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a) \(\frac{2}{3}.\left(\frac{1}{3}+\frac{2}{5}\right)=\frac{2}{3}.\frac{11}{15}=\frac{22}{45}\)
b) 24+25+26+...+99+100
= (100+24).77:2
= 124.77:2
= 4774
c) \(\frac{16.17-5}{16.16+11}=\frac{16.16+(16-5)}{16.16+11}=\frac{16.16+11}{16.16+11}=1\)
d) \(\frac{5}{80}+\frac{5}{90}+\frac{5}{150}+\frac{5}{210}+\frac{5}{270}\)
\(=\frac{1}{16}+\frac{1}{18}+\frac{1}{30}+\frac{1}{42}+\frac{1}{54}\)
\(=\frac{2929}{15120}\)
a)=\(\frac{2}{3}.\left(\frac{5}{15}+\frac{6}{15}\right)\)
= \(\frac{2}{3}.\frac{11}{15}=\frac{22}{45}\)
d) = 5.(\(\frac{1}{80}+\frac{1}{90}+\frac{1}{150}+\frac{1}{210}+\frac{1}{270}\))
= 50........
kq là tự tính:)))))
\(=\frac{5-\frac{5}{3}-\frac{5}{9}-\frac{5}{27}}{8-\frac{8}{3}-\frac{8}{9}-\frac{8}{27}}:\frac{15-\frac{15}{11}+\frac{15}{121}}{16-\frac{16}{11}+\frac{16}{121}}\)
\(=\frac{5\left(1-\frac{1}{3}-\frac{1}{9}-\frac{1}{27}\right)}{8\left(1-\frac{1}{3}-\frac{1}{9}-\frac{1}{27}\right)}:\frac{15\left(1-\frac{1}{11}+\frac{1}{121}\right)}{16\left(1-\frac{1}{11}+\frac{1}{121}\right)}\)
\(=\frac{5}{8}:\frac{15}{16}=\frac{5}{8}.\frac{16}{15}=\frac{2}{3}\)
\(B=\frac{3+\frac{8}{12}+\frac{9}{13}-\frac{12}{17}}{4+\frac{8}{12}+\frac{12}{13}-\frac{16}{17}}+\frac{4+\frac{16}{60}-\frac{24}{213}-\frac{32}{11}}{5+\frac{20}{61}-\frac{36}{213}-\frac{40}{11}}\)
\(\Leftrightarrow B=\frac{3\left(1+\frac{8}{12}+\frac{3}{13}-\frac{4}{17}\right)}{4\left(1+\frac{8}{12}+\frac{3}{13}-\frac{4}{17}\right)}+\frac{4\left(1+\frac{4}{60}-\frac{6}{213}-\frac{8}{11}\right)}{5\left(1+\frac{4}{60}+\frac{6}{213}-\frac{8}{11}\right)}\)
\(\Leftrightarrow B=\frac{3}{4}+\frac{4}{5}\)
\(\Leftrightarrow B=\frac{15}{20}+\frac{16}{20}\)
\(\Leftrightarrow B=\frac{31}{20}\)
a) \(\frac{13}{26}-\frac{1}{3}-\frac{1}{2}+\frac{7}{21}\)
\(=\frac{1}{2}-\frac{1}{3}-\frac{1}{2}+\frac{1}{3}\)
\(=\frac{1}{2}-\frac{1}{2}+\frac{1}{3}-\frac{1}{3}\)
\(=0+0\)
\(=0\)
b) \(\left(\frac{-5}{12}+\frac{6}{11}\right)+\left(\frac{7}{17}+\frac{5}{17}+\frac{5}{12}\right)\)
\(=\frac{-5}{12}+\frac{6}{11}+\frac{7}{17}+\frac{5}{17}+\frac{5}{12}\)
\(=\left(\frac{-5}{12}+\frac{5}{12}\right)+\left(\frac{7}{17}+\frac{5}{17}\right)+\frac{6}{11}\)
\(=0+\frac{12}{17}+\frac{6}{11}\)
\(=\frac{132}{187}+\frac{102}{187}\)
\(=\frac{234}{187}\)
c) \(\left(\frac{13}{5}+\frac{7}{16}\right)-\left(\frac{11}{16}-\frac{12}{10}\right)\)
\(=\left(\frac{13}{5}+\frac{7}{16}\right)-\left(\frac{11}{16}-\frac{6}{5}\right)\)
\(=\frac{13}{5}+\frac{7}{16}-\frac{11}{16}+\frac{6}{5}\)
\(=\left(\frac{13}{5}+\frac{6}{5}\right)+\left(\frac{7}{16}-\frac{11}{16}\right)\)
\(=\frac{19}{5}+\left(\frac{-4}{16}\right)\)
\(=\frac{19}{5}-\frac{1}{4}\)
\(=\frac{76}{20}-\frac{5}{20}\)
\(=\frac{71}{20}\)
d) \(-\left(\frac{3}{10}-\frac{6}{11}\right)-\left(\frac{21}{30}-\frac{5}{11}\right)\)
\(=-\left(\frac{3}{10}-\frac{6}{11}\right)-\left(\frac{7}{10}-\frac{5}{11}\right)\)
\(=-\frac{3}{10}+\frac{6}{11}-\frac{7}{10}+\frac{5}{11}\)
\(=
\left(-\frac{3}{10}-\frac{7}{10}\right)+\left(\frac{6}{11}+\frac{5}{11}\right)\)
\(=\frac{-10}{10}+\frac{11}{11}\)
\(=-1+1\)
\(=0\)
C = \(\dfrac{\dfrac{1}{9}-\dfrac{5}{6}-4}{\dfrac{7}{12}-\dfrac{1}{36}-10}\)
C = \(\dfrac{\dfrac{6-45-216}{54}}{\dfrac{21-1-360}{36}}\)
C = \(\dfrac{\dfrac{-85}{18}}{-\dfrac{85}{9}}\)
C = \(\dfrac{1}{2}\)
Ta có: \(D=\frac{\frac{15}{6x16}+\frac{15}{16x26}+\frac{15}{26x36}}{\frac{33}{6x16}-\frac{63}{16x26}+\frac{93}{26x36}}\)
\(\Rightarrow D=\frac{15.\frac{1}{6x16}+15.\frac{1}{16x26}+15.\frac{1}{26x36}}{3.11.\frac{1}{6x16}-3.21.\frac{1}{16x26}+3.31.\frac{1}{26x36}}\)
\(\Rightarrow D=\frac{15.\left(\frac{1}{6x16}+\frac{1}{16x26}+\frac{1}{26x36}\right)}{3.\left(\frac{11}{6x16}-\frac{21}{16x26}+\frac{31}{26x36}\right)}\)
\(\Rightarrow D=5.\left(\frac{1}{6x16}+\frac{1}{16x26}+\frac{1}{26x36}\right):\left(\frac{11}{6x16}-\frac{21}{16x26}+\frac{31}{26x36}\right)\)
\(A=\frac{16-11}{11.16}+\frac{21-16}{16.21}+...+\frac{66-61}{61.66}\)
\(A=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}=\frac{1}{11}-\frac{1}{66}=\frac{5}{66}\)