\(\eqalign{
& a)\,\,1{4 \over {23}} + {5 \over {21}} - {4 \over {23}} + 0,5 + {{16} \over {21}} \cr
& = \left( {1{4 \over {23}} - {4 \over {23}}} \right) + \left( {{5 \over {21}} + {{16} \over {21}}} \right) + 0,5 \cr
& = 1 + {{21} \over {21}} + 0,5 \cr
& = 1 + 1 + 0,5 = 2,5 \cr
& b)\,\,{3 \over 7}.19{1 \over 3} - {3 \over 7}.33{1 \over 3} \cr
& = {3 \over 7}.\left( {19{1 \over 3} - 33{1 \over 3}} \right) \cr
& = {3 \over 7}.\left( {19 - 33} \right) \cr
& = {3 \over 7}.\left( { - 14} \right) = - 6 \cr
& c)\,\,9.{\left( { - {1 \over 3}} \right)^3} + {1 \over 3} \cr
& = 9.\left( { - {1 \over {27}}} \right) + {1 \over 3} = - {1 \over 3} + {1 \over 3} = 0 \cr
& d)\,\,15.{1 \over 4}:\left( { - {5 \over 7}} \right) - 25{1 \over 4}:\left( { - {5 \over 7}} \right) \cr
& = \left( {15{1 \over 4} - 25{1 \over 4}} \right):\left( { - {5 \over 7}} \right) \cr
& = \left( { - 10} \right):\left( { - {5 \over 7}} \right) \cr
& = \left( { - 10} \right).\left( { - {7 \over 5}} \right) = 14 \cr} \)
