Thực hiện phép tính:
\(a)\dfrac{3}{7} + \dfrac{3}{7}:\left( { - \dfrac{3}{2}} \right) - \dfrac{1}{2}\)
\(b)\,\,2\dfrac{1}{2} - {\left( { - \dfrac{1}{2}} \right)^2} + \dfrac{3}{4}\)
\(c)\left( {\dfrac{3}{8} - 1,25} \right):\left( {\dfrac{3}{4} - 0,25} \right)\)
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\(d)\,\,1\dfrac{2}{5}:\dfrac{{14}}{{15}} + \left( {1\dfrac{1}{3} - 2\dfrac{1}{2}} \right):\dfrac{5}{6}\)
Lý thuyết Quy tắc dấu ngoặc và quy tắc chuyển vế SGK Toán 7 Chân trời sáng tạo (baitapsgk.com)
\(\begin{array}{l}a)\dfrac{3}{7} + \dfrac{3}{7}:\left( { - \dfrac{3}{2}} \right) - \dfrac{1}{2} \\= \dfrac{3}{7} + \dfrac{3}{7}.\left( { - \dfrac{2}{3}} \right) - \dfrac{1}{2}\\ = \dfrac{3}{7}.\left( {1 - \dfrac{2}{3}} \right) - \dfrac{1}{2} = \dfrac{3}{7}.\dfrac{1}{3} - \dfrac{1}{2}\\ = \dfrac{1}{7} - \dfrac{1}{2}= \dfrac{2}{14} - \dfrac{7}{14} = - \dfrac{5}{{14}}\\b)\,\,2\dfrac{1}{2} - {\left( { - \dfrac{1}{2}} \right)^2} + \dfrac{3}{4} = \dfrac{5}{2} - \dfrac{1}{4} + \dfrac{3}{4}\\ = \dfrac{{10}}{4} - \dfrac{1}{4} + \dfrac{3}{4} = \dfrac{{12}}{4} = 3\\c)\left( {\dfrac{3}{8} - 1,25} \right):\left( {\dfrac{3}{4} - 0,25} \right) \\= \left( {\dfrac{3}{8} - \dfrac{5}{4}} \right):{\left( {\dfrac{3}{4} - \dfrac{1}{4}} \right)^2}\\ = \left( {\dfrac{{ - 7}}{8}} \right):{\left( {\dfrac{1}{2}} \right)^2}\\ = \dfrac{{ - 7}}{8}:\dfrac{1}{4} = \dfrac{{ - 7}}{8}.4 = \dfrac{{ - 7}}{2}\\d)\,\,1\dfrac{2}{5}:\dfrac{{14}}{{15}} + \left( {1\dfrac{1}{3} - 2\dfrac{1}{2}} \right):\dfrac{5}{6}\\ = \dfrac{7}{5}:\dfrac{{14}}{{15}} + \left( {\dfrac{4}{3} - \dfrac{5}{2}} \right):\dfrac{5}{6}\\ = \dfrac{7}{5}.\dfrac{{15}}{{14}} + \left( { - \dfrac{7}{6}} \right).\dfrac{6}{5}\\ = \dfrac{3}{2} + \left( {\dfrac{{ - 7}}{5}} \right)\\ =\dfrac{15}{{10}}+\dfrac{-14}{{10}}= \dfrac{1}{{10}}\end{array}\)