Đề bài
Thực hiện phép tính:
a] \[0,58\,.\,{7^2} - \left[ { - 7} \right]\,.\,\left[ { - 0,7} \right]\,.\,15,8;\]
b] \[0,05\,:\,0,5 + 7\,:\,0,7 + 0,9:0,009;\]
c] \[\frac{9}{{11}}\,.\,\frac{{92}}{{121}} + \frac{2}{{ - 121}}\,.\,\frac{9}{{11}}\, + \frac{{31}}{{121}}\,.\,\frac{9}{{11}};\]
d] \[\frac{{20\,212\,021}}{{2\,021}}\,.\,\frac{{2\,020}}{{20\,202\,020}}.\frac{{{2^3}}}{{{3^2}}}\,.\,\frac{{ - 3}}{{{2^2}}}\,\]
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Lời giải chi tiết
a]
\[\begin{array}{l}0,58\,.\,{7^2} - \left[ { - 7} \right]\,.\,\left[ { - 0,7} \right]\,.\,15,8\\ = 0,58\,.\,{7^2} - 7\,.\,0,7\,.\,15,8\\ = 0,58\,.\,{7^2} - 7\,.\,7\,.\,1,58\\ = {7^2}\left[ {0,58 - 1,58} \right]\\ = {7^2}.[ - 1]\\ = - 49\end{array}\]
b]
\[\begin{array}{l}0,05\,:\,0,5 + 7\,:\,0,7 + 0,9:0,009\\ = \frac{5}{{100}}:\frac{5}{{10}} + 7:\frac{7}{{10}} + \frac{9}{{10}}:\frac{9}{{1000}}\\ = \frac{5}{{100}}.\frac{{10}}{5} + 7.\frac{{10}}{7} + \frac{9}{{10}}.\frac{{1000}}{9}\\ = 0,1 + 10 + 100\\ = 110,1.\end{array}\]
c]
\[\begin{array}{l}\frac{9}{{11}}\,.\,\frac{{92}}{{121}} + \frac{2}{{ - 121}}\,.\,\frac{9}{{11}}\, + \frac{{31}}{{121}}\,.\,\frac{9}{{11}}\\ = \frac{9}{{11}}\,.\,\left[ {\frac{{92}}{{121}} + \frac{2}{{ - 121}}\,\, + \frac{{31}}{{121}}} \right]\\ = \frac{9}{{11}}\,.\,\left[ {\frac{{92}}{{121}} + \frac{{ - 2}}{{121}}\,\, + \frac{{31}}{{121}}} \right]\\ = \frac{9}{{11}}\,.\,\frac{{92 + [ - 2] + 31}}{{121}}\\ = \frac{9}{{11}}\,.\,\frac{{121}}{{121}}\\ = \frac{9}{{11}}.\end{array}\]
d]
\[\begin{array}{l}\frac{{20\,212\,021}}{{2\,021}}\,.\,\frac{{2\,020}}{{20\,202\,020}}.\frac{{{2^3}}}{{{3^2}}}\,.\,\frac{{ - 3}}{{{2^2}}}\,\\ = \left[ {\frac{{20\,212\,021}}{{2\,021}}\,.\,\frac{{2\,020}}{{20\,202\,020}}} \right].\left[ {\frac{{{2^3}}}{{{3^2}}}\,.\,\frac{{ - 3}}{{{2^2}}}} \right]\,\\ = \left[ {\frac{{2021.10\,001}}{{2\,021}}\,.\,\frac{{2\,020}}{{2020.10\,001}}} \right].\left[ {\frac{{{2^3}.3.[ - 1]}}{{{3^2}{{.2}^2}}}\,} \right]\,\\ = \frac{{2\,021.10\,001.\,2\,020}}{{2\,021.\,2\,020\,.10\,001}}\,\,.\,\,\frac{{2.[ - 1]}}{3}\\ = 1.\frac{{[ - 2]}}{3}\\ = \frac{{ - 2}}{3}\end{array}\]