Đề bài

Tính giá trị biểu thức \(A = \frac{{ - 3}}{2}.\frac{m}{n} + \frac{3}{{ - 8}}.2\frac{1}{2}\) khi \(\frac{m}{n}\) nhận các giá trị: a) \(\frac{4}{5};\) b) \(\frac{{ - 3}}{8}\) c) \(\frac{0}{{ - 2021}}\) d) \(\frac{5}{2}\)

Lời giải chi tiết

a) Với \(\frac{m}{n} = \frac{4}{5}\) thì  \(A = \frac{{ - 3}}{2}.\frac{4}{5} + \frac{3}{{ - 8}}.2\frac{1}{2} = \frac{{ - 3}}{2}.\frac{4}{5} + \frac{3}{{ - 8}}.\frac{5}{2}\\ = \frac{{ - 6}}{5} + \frac{{ - 15}}{{16}} = \frac{{ - 96}}{{80}} + \frac{{ - 75}}{{80}} = \frac{{ - 171}}{{80}}.\)b) Với \(\frac{m}{n} = \frac{{ - 3}}{8}\) thì  \(A = \frac{{ - 3}}{2}.\frac{{ - 3}}{8} + \frac{3}{{ - 8}}.2\frac{1}{2} = \frac{{ - 3}}{2}.\frac{{ - 3}}{8} + \frac{3}{{ - 8}}.\frac{5}{2}\\ = \frac{9}{{16}} + \frac{{ - 15}}{{16}} = \frac{{ - 6}}{{16}} = \frac{{ - 3}}{8}.\) c) Với \(\frac{m}{n} = \frac{0}{{ - 2021}} = 0\) thì  \(A = \frac{{ - 3}}{2}.0 + \frac{3}{{ - 8}}.2\frac{1}{2} = \frac{3}{{ - 8}}.\frac{5}{2} = \frac{{ - 15}}{{16}}.\)d) Với \(\frac{m}{n} = \frac{5}{2}\) thì \(A = \frac{{ - 3}}{2}.\frac{5}{2} + \frac{3}{{ - 8}}.2\frac{1}{2} = \frac{{ - 3}}{2}.\frac{5}{2} + \frac{3}{{ - 8}}.\frac{5}{2}\\ = \left( {\frac{{ - 3}}{2} + \frac{3}{{ - 8}}} \right).\frac{5}{2} = \frac{{ - 15}}{8}.\frac{5}{2} = \frac{{ - 75}}{{16}}.\)