти значение числового выражения: 1) \(-\frac{2}{3} \cdot \left(1\frac{1}{2} - \frac{2}{5}\right)\); 2) \(\frac{5}{6} : \left(-1\frac{2}{3} + \frac{1}{4}\right)\); 3) \(-5\frac{1}{3} - 1\frac{1}{3} \cdot 0{,}5\); 4) \(-2\frac{3}{4} + 1\frac{1}{4} \cdot 0{,}4\); 5) \(\frac{16 - 2\frac{1}{3}}{-4}\); 6) \(\frac{5}{4\frac{1}{7} - 15}\); 7) \(-3\frac{1}{6} - 2\frac{5}{8} : 2\frac{1}{4}\); 8) \(-2\frac{2}{5} + 3\frac{1}{15} : 2\frac{1}{11}\).
Деление на дробь заменяется умножением на дробь, обратную делителю; дробная черта в пунктах 5) и 6) заменяет знак деления.
1) \[\begin{aligned} &-\frac{2}{3} \cdot \left(1\frac{1}{2} - \frac{2}{5}\right) = -\frac{2}{3} \cdot \left(\frac{15}{10} - \frac{4}{10}\right) = {} \\ &= -\frac{2}{3} \cdot \frac{11}{10} = -\frac{22}{30} = -\frac{11}{15}. \end{aligned}\]
2) \[\begin{aligned} &\frac{5}{6} : \left(-1\frac{2}{3} + \frac{1}{4}\right) = \frac{5}{6} : \left(-\frac{20}{12} + \frac{3}{12}\right) = {} \\ &= \frac{5}{6} : \left(-\frac{17}{12}\right) = \frac{5}{6} \cdot \left(-\frac{12}{17}\right) = -\frac{10}{17}. \end{aligned}\]
3) \[\begin{aligned} &-5\frac{1}{3} - 1\frac{1}{3} \cdot 0{,}5 = -\frac{16}{3} - \frac{4}{3} \cdot \frac{1}{2} = {} \\ &= -\frac{16}{3} - \frac{2}{3} = -\frac{18}{3} = -6. \end{aligned}\]
4) \[\begin{aligned} &-2\frac{3}{4} + 1\frac{1}{4} \cdot 0{,}4 = -\frac{11}{4} + \frac{5}{4} \cdot \frac{2}{5} = {} \\ &= -\frac{11}{4} + \frac{2}{4} = -\frac{9}{4} = -2\frac{1}{4}. \end{aligned}\]
5) \[\begin{aligned} &\frac{16 - 2\frac{1}{3}}{-4} = \left(16 - 2\frac{1}{3}\right) : (-4) = 13\frac{2}{3} : (-4) = {} \\ &= -\frac{41}{3} \cdot \frac{1}{4} = -\frac{41}{12} = -3\frac{5}{12}. \end{aligned}\]
6) \[\begin{aligned} &\frac{5}{4\frac{1}{7} - 15} = 5 : \left(4\frac{1}{7} - 15\right) = 5 : \left(\frac{29}{7} - \frac{105}{7}\right) = {} \\ &= 5 : \left(-\frac{76}{7}\right) = 5 \cdot \left(-\frac{7}{76}\right) = -\frac{35}{76}. \end{aligned}\]
7) \[\begin{aligned} &-3\frac{1}{6} - 2\frac{5}{8} : 2\frac{1}{4} = -\frac{19}{6} - \frac{21}{8} \cdot \frac{4}{9} = {} \\ &= -\frac{19}{6} - \frac{7}{6} = -\frac{26}{6} = -\frac{13}{3} = -4\frac{1}{3}. \end{aligned}\]
8) \[\begin{aligned} &-2\frac{2}{5} + 3\frac{1}{15} : 2\frac{1}{11} = -\frac{12}{5} + \frac{46}{15} \cdot \frac{11}{23} = {} \\ &= -\frac{12}{5} + \frac{22}{15} = -\frac{36}{15} + \frac{22}{15} = -\frac{14}{15}. \end{aligned}\]
Ответ: 1) \(-\frac{11}{15}\); 2) \(-\frac{10}{17}\); 3) \(-6\); 4) \(-2\frac{1}{4}\); 5) \(-3\frac{5}{12}\); 6) \(-\frac{35}{76}\); 7) \(-4\frac{1}{3}\); 8) \(-\frac{14}{15}\).
