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\(\frac{22}{29}=1-\frac{7}{29}\)
\(\frac{34}{41}=1-\frac{7}{41}\)
\(\frac{7}{29}\)>\(\frac{7}{41}\Rightarrow\frac{22}{29}\)<\(\frac{34}{41}\)
Ta có: \(\frac{22}{29}< \frac{22}{28}=\frac{11}{14}=\frac{33}{42}< \frac{34}{42}< \frac{34}{41}\)
Vậy \(\frac{22}{29}< \frac{34}{41}\)
\(-23\frac{2}{7};-24\frac{2}{5}\)
Ta có : -23 > -24 \(\Leftrightarrow\)\(-23\frac{2}{7}>-24\frac{2}{5}\)
\(VP=\dfrac{2013}{1}+\dfrac{2012}{2}+...+\dfrac{2}{2012}+\dfrac{1}{2013}\)
\(VP=2013+\dfrac{2012}{2}+...+\dfrac{2}{2012}+\dfrac{1}{2013}\)
\(VP=1+\left(\dfrac{2012}{2}+1\right)+....+\left(\dfrac{2}{2012}+1\right)+\left(\dfrac{1}{2013}+1\right)\)
\(VP=\dfrac{2014}{2014}+\dfrac{2014}{2}+...+\dfrac{2014}{2012}+\dfrac{2014}{2013}\)
\(VP=2014\left(\dfrac{1}{2}+..+\dfrac{1}{2012}+\dfrac{1}{2013}+\dfrac{1}{2014}\right)\)
\(VP-VT=2014\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2014}\right)-x\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2014}\right)=0\)
\(\Rightarrow\left(2014-x\right)\left(\dfrac{1}{2}+\dfrac{1}{3}+....+\dfrac{1}{2014}\right)=0\)
\(\Rightarrow x=2014\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2014}\ne0\right)\)
\(\frac{34}{43}\)và \(\frac{35}{42}\)
Chon phân số trung gian là : \(\frac{34}{42}\)
Vì \(\frac{34}{43}< \frac{34}{42};\frac{34}{42}< \frac{35}{42}\)nên \(\frac{34}{43}< \frac{35}{42}\)
\(\frac{47}{15}\)và \(\frac{29}{35}\)
Chọn phân số trung gian là : \(\frac{47}{35}\)
Vì \(\frac{47}{15}>\frac{47}{35};\frac{47}{35}>\frac{29}{35}\)nên \(\frac{47}{15}>\frac{29}{35}\)
Ta có :
\(\frac{34}{43}< \frac{34}{42}\left(43>42\right)\)
Mà \(\frac{34}{42}< \frac{35}{42}\left(34< 35\right)\)
\(\Rightarrow\frac{34}{43}< \frac{35}{42}\)
Ta có :
\(\frac{47}{15}>\frac{47}{35}\left(15< 35\right)\)
Mà \(\frac{29}{35}< \frac{47}{35}\left(29< 47\right)\)
\(\Rightarrow\frac{47}{15}>\frac{29}{35}\)
~ Ủng hộ nhé
Ta có: \(22\frac{2}{9}=\frac{200}{9}\)
\(34\frac{4}{1}=38=\frac{342}{9}\)
Vì \(\frac{200}{9}< \frac{342}{9}\)nên \(22\frac{2}{9}< 34\frac{4}{1}\)
Vậy \(22\frac{2}{9}< 34\frac{4}{1}\)