Bài 96. Thực hiện phép tính (bằng cách hợp lí nếu có thể):
a) \(1{4 \over {23}} + {5 \over {21}} - {4 \over {23}} + 0,5 + {{16} \over {21}}\)
b) \({3 \over 7}.19{1 \over 3} - {3 \over 7}.33{1 \over 3}\)
c) \(9.{\left( { - {1 \over 3}} \right)^3} + {1 \over 3}\)
d) \(15.{1 \over 4}:\left( { - {5 \over 7}} \right) - 25{1 \over 4}:\left( { - {5 \over 7}} \right)\)
a) \(1{4 \over {23}} + {5 \over {21}} - {4 \over {23}} + 0,5 + {{16} \over {21}}\)
\( = \left( {1{4 \over {23}} - {4 \over {23}}} \right) + \left( {{5 \over {21}} + {{16} \over {21}}} \right) + 0,5 = 2,5\)
b) \({3 \over 7}.19{1 \over 3} - {3 \over 7}.33{1 \over 3}\)
\( = {3 \over 7}\left( {19{1 \over 3} - 33{1 \over 3}} \right)\)
\( = {3 \over 7}\left( {19 - 33} \right)\)
\( = {3 \over 7}\left( { - 14} \right) = - 6\)
c) \(9{\left( { - {1 \over 3}} \right)^3} + {1 \over 3} = 9\left( { - {1 \over {27}}} \right) + {1 \over 3} = - {1 \over 3} + {1 \over 3} = 0\)
d) \(15{1 \over 4}:\left( { - {5 \over 7}} \right) - 25{1 \over 4}:\left( { - {5 \over 7}} \right)\)
\( = \left( {15{1 \over 4} - 25{1 \over 4}} \right):\left( { - {5 \over 7}} \right)\)
\( = - 10\left( { - {7 \over 5}} \right) = 14\)