27/31<2727/3131

11/31<111/311

\(2^{111}=\left(2^3\right)^{37}=8^{37}\)

\(3^{77}>3^{74}=\left(3^2\right)^{37}=9^{37}\)

Vì \(8^{37}< 9^{37}\Rightarrow2^{111}< 9^{37}< 3^{77}\)

Ta có:

\(\dfrac{199}{115}>\dfrac{115}{115}=1\\ \dfrac{111}{116}< \dfrac{116}{116}=1\)

Vậy \(\dfrac{199}{115}>\dfrac{111}{116}\)

199/115>111/116

-111/5  x  3= -333/15

do -15 lớn hơn -17 => -111/5 >-333/17

-337/339= -115/339 - 222/339

-115/339 > -155/133   => -337/339 > -155/133

\(\frac{3}{13}+4\frac{7}{26}+1\frac{1}{12}=5+\left(\frac{3}{13}+\frac{7}{26}+\frac{1}{12}\right)=5\frac{7}{12}\)

\(\frac{2}{3}+\frac{4}{37}+5\frac{5}{11}=5+\left(\frac{2}{3}+\frac{4}{27}+\frac{5}{111}\right)\)ta thấy 2/3 > 7/12

Nên \(\frac{3}{13}+4\frac{7}{26}+1\frac{1}{2}\)< \(\frac{2}{3}+\frac{4}{37}+5\frac{5}{111}\)

Cai sau lớn hơn