Giải bài 2 trang 25 sách bài tập Toán 6 – Chân trời sáng tạo Tập 2

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

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)

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