\(a,A=\frac{13}{20}-\frac{6}{7}:\frac{10}{21}\)
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Ta có: \(10A=\frac{10^{21}-60}{10^{21}-6}=\frac{10^{21}-6-54}{10^{21}-6}=1-\frac{54}{10^{21}-6}\)
\(10B=\frac{10^{22}-60}{10^{22}-6}=\frac{10^{22}-6-54}{10^{22}-6}=1-\frac{54}{10^{22}-6}\)
ta có: \(10^{21}-6<10^{22}-6\)
=>\(\frac{54}{10^{21}-6}>\frac{54}{10^{22}-6}\)
=>\(-\frac{54}{10^{21}-6}<-\frac{54}{10^{22}-6}\)
=>\(-\frac{54}{10^{21}-6}+1<-\frac{54}{10^{22}-1}+1\)
=>\(\frac{A}{10}<\frac{B}{10}\)
=>A<B
b) \(\frac{\frac{2}{3}+\frac{5}{7}+\frac{4}{21}}{\frac{5}{6}+\frac{11}{7}-\frac{7}{21}}\)
\(=\frac{\frac{29}{21}+\frac{4}{21}}{\frac{101}{42}-\frac{7}{21}}\)
\(=\frac{\frac{11}{7}}{\frac{29}{14}}\)
\(=\frac{22}{29}.\)
Chúc bạn học tốt!
\(A=\frac{7}{6}+\frac{13}{12}+\frac{21}{20}+...+\frac{9901}{9900}=\left(1+\frac{1}{2.3}\right)+\left(1+\frac{1}{3.4}\right)+\left(1+\frac{1}{4.5}\right)+...+\left(1+\frac{1}{99.100}\right)\)\(=\left(1+1+1+...+1\right)+\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\right)\)
\(=98+\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\right)=98+\left(\frac{1}{2}-\frac{1}{100}\right)\)
\(=98+\frac{49}{100}=98\frac{49}{100}\)
\(\frac{3}{5}-\frac{-7}{10}+\frac{13}{20}=\frac{12}{20}-\frac{-14}{20}+\frac{13}{20}=\frac{12-\left(-14\right)+13}{20}=\frac{12+14+13}{20}=\frac{39}{20}< \frac{40}{20}=2\)
Vậy \(\frac{3}{5}-\frac{-7}{10}+\frac{13}{20}< 2\)
\(\frac{3-\frac{3}{7}+\frac{3}{13}-\frac{3}{2018}}{7-\frac{7}{20}+\frac{7}{13}-\frac{7}{2018}}\)
\(=\frac{3\left(1-\frac{1}{20}+\frac{1}{13}-\frac{1}{2018}\right)}{7\left(1-\frac{1}{20}+\frac{1}{13}-\frac{1}{2018}\right)}\)
\(=\frac{3}{7}\)