a) Ta có :

\(\frac{19}{23}=\frac{19.101}{23.101}=\frac{1919}{2323}\)

\(\Rightarrow\frac{19}{23}=\frac{1919}{2323}\)

b) Ta có 

\(\frac{10}{60}=\frac{10.10101}{60.10101}=\frac{101010}{606060}\)

\(\Rightarrow\frac{10}{60}=\frac{101010}{606060}\)

c) Ta có 

\(\frac{123}{124}=\frac{123.1001}{124.1001}=\frac{123123}{124124}\)

\(\Rightarrow\frac{123}{124}=\frac{123123}{124124}\)

Xét :

\(\frac{122}{123}-1=-\frac{1}{123}\)

\(\frac{123}{124}-1=-\frac{1}{124}\)

Vì \(-\frac{1}{123}< -\frac{1}{124}\)

\(\Rightarrow\frac{122}{123}< \frac{123}{124}\)

\(\Rightarrow\frac{122}{123}< \frac{123123}{124124}\)

Ta có : \(\frac{124124}{125125}=\frac{124124:1001}{125125:1001}=\frac{124}{125}\)

\(\frac{123}{124}=1-\frac{1}{124}\); \(\frac{124}{125}=1-\frac{1}{125}\)

Vì 1/124 < 1/125 => 123/124 > 123/125 => 123/124 > 124124/125125

ta có: \(\frac{124124}{125125}=\frac{124}{125}\)

Lại có: \(1-\frac{123}{124}=\frac{1}{124};1-\frac{124}{125}=\frac{1}{125}\)

\(\Rightarrow\frac{1}{124}>\frac{1}{125}\Rightarrow1-\frac{123}{124}>1-\frac{124}{125}\)

\(\Rightarrow\frac{123}{124}< \frac{124}{125}\Rightarrow\frac{123}{124}< \frac{124124}{125125}\)

So sánh 2 phân số : 123 / 124 và 124124 / 125125

124124 / 125125 = 124 / 125

123 / 124 = 1 - 123 / 124 = 1/124

124 / 125 = 1 - 124 / 125 = 1/125 

Vì 1/ 124 > 1/125 => 123/124 > 124124/125125

Vậy 123/124 > 124124/125125

232323/434343=23/43=161/301

6/7=258/301

mà 161<258

nên 232323/434343<6/7

2 phân số này đều bằng nhau vì 2 phân số đều có số chung là 19/21

1919/2121=19/21

191919/212121=19/21

Vậy 2 phân số bằng nhau.

Ta có : \(\frac{1919}{2121}=\frac{19}{21}\)

             \(\frac{191919}{212121}=\frac{19}{21}\)

Vì \(\frac{19}{21}=\frac{19}{21}\) \(\Rightarrow\) \(\frac{1919}{2121}=\frac{191919}{212121}\)

k nhá

Ta có:\(\dfrac{2323}{9999}=\dfrac{23.101}{99.101}=\dfrac{23}{99}\)

         \(\dfrac{232323}{999999}=\dfrac{23.10101}{99.10101}=\dfrac{23}{99}\)

\(\Rightarrow\dfrac{2323}{9999}=\dfrac{232323}{999999}\)

\(\dfrac{2323}{9999}=\dfrac{232323}{999999}\)

Ta có:
\(\dfrac{3434}{7878}=\dfrac{3434:202}{7878:202}=\dfrac{17}{39}\)
\(\Rightarrow\dfrac{3434}{7878}< \dfrac{20}{39}\)
\(-------\)
Ta có:
\(\dfrac{123123}{405405}=\dfrac{123123:1001}{405405:1001}=\dfrac{123}{405}\)
\(\Rightarrow\dfrac{123123}{405405}>\dfrac{123}{1109}\)
\(---------\)
Ta có:
\(\dfrac{666666}{323232}=\dfrac{666666:80808}{323232:80808}=\dfrac{8,25}{4}\)
\(\Rightarrow\dfrac{666666}{323232}< \dfrac{25}{4}\)