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a)Ta có:
\(\dfrac{-3}{7}=\dfrac{\left(-3\right)\cdot111}{7.111}=\dfrac{-333}{7}\)
b)\(15\%=\dfrac{3}{20}=0,15\)
\(5\%=\dfrac{1}{20}=0,05\)
c)\(-5\dfrac{1}{2}=-\dfrac{11}{2}\Rightarrow\)số nghịch đảo của nó là:\(-\dfrac{2}{11}\)
\(\)\(1,3=\dfrac{13}{10}\Rightarrow\)số nghịch đảo của nó là:\(\dfrac{10}{13}\)
\(\dfrac{48}{25}\cdot\dfrac{27}{55}+2\dfrac{4}{9}\cdot\dfrac{14}{33}\)
\(=\dfrac{1296}{1375}+\dfrac{22}{9}\cdot\dfrac{14}{33}\\ =\dfrac{1296}{1375}+\dfrac{28}{27}\\ =\dfrac{34992}{37125}+\dfrac{38500}{37125}\\ =\dfrac{73492}{37125}\)
\(1\dfrac{19}{22}\cdot\left(\dfrac{47}{77}-\dfrac{16}{15}\right)\\ =\dfrac{41}{22}\cdot\dfrac{-527}{1155}\\ =\dfrac{-21607}{25410}\)
\(\left(3\dfrac{10}{99}+4\dfrac{11}{99}-5\dfrac{8}{299}\right)-\left(\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{6}\right)\\ =\left(\dfrac{307}{99}+\dfrac{37}{99}-\dfrac{1503}{299}\right)-0\\ =\dfrac{344}{99}-\dfrac{1053}{299}\\ =-\dfrac{107}{2277}\)
\(A=\dfrac{1}{7}\left(\dfrac{555}{777}+\dfrac{4444}{12221}+\dfrac{33333}{244442}+\dfrac{11}{30}+\dfrac{13}{30}\right)\)
\(=\dfrac{1}{7}\left(\dfrac{5}{7}+\dfrac{4}{11}+\dfrac{3}{22}+\dfrac{23}{30}\right)\\ =\dfrac{1}{7}\left(\dfrac{5}{7}+\dfrac{1}{2}+\dfrac{23}{30}\right)\\ =\dfrac{1}{7}\cdot\dfrac{208}{105}\\ =\dfrac{208}{735}\)
a)
\(\dfrac{1}{2\cdot3}x+\dfrac{1}{3\cdot4}x+...+\dfrac{1}{49\cdot50}x=1\\ x\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{49}-\dfrac{1}{50}\right)=1\\ x\left(\dfrac{1}{2}-\dfrac{1}{50}\right)=1\\ x\cdot\dfrac{12}{25}=1\\ x=1:\dfrac{12}{25}=1\cdot\dfrac{25}{12}=\dfrac{25}{12}\)
\(\dfrac{333}{777}+\dfrac{22}{55}=\dfrac{333:111}{777:111}+\dfrac{22:11}{55:11}\\ =\dfrac{3}{7}+\dfrac{2}{5}=\dfrac{3\times5+2\times7}{35}\\ =\dfrac{15+14}{35}=\dfrac{29}{35}\)