Giải Bài 4 trang 10 sách bài tập toán 7 tập 1 - Chân trời sáng tạo

Đề bài

Tính

a) \(\dfrac{6}{7}.\left( { - \dfrac{1}{8}} \right) + \dfrac{6}{7}.\left( { - \dfrac{3}{4}} \right)\)

b) \(\left( {\dfrac{{ - 7}}{{17}}} \right).\dfrac{5}{{12}} + \left( {\dfrac{{ - 7}}{{17}}} \right).\dfrac{7}{{12}} + \left( {\dfrac{{ - 10}}{{17}}} \right)\)

c) \(\left[ {\dfrac{3}{5} + \left( {\dfrac{{ - 1}}{4}} \right)} \right]:\dfrac{3}{7} + \left[ {\left( {\dfrac{{ - 3}}{4}} \right) + \dfrac{2}{5}} \right]:\dfrac{3}{7}\)

d) \(\dfrac{7}{8}:\left( {\dfrac{2}{9} - \dfrac{1}{{18}}} \right) + \dfrac{7}{8}:\left( {\dfrac{1}{{36}} - \dfrac{5}{{12}}} \right)\)

Lời giải chi tiết

\(\begin{array}{l}a)\dfrac{6}{7}.\left( { - \dfrac{1}{8}} \right) + \dfrac{6}{7}.\left( { - \dfrac{3}{4}} \right) = \dfrac{6}{7}.\left( { - \dfrac{1}{8} - \dfrac{3}{4}} \right) = \dfrac{6}{7}.\left( { - \dfrac{1}{8} - \dfrac{6}{8}} \right) = \dfrac{6}{7}.\left( { - \dfrac{7}{8}} \right) =  - \dfrac{6}{8} =  - \dfrac{3}{4}\\b)\left( {\dfrac{{ - 7}}{{17}}} \right).\dfrac{5}{{12}} + \left( {\dfrac{{ - 7}}{{17}}} \right).\dfrac{7}{{12}} + \left( {\dfrac{{ - 10}}{{17}}} \right) = \left( {\dfrac{{ - 7}}{{17}}} \right)\left( {\dfrac{5}{{12}} + \dfrac{7}{{12}}} \right) + \left( {\dfrac{{ - 10}}{{17}}} \right) = \left( {\dfrac{{ - 7}}{{17}}} \right).1 + \left( {\dfrac{{ - 10}}{{17}}} \right) = \dfrac{{ - 17}}{{17}} =  - 1\\c)\left[ {\dfrac{3}{5} + \left( {\dfrac{{ - 1}}{4}} \right)} \right]:\dfrac{3}{7} + \left[ {\left( {\dfrac{{ - 3}}{4}} \right) + \dfrac{2}{5}} \right]:\dfrac{3}{7} = \left( {\dfrac{{12}}{{20}} - \dfrac{5}{{20}}} \right):\dfrac{3}{7} + \left( {\dfrac{{ - 15}}{{20}} + \dfrac{8}{{20}}} \right):\dfrac{3}{7} = \dfrac{7}{{20}}:\dfrac{3}{7} + \dfrac{{ - 7}}{{20}}:\dfrac{3}{7} = \left( {\dfrac{7}{{20}} + \dfrac{{ - 7}}{{20}}} \right):\dfrac{3}{7} = 0.\dfrac{7}{3} = 0\\d)\dfrac{7}{8}:\left( {\dfrac{2}{9} - \dfrac{1}{{18}}} \right) + \dfrac{7}{8}:\left( {\dfrac{1}{{36}} - \dfrac{5}{{12}}} \right) = \dfrac{7}{8}:\left( {\dfrac{4}{{18}} - \dfrac{1}{{18}}} \right) + \dfrac{7}{8}:\left( {\dfrac{1}{{36}} - \dfrac{{15}}{{36}}} \right) = \dfrac{7}{8}:\left( {\dfrac{1}{6}} \right) + \dfrac{7}{8}:\left( {\dfrac{{ - 7}}{{18}}} \right) = \dfrac{7}{8}.6 + \dfrac{7}{8}.\dfrac{{ - 18}}{7} = \dfrac{{42}}{8} + \dfrac{{ - 18}}{8} = \dfrac{{24}}{8} = 3\end{array}\)