Вопрос:

Найдите значение выражения: 1) $$\frac{(152\frac{3}{4}-148\frac{3}{8})\cdot 0,3}{0,2}$$; 2) $$\frac{(6,6-3\frac{3}{14})\cdot 5\frac{5}{6}}{(21-1,25):2,5}$$; 3) $$\frac{215\frac{9}{16}-208\frac{3}{4}+0,5}{0,0001:0,005}$$

Ответ:

Решение:

1)

$$\frac{(152\frac{3}{4}-148\frac{3}{8})\cdot 0,3}{0,2} = \frac{(\frac{611}{4}-\frac{1187}{8})\cdot 0,3}{0,2} =$$ $$\frac{(\frac{1222}{8}-\frac{1187}{8})\cdot 0,3}{0,2} = \frac{\frac{35}{8}\cdot 0,3}{0,2} = \frac{\frac{35}{8}\cdot \frac{3}{10}}{\frac{2}{10}} = $$ $$\frac{\frac{105}{80}}{\frac{2}{10}} = \frac{105}{80} \cdot \frac{10}{2} = \frac{105}{80} \cdot 5 = \frac{105}{16} = 6\frac{9}{16}$$

2)

$$\frac{(6,6-3\frac{3}{14})\cdot 5\frac{5}{6}}{(21-1,25):2,5} = \frac{(6,6-\frac{45}{14})\cdot \frac{35}{6}}{(19,75):2,5} = $$ $$\frac{(\frac{66}{10}-\frac{45}{14})\cdot \frac{35}{6}}{(19,75):2,5} = \frac{(\frac{33}{5}-\frac{45}{14})\cdot \frac{35}{6}}{(19,75):2,5} = $$ $$\frac{(\frac{462}{70}-\frac{225}{70})\cdot \frac{35}{6}}{7,9} = \frac{\frac{237}{70}\cdot \frac{35}{6}}{7,9} = \frac{\frac{237}{2\cdot 35}\cdot \frac{35}{6}}{7,9} = $$ $$\frac{\frac{237}{12}}{7,9} = \frac{237}{12} : 7,9 = \frac{237}{12} : \frac{79}{10} = \frac{237}{12} \cdot \frac{10}{79} = $$ $$\frac{237}{6} \cdot \frac{5}{79} = \frac{79 \cdot 3}{6} \cdot \frac{5}{79} = \frac{3}{6} \cdot 5 = \frac{1}{2} \cdot 5 = 2,5$$

3)

$$\frac{215\frac{9}{16}-208\frac{3}{4}+0,5}{0,0001:0,005} = \frac{215\frac{9}{16}-208\frac{12}{16}+\frac{1}{2}}{0,0001:0,005} = $$ $$\frac{214\frac{25}{16}-208\frac{12}{16}}{0,0001:0,005} = \frac{6\frac{13}{16}+\frac{8}{16}}{\frac{1}{10000}:\frac{5}{1000}} = \frac{6\frac{21}{16}}{\frac{1}{10000} \cdot \frac{1000}{5}} = $$ $$\frac{6\frac{21}{16}}{\frac{1}{10 \cdot 5}} = \frac{6\frac{21}{16}}{\frac{1}{50}} = \frac{\frac{117}{16}}{\frac{1}{50}} = \frac{117}{16} \cdot 50 = \frac{117}{8} \cdot 25 = \frac{2925}{8} = 365\frac{5}{8}$$

Ответ:

1) $$6\frac{9}{16}$$

2) $$2,5$$

3) $$365\frac{5}{8}$$

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