1. Вычислите. 1) 5 - 2 1/4 =

### 1. Вычислите. 1) $5 - 2\frac{1}{4} = 4\frac{4}{4} - 2\frac{1}{4} = 2\frac{3}{4}$ 2) $5\frac{3}{4} + 2\frac{1}{6} = 5\frac{9}{12} + 2\frac{2}{12} = 7\frac{11}{12}$ 3) $1\frac{1}{8} \div \frac{7}{9} \div 1\frac{3}{4} = \frac{9}{8} \cdot \frac{9}{7} \div \frac{7}{4} = \frac{81}{56} \cdot \frac{4}{7} = \frac{81}{14 \cdot 7} = \frac{81}{98}$ 4) $\frac{8}{9} \cdot \frac{10}{3} \cdot \frac{4}{3} = \frac{8 \cdot 10 \cdot 4}{9 \cdot 3 \cdot 3} = \frac{320}{81} = 3\frac{77}{81}$ ### 2. Преобразуйте в десятичную дробь. $1/5 = 0,2$; $1/4 = 0,25$; $7/20 = 0,35$; $3/4 = 0,75$; $11/25 = 0,44$; $7/125 = 0,056$. ### 3. Вычислите. 1) $0,5 \cdot 1,3 = 0,65$ 2) $0,42 \div 0,07 = 42 \div 7 = 6$ 3) $0,13 \cdot 7 = 0,91$ 4) $0,06 \div 0,1 = 0,6$ 5) $\frac{4,4}{0,11} + \frac{5,2}{1,3} + \frac{18}{0,3} = 40 + 4 + 60 = 104$ 6) $\frac{0,6 \cdot 1,8}{0,012 \cdot 0,9} - \frac{1,3}{0,13} = \frac{1,08}{0,0108} - 10 = 100 - 10 = 90$ 7) $\frac{3}{14} - 1\frac{1}{7}(0,25 - 0,125) = \frac{3}{14} - \frac{8}{7} \cdot 0,125 = \frac{3}{14} - \frac{8}{7} \cdot \frac{1}{8} = \frac{3}{14} - \frac{1}{7} = \frac{3}{14} - \frac{2}{14} = \frac{1}{14}$ 8) $\frac{1}{2 \cdot 3} + \frac{1}{3 \cdot 4} + \frac{1}{4 \cdot 5} = \frac{1}{6} + \frac{1}{12} + \frac{1}{20} = \frac{10}{60} + \frac{5}{60} + \frac{3}{60} = \frac{18}{60} = \frac{3}{10} = 0,3$ ### 4. Вычислите. 1) $-3 - 6 = -9$ 2) $-2 - (-9) = -2 + 9 = 7$ 3) $\frac{1}{3} - 5 = -4\frac{2}{3}$ 4) $1\frac{3}{7} - 4 = -2\frac{4}{7}$ 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) $16 : x = 8 : 4 \Rightarrow 16 : x = 2 \Rightarrow x = 8$ 2) $\frac{7}{18} : a = \frac{5}{9} : \frac{4}{7} \Rightarrow \frac{7}{18} : a = \frac{5}{9} \cdot \frac{7}{4} \Rightarrow \frac{7}{18} : a = \frac{35}{36} \Rightarrow a = \frac{7}{18} \cdot \frac{36}{35} = \frac{1}{1} \cdot \frac{2}{5} = \frac{2}{5} = 0,4$ 3) $(27 - x) : 3 - 4 = 2 \Rightarrow (27 - x) : 3 = 6 \Rightarrow 27 - x = 18 \Rightarrow x = 9$ 4) $-5(-1 + x) = 14 - 4(-3 + x) \Rightarrow 5 - 5x = 14 + 12 - 4x \Rightarrow 5 - 5x = 26 - 4x \Rightarrow -x = 21 \Rightarrow x = -21$ 5) $\frac{4 - x}{4} - \frac{x - 1}{3} = 1 - \frac{5x - 8}{6}$ (умножим на 12) $\Rightarrow 3(4 - x) - 4(x - 1) = 12 - 2(5x - 8) \Rightarrow 12 - 3x - 4x + 4 = 12 - 10x + 16 \Rightarrow 16 - 7x = 28 - 10x \Rightarrow 3x = 12 \Rightarrow x = 4$