Giải bài 39 trang 40 sách bài tập Toán 6 – Cánh Diều Tập 2


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) \(\left( {1 - \frac{5}{{17}}} \right).\left( {\frac{3}{8} - \frac{{{5^2}}}{{24}}} \right) = \left( {\frac{{17}}{{17}} - \frac{5}{{17}}} \right).\left( {\frac{9}{{24}} - \frac{{25}}{{24}}} \right) = \frac{{12}}{{17}}.\frac{{ - 16}}{{24}} = \frac{{12}}{{17}}.\frac{{( - 8).2}}{{2.12}} = \frac{{ - 8}}{{17}}\)


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