Đề bài
a] \[{3 \over 4} + {{ - 5} \over {13}}.{{13} \over {10}}\]
b] \[\left[ {{{ - 3} \over 7} + {1 \over 4}} \right]:{{15} \over {28}}\]
c] \[2{1 \over 2}:\left[ {{5 \over 2} - 3{3 \over 4}} \right] + {\left[ {{{ - 1} \over 2}} \right]^2}\]
d] \[\left[ {3 - 2{3 \over 5}} \right].4{1 \over 6} - 1{3 \over 5}:1{1 \over {15}}\]
e] \[{5 \over 6} + 6{5 \over 6}\left[ {11{5 \over {20}} - 9{1 \over 4}} \right]:8{1 \over 3}\]
f] \[{{11} \over 9}.{{15} \over 4} - {{11} \over 4}.{7 \over 9} - {{11} \over 9}.{5 \over 4}\]
g] \[\left[ { - 3,6 + 5{1 \over 3}:0,4} \right].{{10} \over {73}} - {1 \over 3}:\left[ {4,8 - 5{1 \over 2}} \right]\]
Lời giải chi tiết
\[\eqalign{ & a]{3 \over 4} + {{ - 5} \over {13}}.{{13} \over {10}} = {3 \over 4} + {{ - 1} \over 2} = {3 \over 4} + {{ - 2} \over 4} = {1 \over 4} \cr & b]\left[ {{{ - 3} \over 7} + {1 \over 4}} \right]:{{15} \over {28}} = \left[ {{{ - 12} \over {28}} + {7 \over {28}}} \right]:{{15} \over {28}} = {{ - 5} \over {28}}.{{28} \over {15}} = {{ - 1} \over 3} \cr & c]2{1 \over 2}:\left[ {{5 \over 2} - 3{3 \over 4}} \right] + {\left[ {{{ - 1} \over 2}} \right]^2} = {5 \over 2}:\left[ {{5 \over 2} - {{15} \over 4}} \right] + {1 \over 4} \cr & = {5 \over 2}:\left[ {{{10} \over 4} - {{15} \over 4}} \right] + {1 \over 4} = {5 \over 2}:{{ - 5} \over 4} + {1 \over 4} = {5 \over 2}.{{ - 4} \over 5} + {1 \over 4} = - 2 + {1 \over 4} \cr & = {{ - 8} \over 4} + {1 \over 4} = {{ - 7} \over 4} = - 1{3 \over 4} \cr & d]\left[ {3 - 2{3 \over 5}} \right].4{1 \over 6} - 1{3 \over 5}:1{1 \over {15}} = \left[ {2{5 \over 5} - 2{3 \over 5}} \right].{{25} \over 6} - {8 \over 5}:{{16} \over {15}} \cr & = {2 \over 5}.{{25} \over 6} - {8 \over 5}.{{15} \over {16}} = {5 \over 3} - {3 \over 2} = {{10} \over 6} - {9 \over 6} = {1 \over 6} \cr & e]{5 \over 6} + 6{5 \over 6}\left[ {11{5 \over {20}} - 9{1 \over 4}} \right]:8{1 \over 3} = {5 \over 6} + {{41} \over 6}\left[ {11{5 \over {20}} - 9{5 \over {20}}} \right]:{{25} \over 3} \cr & = {5 \over 6} + {{41} \over 6}.2:{{25} \over 3} = {5 \over 6} + {{41} \over 3}.{3 \over {25}} \cr & = {5 \over 6} + {{41} \over 3}.{3 \over {25}} = {5 \over 6} + {{41} \over {25}} = {{125} \over {150}} + {{246} \over {150}} = {{371} \over {150}} = 2{{71} \over {150}} \cr & f]{{11} \over 9}.{{15} \over 4} - {{11} \over 4}.{7 \over 9} - {{11} \over 9}.{5 \over 4} = {{11} \over 9}.{{15} \over 4} - {{11} \over 9}.{7 \over 4} \cr & = {{11} \over 9}.\left[ {{{15} \over 4} - {7 \over 4} - {5 \over 4}} \right] = {{11} \over 9}.{3 \over 4} = {{11} \over {12}}. \cr & g]\left[ { - 3,6 + 5{1 \over 3}:0,4} \right].{{10} \over {73}} - {1 \over 3}:\left[ {4,8 - 5{1 \over 2}} \right] = \left[ {{{ - 18} \over 5} + {{16} \over 3}:{2 \over 5}} \right].{{10} \over {73}} - {1 \over 3}:\left[ {{{24} \over 5} - {{11} \over 2}} \right] \cr & = \left[ {{{ - 18} \over 5} + {{16} \over 3}.{5 \over 2}} \right].{{10} \over {73}} - {1 \over 3}:\left[ {{{48} \over {10}} - {{55} \over {10}}} \right] = \left[ {{{ - 18} \over 5} + {{40} \over 3}} \right].{{10} \over {73}} - {1 \over 3}:{{ - 7} \over {10}} \cr & = \left[ {{{ - 54} \over {15}} + {{200} \over {15}}} \right].{{10} \over {73}} - {1 \over 3}.{{10} \over { - 7}} = {{146} \over {15}}.{{10} \over {73}} - {{ - 10} \over {21}} = {4 \over 3} + {{10} \over {21}} = {{28} \over {21}} + {{10} \over {21}} = {{38} \over {21}} = 1{{17} \over {21}}. \cr} \]