Вопрос:
Вычислите: а) 2 3/4 · 5 7/33; б) −3 1/2 · 2 2/5; в) −4 5/7 · (−2 6/11); г) −3 1/2 · 2 2/7; д) 4 1/3 : 2 5/6; е) −7 3/8 : (−2 1/16); ж) −1 1/3 : 3 1/6; з) 4 1/5 : 7 1/25.
Ответ:
- \(2\frac{3}{4}\cdot5\frac{7}{33}=\frac{11}{4}\cdot\frac{172}{33}=\frac{473}{33}=14\frac{11}{33}=14\frac{1}{3}\).
- \(-3\frac{1}{2}\cdot2\frac{2}{5}=-\frac{7}{2}\cdot\frac{12}{5}=-\frac{42}{5}=-8\frac{2}{5}\).
- \(-4\frac{5}{7}\cdot\left(-2\frac{6}{11}\right)=-\frac{33}{7}\cdot\left(-\frac{28}{11}\right)=12\).
- \(-3\frac{1}{2}\cdot2\frac{2}{7}=-\frac{7}{2}\cdot\frac{16}{7}=-8\).
- \(4\frac{1}{3}:2\frac{5}{6}=\frac{13}{3}:\frac{17}{6}=\frac{13}{3}\cdot\frac{6}{17}=\frac{26}{17}=1\frac{9}{17}\).
- \(-7\frac{3}{8}:\left(-2\frac{1}{16}\right)=-\frac{59}{8}:\left(-\frac{33}{16}\right)=\frac{59}{8}\cdot\frac{16}{33}=\frac{118}{33}=3\frac{19}{33}\).
- \(-1\frac{1}{3}:3\frac{1}{6}=-\frac{4}{3}:\frac{19}{6}=-\frac{4}{3}\cdot\frac{6}{19}=-\frac{8}{19}\).
- \(4\frac{1}{5}:7\frac{1}{25}=\frac{21}{5}:\frac{176}{25}=\frac{21}{5}\cdot\frac{25}{176}=\frac{105}{176}\).