Đề bài
Tính giá trị của biểu thức:
a] \[\frac{{10}}{{ - 13}}:\frac{{ - 4}}{{13}}.\frac{{11}}{{ - 10}};\]
b] \[\frac{{ - 3}}{{17}}.\left[ {\frac{{12}}{{ - 11}}.\frac{{ - 34}}{{21}}} \right];\]
c] \[\frac{{105}}{{146}}.\frac{6}{{ - 5}} + \frac{{105}}{{146}}.\frac{{ - 5}}{8};\]
d] \[\frac{{ - 5}}{8}.\frac{{25}}{{111}} + \frac{{25}}{{111}}.\frac{3}{{ - 10}};\]
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Lời giải chi tiết
a]
\[\begin{array}{l}\frac{{10}}{{ - 13}}:\frac{{ - 4}}{{13}}.\frac{{11}}{{ - 10}} = \left[ {\frac{{10}}{{ - 13}}:\frac{{ - 4}}{{13}}} \right].\frac{{11}}{{ - 10}} = \left[ {\frac{{10}}{{ - 13}}.\frac{{13}}{{ - 4}}} \right].\frac{{11}}{{ - 10}}\\ = \frac{{130}}{{52}}.\frac{{11}}{{ - 10}} = \frac{5}{2}.\frac{{11}}{{ - 10}} = \frac{{5.11}}{{2.\left[ { - 10} \right]}} = \frac{{55}}{{ - 20}} = \frac{{ - 11}}{4};\end{array}\]
b]
\[\begin{array}{l}\frac{{ - 3}}{{17}}.\left[ {\frac{{12}}{{ - 11}}.\frac{{ - 34}}{{21}}} \right] = \frac{{12}}{{ - 11}}.\left[ {\frac{{ - 3}}{{17}}.\frac{{ - 34}}{{21}}} \right] = \frac{{12}}{{ - 11}}.\frac{{[ - 3]\left[ { - 34} \right]}}{{17.21}}\\ = \frac{{12}}{{ - 11}}.\frac{{[ - 3].17.\left[ { - 2} \right]}}{{17.3.7}} = \frac{{12}}{{ - 11}}.\frac{2}{7} = \frac{{24}}{{ - 77}} = \frac{{ - 24}}{{77}};\end{array}\]
c]
\[\begin{array}{l}\frac{{105}}{{146}}.\frac{6}{{ - 5}} + \frac{{105}}{{146}}.\frac{{ - 5}}{8} = \frac{{105}}{{146}}.\left[ {\frac{6}{{ - 5}} + \frac{{ - 5}}{8}} \right] = \frac{{105}}{{146}}.\left[ {\frac{{ - 48}}{{40}} + \frac{{ - 25}}{{40}}} \right]\\ = \frac{{105}}{{146}}.\frac{{ - 73}}{{40}} = \frac{{105.[ - 73]}}{{146.40}} = \frac{{5.21.[ - 73]}}{{73.2.8.5}} = \frac{{[ - 21].5.73}}{{16.5.73}} = \frac{{ - 21}}{{16}};\end{array}\]
d]
\[\begin{array}{l}\frac{{ - 5}}{8}.\frac{{25}}{{111}} + \frac{{25}}{{111}}.\frac{3}{{ - 10}} = \frac{{25}}{{111}}.\frac{{ - 5}}{8} + \frac{{25}}{{111}}.\frac{3}{{ - 10}} = \frac{{25}}{{111}}.\left[ {\frac{{ - 5}}{8} + \frac{3}{{ - 10}}} \right]\\ = \frac{{25}}{{111}}.\left[ {\frac{{ - 25}}{{40}} + \frac{{ - 12}}{{40}}} \right] = \frac{{25}}{{111}}.\frac{{ - 37}}{{40}} = \frac{{25.[ - 37]}}{{111.40}} = \frac{{[ - 5].37.5}}{{24.37.5}} = \frac{{ - 5}}{{24}};\end{array}\]