Cho \({\rm{D}} = \frac{{ - 5}}{{18}}:\left( {\frac{1}{{11}} - \frac{{13}}{{22}}} \right) - \frac{5}{{18}}:\left( {\frac{1}{6} - \frac{1}{2}} \right) - \frac{{25}}{{18}}\). Xét tính đúng/sai c

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

a) Đúng. \(\frac{1}{{11}} - \frac{{13}}{{22}} = \frac{2}{{22}} - \frac{{13}}{{22}} = \frac{{ - 11}}{{22}} = \frac{{ - 1}}{2}.\) Vậy a) đúng.

b) Sai. \(\frac{1}{6} - \frac{1}{2} = \frac{1}{6} - \frac{3}{6} = \frac{{ - 2}}{6} = \frac{{ - 1}}{3}.\) Vậy b) sai.

c) Sai. \({\rm{D}} = \frac{{ - 5}}{{18}}:\left( {\frac{1}{{11}} - \frac{{13}}{{22}}} \right) - \frac{5}{{18}}:\left( {\frac{1}{6} - \frac{1}{2}} \right) - \frac{{25}}{{18}}\)

\( = \frac{{ - 5}}{{18}}:\frac{{ - 1}}{2} - \frac{5}{{18}}:\frac{{ - 1}}{3} - \frac{{25}}{{18}}\)

\( = \frac{5}{{18}} \cdot 2 - \frac{5}{{18}} \cdot \left( { - 3} \right) - 5 \cdot \frac{5}{{18}}\)

\( = \frac{5}{{18}} \cdot 2 + \frac{5}{{18}} \cdot 3 - 5 \cdot \frac{5}{{18}}.\)

Vậy c) sai.

d) Đúng. \({\rm{D}} = \frac{5}{{18}} \cdot 2 + \frac{5}{{18}} \cdot 3 - 5 \cdot \frac{5}{{18}} = \frac{5}{{18}} \cdot \left( {2 + 3 - 5} \right) = \frac{5}{{18}} \cdot 0 = 0.\)

Vậy D = 0.