Thực hiện các phép tính sau:
a) \(\frac{5}{{12}} + \frac{{21}}{8}.\frac{1}{{14}}\)
b) \(\frac{8}{{15}}.\frac{3}{{64}} - \frac{{13}}{{25}}.\)
c) \(\left( {\frac{{19}}{{21}} - \frac{2}{3}} \right).\frac{{28}}{{10}}\)
d) \(\left( {1 - \frac{5}{{17}}} \right).\left( {\frac{3}{8} - \frac{{{5^2}}}{{24}}} \right)\)
Quy tắc nhân phân số:
\(\frac{a}{b}.\frac{c}{d} = \frac{{a.c}}{{b.d}}\;\;(b \ne 0,d \ne 0)\)
a) \(\frac{5}{{12}} + \frac{{21}}{8}.\frac{1}{{14}} = \frac{5}{{12}} + \frac{3}{{16}} = \frac{20}{{48}} + \frac{9}{{48}} = \frac{{29}}{{48}}\)
b) \(\frac{8}{{15}}.\frac{3}{{64}} - \frac{{13}}{{25}} = \frac{{8.3}}{{15.64}} - \frac{{13}}{{25}} = \frac{1}{{40}} - \frac{{13}}{{25}} \\= \frac{5}{{200}} - \frac{{104}}{{200}} = \frac{{ - 99}}{{200}}\)
c) \(\left( {\frac{{19}}{{21}} - \frac{2}{3}} \right).\frac{{28}}{{10}} = \left( {\frac{{19}}{{21}} - \frac{{14}}{{21}}} \right).\frac{{28}}{{10}} = \frac{5}{{21}}.\frac{{14}}{{5}} \\= \frac{2}{3}\)
d) \(\left( {1 - \frac{5}{{17}}} \right).\left( {\frac{3}{8} - \frac{{{5^2}}}{{24}}} \right) = \left( {\frac{{17}}{{17}} - \frac{5}{{17}}} \right).\left( {\frac{9}{{24}} - \frac{{25}}{{24}}} \right) \\= \frac{{12}}{{17}}.\frac{{ - 16}}{{24}} = \frac{{ - 8}}{{17}}\)