Tính bằng cách thuận tiện: a) 9/8 + 5/7 + 3/8 + 4/7 + 7/8 − 3/8 + 3/7 + 2/7

a) \[\frac{9}{8} + \frac{5}{7} + \frac{3}{8} + \frac{4}{7} + \frac{7}{8} - \frac{3}{8} + \frac{3}{7} + \frac{2}{7}\]

\[ = \left( {\frac{9}{8} + \frac{3}{8} + \frac{7}{8} - \frac{3}{8}} \right) + \left( {\frac{5}{7} + \frac{4}{7} + \frac{3}{7} + \frac{2}{7}} \right)\]

\[ = \frac{{16}}{8} + \frac{{14}}{7}\]

= 2 + 2 = 4

b) \[\frac{2}{3} \times \frac{5}{4} + \frac{2}{3} \times \frac{3}{8} + \frac{2}{3}\]

\[ = \frac{2}{3} \times \left( {\frac{5}{4} + \frac{3}{8} + 1} \right)\]

\[ = \frac{2}{3} \times \left( {\frac{{10}}{8} + \frac{3}{8} + \frac{8}{8}} \right)\]

\[ = \frac{2}{3} \times \frac{{21}}{8}\]

\[ = \frac{7}{4}\]

c) \[\frac{5}{7} \times \frac{1}{9} + \frac{5}{7} \times \frac{2}{9} + \frac{5}{7}:\frac{3}{7}\]

\[ = \frac{5}{7} \times \frac{1}{9} + \frac{5}{7} \times \frac{2}{9} + \frac{5}{7} \times \frac{7}{3}\]

\[ = \frac{5}{7} \times \left( {\frac{1}{9} + \frac{2}{9} + \frac{7}{3}} \right)\]

\[ = \frac{5}{7} \times \left( {\frac{1}{9} + \frac{2}{9} + \frac{{21}}{9}} \right)\]

\[ = \frac{5}{7} \times \frac{{24}}{9}\]

\[ = \frac{{40}}{{21}}\]

d) \[\frac{4}{9}:\frac{2}{5} + \frac{3}{5}:\frac{9}{4} - \frac{2}{3}:\frac{9}{4}\]

\[ = \frac{4}{9} \times \frac{5}{2} + \frac{3}{5} \times \frac{4}{9} - \frac{2}{3} \times \frac{4}{9}\]

\[ = \frac{4}{9} \times \left( {\frac{5}{2} + \frac{3}{5} - \frac{2}{3}} \right)\]

\[ = \frac{4}{9} \times \left( {\frac{{75}}{{30}} + \frac{{18}}{{30}} - \frac{{20}}{{30}}} \right)\]

\[ = \frac{4}{9} \times \frac{{73}}{{30}}\]

\[ = \frac{{146}}{{135}}\]