15. 1) \(7\frac{2}{3}a-1,5b-\frac{5}{6}c\), вычислить при \(a=\frac{5}{46}\); \(b=-\frac{4}{9}\); \(c=\frac{14}{15}\). 2) \(4\frac{2}{9}a+8\frac{1}{6}b+\frac{14}{81}c\), вычислить при \(a=\frac{3}{19}\); \(b=-3\frac{3}{7}\); \(c=1\frac{13}{14}\). 3) \(1,4a-\frac{51}{92}b+\frac{11}{25}c\), вычислить при \(a=\frac{25}{42}\); \(b=1\frac{6}{17}\); \(c=-1\frac{17}{33}\).

1)

Подставим значения переменных:

\[7\frac{2}{3}a-1,5b-\frac{5}{6}c=\frac{23}{3}\cdot\frac{5}{46}-\frac{3}{2}\cdot\left(-\frac{4}{9}\right)-\frac{5}{6}\cdot\frac{14}{15}.\]

\[=\frac{5}{6}+\frac{2}{3}-\frac{7}{9}=\frac{15+12-14}{18}=\frac{13}{18}.\]

2)

\[4\frac{2}{9}a+8\frac{1}{6}b+\frac{14}{81}c=\frac{38}{9}\cdot\frac{3}{19}+\frac{49}{6}\cdot\left(-\frac{24}{7}\right)+\frac{14}{81}\cdot\frac{27}{14}.\]

\[=\frac{2}{3}-28+\frac{1}{3}=1-28=-27.\]

3)

\[1,4a-\frac{51}{92}b+\frac{11}{25}c=\frac{7}{5}\cdot\frac{25}{42}-\frac{51}{92}\cdot\frac{23}{17}+\frac{11}{25}\cdot\left(-\frac{50}{33}\right).\]

\[=\frac{5}{6}-\frac{3}{4}-\frac{2}{3}=\frac{10-9-8}{12}=-\frac{7}{12}.\]

Ответ: 1) \(\frac{13}{18}\); 2) \(-27\); 3) \(-\frac{7}{12}\).