Bài 2 trang 25 SBT Toán 6 - Chân trời sáng tạo Tập 2: Tính giá trị của biểu thức: \(\frac{{10}}{{ - 13}}: \frac{{ - 4}}{{13}}. \frac{{11}}{{ - 10}};\) \(\frac{{ - 3}}{{17}}....

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) \(\frac{{ - 5}}{8}.\frac{{25}}{{111}} + \frac{{25}}{{111}}.\frac{3}{{ - 10}};\)

Tính theo thứ tự thông thường, có thể sử dụng các tính chất giao hoán, kết hợp, phân phối.

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)

\(\begin{array}{l}\frac{{ - 5}}{8}.\frac{{25}}{{111}} + \frac{{25}}{{111}}.\frac{3}{{ - 10}} = \frac{{25}}{{111}}.\frac{{ - 5}}{8} + \frac{{25}}{{111}}.\frac{3}{{ - 10}} = \frac{{25}}{{111}}.\left( {\frac{{ - 5}}{8} + \frac{3}{{ - 10}}} \right)\\ = \frac{{25}}{{111}}.\left( {\frac{{ - 25}}{{40}} + \frac{{ - 12}}{{40}}} \right) = \frac{{25}}{{111}}.\frac{{ - 37}}{{40}} = \frac{{25.( - 37)}}{{111.40}} = \frac{{( - 5).37.5}}{{24.37.5}} = \frac{{ - 5}}{{24}};\end{array}\)