Tính bằng cách thuận tiện: a) \(\frac{{15}}{{31}} + \frac{{31}}{{15}} + \frac{{16}}{{31}} - \frac{{16}}{{15}}\)

a) \(\frac{{15}}{{31}} + \frac{{31}}{{15}} + \frac{{16}}{{31}} - \frac{{16}}{{15}}\)

\( = \left( {\frac{{15}}{{31}} + \frac{{16}}{{31}}} \right) + \left( {\frac{{31}}{{15}} - \frac{{16}}{{15}}} \right)\)

\( = \frac{{31}}{{31}} + \frac{{15}}{{15}}\)

= 1 + 1

= 2

b) \(\frac{{23}}{{174}} \times \,\frac{{25}}{{283}} \times \frac{{174}}{{25}} \times \frac{{283}}{{23}}\)

\( = \left( {\frac{{23}}{{174}} \times \frac{{174}}{{25}}} \right) \times \left( {\frac{{25}}{{283}} \times \frac{{283}}{{23}}} \right)\)

\( = \frac{{23}}{{25}} \times \frac{{25}}{{23}}\)

= 1