1. Решите пропорцию: a) 2: x = 5:7 3 6)=2: y 4 2. :6; 3' r) = (1,2b): 6 4,8 7 1- 9 4 1913 -1.32-0.72 д) 9 ; 0,72 13 в) 2: (1,5а) = : 0,8. 7 5 14

Решим пропорции:

1. a) 2 : x = 5 : 7 $$x = \frac{2 \cdot 7}{5} = \frac{14}{5} = 2,8$$ Ответ: x = 2,8
2. б) $$\frac{0,8}{y} = 2 : \frac{3}{4}$$ $$\frac{0,8}{y} = \frac{2 \cdot 4}{3}$$ $$\frac{0,8}{y} = \frac{8}{3}$$ $$y = \frac{0,8 \cdot 3}{8} = \frac{2,4}{8} = 0,3$$ Ответ: y = 0,3
3. в) $$2\frac{1}{7} : (1,5a) = \frac{5}{14} : 0,8$$ $$\frac{15}{7} : (1,5a) = \frac{5}{14} : \frac{8}{10}$$ $$\frac{15}{7} : (1,5a) = \frac{5}{14} : \frac{4}{5}$$ $$\frac{15}{7} : (1,5a) = \frac{5 \cdot 5}{14 \cdot 4}$$ $$\frac{15}{7} : (1,5a) = \frac{25}{56}$$ $$1,5a = \frac{15}{7} : \frac{25}{56}$$ $$1,5a = \frac{15 \cdot 56}{7 \cdot 25}$$ $$1,5a = \frac{3 \cdot 8}{1 \cdot 5}$$ $$1,5a = \frac{24}{5}$$ $$1,5a = 4,8$$ $$a = \frac{4,8}{1,5} = \frac{48}{15} = \frac{16}{5} = 3,2$$ Ответ: a = 3,2
4. г) $$\frac{4,8}{1\frac{7}{9}} = (1,2b) : 6\frac{2}{3}$$ $$\frac{4,8}{\frac{16}{9}} = (1,2b) : \frac{20}{3}$$ $$\frac{4,8 \cdot 9}{16} = (1,2b) : \frac{20}{3}$$ $$\frac{43,2}{16} = (1,2b) : \frac{20}{3}$$ $$2,7 = (1,2b) : \frac{20}{3}$$ $$1,2b = 2,7 \cdot \frac{20}{3}$$ $$1,2b = 2,7 \cdot 6\frac{2}{3}$$ $$1,2b = 18$$ $$b = \frac{18}{1,2} = \frac{180}{12} = 15$$ Ответ: b = 15
5. д) $$\frac{19\frac{4}{9}}{13} = \frac{1,3z-0,72}{0,72}$$ $$\frac{\frac{175}{9}}{13} = \frac{1,3z-0,72}{0,72}$$ $$\frac{175}{9 \cdot 13} = \frac{1,3z-0,72}{0,72}$$ $$\frac{175}{117} = \frac{1,3z-0,72}{0,72}$$ $$1,3z - 0,72 = \frac{175 \cdot 0,72}{117}$$ $$1,3z - 0,72 = \frac{126}{117}$$ $$1,3z - 0,72 = \frac{14}{13}$$ $$1,3z - 0,72 = 1\frac{1}{13}$$ $$1,3z - 0,72 \approx 1,077$$ $$1,3z = 1,077 + 0,72$$ $$1,3z = 1,797$$ $$z = \frac{1,797}{1,3} \approx 1,382$$ Ответ: z \approx 1,382