a) \({{ – 5} \over 9} + {2 \over {11}} + {{ – 4} \over {11}}\) ;
b) \({{ – 5} \over {24}} + {{ – 7} \over {24}} + {9 \over {18}}\) ;
c ) \({{ – 4} \over {13}} + \left( {{{ – 9} \over {13}} + 1} \right)\) ;
d) \({5 \over 9} + {{ – 2} \over 7} + {4 \over 9} + {{ – 5} \over 7} + {2 \over 3}\).
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\(\eqalign{ & a){{ – 5} \over 9} + {2 \over {11}} + {{ – 4} \over {11}} = {{ – 5} \over 9} + {{2 – 4} \over {11}} = {{ – 5} \over 9} + {{ – 2} \over {11}} = {{ – 55} \over {99}} + {{ – 18} \over {99}} = {{ – 73} \over {99}}. \cr & b){{ – 5} \over {24}} + {{ – 7} \over {24}} + {9 \over {18}} = {{( – 5) + ( – 7)} \over {24}} + {1 \over 2} = {{ – 12} \over {24}} + {1 \over 2} = {{ – 1} \over 2} + {1 \over 2} = 0. \cr & c){{ – 4} \over {13}} + \left( {{{ – 9} \over {13}} + 1} \right) = {{ – 4} \over {13}} – {9 \over {13}} + 1 = {{ – 4 – 9} \over {13}} + 1 = {{ – 13} \over {13}} + 1 = – 1 + 1 = 0. \cr & d){5 \over 9} + {{ – 2} \over 7} + {4 \over 9} + {{ – 5} \over 7} + {2 \over 3} = \left( {{5 \over 9} + {4 \over 9}} \right) + \left( {{{ – 2} \over 7} + {{ – 5} \over 7}} \right) + {2 \over 3} \cr & = {{5 + 4} \over 9} + {{ – 2 – 5} \over 7} + {2 \over 3} = {9 \over 9} + {{ – 7} \over 7} + {2 \over 3} = 1 + ( – 1) + {2 \over 3} = 0 + {2 \over 3} = {2 \over 3}. \cr} \)