Đề bài
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] \[\left[ {1 - \frac{5}{{17}}} \right].\left[ {\frac{3}{8} - \frac{{{5^2}}}{{24}}} \right]\]
Phương pháp giải - Xem chi tiết
Quy tắc nhân phân số:
\[\frac{a}{b}.\frac{c}{d} = \frac{{a.c}}{{b.d}}\;\;[b \ne 0,d \ne 0];\;\;\;m.\frac{a}{b} = \frac{a}{b}.m = \frac{{a.m}}{b}\]
Lời giải chi tiết
a] \[\frac{5}{{12}} + \frac{{21}}{8}.\frac{1}{{14}} = \frac{5}{{12}} + \frac{{21.1}}{{8.14}} = \frac{5}{{12}} + \frac{{3.7}}{{8.2.7}} = \frac{5}{{12}} + \frac{3}{{16}} = \frac{{29}}{{48}}\]
b] \[\frac{8}{{15}}.\frac{3}{{64}} - \frac{{13}}{{25}} = \frac{{8.3}}{{15.64}} - \frac{{13}}{{25}} = \frac{{2.2.2.3}}{{{{3.5.2}^6}}} - \frac{{13}}{{25}} = \frac{1}{{{{5.2}^3}}} - \frac{{13}}{{25}} = \frac{1}{{40}} - \frac{{13}}{{25}} = \frac{{ - 99}}{{200}}\]
c] \[\left[ {\frac{{19}}{{21}} - \frac{2}{3}} \right].\frac{{28}}{{10}} = \left[ {\frac{{19}}{{21}} - \frac{{14}}{{21}}} \right].\frac{{28}}{{10}} = \frac{5}{{21}}.\frac{{28}}{{10}} = \frac{{5.28}}{{21.10}} = \frac{{5.2.2.7}}{{3.7.2.5}} = \frac{2}{3}\]
d] \[\left[ {1 - \frac{5}{{17}}} \right].\left[ {\frac{3}{8} - \frac{{{5^2}}}{{24}}} \right] = \left[ {\frac{{17}}{{17}} - \frac{5}{{17}}} \right].\left[ {\frac{9}{{24}} - \frac{{25}}{{24}}} \right] = \frac{{12}}{{17}}.\frac{{ - 16}}{{24}} = \frac{{12}}{{17}}.\frac{{[ - 8].2}}{{2.12}} = \frac{{ - 8}}{{17}}\]