PHẦN II. TỰ LUẬN

Thực hiện phép tính (tính hợp lí nếu có thể):

a) \[25\% - 1\frac{1}{4} + 0,2:\frac{6}{5}\];

b) \[\frac{8}{9} + \frac{1}{9}.\frac{2}{9} + \frac{1}{9}.\frac{7}{9}\];

c) \(\frac{5}{{39}}\,\, \cdot \,\left( {\,7\frac{4}{5}\,\, \cdot \,1\frac{2}{3}\,\, + \,\,8\frac{1}{3}\, \cdot \,7\frac{4}{5}\,} \right)\)

Hướng dẫn giải:

a) \[25\% - 1\frac{1}{4} + 0,2:\frac{6}{5}\]

\[ = \frac{{25}}{{100}} - \frac{5}{4} + \frac{1}{5}:\frac{6}{5}\]

\[ = \frac{1}{4} - \frac{5}{4} + \frac{1}{5}.\frac{5}{6}\]

\[ = \left( {\frac{1}{4} - \frac{5}{4}} \right) + \frac{{1.5}}{{5.6}}\]

\[ = \frac{{ - 4}}{4} + \frac{1}{6}\]

\[ = - 1 + \frac{1}{6}\]

\[ = \frac{{ - 6}}{6} + \frac{1}{6}\]

\[ = \frac{{ - 5}}{6}\]

b) \[\frac{8}{9} + \frac{1}{9}.\frac{2}{9} + \frac{1}{9}.\frac{7}{9}\]

\[ = \frac{8}{9} + \left( {\frac{1}{9}.\frac{2}{9} + \frac{1}{9}.\frac{7}{9}} \right)\]

\[ = \frac{8}{9} + \frac{1}{9}.\left( {\frac{2}{9} + \frac{7}{9}} \right)\]

\[ = \frac{8}{9} + \frac{1}{9}.\frac{9}{9}\]

\[ = \frac{8}{9} + \frac{1}{9}.1\]

\( = \frac{8}{9} + \frac{1}{9}\)

\( = \frac{9}{9}\)

= 1.

c) \(\frac{5}{{39}}{\mkern 1mu} {\mkern 1mu} \, \cdot {\mkern 1mu} \,\left( {{\mkern 1mu} 7\frac{4}{5}\,{\mkern 1mu} {\mkern 1mu} \cdot \,1\frac{2}{3}{\mkern 1mu} {\mkern 1mu} \, + {\mkern 1mu} {\mkern 1mu} \,8\frac{1}{3}\,\, \cdot \,\,7\frac{4}{5}{\mkern 1mu} } \right)\)

\( = \,{\mkern 1mu} \frac{5}{{39}}{\mkern 1mu} {\mkern 1mu}  \cdot \,{\mkern 1mu} \left[ {{\mkern 1mu} 7{\mkern 1mu} \frac{4}{5}\,{\mkern 1mu} \cdot \,{\mkern 1mu} \left( {1\frac{2}{3} + {\mkern 1mu} {\mkern 1mu} 8\frac{1}{3}{\mkern 1mu} } \right)} \right]\)

\( = \,{\mkern 1mu} \frac{5}{{39}}{\mkern 1mu} \, \cdot \,\frac{{39}}{5}{\mkern 1mu} \,\left( {1 + \frac{2}{3} + 8 + \frac{1}{3}} \right){\mkern 1mu} \)

\( = \,{\mkern 1mu} {\mkern 1mu} \frac{{5.39}}{{39.5}}{\mkern 1mu} {\mkern 1mu} \cdot\,{\mkern 1mu} \,\left( {9 + \frac{2}{3} + \frac{1}{3}} \right){\mkern 1mu} \)

\( = \,1{\mkern 1mu} \cdot\,\left( {9\, + \frac{3}{3}} \right){\mkern 1mu} \)

= 9 + 1

= 10.