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\(\begin{array}{l}\left( {\frac{{20}}{7}.\frac{{ - 4}}{{ - 5}}} \right) + \left( {\frac{{20}}{7}.\frac{3}{{ - 5}}} \right) = \frac{{20}}{7}.\left( {\frac{{ - 4}}{{ - 5}} + \frac{3}{{ - 5}}} \right)\\ = \frac{{20}}{7}.\left( {\frac{{ - 1}}{{ - 5}}} \right) = \frac{{20}}{7}.\frac{1}{5} = \frac{{20}}{{35}} = \frac{4}{7}\end{array}\)
a) Cách 1:
\(\begin{array}{l}\left( {\frac{{ - 2}}{{ - 5}} + \frac{{ - 5}}{{ - 6}}} \right) + \frac{4}{5} = \frac{2}{5} + \frac{5}{6} + \frac{4}{5}\\ = \frac{{12}}{{30}} + \frac{{25}}{{30}} + \frac{{24}}{{30}} = \frac{{61}}{{30}}\end{array}\)
Cách 2:
\(\begin{array}{l}\left( {\frac{{ - 2}}{{ - 5}} + \frac{{ - 5}}{{ - 6}}} \right) + \frac{4}{5} = \left( {\frac{2}{5} + \frac{4}{5}} \right) + \frac{5}{6}\\ = \frac{6}{5} + \frac{5}{6} = \frac{{36}}{{30}} + \frac{{25}}{{30}} = \frac{{61}}{{30}}\end{array}\)
b) Cách 1:
\(\begin{array}{l}\frac{{ - 3}}{{ - 4}} + \left( {\frac{{11}}{{ - 15}} + \frac{{ - 1}}{2}} \right) = \frac{3}{4} + \frac{{ - 11}}{{15}} + \frac{{ - 1}}{2}\\ = \frac{{45}}{{60}} + \frac{{ - 44}}{{60}} + \frac{{ - 30}}{{60}}\\ = \frac{{ - 29}}{{60}}\end{array}\).
Cách 2:
\(\begin{array}{l}\frac{{ - 3}}{{ - 4}} + \left( {\frac{{11}}{{ - 15}} + \frac{{ - 1}}{2}} \right) = \frac{3}{4} + \frac{{ - 11}}{{15}} + \frac{{ - 1}}{2}\\ = \left( {\frac{3}{4} + \frac{{ - 1}}{2}} \right) + \frac{{ - 11}}{{15}}\\ = \left( {\frac{3}{4} + \frac{{ - 2}}{4}} \right) + \frac{{ - 11}}{{15}}\\ = \frac{1}{4} + \frac{{ - 11}}{{15}}\\ = \frac{{15}}{{60}} + \frac{{ - 44}}{{60}}\\ = \frac{{ - 29}}{{60}}\end{array}\)
\(\begin{array}{l}\left( {\frac{3}{5} + \frac{{ - 2}}{7}} \right) + \frac{{ - 1}}{5} = \left( {\frac{3}{5} + \frac{{ - 1}}{5}} \right) + \frac{{ - 2}}{7}\\ = \frac{2}{5} + \frac{{ - 2}}{7} = \frac{{14}}{{35}} + \frac{{ - 10}}{{35}} = \frac{4}{{35}}\end{array}\).
