1. Вычислите. 1) 5 - 2 1/4 =

### Задание 1 1) $5 - 2\frac{1}{4} = 5 - 2.25 = 2.75 = 2\frac{3}{4}$ 2) $5\frac{3}{4} + 2\frac{1}{6} = 5\frac{9}{12} + 2\frac{2}{12} = 7\frac{11}{12}$ 3) $1\frac{1}{8} : 1\frac{3}{4} = \frac{9}{8} : \frac{7}{4} = \frac{9}{8} \cdot \frac{4}{7} = \frac{9}{14}$ 4) $\frac{8}{9} \cdot \frac{10}{3} : \frac{4}{3} = \frac{80}{27} \cdot \frac{3}{4} = \frac{20}{9} = 2\frac{2}{9}$ ### Задание 2 1) $1/5 = 0.2$ 2) $1/4 = 0.25$ 3) $7/20 = 0.35$ 4) $3/4 = 0.75$ 5) $11/25 = 0.44$ 6) $7/125 = 0.056$ ### Задание 3 1) $0.5 \cdot 1.3 = 0.65$ 2) $0.42 : 0.07 = 6$ 3) $0.13 \cdot 7 = 0.91$ 4) $0.06 : 0.1 = 0.6$ 5) $4.4/0.11 + 5.2/1.3 + 18/0.3 = 40 + 4 + 60 = 104$ 6) $(0.6 \cdot 1.8) / (0.012 \cdot 0.9) - 1.3/0.13 = 1.08 / 0.0108 - 10 = 100 - 10 = 90$ 7) $3/14 - 1/7 \cdot (0.25 - 0.125) = 3/14 - 1/7 \cdot 0.125 = 3/14 - 1/7 \cdot 1/8 = 3/14 - 1/56 = 12/56 - 1/56 = 11/56$ 8) $1/(2\cdot 3) + 1/(3\cdot 4) + 1/(4\cdot 5) = 1/6 + 1/12 + 1/20 = 10/60 + 5/60 + 3/60 = 18/60 = 3/10 = 0.3$ ### Задание 4 1) $-3 - 6 = -9$ 2) $-2 - (-9) = -2 + 9 = 7$ 3) $1/3 - 5 = -4\frac{2}{3}$ 4) $1\frac{3}{7} - 4 = 1\frac{3}{7} - 3\frac{7}{7} = -2\frac{4}{7}$ 5) $-7 - (-4 - (-3 + 1)) - 5 = -7 - (-4 - (-2)) - 5 = -7 - (-4 + 2) - 5 = -7 - (-2) - 5 = -7 + 2 - 5 = -10$ 6) $-3^2 + 2 \cdot 3^2 - (-4)^2 \cdot 1/8 = -9 + 2 \cdot 9 - 16 \cdot 1/8 = -9 + 18 - 2 = 7$ ### Задание 5 1) $16:x = 8:4 \Rightarrow 16:x = 2 \Rightarrow x = 8$ 2) $7/18 : a = 5/9 : 4/7 \Rightarrow 7/18 : a = 5/9 \cdot 7/4 \Rightarrow 7/18 : a = 35/36 \Rightarrow a = 7/18 \cdot 36/35 = 2/5 = 0.4$ 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) $(4-x)/4 - (x-1)/3 = 1 - (5x-8)/6 \Rightarrow (12-3x - 4x+4)/12 = (6 - 5x + 8)/6 \Rightarrow (16-7x)/12 = (14-5x)/6 \Rightarrow 16-7x = 2(14-5x) \Rightarrow 16-7x = 28 - 10x \Rightarrow 3x = 12 \Rightarrow x = 4$