Вычислите:
$$\cfrac{\left(5\cfrac{4}{45} - 4\cfrac{1}{6}\right): 5\cfrac{8}{15}}{\left(4\cfrac{2}{3} + 0,75\right) \cdot 3\cfrac{9}{13}} \cdot 34\cfrac{2}{7}+\cfrac{0,3:0,01}{70}+\cfrac{2}{7}$$
Решение:
$$ 5\frac{4}{45} - 4\frac{1}{6} = 1\frac{8}{90} - \frac{15}{90} = \frac{98}{90} - \frac{15}{90} = \frac{83}{90} $$
$$ \frac{83}{90} : 5\frac{8}{15} = \frac{83}{90} : \frac{5 \cdot 15+8}{15} = \frac{83}{90} \cdot \frac{15}{83} = \frac{15}{90} = \frac{1}{6}$$
$$ 4\frac{2}{3} + 0,75 = 4\frac{2}{3} + \frac{3}{4} = 4\frac{8}{12} + \frac{9}{12} = \frac{56}{12} + \frac{9}{12} = \frac{65}{12} $$
$$ \frac{65}{12} \cdot \frac{3 \cdot 13+9}{13} = \frac{65}{12} \cdot \frac{48}{13} = 5 \cdot 4 = 20 $$
$$ \frac{\frac{1}{6}}{20} \cdot 34\frac{2}{7}= \frac{1}{120} \cdot \frac{34 \cdot 7+2}{7} = \frac{240}{120 \cdot 7}= \frac{2}{7}$$
$$\frac{0,3:0,01}{70} = \frac{0,3:\cfrac{1}{100}}{70} = \frac{0,3 \cdot 100}{70} = \frac{3}{7}$$
$$\frac{2}{7}+\frac{3}{7} +\frac{2}{7} = 1$$