Tính bằng cách thuận tiện

\(\begin{array}{l}\frac{{15}}{{31}}\,\, + \,\,\frac{{31}}{{15}}\,\, + \,\,\frac{{16}}{{31}}\,\, - \,\,\frac{{16}}{{15}}\\ = \left( {\frac{{15}}{{31}} + \frac{{16}}{{31}}} \right) + \left( {\frac{{31}}{{15}} - \frac{{16}}{{15}}} \right)\\ = \frac{{31}}{{31}} + \frac{{15}}{{15}}\\ = 1 + 1\\ = 2\end{array}\)

\(\begin{array}{l}\frac{{23}}{{174}}\,\, \times \,\,\frac{{25}}{{283}}\,\, \times \,\,\frac{{174}}{{25}}\,\, \times \,\,\frac{{283}}{{23}}\\ = \left( {\frac{{23}}{{174}} \times \frac{{174}}{{25}}} \right) \times \left( {\frac{{25}}{{283}} \times \frac{{283}}{{23}}} \right)\\ = \frac{{23}}{{25}} \times \frac{{25}}{{23}}\\ = 1\end{array}\)