Bài 71 trang 20 SBT toán 6 tập 2

Đề bài

Tính nhanh: 

\(\displaystyle{\rm{A}} = {5 \over {13}} + {{ - 5} \over 7} + {{ - 20} \over {41}} + {8 \over {13}} + {{ - 21} \over {41}};\)

\(\displaystyle B = {{ - 5} \over 9} + {8 \over {15}} + {{ - 2} \over {11}} + {4 \over { - 9}} + {7 \over {15}}.\)

Lời giải chi tiết

\(\displaystyle {\rm{A}} = {5 \over {13}} + {{ - 5} \over 7} + {{ - 20} \over {41}} + {8 \over {13}} + {{ - 21} \over {41}} \)

\(\displaystyle = \left( {{5 \over {13}} + {8 \over {13}}} \right) + \left( {{{ - 20} \over {41}} + {{ - 21} \over {41}}} \right) \)\(\displaystyle + {{ - 5} \over 7} \)

\(\displaystyle =  {{5+8} \over {13}} + {{ (- 20)+(-21)} \over {41}}  \)\(\displaystyle + {{ - 5} \over 7} \)

\(\displaystyle =  {{13} \over {13}} + {{ -41} \over {41}}  \)\(\displaystyle + {{ - 5} \over 7} \)
\(\displaystyle = 1 + \left( { - 1} \right) + {{ - 5} \over 7} =0+ {{ - 5} \over 7}= {{ - 5} \over 7} \)

\(\displaystyle B = {{ - 5} \over 9} + {8 \over {15}} + {{ - 2} \over {11}} + {-4 \over { 9}} + {7 \over {15}} \)

\(\displaystyle= \left( {{{ - 5} \over 9} + {{ - 4} \over 9}} \right) + \left( {{8 \over {15}} + {7 \over {15}}} \right) \)\(\displaystyle+ {{ - 2} \over {11}} \)

\(\displaystyle=  {{ (- 5)+(-4) } \over 9} + {{8 +7}\over {15}}  \)\(\displaystyle+ {{ - 2} \over {11}} \)

\(\displaystyle=  {{ -9 } \over 9} + {{15}\over {15}}  \)\(\displaystyle+ {{ - 2} \over {11}} \)
\(\displaystyle = - 1 + 1 + {{ - 2} \over {11}} =0+{{ - 2} \over {11}}= {{ - 2} \over {11}}  \)

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