Номер №19 — ГДЗ по алгебре за 7 класс, Макарычев
Вычислите:
а) \(6\dfrac{1}{3} - 8\);
б) \(-2\dfrac{2}{7} + 4\dfrac{3}{5}\);
в) \(5\dfrac{1}{3} - 6\dfrac{1}{4}\);
г) \(\dfrac{3}{8} : \left(-\dfrac{9}{16}\right)\);
д) \(\dfrac{5}{12} \cdot (-6)\);
е) \(-3\dfrac{2}{9} \cdot 3\);
ж) \(\dfrac{4}{7} \cdot (-49)\);
з) \(-16 : \left(-\dfrac{4}{9}\right)\);
и) \(-3\dfrac{1}{2} \cdot \left(-1\dfrac{3}{7}\right)\).
Выполняем действия с рациональными числами.
а) \(6\tfrac{1}{3} - 8 = \dfrac{19}{3} - \dfrac{24}{3} = -\dfrac{5}{3} = -1\tfrac{2}{3}\).
б) \(-2\tfrac{2}{7} + 4\tfrac{3}{5} = -\dfrac{16}{7} + \dfrac{23}{5} = -\dfrac{80}{35} + \dfrac{161}{35} = \dfrac{81}{35} = 2\tfrac{11}{35}\).
в) \(5\tfrac{1}{3} - 6\tfrac{1}{4} = \dfrac{16}{3} - \dfrac{25}{4} = \dfrac{64}{12} - \dfrac{75}{12} = -\dfrac{11}{12}\).
г) \(\dfrac{3}{8} : \left(-\dfrac{9}{16}\right) = -\dfrac{3}{8} \cdot \dfrac{16}{9} = -\dfrac{48}{72} = -\dfrac{2}{3}\).
д) \(\dfrac{5}{12} \cdot (-6) = -\dfrac{30}{12} = -\dfrac{5}{2} = -2\tfrac{1}{2}\).
е) \(-3\tfrac{2}{9} \cdot 3 = -\dfrac{29}{9} \cdot 3 = -\dfrac{87}{9} = -\dfrac{29}{3} = -9\tfrac{2}{3}\).
ж) \(\dfrac{4}{7} \cdot (-49) = -\dfrac{4 \cdot 49}{7} = -4 \cdot 7 = -28\).
з) \(-16 : \left(-\dfrac{4}{9}\right) = 16 \cdot \dfrac{9}{4} = \dfrac{144}{4} = 36\).
и) \(-3\tfrac{1}{2} \cdot \left(-1\tfrac{3}{7}\right) = \left(-\dfrac{7}{2}\right) \cdot \left(-\dfrac{10}{7}\right) = \dfrac{70}{14} = 5\).
Ответ: а) \(-1\tfrac{2}{3}\); б) \(2\tfrac{11}{35}\); в) \(-\dfrac{11}{12}\); г) \(-\dfrac{2}{3}\); д) \(-2\tfrac{1}{2}\); е) \(-9\tfrac{2}{3}\); ж) \(-28\); з) \(36\); и) \(5\).
Вычислите:
а) \(6\dfrac{1}{3} - 8\);
б) \(-2\dfrac{2}{7} + 4\dfrac{3}{5}\);
в) \(5\dfrac{1}{3} - 6\dfrac{1}{4}\);
г) \(\dfrac{3}{8} : \left(-\dfrac{9}{16}\right)\);
д) \(\dfrac{5}{12} \cdot (-6)\);
е) \(-3\dfrac{2}{9} \cdot 3\);
ж) \(\dfrac{4}{7} \cdot (-49)\);
з) \(-16 : \left(-\dfrac{4}{9}\right)\);
и) \(-3\dfrac{1}{2} \cdot \left(-1\dfrac{3}{7}\right)\).
а) \(6\tfrac{1}{3} - 8 = -1\tfrac{2}{3}\).
б) \(-2\tfrac{2}{7} + 4\tfrac{3}{5} = -\dfrac{80}{35} + \dfrac{161}{35} = \dfrac{81}{35} = 2\tfrac{11}{35}\).
в) \(5\tfrac{1}{3} - 6\tfrac{1}{4} = \dfrac{64}{12} - \dfrac{75}{12} = -\dfrac{11}{12}\).
г) \(\dfrac{3}{8} : \left(-\dfrac{9}{16}\right) = -\dfrac{3}{8} \cdot \dfrac{16}{9} = -\dfrac{2}{3}\).
д) \(\dfrac{5}{12} \cdot (-6) = -\dfrac{5}{2} = -2\tfrac{1}{2}\).
е) \(-3\tfrac{2}{9} \cdot 3 = -\dfrac{29}{3} = -9\tfrac{2}{3}\).
ж) \(\dfrac{4}{7} \cdot (-49) = -28\).
з) \(-16 : \left(-\dfrac{4}{9}\right) = 16 \cdot \dfrac{9}{4} = 36\).
и) \(-3\tfrac{1}{2} \cdot \left(-1\tfrac{3}{7}\right) = \dfrac{7}{2} \cdot \dfrac{10}{7} = 5\).
Ответ: а) \(-1\tfrac{2}{3}\); б) \(2\tfrac{11}{35}\); в) \(-\dfrac{11}{12}\); г) \(-\dfrac{2}{3}\); д) \(-2\tfrac{1}{2}\); е) \(-9\tfrac{2}{3}\); ж) \(-28\); з) \(36\); и) \(5\).
