1. Вычислите. 1) 5-2 1/4 = ...

Решение заданий: **1. Вычислите:** 1) $5 - 2\frac{1}{4} = 5 - 2,25 = 2,75$ 2) $5\frac{3}{4} + 2\frac{1}{6} = 5\frac{9}{12} + 2\frac{2}{12} = 7\frac{11}{12}$ 3) $1\frac{1}{8} : \frac{7}{9} : 1\frac{3}{4} = \frac{9}{8} : \frac{7}{9} : \frac{7}{4} = (\frac{9}{8} \cdot \frac{9}{7}) : \frac{7}{4} = \frac{81}{56} \cdot \frac{4}{7} = \frac{81}{14 \cdot 7} = \frac{81}{98}$ 4) $\frac{8}{9} \cdot \frac{4}{3} : \frac{10}{3} = (\frac{32}{27}) \cdot \frac{3}{10} = \frac{32 \cdot 3}{27 \cdot 10} = \frac{32}{9 \cdot 10} = \frac{32}{90} = \frac{16}{45}$ **4. Вычислите:** 1) $-3 - 6 = -9$ 2) $-2 - (-9) = -2 + 9 = 7$ 3) $\frac{1}{3} - 5 = \frac{1}{3} - \frac{15}{3} = -\frac{14}{3} = -4\frac{2}{3}$ 4) $1\frac{3}{7} - 4 = \frac{10}{7} - \frac{28}{7} = -\frac{18}{7} = -2\frac{4}{7}$ 5) $-7 - (-4 - (-3 + 1)) - 5 = -7 - (-4 - (-2)) - 5 = -7 - (-4 + 2) - 5 = -7 - (-2) - 5 = -7 + 2 - 5 = -10$ 6) $-3^2 + 2 \cdot 3^2 - (-4)^2 \cdot \frac{1}{8} = -9 + 2 \cdot 9 - 16 \cdot \frac{1}{8} = -9 + 18 - 2 = 7$ **5. Решите уравнения:** 1) $16 : x = 8 : 4$ $16 : x = 2$ $x = 16 : 2$ $x = 8$ 2) $\frac{7}{18} : a = \frac{5}{9} : \frac{4}{7}$ $\frac{7}{18} : a = \frac{5}{9} \cdot \frac{7}{4} = \frac{35}{36}$ $a = \frac{7}{18} : \frac{35}{36} = \frac{7}{18} \cdot \frac{36}{35} = \frac{1}{1} \cdot \frac{2}{5} = \frac{2}{5} = 0,4$ 3) $(27 - x) : 3 - 4 = 2$ $(27 - x) : 3 = 6$ $27 - x = 18$ $x = 27 - 18$ $x = 9$ 4) $-5(-1 + x) = 14 - 4(-3 + x)$ $5 - 5x = 14 + 12 - 4x$ $5 - 5x = 26 - 4x$ $-5x + 4x = 26 - 5$ $-x = 21$ $x = -21$