Thực hiện phép tính, tính nhanh (nếu có thể): (a) ( 2/3 − 7/18 ) : 5/6 . (b) 25/19 + − 37/14 − 25/19 + 9/14 + 13/8 .
Giải thích
a) \(\left( {\frac{2}{3} - \frac{7}{{18}}} \right):\frac{5}{6}\)
\( = \frac{5}{{18}}:\frac{5}{6}\)
\( = \frac{5}{{18}} \cdot \frac{6}{5}\)
\( = \frac{6}{{18}} = \frac{1}{3}\).
b) \(\frac{{25}}{{19}} + \frac{{ - 37}}{{14}} - \frac{{25}}{{19}} + \frac{9}{{14}} + \frac{{13}}{8}\)
\( = \left( {\frac{{25}}{{19}} - \frac{{25}}{{19}}} \right) + \left( {\frac{{ - 37}}{{14}} + \frac{9}{{14}}} \right) + \frac{{13}}{8}\)
\( = 0 + \left( { - 2} \right) + \frac{{13}}{8}\)
\( = \frac{{ - 3}}{8}\).
c) \(3\frac{2}{5}.\frac{{14}}{{25}} + 3\frac{2}{5}.\frac{{11}}{{25}} - \frac{2}{5}\)
\( = 3\frac{2}{5}.\left( {\frac{{14}}{{25}} + \frac{{11}}{{25}}} \right) - \frac{2}{5}\)
\( = 3\frac{2}{5} - \frac{2}{5}\)
\( = 3 + \frac{2}{5} - \frac{2}{5} = 3\).