Bài 119 trang 32 SBT toán 6 tập 2

Đề bài

Tính một cách hợp lí: 

a) \(\displaystyle {\rm{4}}{3 \over 4} + \left( { - 0,37} \right) + {1 \over 8} + \left( { - 1,28} \right) \)\(\displaystyle+ \left( { - 2,5} \right) + 3{1 \over {12}}\) 

b) \(\displaystyle {3 \over {5.7}} + {3 \over {7.9}} + .. + {3 \over {59.61}}\) 

c) \(\displaystyle {\displaystyle {{5 \over {22}} + {3 \over {13}} - {1 \over 2}} \over {\displaystyle {4 \over {13}} - {2 \over {11}} + {3 \over 2}}}\) 

Lời giải chi tiết

a) \(\displaystyle {\rm{4}}{3 \over 4} + \left( { - 0,37} \right) + {1 \over 8} + \left( { - 1,28} \right) \)\(\displaystyle+ \left( { - 2,5} \right) + 3{1 \over {12}}\) 

\(\displaystyle = \left( {4{3 \over 9} + {1 \over 8} + 3{1 \over {12}}} \right) \)\(\displaystyle- \left( {0,37 + 1,28 + 2,5} \right) \) 
\(\displaystyle = \left( {4{{18} \over {24}} + {3 \over {24}} + 3{2 \over {24}}} \right) -  {4,15}  \)
\(\displaystyle = 7{{23} \over {24}} - 4{3 \over {20}} = 7{{115} \over {120}} - 4{{18} \over {120}} \)

\(\displaystyle = (7-4)+\left({{115} \over {120}}-{{18} \over {120}}\right)\)

\(\displaystyle= 3{{97} \over {120}}  \)

\(\displaystyle \eqalign{
& b){3 \over {5.7}} + {3 \over {7.9}} + .. + {3 \over {59.61}} \cr 
& = {3 \over 2}.\left( {{2 \over {5.7}} + {2 \over {7.9}} + .. + {2 \over {59.61}}} \right) \cr 
& = {3 \over 2}.\left( {{1 \over 5} - {1 \over 7} + {1 \over 7} - {1 \over 9} + ... + {1 \over {59}} - {1 \over {61}}} \right) \cr 
& = {3 \over 2}.\left( {{1 \over 5} - {1 \over {61}}} \right) \cr & = {3 \over 2}.\left( {{61 \over 305} - {5 \over {305}}} \right) \cr
& = {3 \over 2}.{{56} \over {305}} = {{84} \over {305}} \cr} \) 

\(\displaystyle  c){\displaystyle{{5 \over {22}} + {3 \over {13}} - {1 \over 12}} \over {\displaystyle {4 \over {13}} - {2 \over {11}} + {3 \over 2}}} \)\(\displaystyle= {{\left( \displaystyle {{5 \over {22}} + {3 \over {13}} - {1 \over 12}} \right).\left( {2.11.13} \right)}  \over {\left( \displaystyle {{4 \over {13}} - {2 \over {11}} + {3 \over 2}} \right).\left( {2.11.13} \right)}} \)

\( = \dfrac{{\dfrac{5}{{22}}.2.11.13 + \dfrac{3}{{13}}.2.11.13 - \dfrac{1}{2}.2.11.13}}{{\dfrac{4}{{13}}.2.11.13 - \dfrac{2}{{11}}.2.11.13 + \dfrac{3}{2}.2.11.13}}\)
\(\displaystyle = {{65 + 66 - 143} \over {88 - 52 + 429}} = {{ - 12} \over {465}} = {{ - 4} \over {155}} . \)

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