Thực hiện phép tính:

a) (15,25 + 3,75).4 + (20,71 + 5,29).5;

b) \[\frac{4}{{20}} + \frac{{16}}{{42}} + \frac{6}{{15}} + \frac{{ - 3}}{5} + \frac{2}{{21}} + \frac{{ - 10}}{{21}} + \frac{3}{{20}}\];

c) \[\frac{5}{{11}}.\frac{5}{7} + \frac{5}{{11}}.\frac{2}{7} + \frac{6}{{11}};\]

d) \(\left( { - \frac{5}{{24}} + 0,75 + \frac{7}{{12}}} \right):\left( { - 2\frac{1}{8}} \right)\).

Hướng dẫn giải:

a) (15,25 + 3,75).4 + (20,71 + 5,29).5

= 19.4 + 26.5

= 76 + 130

= 206

b) \[\frac{4}{{20}} + \frac{{16}}{{42}} + \frac{6}{{15}} + \frac{{ - 3}}{5} + \frac{2}{{21}} + \frac{{ - 10}}{{21}} + \frac{3}{{20}}\]

\[ = \frac{1}{5} + \frac{8}{{21}} + \frac{2}{5} + \frac{{ - 3}}{5} + \frac{2}{{21}} + \frac{{ - 10}}{{21}} + \frac{3}{{20}}\]

\[ = \frac{1}{5} + \frac{2}{5} + \frac{{ - 3}}{5} + \frac{8}{{21}} + \frac{2}{{21}} + \frac{{ - 10}}{{21}} + \frac{3}{{20}}\]

\[ = \left( {\frac{1}{5} + \frac{2}{5} + \frac{{ - 3}}{5}} \right) + \left( {\frac{8}{{21}} + \frac{2}{{21}} + \frac{{ - 10}}{{21}}} \right) + \frac{3}{{20}}\]

\[ = \frac{{1 + 2 + \left( { - 3} \right)}}{5} + \frac{{8 + 2 + \left( { - 10} \right)}}{{21}} + \frac{3}{{20}}\]

\( = \frac{0}{5} + \frac{0}{{21}} + \frac{3}{{20}}\)

\( = 0 + 0 + \frac{3}{{20}}\)

\[ = \frac{3}{{20}}\]

c) \[\frac{5}{{11}}.\frac{5}{7} + \frac{5}{{11}}.\frac{2}{7} + \frac{6}{{11}}\]

\[ = \left( {\frac{5}{{11}}.\frac{5}{7} + \frac{5}{{11}}.\frac{2}{7}} \right) + \frac{6}{{11}}\]

\[ = \frac{5}{{11}}.\left( {\frac{5}{7} + \frac{2}{7}} \right) + \frac{6}{{11}}\]

\( = \frac{5}{{11}}.\frac{7}{7} + \frac{6}{{11}}\)

\( = \frac{5}{{11}}.1 + \frac{6}{{11}}\)

\[ = \frac{5}{{11}} + \frac{6}{{11}}\]

\( = \frac{{5 + 6}}{{11}}\)

\( = \frac{{11}}{{11}}\)

= 1.

d) \(\left( { - \frac{5}{{24}} + 0,75 + \frac{7}{{12}}} \right):\left( { - 2\frac{1}{8}} \right)\)

\( = \left( { - \frac{5}{{24}} + \frac{3}{4} + \frac{7}{{12}}} \right):\left( { - \frac{{17}}{8}} \right)\)

\( = \left( { - \frac{5}{{24}} + \frac{{18}}{{24}} + \frac{{14}}{{24}}} \right):\left( { - \frac{{17}}{8}} \right)\)

\( = \frac{{ - 5 + 18 + 14}}{{24}}:\left( { - \frac{{17}}{8}} \right)\)

\( = \frac{9}{8}.\left( { - \frac{8}{{17}}} \right)\)

\[ = \frac{{9.\left( { - 8} \right)}}{{8.17}}\]

\[ = - \frac{9}{{17}}\]