Tính:
a) \({\rm{}}{2 \over 3} + {1 \over 5}.{{10} \over 7}\)
b) \({7 \over {12}} - {{27} \over 1}.{1 \over {18}}\)
c) \(\left( {{{23} \over {41}} - {{15} \over {82}}} \right).{{41} \over {25}}\)
d) \({\rm{}}\left( {{4 \over 5} + {1 \over 2}} \right).\left( {{3 \over {13}} - {8 \over {13}}} \right)\)
Giải
a) \({\rm{}}{2 \over 3} + {1 \over 5}.{{10} \over 7} \)
\(= {2 \over 3} + {{1.10} \over {5.7}} \)
\(= {2 \over 3} + {2 \over 7} \)
\(= {{14} \over {21}} + {6 \over {21}}\)
\(= {{20} \over {21}}\)
b) \({7 \over {12}} - {{27} \over 1}.{1 \over {18}} \)
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\(= {7 \over 2} - {{27.1} \over {7.18}} \)
\(= {7 \over 2} - {3 \over {14}} \)
\(= {{49} \over {14}} + {{ - 3} \over {14}} \)
\(= {{46} \over {14}} = {{23} \over 7}\)
c) \(\left( {{{23} \over {41}} - {{15} \over {82}}} \right).{{41} \over {25}} \)
\(= \left( {{{46} \over {82}} + {{ - 15} \over {82}}} \right).{{41} \over {25}} \)
\(= {{31} \over {82}}.{{41} \over {25}} \)
\(= {{31.41} \over {82.25}} = {{31} \over {50}}\)
d) \({\rm{}}\left( {{4 \over 5} + {1 \over 2}} \right).\left( {{3 \over {13}} - {8 \over {13}}} \right) \)
\(= \left( {{8 \over {10}} + {5 \over {10}}} \right).\left( {{3 \over {13}} + {{ - 8} \over {13}}} \right)\)
\(= {{13} \over {10}}.{{ - 5} \over {13}} = {{13.( - 5)} \over {10.13}} = {{ - 1} \over 2}\)