51. Найдите значение выражения: 1) 12 : 3 3/8 − 1 1/4 : 15/32; 2) 1 31/35 : (2 − 8/9 · 1 19/45); 3) (1 1/35 : 4/5 − 1 8/35) · 3; 4) (7 − 1 5/9 : 7/24) : 20/27.

Question

Accepted Answer

\(12 : 3\frac{3}{8} - 1\frac{1}{4} : \frac{15}{32}\)
\(3\frac{3}{8}=\frac{27}{8},\quad 1\frac{1}{4}=\frac{5}{4}\).
\(12 : \frac{27}{8}=12\cdot\frac{8}{27}=\frac{32}{9}\).
\(\frac{5}{4}:\frac{15}{32}=\frac{5}{4}\cdot\frac{32}{15}=\frac{8}{3}\).
\(\frac{32}{9}-\frac{8}{3}=\frac{32}{9}-\frac{24}{9}=\frac{8}{9}\).
\(1\frac{31}{35}:\left(2-\frac{8}{9}\cdot1\frac{19}{45}\right)\)
\(1\frac{31}{35}=\frac{66}{35},\quad 1\frac{19}{45}=\frac{64}{45}\).
\(\frac{8}{9}\cdot\frac{64}{45}=\frac{512}{405}\), поэтому \(2-\frac{512}{405}=\frac{298}{405}\).
\(\frac{66}{35}:\frac{298}{405}=\frac{66}{35}\cdot\frac{405}{298}=\frac{2673}{1043}\).
\(\left(1\frac{1}{35}:\frac{4}{5}-1\frac{8}{35}\right)\cdot3\)
\(1\frac{1}{35}=\frac{36}{35},\quad 1\frac{8}{35}=\frac{43}{35}\).
\(\frac{36}{35}:\frac{4}{5}=\frac{36}{35}\cdot\frac{5}{4}=\frac{9}{7}=\frac{45}{35}\).
\(\left(\frac{45}{35}-\frac{43}{35}\right)\cdot3=\frac{2}{35}\cdot3=\frac{6}{35}\).
\(\left(7-1\frac{5}{9}:\frac{7}{24}\right):\frac{20}{27}\)
\(1\frac{5}{9}=\frac{14}{9}\).
\(\frac{14}{9}:\frac{7}{24}=\frac{14}{9}\cdot\frac{24}{7}=\frac{16}{3}\).
\(7-\frac{16}{3}=\frac{5}{3}\).
\(\frac{5}{3}:\frac{20}{27}=\frac{5}{3}\cdot\frac{27}{20}=\frac{9}{4}\).

Ответ: 1) \(\frac{8}{9}\); 2) \(\frac{2673}{1043}\); 3) \(\frac{6}{35}\); 4) \(\frac{9}{4}\).