584. Выполните действия: 1) (3/4 + 1/20) · 1/2; 2) (7/12 − 1/3) · 16/19; 3) (7 3/5 − 2 4/15) · 9/32; 4) (11/24 + 1/6) · 1 3/5; 5) (5 1/2 + 2 3/5) · 5/9; 6) (7 − 2 5/16) · 4/25.

Question

Вопрос:

Accepted Answer

\(\left(\frac{3}{4}+\frac{1}{20}\right)\cdot\frac{1}{2}=\left(\frac{15}{20}+\frac{1}{20}\right)\cdot\frac{1}{2}=\frac{16}{20}\cdot\frac{1}{2}=\frac{4}{5}\cdot\frac{1}{2}=\frac{2}{5}\).
\(\left(\frac{7}{12}-\frac{1}{3}\right)\cdot\frac{16}{19}=\left(\frac{7}{12}-\frac{4}{12}\right)\cdot\frac{16}{19}=\frac{3}{12}\cdot\frac{16}{19}=\frac{1}{4}\cdot\frac{16}{19}=\frac{4}{19}\).
\(\left(7\frac{3}{5}-2\frac{4}{15}\right)\cdot\frac{9}{32}=\left(7\frac{9}{15}-2\frac{4}{15}\right)\cdot\frac{9}{32}=5\frac{5}{15}\cdot\frac{9}{32}=\frac{16}{3}\cdot\frac{9}{32}=\frac{3}{2}=1\frac{1}{2}\).
\(\left(\frac{11}{24}+\frac{1}{6}\right)\cdot1\frac{3}{5}=\left(\frac{11}{24}+\frac{4}{24}\right)\cdot\frac{8}{5}=\frac{15}{24}\cdot\frac{8}{5}=\frac{5}{8}\cdot\frac{8}{5}=1\).
\(\left(5\frac{1}{2}+2\frac{3}{5}\right)\cdot\frac{5}{9}=\left(\frac{11}{2}+\frac{13}{5}\right)\cdot\frac{5}{9}=\left(\frac{55}{10}+\frac{26}{10}\right)\cdot\frac{5}{9}=\frac{81}{10}\cdot\frac{5}{9}=\frac{9}{2}=4\frac{1}{2}\).
\(\left(7-2\frac{5}{16}\right)\cdot\frac{4}{25}=\left(\frac{112}{16}-\frac{37}{16}\right)\cdot\frac{4}{25}=\frac{75}{16}\cdot\frac{4}{25}=\frac{3}{4}\).

Ответ: 1) \(\frac{2}{5}\); 2) \(\frac{4}{19}\); 3) \(1\frac{1}{2}\); 4) \(1\); 5) \(4\frac{1}{2}\); 6) \(\frac{3}{4}\).