Thực hiện phép tính (tính hợp lý nếu có thể): (a) 3/5 + − 14/15 : − 7/3 . (b) 31/27 − 5/23 + − 18/23 − 4/27 − 3/− 7 .
Giải thích
a) \[\frac{3}{5} + \frac{{ - 14}}{{15}}:\frac{{ - 7}}{3}\]
\[ = \frac{3}{5} + \frac{{ - 14}}{{15}}.\frac{{ - 3}}{7}\]
\[ = \frac{3}{5} + \frac{2}{5} = 1.\]
b) \[\frac{{31}}{{27}} - \frac{5}{{23}} + \frac{{ - 18}}{{23}} - \frac{4}{{27}} - \frac{3}{{ - 7}}\]
\[ = \left( {\frac{{31}}{{27}} + \frac{{ - 4}}{{27}}} \right) + \left( {\frac{{ - 5}}{{23}} + \frac{{ - 18}}{{23}}} \right) + \frac{3}{7}\]
\[ = - 1 + 1 + \frac{3}{7} = \frac{3}{7}.\]
c) \[\frac{{ - 2}}{7}.\frac{3}{5} + \frac{{ - 2}}{7}.\frac{4}{5} + 2\frac{1}{5}\]
\[ = \frac{{ - 2}}{7}.\left( {\frac{3}{5} + \frac{4}{5}} \right) + \frac{{11}}{{10}}\]
\[ = \frac{{ - 2}}{7}.\frac{7}{5} + \frac{{11}}{{10}}\]
\[ = \frac{{ - 2}}{5} + \frac{{11}}{5} = \frac{9}{5}.\]