Đề bài

Tính bằng hai cách :  a) \(3{5 \over 9} + 2{1 \over 4}\)          b) \(5{1 \over 6} - 3{2 \over 5}\)  c) \(5 - 3{4 \over 7}\)              d) \(8{2 \over 7} - \left( {3{4 \over 9} + 4{2 \over 7}} \right)\).

Lời giải chi tiết

a)Cách 1: \(3{5 \over 9} + 2{1 \over 4} = {{32} \over 9} + {9 \over 4} = {{128} \over {36}} + {{81} \over {36}} = {{209} \over {36}} = 5{{29} \over {36}}.\)Cách 2: \(3{5 \over 9} + 2{1 \over 4} = 3{{20} \over {36}} + 2{9 \over {36}} = 5{{29} \over {36}}.\)b) Cách 1: \(5{1 \over 6} - 3{2 \over 5} = {{31} \over 6} - {{17} \over 5} = {{155} \over {30}} - {{102} \over {30}} = {{53} \over {30}} = 1{{23} \over {30}}.\)Cách 2: \(5{1 \over 6} - 3{2 \over 5} = 5{5 \over {30}} - 3{{12} \over {30}} = 4{{35} \over {30}} - 3{{12} \over {30}} = 1{{23} \over {30}}.\)c) Cách 1: \(5 - 3{4 \over 7} = 5 - {{25} \over 7} = {{35} \over 7} - {{25} \over 7} = {{10} \over 7} = 1{3 \over 7}.\)Cách 2: \(5 - 3{4 \over 7} = 4{7 \over 7} - 3{4 \over 7} = 1{3 \over 7}.\)d) Cách 1:\(\eqalign{  & 8{2 \over 7} - \left( {3{4 \over 9} + 4{2 \over 7}} \right) = {{58} \over 7} - \left( {{{31} \over 9} + {{30} \over 7}} \right)  \cr  &  = {{58} \over 7} - {{31} \over 9} - {{30} \over 7} = {{522} \over {63}} - {{217} \over {63}} - {{270} \over {63}} = {{35} \over {63}} = {5 \over 9}. \cr} \) Cách 2: \(8{2 \over 7} - \left( {3{4 \over 9} + 4{2 \over 7}} \right) = \left( {8{2 \over 7} - 4{2 \over 7}} \right) - 3{4 \over 9} = 4 - 3{4 \over 9} = 3{9 \over 9} - 3{4 \over 9} = {5 \over 9}.\)

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