Advertisements (Quảng cáo)
Tính bằng cách hợp lí :
a) \(4{3 \over 4} + \left( { – 0,37} \right) + {1 \over 8} + \left( { – 1,28} \right) + \left( { – 2,5} \right) + 3\)
b) \({3 \over {5.7}} + {3 \over {7.9}} + … + {3 \over {59.61}}\)
c) \({{{5 \over {22}} + {3 \over {13}} – {1 \over 2}} \over {{4 \over {13}} – {2 \over {11}} + {3 \over 2}}}\).
Advertisements (Quảng cáo)
\(\eqalign{ & a)4{3 \over 4} + ( – 0,37) + {1 \over 8} + ( – 1,28) + ( – 2,5) + 3 \cr & = 4,75 + ( – 0,37) + 0,125 + ( – 1,28) + ( – 2,5) + 3 \cr & = (4,75 + 0,125 + 3) + ( – 0,37 – 1,28 – 2,5) = 7,875 + ( – 4,15) = 3,725 \cr & b){3 \over {5.7}} + {3 \over {7.9}} + … + {3 \over {59.61}} = {3 \over 2}.\left( {{2 \over {5.7}} + {2 \over {7.9}} + … + {2 \over {59.61}}} \right) \cr & = {3 \over 2}.\left( {{1 \over 5} – {1 \over 7} + {1 \over 7} – {1 \over 9} + … + {1 \over {59}} – {1 \over {61}}} \right) = {3 \over 2}.\left( {{1 \over 5} – {1 \over {61}}} \right) \cr & = {3 \over 2}.\left( {{{61} \over {305}} – {5 \over {305}}} \right) = {3 \over 2}.{{56} \over {305}} = {{84} \over {305}}. \cr & c){{{5 \over {22}} + {3 \over {13}} – {1 \over 2}} \over {{4 \over {13}} – {2 \over {11}} + {3 \over 2}}} = {{{{65} \over {286}} + {{66} \over {286}} – {{143} \over {286}}} \over {{{88} \over {286}} – {{52} \over {286}} + {{429} \over {286}}}} = {{{{ – 12} \over {286}}} \over {{{465} \over {286}}}} = {{ – 12} \over {465}} = {{ – 4} \over {155}}. \cr} \)