Найдите значение выражения: а) \(\frac{2,8}{16,8};\) б) \(2\frac{1}{4}:\frac{3\frac{2}{3}}{1\frac{1}{8}};\) в) \(\frac{1,21}{3\frac{2}{3}}.\)

Решение:

1. a) \(\frac{2,8}{16,8} = \frac{28}{168} = \frac{1}{6}\)
2. б) \(2\frac{1}{4}:\frac{3\frac{2}{3}}{1\frac{1}{8}} = \frac{9}{4} : \frac{\frac{11}{3}}{\frac{9}{8}} = \frac{9}{4} : (\frac{11}{3} \cdot \frac{8}{9}) = \frac{9}{4} : \frac{11 \cdot 8}{3 \cdot 9} = \frac{9}{4} : \frac{11 \cdot 8}{3 \cdot 9} = \frac{9}{4} : \frac{88}{27} = \frac{9}{4} \cdot \frac{27}{88} = \frac{9 \cdot 27}{4 \cdot 88} = \frac{243}{352}\)
3. в) \(\frac{1,21}{3\frac{2}{3}} = \frac{1,21}{\frac{11}{3}} = 1,21 : \frac{11}{3} = 1,21 \cdot \frac{3}{11} = \frac{121}{100} \cdot \frac{3}{11} = \frac{11}{100} \cdot 3 = \frac{33}{100} = 0,33\)

Ответ: а) \(\frac{1}{6}\); б) \(\frac{243}{352}\); в) 0,33