2.539 Вычислите значение дробного выражения: a) \(\frac{2,16 \cdot 0,55 \cdot 4,5}{2,7 \cdot 0,15 \cdot 1,2};\) б) \(\frac{2\frac{2}{3} \cdot 2\frac{3}{7} \cdot \frac{9}{11}}{3\frac{3}{7} \cdot 5\frac{2}{3} \cdot \frac{1}{11}};\) в) \(\frac{11-\frac{1}{4}}{21\frac{1}{3} \cdot 5-\frac{1}{4}};\) г) \(\frac{30,6 : 14\frac{4}{7}}{1-\frac{5}{16}}.\)

• a) \(\frac{2,16 \cdot 0,55 \cdot 4,5}{2,7 \cdot 0,15 \cdot 1,2} = \frac{216 \cdot 55 \cdot 45}{27 \cdot 15 \cdot 12} \cdot \frac{1}{100} = \frac{8 \cdot 11 \cdot 3}{1 \cdot 1 \cdot 4} \cdot \frac{1}{10} = \frac{264}{40} = \frac{66}{10} = 6,6\)
• б) \(\frac{2\frac{2}{3} \cdot 2\frac{3}{7} \cdot \frac{9}{11}}{3\frac{3}{7} \cdot 5\frac{2}{3} \cdot \frac{1}{11}} = \frac{\frac{8}{3} \cdot \frac{17}{7} \cdot \frac{9}{11}}{\frac{24}{7} \cdot \frac{17}{3} \cdot \frac{1}{11}} = \frac{8 \cdot 17 \cdot 9 \cdot 7 \cdot 3 \cdot 11}{3 \cdot 7 \cdot 11 \cdot 24 \cdot 17 \cdot 1} = \frac{8 \cdot 9}{3 \cdot 24} = \frac{72}{72} = 1\)
• в) \(\frac{11-\frac{1}{4}}{21\frac{1}{3} \cdot 5-\frac{1}{4}} = \frac{\frac{44-1}{4}}{\frac{64}{3} \cdot \frac{19}{4}} = \frac{\frac{43}{4}}{\frac{16}{3} \cdot 19} = \frac{43 \cdot 3}{4 \cdot 16 \cdot 19} = \frac{129}{1216} \approx 0,106\)
• г) \(\frac{30,6 : 14\frac{4}{7}}{1-\frac{5}{16}} = \frac{30,6 : \frac{102}{7}}{\frac{16-5}{16}} = \frac{\frac{306}{10} : \frac{102}{7}}{\frac{11}{16}} = \frac{\frac{306}{10} \cdot \frac{7}{102}}{\frac{11}{16}} = \frac{\frac{3 \cdot 7}{10}}{\frac{11}{16}} = \frac{21 \cdot 16}{10 \cdot 11} = \frac{336}{110} = \frac{168}{55} \approx 3,055\)

Ответ: a) 6,6; б) 1; в) \(\frac{129}{1216}\); г) \(\frac{168}{55}\)