Thử tài bạn 10 trang 18 Tài liệu dạy – học Toán 7 tập 1

a) \(\left( {{{ - 1} \over 3} + {3 \over {11}}} \right).{2 \over {2015}} + \left( {{1 \over 3} + {8 \over {11}}} \right).{2 \over {2015}}\)                     

b) \({5 \over {23}}:\left( {{3 \over {26}} + {7 \over 9}} \right) - {5 \over {23}}:\left( {{{23} \over {26}} + {2 \over 9}} \right).\)

Lời giải:

\(\eqalign{  & a)\left( { - {1 \over 3} + {3 \over {11}}} \right).{2 \over {2015}} + \left( {{1 \over 3} + {8 \over {11}}} \right).{2 \over {2015}} = {2 \over {2015}}\left( { - {1 \over 3} + {3 \over {11}} + {1 \over 3} + {8 \over {11}}} \right)  \cr  &  = {2 \over {2015}}\left[ {\left( { - {1 \over 3} + {1 \over 3}} \right) + \left( {{3 \over {11}} + {8 \over {11}}} \right)} \right] = {2 \over {2015}}\left( {0 + 1} \right) = {2 \over {2015}}  \cr  & b){5 \over {23}}:\left( {{3 \over {26}} + {7 \over 9}} \right) - {5 \over {23}}:\left( {{{23} \over {26}} + {2 \over 9}} \right) = {5 \over {23}}:\left( {{{27} \over {234}} + {{182} \over {234}}} \right) - {5 \over {23}}:\left( {{{207} \over {234}} + {{52} \over {234}}} \right)  \cr  &  = {5 \over {23}}:{{209} \over {234}} - {5 \over {23}}:{{259} \over {234}} = {5 \over {23}}.{{234} \over {209}} - {5 \over {23}}.{{234} \over {259}}  \cr  &  = {5 \over {23}}.234.\left( {{1 \over {209}} - {1 \over {259}}} \right)  \cr  &  = {{5.234.50} \over {23.209.259}} = {{58500} \over {1245013}} \cr} \)