5. Старый банк. Найдите значение выражения: 1) (10/13 + 15/4) · 26/5; 2) (1/6 + 1/4) · 9; 3) (1 11/16 − 3 7/8) · 4; 4) 3 3/8 : (1 35/48 − 2 7/24); 5) 1/(1/36 + 1/45); 6) 21 · (1/7)^2 − 10 · 1/7.

Question

Вопрос:

Accepted Answer

\(\left(\frac{10}{13}+\frac{15}{4}\right)\cdot\frac{26}{5}=\left(\frac{40}{52}+\frac{195}{52}\right)\cdot\frac{26}{5}=\frac{235}{52}\cdot\frac{26}{5}=\frac{47}{2}\).
\(\left(\frac{1}{6}+\frac{1}{4}\right)\cdot9=\frac{5}{12}\cdot9=\frac{15}{4}=3\frac{3}{4}\).
\(\left(1\frac{11}{16}-3\frac{7}{8}\right)\cdot4=\left(\frac{27}{16}-\frac{62}{16}\right)\cdot4=-\frac{35}{16}\cdot4=-\frac{35}{4}=-8\frac{3}{4}\).
\(3\frac{3}{8}:\left(1\frac{35}{48}-2\frac{7}{24}\right)=\frac{27}{8}:\left(\frac{83}{48}-\frac{55}{24}\right)=\frac{27}{8}:\left(\frac{83}{48}-\frac{110}{48}\right)=\frac{27}{8}:\left(-\frac{27}{48}\right)=-6\).
\(\frac{1}{\frac{1}{36}+\frac{1}{45}}=\frac{1}{\frac{5}{180}+\frac{4}{180}}=\frac{1}{\frac{1}{20}}=20\).
\(21\cdot\left(\frac{1}{7}\right)^2-10\cdot\frac{1}{7}=21\cdot\frac{1}{49}-\frac{10}{7}=\frac{3}{7}-\frac{10}{7}=-1\).

Ответ: 1) \(\frac{47}{2}\); 2) \(3\frac{3}{4}\); 3) \(-8\frac{3}{4}\); 4) \(-6\); 5) 20; 6) \(-1\).