221. Найдите значение выражения: а) 61/64 − (7/12 − 5/14) · (13/16 + 1/2); б) (1 − 11/17) · (3/4 − 5/12 + 11/18); в) (3,5 − 2,9) · (4 1/22 − 3 7/33); г) (5 3/14 − 4 4/7) · (3 11/15 − 1 2/5).

Question

Вопрос:

Accepted Answer

а)

\(\frac{7}{12}-\frac{5}{14}=\frac{19}{84}\), а \(\frac{13}{16}+\frac{1}{2}=\frac{21}{16}\).

\(\frac{61}{64}-\frac{19}{84}\cdot\frac{21}{16}=\frac{61}{64}-\frac{19}{64}=\frac{42}{64}=\frac{21}{32}\).

б)

\(1-\frac{11}{17}=\frac{6}{17}\).

\(\frac{3}{4}-\frac{5}{12}+\frac{11}{18}=\frac{27-15+22}{36}=\frac{34}{36}=\frac{17}{18}\).

\(\frac{6}{17}\cdot\frac{17}{18}=\frac{1}{3}\).

в)

\(3{,}5-2{,}9=0{,}6=\frac{3}{5}\).

\(4\frac{1}{22}-3\frac{7}{33}=\frac{89}{22}-\frac{106}{33}=\frac{267-212}{66}=\frac{55}{66}=\frac{5}{6}\).

\(\frac{3}{5}\cdot\frac{5}{6}=\frac{1}{2}\).

г)

\(5\frac{3}{14}-4\frac{4}{7}=\frac{73}{14}-\frac{64}{14}=\frac{9}{14}\).

\(3\frac{11}{15}-1\frac{2}{5}=\frac{56}{15}-\frac{21}{15}=\frac{7}{3}\).

\(\frac{9}{14}\cdot\frac{7}{3}=\frac{3}{2}=1\frac{1}{2}\).

Ответ: а) \(\frac{21}{32}\); б) \(\frac{1}{3}\); в) \(\frac{1}{2}\); г) \(1\frac{1}{2}\).