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) $\frac{{10}}{{ - 13}}:\frac{{ - 4}}{{13}}.\frac{{11}}{{ - 10}}$

$\begin{array}{l}= \left( {\frac{{10}}{{ - 13}}:\frac{{ - 4}}{{13}}} \right).\frac{{11}}{{ - 10}} = \left( {\frac{{10}}{{ - 13}}.\frac{{13}}{{ - 4}}} \right).\frac{{11}}{{ - 10}}\\ = \frac{{2.5.13}}{{(-13).(-2).2}}.\frac{{11}}{{ - 10}} = \frac{5}{2}.\frac{{11}}{{ - 10}} = \frac{{5.11}}{{2.\left( { - 10} \right)}} = \frac{{55}}{{ - 20}} = \frac{{ - 11}}{4};\end{array}$

b) $\frac{{ - 3}}{{17}}.\left( {\frac{{12}}{{ - 11}}.\frac{{ - 34}}{{21}}} \right)$

$\begin{array}{l}= \frac{{12}}{{ - 11}}.\left( {\frac{{ - 3}}{{17}}.\frac{{ - 34}}{{21}}} \right) = \frac{{12}}{{ - 11}}.\frac{{( - 3)\left( { - 34} \right)}}{{17.21}}\\ = \frac{{12}}{{ - 11}}.\frac{{( - 3).17.\left( { - 2} \right)}}{{17.3.7}} = \frac{{12}}{{ - 11}}.\frac{2}{7} = \frac{{24}}{{ - 77}} = \frac{{ - 24}}{{77}};\end{array}$

c) $\frac{{105}}{{146}}.\frac{6}{{ - 5}} + \frac{{105}}{{146}}.\frac{{ - 5}}{8}$

$\begin{array}{l}= \frac{{105}}{{146}}.\left( {\frac{6}{{ - 5}} + \frac{{ - 5}}{8}} \right) = \frac{{105}}{{146}}.\left( {\frac{{ - 48}}{{40}} + \frac{{ - 25}}{{40}}} \right)\\ = \frac{{105}}{{146}}.\frac{{ - 73}}{{40}} = \frac{{105.( - 73)}}{{146.40}} = \frac{{5.21.( - 73)}}{{73.2.8.5}} \\= \frac{{( - 21).5.73}}{{16.5.73}} = \frac{{ - 21}}{{16}};\end{array}$

d) $\frac{{ - 5}}{8}.\frac{{25}}{{111}} + \frac{{25}}{{111}}.\frac{3}{{ - 10}}$

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