Cho \({\rm{C}} = \frac{1}{5} + \frac{2}{{11}} - \frac{2}{7} - \left( {\frac{{ - 3}}{4}} \right) + \frac{{38}}{{35}} - \frac{{85}}{{44}} + \frac{{ - 4}}{3}.\) Xét tính đúng/sai của mỗi khẳng đ

Đáp án: a) Đúng. b) Đúng. c) Sai. d) Sai.

a) Đúng. \({\rm{C}} = \frac{1}{5} + \frac{2}{{11}} - \frac{2}{7} - \left( {\frac{{ - 3}}{4}} \right) + \frac{{38}}{{35}} - \frac{{85}}{{44}} + \frac{{ - 4}}{3}\)

\( = \frac{1}{5} + \frac{2}{{11}} - \frac{2}{7} + \frac{3}{4} + \frac{{38}}{{35}} - \frac{{85}}{{44}} - \frac{4}{3}\)

\( = \left( {\frac{1}{5} - \frac{2}{7} + \frac{{38}}{{35}}} \right) + \left( {\frac{2}{{11}} + \frac{3}{4} - \frac{{85}}{{44}}} \right) - \frac{4}{3}.\)

Vậy a) đúng.

b) Đúng. \(\frac{1}{5} - \frac{2}{7} + \frac{{38}}{{35}} = \frac{7}{{35}} - \frac{{10}}{{35}} + \frac{{38}}{{35}} = \frac{{35}}{{35}} = 1.\) Vậy b) đúng.

c) Sai. \(\frac{2}{{11}} + \frac{3}{4} - \frac{{85}}{{44}} = \frac{8}{{44}} + \frac{{33}}{{44}} - \frac{{85}}{{44}} = \frac{{ - 44}}{{44}} = - 1.\) Vậy c) sai.

d) Sai. \({\rm{C}} = \left( {\frac{1}{5} - \frac{2}{7} + \frac{{38}}{{35}}} \right) + \left( {\frac{2}{{11}} + \frac{3}{4} - \frac{{85}}{{44}}} \right) - \frac{4}{3}\)

\( = 1 + \left( { - 1} \right) - \frac{4}{3} = \frac{{ - 4}}{3}\).

Vậy C < 0.