Câu 119 trang 32 SBT Toán Lớp 6 tập 2: Tính một cách hợp lý....

Tính một cách hợp lý

a) ({ m{4}}{3 over 4} + left( { – 0,37} ight) + {1 over 8} + left( { – 1,28} ight) + left( { – 2,5} ight) + 3{1 over {12}}) 

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}}}) 

Giải

a) ({ m{4}}{3 over 4} + left( { – 0,37} ight) + {1 over 8} + left( { – 1,28} ight) + left( { – 2,5} ight) + 3{1 over {12}}) 

(eqalign{
& = left( {4{3 over 9} + {1 over 8} + 3{1 over {12}}} ight) – left( {0,37 + 1,28 + 2,5} ight) cr
& = left( {4{{18} over {24}} + {3 over {24}} + 3{2 over {24}}} ight) – left( {4,15} ight) cr
& = 7{{23} over {24}} – 4{3 over {20}} = 7{{115} over {120}} – 4{{18} over {120}} = 3{{97} over {120}} cr} )

(eqalign{
& b){3 over {5.7}} + {3 over {7.9}} + .. + {3 over {59.61}} cr
& = {3 over 2}.left( {{2 over {5.7}} + {2 over {7.9}} + .. + {2 over {59.61}}} ight) cr
& = {3 over 2}.left( {{1 over 5} – {1 over 7} + {1 over 7} – {1 over 9} + … + {1 over {59}} – {1 over {61}}} ight) cr
& = {3 over 2}.left( {{1 over 5} – {1 over {61}}} ight) cr
& = {3 over 2}.{{56} over {305}} = {{84} over {305}} cr} )

(eqalign{
& c){{{5 over {22}} + {3 over {13}} – {1 over 12}} over {{4 over {13}} – {2 over {11}} + {3 over 2}}} = {{left( {{5 over {22}} + {3 over {13}} – {1 over 12}} ight).left( {2.11.13} ight)} over {left( {{4 over {13}} – {2 over {11}} + {3 over 2}} ight).left( {2.11.13} ight)}} cr
& = {{65 + 66 – 143} over {88 – 52 + 429}} = {{ – 12} over {465}} = {{ – 4} over {155}} cr} )