23. Вычислите: а) 5 2/5 · 1 1/9 − 4 4/7 · 1 3/4; б) 7 1/3 : 1 2/9 + 4 8/9 · 9/11; в) 2 1/3 : (2 − 17 1/3 : 13); г) (3 3/8 · 1 7/9 − 3) : 3/5.

а)

\(5\frac{2}{5}=\frac{27}{5}\), \(1\frac{1}{9}=\frac{10}{9}\), \(4\frac{4}{7}=\frac{32}{7}\), \(1\frac{3}{4}=\frac{7}{4}\).

\(\frac{27}{5}\cdot\frac{10}{9}-\frac{32}{7}\cdot\frac{7}{4}=6-8=-2\).

б)

\(7\frac{1}{3}=\frac{22}{3}\), \(1\frac{2}{9}=\frac{11}{9}\), \(4\frac{8}{9}=\frac{44}{9}\).

\(\frac{22}{3}:\frac{11}{9}+\frac{44}{9}\cdot\frac{9}{11}=6+4=10\).

в)

\(2\frac{1}{3}=\frac{7}{3}\), \(17\frac{1}{3}=\frac{52}{3}\).

\(\frac{52}{3}:13=\frac{4}{3}\), поэтому

\(\frac{7}{3}:\left(2-\frac{4}{3}\right)=\frac{7}{3}:\frac{2}{3}=\frac{7}{2}=3\frac{1}{2}\).

г)

\(3\frac{3}{8}=\frac{27}{8}\), \(1\frac{7}{9}=\frac{16}{9}\).

\(\left(\frac{27}{8}\cdot\frac{16}{9}-3\right):\frac{3}{5}=(6-3):\frac{3}{5}=3\cdot\frac{5}{3}=5\).

Ответ: а) −2; б) 10; в) 3 1/2; г) 5.