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Câu hỏi: Tính:
\(\displaystyle {\rm{a)}}{{ - 1} \over {39}} + {{ - 1} \over {52}}\)
\(\displaystyle b){{ - 6} \over 9} + {{ - 12} \over {16}}\)
\(\displaystyle c){{ - 2} \over 5} - {{ - 3} \over {11}}\)
\(\displaystyle {\rm{d)}}{{ - 34} \over {37}}.{{74} \over { - 85}}\)
\(\displaystyle {\rm{e)}}{{ - 5} \over 9}:{{ - 7} \over {18}}\)
\(\displaystyle {\rm{a)}}{{ - 1} \over {39}} + {{ - 1} \over {52}}\)
\(\displaystyle b){{ - 6} \over 9} + {{ - 12} \over {16}}\)
\(\displaystyle c){{ - 2} \over 5} - {{ - 3} \over {11}}\)
\(\displaystyle {\rm{d)}}{{ - 34} \over {37}}.{{74} \over { - 85}}\)
\(\displaystyle {\rm{e)}}{{ - 5} \over 9}:{{ - 7} \over {18}}\)
Phương pháp giải
Sử dụng:
\(\dfrac{a}{b} + \dfrac{c}{d} = \dfrac{{ad}}{{bd}} + \dfrac{{cb}}{{bd}} = \dfrac{{ad + cb}}{{bd}}\)
\(\dfrac{a}{b} - \dfrac{c}{d} =\dfrac{a}{b} + \dfrac{-c}{d}= \dfrac{{ad}}{{bd}} + \dfrac{{-cb}}{{bd}} \)\( = \dfrac{{ad - cb}}{{bd}}\)
\( \dfrac{a}{b} . \dfrac{c}{d} =\dfrac{a.c}{b.d}\)
\( \dfrac{a}{b} : \dfrac{c}{d}=\dfrac{a}{b}.\dfrac{d}{c} = \dfrac{a.d}{b.c}\)
Chú ý: Ta có thể rút gọn các phân số về dạng tối giản rồi thực hiện phép tính.
Lời giải chi tiết
\(\displaystyle{\rm{a)}}{{ - 1} \over {39}} + {{ - 1} \over {52}} = {{ - 4} \over {156}} + {{ - 3} \over {156}} = {{ - 7} \over {156}}\)
\(\displaystyle b){{ - 6} \over 9} + {{ - 12} \over {16}} = {{ - 2} \over 3} + {{ - 3} \over 4} \)\( \displaystyle= {{ - 8} \over {12}} + {{ - 9} \over {12}} = {{ - 17} \over {12}}\)
\(\displaystyle c){{ - 2} \over 5} - {{ - 3} \over {11}} = {{ - 22} \over {55}} - {{ - 15} \over {55}} \)\( \displaystyle =\frac{{ - 22}}{{55}} + \frac{{15}}{{55}} = \frac{{ - 22 + 15}}{{55}}= {{ - 7} \over {55}}\)
\(\displaystyle {\rm{d)}}{{ - 34} \over {37}}.{{74} \over { - 85}} = {{ (- 17).2.37.2} \over {37.( - 17).5}} = {4 \over 5}\)
\(\displaystyle {\rm{e)}}{{ - 5} \over 9}:{{ - 7} \over {18}} = {{ - 5} \over 9}.{{ - 18} \over 7}\)\( \displaystyle =\frac{{\left( { - 5} \right).\left( { - 2} \right)}}{{1.7}} = {{10} \over 7}\)
Sử dụng:
\(\dfrac{a}{b} + \dfrac{c}{d} = \dfrac{{ad}}{{bd}} + \dfrac{{cb}}{{bd}} = \dfrac{{ad + cb}}{{bd}}\)
\(\dfrac{a}{b} - \dfrac{c}{d} =\dfrac{a}{b} + \dfrac{-c}{d}= \dfrac{{ad}}{{bd}} + \dfrac{{-cb}}{{bd}} \)\( = \dfrac{{ad - cb}}{{bd}}\)
\( \dfrac{a}{b} . \dfrac{c}{d} =\dfrac{a.c}{b.d}\)
\( \dfrac{a}{b} : \dfrac{c}{d}=\dfrac{a}{b}.\dfrac{d}{c} = \dfrac{a.d}{b.c}\)
Chú ý: Ta có thể rút gọn các phân số về dạng tối giản rồi thực hiện phép tính.
Lời giải chi tiết
\(\displaystyle{\rm{a)}}{{ - 1} \over {39}} + {{ - 1} \over {52}} = {{ - 4} \over {156}} + {{ - 3} \over {156}} = {{ - 7} \over {156}}\)
\(\displaystyle b){{ - 6} \over 9} + {{ - 12} \over {16}} = {{ - 2} \over 3} + {{ - 3} \over 4} \)\( \displaystyle= {{ - 8} \over {12}} + {{ - 9} \over {12}} = {{ - 17} \over {12}}\)
\(\displaystyle c){{ - 2} \over 5} - {{ - 3} \over {11}} = {{ - 22} \over {55}} - {{ - 15} \over {55}} \)\( \displaystyle =\frac{{ - 22}}{{55}} + \frac{{15}}{{55}} = \frac{{ - 22 + 15}}{{55}}= {{ - 7} \over {55}}\)
\(\displaystyle {\rm{d)}}{{ - 34} \over {37}}.{{74} \over { - 85}} = {{ (- 17).2.37.2} \over {37.( - 17).5}} = {4 \over 5}\)
\(\displaystyle {\rm{e)}}{{ - 5} \over 9}:{{ - 7} \over {18}} = {{ - 5} \over 9}.{{ - 18} \over 7}\)\( \displaystyle =\frac{{\left( { - 5} \right).\left( { - 2} \right)}}{{1.7}} = {{10} \over 7}\)