a)
\(\begin{array}{l}\left( {\frac{{ - 2}}{{ - 5}}:\frac{3}{{ - 4}}} \right).\frac{4}{5} = \left( {\frac{2}{5}.\frac{{ - 4}}{3}} \right).\frac{4}{5}\\ = \frac{{ - 8}}{{15}}.\frac{4}{5} = \frac{{ - 32}}{{75}}\end{array}\)
b)
\(\begin{array}{l}\frac{{ - 3}}{{ - 4}}:\left( {\frac{7}{{ - 5}}.\frac{{ - 3}}{2}} \right) = \frac{3}{4}:\frac{{ - 21}}{{ - 10}}\\ = \frac{3}{4}.\frac{{10}}{{21}} = \frac{{30}}{{84}} = \frac{5}{14}\end{array}\)
c)
\(\begin{array}{l}\frac{{ - 1}}{9}.\frac{{ - 3}}{5} + \frac{5}{{ - 6}}.\frac{{ - 3}}{5} + \frac{5}{2}.\frac{{ - 3}}{5}.\\ = \frac{{ - 3}}{5}.\left( {\frac{{ - 1}}{9} + \frac{5}{{ - 6}} + \frac{5}{2}} \right)\\ = \frac{{ - 3}}{5}.\left( {\frac{{ - 2}}{{18}} + \frac{{ - 15}}{{18}} + \frac{{45}}{{18}}} \right)\\ = \frac{{ - 3}}{5}.\frac{{28}}{{18}}\\ = \frac{{ - 3}}{5}.\frac{{14}}{9}\\ = \frac{{ - 14}}{{15}}\end{array}\)
\(A=\left(4+\frac{1}{5}\right).\frac{19}{8}+\left(2+\frac{5}{8}\right).\frac{21}{5}\) =\(\frac{21}{5}.\frac{19}{8}+\frac{21}{8}.\frac{21}{5}\) =\(\frac{21}{5}.\left(\frac{19}{8}+\frac{21}{8}\right)\) = \(\frac{21}{5}.5\) =21 \(B=\frac{25}{2}.\left(3+\frac{2}{7}\right)-\frac{23}{7}.\left(5+\frac{1}{2}\right)\) =\(\frac{25}{2}.\frac{23}{7}-\frac{23}{7}.\frac{11}{2}\) =\(\frac{23}{7}.\left(\frac{25}{2}-\frac{11}{2}\right)\) =\(\frac{23}{7}.7=23\)
\(M=\frac{5}{7}\left(\frac{8}{5}+\frac{2}{5}\right)+\frac{5}{7}\left(\frac{6}{5}+\frac{9}{5}\right)\)
Cách 1 : \(M=\frac{5}{7}\left(\frac{8}{5}+\frac{2}{5}\right)+\frac{5}{7}\left(\frac{6}{5}+\frac{9}{5}\right)\)
\(M=\frac{5}{7}\cdot\left(\frac{8}{5}+\frac{2}{5}+\frac{6}{5}+\frac{9}{5}\right)=\frac{5}{7}.\frac{25}{5}=\frac{25}{7}\)
Cách 2:
\(M=\frac{5}{7}\left(\frac{8}{5}+\frac{2}{5}\right)+\frac{5}{7}\left(\frac{6}{5}+\frac{9}{5}\right)\)
\(M=\frac{10}{5}.\frac{5}{7}+\frac{15}{5}.\frac{5}{7}=\frac{10}{7}+\frac{15}{7}=\frac{25}{7}\)
Cách 3 :
\(M=\frac{5}{7}\left(\frac{8}{5}+\frac{2}{5}\right)+\frac{5}{7}\left(\frac{6}{5}+\frac{9}{5}\right)\)
\(M=\frac{8}{5}.\frac{5}{7}+\frac{2}{5}.\frac{5}{7}+\frac{6}{5}.\frac{5}{7}+\frac{9}{5}.\frac{5}{7}=\frac{8}{7}+\frac{2}{7}+\frac{6}{7}+\frac{9}{7}=\frac{25}{7}\)
Cách 1 :
\(M=\left(\frac{8}{5}+\frac{2}{5}\right).\frac{5}{7}+\left(\frac{6}{5}+\frac{9}{5}\right).\frac{5}{7}\)
\(M=2.\frac{5}{7}+3.\frac{5}{7}\)
\(M=\frac{10}{7}+\frac{15}{7}\)
\(M=\frac{25}{7}\)
Cách 2
\(M=\left(\frac{8}{5}+\frac{2}{5}\right).\frac{5}{7}+\left(\frac{6}{5}+\frac{9}{5}\right).\frac{5}{7}\)
\(M=2.\frac{5}{7}+3.\frac{5}{7}\)
\(M=\left(2+3\right).\frac{5}{7}\)
\(M=5.\frac{5}{7}\)
\(M=\frac{25}{7}\)
Cách 3 :
\(M=\left(\frac{8}{5}+\frac{2}{5}\right).\frac{5}{7}+\left(\frac{6}{5}+\frac{9}{5}\right).\frac{5}{7}\)
\(M=\left[\left(\frac{8}{5}+\frac{2}{5}\right)+\left(\frac{6}{5}+\frac{9}{5}\right)\right].\frac{5}{7}\)
\(M=\left[2+3\right].\frac{5}{7}\)
\(M=5.\frac{5}{7}\)
\(M=\frac{25}{7}\)
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