Умножение рациональных чисел 3 Уровень С 1. (-1) 2.-2(-1) 3.-(-4)(2) 4. (-2) 5. -2-3-(-12) 6. 5,07 (-3,07) 7.-46 8.--(-3) 2 9. (-1) 10.-5(-) 11.-6.7-(-2,4) 12.-12 13.-2() 14.-11 15.-8,4-(-)(-1) 16. 1,05 10,4 17. (-2) 18.-2-(-2)-0,5 19.()(-4) 20. -6,5 (-)(-8,9)

Шаг 1: (-1)^(3)

\[(-1)^3 = -1 \times -1 \times -1 = -1\]

Шаг 2: -2 3/7 * (-1 1/12)

\[-2\frac{3}{7} \times \left(-1\frac{1}{12}\right) = -\frac{17}{7} \times \left(-\frac{13}{12}\right) = \frac{17 \times 13}{7 \times 12} = \frac{221}{84}\]

Шаг 3: -2/5 * (-4) * (-2/5)

\[-\frac{2}{5} \times (-4) \times \left(-\frac{2}{5}\right) = -\frac{2 \times 4 \times 2}{5 \times 5} = -\frac{16}{25}\]

Шаг 4: (-2 3/2)^2

\[\left(-2\frac{3}{2}\right)^2 = \left(-\frac{7}{2}\right)^2 = \left(-\frac{7}{2}\right) \times \left(-\frac{7}{2}\right) = \frac{49}{4}\]

Шаг 5: -2 3/6 * (-12)

\[-2\frac{3}{6} \times (-12) = -\frac{15}{6} \times (-12) = \frac{15 \times 12}{6} = \frac{180}{6} = 30\]

Шаг 6: 5,07 * (-3,07)

5,07 * (-3,07) = -15,5649

Шаг 7: -4 2/5 * 6

\[-4\frac{2}{5} \times 6 = -\frac{22}{5} \times 6 = -\frac{22 \times 6}{5} = -\frac{132}{5}\]

Шаг 8: -10/21 * (-3 1/2)^2

\[-\frac{10}{21} \times \left(-3\frac{1}{2}\right)^2 = -\frac{10}{21} \times \left(-\frac{7}{2}\right)^2 = -\frac{10}{21} \times \frac{49}{4} = -\frac{10 \times 49}{21 \times 4} = -\frac{490}{84} = -\frac{35}{6}\]

Шаг 9: (-1 1/4)^2

\[\left(-1\frac{1}{4}\right)^2 = \left(-\frac{5}{4}\right)^2 = \left(-\frac{5}{4}\right) \times \left(-\frac{5}{4}\right) = \frac{25}{16}\]

Шаг 10: -5 5/6 * (-2/7)

\[-5\frac{5}{6} \times \left(-\frac{2}{7}\right) = -\frac{35}{6} \times \left(-\frac{2}{7}\right) = \frac{35 \times 2}{6 \times 7} = \frac{70}{42} = \frac{5}{3}\]

Шаг 11: -6,7 * 5/24 * (-2,4)

\[-6.7 \times \frac{5}{24} \times (-2.4) = \frac{-6.7 \times 5 \times -2.4}{24} = \frac{80.4}{24} = 3.35\]

Шаг 12: -1 1/8 * 2 1/3

\[-1\frac{1}{8} \times 2\frac{1}{3} = -\frac{9}{8} \times \frac{7}{3} = -\frac{9 \times 7}{8 \times 3} = -\frac{63}{24} = -\frac{21}{8}\]

Шаг 13: -2 5/7 * (1/3)^3

\[-2\frac{5}{7} \times \left(\frac{1}{3}\right)^3 = -\frac{19}{7} \times \frac{1}{27} = -\frac{19 \times 1}{7 \times 27} = -\frac{19}{189}\]

Шаг 14: -1 1/8 * 1 7/33

\[-1\frac{1}{8} \times 1\frac{7}{33} = -\frac{9}{8} \times \frac{40}{33} = -\frac{9 \times 40}{8 \times 33} = -\frac{360}{264} = -\frac{15}{11}\]

Шаг 15: -8,4 * (-7/12) * (-1)

\[-8.4 \times \left(-\frac{7}{12}\right) \times (-1) = -8.4 \times \frac{7}{12} = -\frac{8.4 \times 7}{12} = -\frac{58.8}{12} = -4.9\]

Шаг 16: -1,05 * 10,4

-1,05 * 10,4 = -10,92

Шаг 17: (-2 1/2)^2 * 5/24

\[\left(-2\frac{1}{2}\right)^2 \times \frac{5}{24} = \left(-\frac{5}{2}\right)^2 \times \frac{5}{24} = \frac{25}{4} \times \frac{5}{24} = \frac{25 \times 5}{4 \times 24} = \frac{125}{96}\]

Шаг 18: -2 2/3 * (-2 1/4) * (-0,5)

\[-2\frac{2}{3} \times \left(-2\frac{1}{4}\right) \times (-0.5) = -\frac{8}{3} \times \left(-\frac{9}{4}\right) \times (-0.5) = -\frac{8 \times 9 \times 0.5}{3 \times 4} = -\frac{36}{12} = -3\]

Шаг 19: (3/4)^2 * (-4)

\[\left(\frac{3}{4}\right)^2 \times (-4) = \frac{9}{16} \times (-4) = -\frac{9 \times 4}{16} = -\frac{36}{16} = -\frac{9}{4}\]

Шаг 20: -6,5 * (-5/24) * (-8,9)

\[-6.5 \times \left(-\frac{5}{24}\right) \times (-8.9) = -6.5 \times \frac{5}{24} \times 8.9 = -\frac{6.5 \times 5 \times 8.9}{24} = -\frac{289.25}{24} = -12.052083333333334\]