Tính giá trị các biểu thức sau một cách hợp lí :
a) \(A = {5 \over {19}}.{7 \over {11}} + {5 \over {19}}.{4 \over {11}} + {{14} \over {19}}\)
b) \(B = {5 \over 9}.{7 \over {17}} + {5 \over 9}.{{12} \over {17}} - {5 \over 9}.{2 \over {17}}\)
c) \(C = {{ - 6} \over 7}.{1 \over 4} + {1 \over 3}.\left( {{{ - 6} \over 7}} \right) - {1 \over 2}:\left( {{{ - 7} \over 6}} \right)\)
Advertisements (Quảng cáo)
d) \(D = \left( {{{67} \over {111}} + {2 \over {33}} - {{15} \over {117}}} \right).\left( {{1 \over 3} - {1 \over 4} - {1 \over {12}}} \right)\)
\(\eqalign{ & a)A = {5 \over {19}}.{7 \over {11}} + {5 \over {19}}.{4 \over {11}} + {{14} \over {19}} = {5 \over {19}}.\left( {{7 \over {11}} + {4 \over {11}}} \right) + {{14} \over {19}} = {5 \over {19}}.1 + {{14} \over {19}} = {5 \over {19}} + {{14} \over {19}} = 1 \cr & b)B = {5 \over 9}.{7 \over {17}} + {5 \over 9}.{2 \over {17}} - {5 \over 9}.{2 \over {17}} = {5 \over 9}.\left( {{7 \over {17}} + {{12} \over {17}} - {2 \over {17}}} \right) = {5 \over 9}.\left( {{{7 + 12 - 2} \over {17}}} \right) = {5 \over 9}.1 = {5 \over 9} \cr & c)C = {{ - 6} \over 7}.{1 \over 4} + {1 \over 3}.\left( {{{ - 6} \over 7}} \right) - {1 \over 2}:\left( {{{ - 7} \over 6}} \right) = {{ - 6} \over 7}.{1 \over 4} + {1 \over 3}.\left( {{{ - 6} \over 7}} \right) - {1 \over 2}.\left( {{{ - 6} \over 7}} \right) = {{ - 6} \over 7}.\left( {{1 \over 4} + {1 \over 3} - {1 \over 2}} \right) \cr & = {{ - 6} \over 7}.\left( {{3 \over {12}} + {4 \over {12}} - {6 \over {12}}} \right) = {{ - 6} \over 7}.\left( {{{3 + 4 - 6} \over {12}}} \right) = {{ - 6} \over 7}.{1 \over {12}} = {{ - 6.1} \over {7.12}} = {{ - 1} \over {14}}. \c & d)D = \left( {{{67} \over {111}} + {2 \over {33}} - {{15} \over {117}}} \right).\left( {{1 \over 3} - {1 \over 4} - {1 \over {12}}} \right) \cr & = \left( {{{67} \over {111}} + {2 \over {33}} - {{15} \over {117}}} \right).\left( {{4 \over {12}} + {{ - 3} \over {12}} + {{ - 1} \over {12}}} \right) = \left( {{{67} \over {111}} + {2 \over {33}} - {{15} \over {117}}} \right).0 = 0 \cr} \)