Cho \(A = \frac{{\frac{{ - 1}}{2} - 5\,.\,{{\left( {\frac{3}{2}} \right)}^2}}}{{15\frac{2}{9} + {{\left( { - \frac{2}{3}} \right)}^2}}}\); \(B = \frac{7}{{12}}\,.\,3,4 - \frac{7}{{12}}\,.\,8,8\). Tính A – 5B.

Lời giải:

\(A = \frac{{\frac{{ - 1}}{2} - 5\,.\,{{\left( {\frac{3}{2}} \right)}^2}}}{{15\frac{2}{9} + {{\left( { - \frac{2}{3}} \right)}^2}}} = \frac{{\frac{{ - 1}}{2} - 5\frac{9}{4}}}{{\frac{{137}}{9} + \frac{4}{9}}}\)

\( = \frac{{\frac{{ - 2}}{4} - \frac{{45}}{4}}}{{\frac{{47}}{3}}} = \frac{{\frac{{ - 47}}{4}}}{{\frac{{47}}{3}}} = \frac{{ - 47}}{4}:\frac{{47}}{3}\)

\( = \frac{{ - 47}}{4}.\frac{3}{{47}} = \frac{{ - 3}}{4}\);

\(B = \frac{7}{{12}}\,.\,3,4 - \frac{7}{{12}}\,.\,8,8 = \frac{7}{{12}}\,.\,(3,4 - 8,8)\)

\( = \frac{7}{{12}}\,.\,( - 5,4) = \frac{7}{{12}}\,.\,\frac{{ - 27}}{5} = \frac{{ - 63}}{{20}}\).

Do đó \(A - 5B = \frac{{ - 3}}{4} - 5\,.\,\,\frac{{ - 63}}{{20}} = \frac{{ - 3}}{4} + \frac{{63}}{4} = 15\).

Vậy A – 5B = 15.