Giải Bài 2 trang 10 sách bài tập toán 7 tập 1 - Chân trời sáng tạo

Đề bài

Tính

a) \( - 0,375 + \dfrac{1}{4} - \left( { - \dfrac{1}{5}} \right)\)

b) \(\dfrac{2}{3} + \left( {\dfrac{{ - 5}}{{12}}} \right) + \left( {\dfrac{{ - 7}}{{15}}} \right) + ( - 0,2)\)

c) \(0,275 + \left( {\dfrac{{ - 8}}{{17}}} \right) + \dfrac{{29}}{{40}} + \left( {\dfrac{{ - 9}}{{17}}} \right) - 1\dfrac{1}{3}\)

d) \(\left( { - 5} \right).\left( {\dfrac{{ - 34}}{{21}}} \right).\left( {\dfrac{{ - 7}}{{10}}} \right).\left( { - \dfrac{3}{{17}}} \right)\)

e) \(\left( {\dfrac{{13}}{{18}}:\dfrac{{26}}{9}} \right).\dfrac{4}{7}\)

f) \(\left[ {\left( { - \dfrac{5}{{33}}} \right):\dfrac{2}{{11}}} \right].0,15\)

Lời giải chi tiết

\(\begin{array}{l}a) - 0,375 + \dfrac{1}{4} - \left( { - \dfrac{1}{5}} \right) = \dfrac{{ - 3}}{8} + \dfrac{1}{4} + \dfrac{1}{5} = \dfrac{{ - 15}}{{40}} + \dfrac{{10}}{{40}} + \dfrac{8}{{40}} = \dfrac{3}{{40}}\\b)\dfrac{2}{3} + \left( {\dfrac{{ - 5}}{{12}}} \right) + \left( {\dfrac{{ - 7}}{{15}}} \right) + ( - 0,2) = \dfrac{2}{3} - \dfrac{5}{{12}} - \left( {\dfrac{7}{{15}} - \dfrac{1}{5}} \right)\\ = \left( {\dfrac{2}{3} - \dfrac{5}{{12}}} \right) - \left( {\dfrac{7}{{15}} + \dfrac{1}{5}} \right) = \left( {\dfrac{8}{{12}} - \dfrac{5}{{12}}} \right) - \left( {\dfrac{7}{{15}} + \dfrac{3}{{15}}} \right)\\ = \dfrac{3}{{12}} - \dfrac{{10}}{{15}} = \dfrac{3}{{12}} - \dfrac{8}{{12}} = \dfrac{{ - 5}}{{12}}\\c)0,275 + \left( {\dfrac{{ - 8}}{{17}}} \right) + \dfrac{{29}}{{40}} + \left( {\dfrac{{ - 9}}{{17}}} \right) - 1\dfrac{1}{3}\\ = \dfrac{{11}}{{40}} + \left( {\dfrac{{ - 8}}{{17}}} \right) + \dfrac{{29}}{{40}} + \left( {\dfrac{{ - 9}}{{17}}} \right) - \dfrac{4}{3}\\ = \left( {\dfrac{{11}}{{40}} + \dfrac{{29}}{{40}}} \right) + \left[ {\left( {\dfrac{{ - 8}}{{17}}} \right) + \left( {\dfrac{{ - 9}}{{17}}} \right)} \right] - \dfrac{4}{3}\\ = 1 + ( - 1) - \dfrac{4}{3} =  - \dfrac{4}{3}\\d)\left( { - 5} \right).\left( {\dfrac{{ - 34}}{{21}}} \right).\left( {\dfrac{{ - 7}}{{10}}} \right).\left( { - \dfrac{3}{{17}}} \right)\\ = 5.\dfrac{{34}}{{21}}.\dfrac{7}{{10}}.\dfrac{3}{{17}} = \dfrac{{5.34.7.3}}{{21.10.17}} = \dfrac{{5.17.2.7.3}}{{7.3.5.2.17}} = 1\\e)\left( {\dfrac{{13}}{{18}}:\dfrac{{26}}{9}} \right).\dfrac{4}{7} = \dfrac{{13}}{{18}}.\dfrac{9}{{26}}.\dfrac{4}{7} = \dfrac{{13.9.4}}{{18.26.7}} = \dfrac{{13.9.2.2}}{{2.9.13.2.7}} = \dfrac{1}{7}\\f)\left[ {\left( { - \dfrac{5}{{33}}} \right):\dfrac{2}{{11}}} \right].0,15 = \dfrac{{ - 5}}{{33}}.\dfrac{{11}}{2}.\dfrac{3}{{20}} =  - \dfrac{{5.11.3}}{{3.11.2.4.5}} = \dfrac{{ - 1}}{8}\end{array}\)