`1.`

`a) 12/14 ; 1212/1414 ; 121212/141414`

`12/14 = `$\dfrac{12 : 2}{14 : 2}$` = 6/7.`

`1212/1414 = `$\dfrac{1212 : 202}{1414 : 202}$` = 6/7.`

`121212/141414 = `$\dfrac{121212 : 20202}{141414 : 20202}$` = 6/7`

$\text{Vì }$`6/7 = 6/7 = 6/7`

`=> 12/14 = 1212/1414 =  121212/141414.`

`b) 24/35 ; 2424/3535 ; 242424/353535`

`2424/3535 = `$\dfrac{2424 : 101}{3535 : 101}$` = 24/35.`

`242424/353535 = `$\dfrac{242424 : 10101}{353535 : 10101}$` = 24/35.`

$\text{Vì }$`24/35 = 24/35 = 24/35`

`=> 24/35 = 2424/3535 =  242424/353535.`

`c) `$\dfrac{ab}{cd}$` ; `$\dfrac{abab}{cdcd}$` ; `$\dfrac{ababab}{cdcdcd}$

$\dfrac{ababa}{cdcd}$ `= `$\dfrac{abab : 101}{cdcd : 101}$` = `$\dfrac{ab}{cd}$.

$\dfrac{ababab}{cdcdcd}$` = `$\dfrac{ababab : 10101}{cdcdcd : 10101}$` = `$\dfrac{ab}{cd}$.

$\text{Vì }$ $\dfrac{ab}{cd}$` = `$\dfrac{ab}{cd}$` = `$\dfrac{ab}{cd}$

`=> `$\dfrac{ab}{cd}$` = `$\dfrac{abab}{cdcd}$` =  `$\dfrac{ababab}{cdcdcd}$`.`

`d) 123/145 ; 123123/145145 ; 123123123/145145145`

`123123/145145 = `$\dfrac{123123 : 1001}{145145 : 1001}$` = 123/145.`

`123123123/145145145 = `$\dfrac{123123123 : 1001001}{145145145 : 1001001}$` = 123/145.`

$\text{Vì }$`123/145 = 123/145 = 123/145`

`=> 123/145 = 123123/145145 =  123123123/145145145.`

`e) 122436/132639 và 12/13`

`122436/132639 = `$\dfrac{122436 : 10203}{132639 : 10203}$` = 12/13`

`Vì 12/13 = 12/13`

`=> 122436/132639 = 12/13.`

`f) 22/25 và 224466/255075`

`224466/255075 = `$\dfrac{224466 : 10203}{255075 : 10203}$` = 22/25.`

`Vì 22/25 = 22/25`

`=> 224466/255075 = 22/25.`

`2.`

`a) 12/14 ; 1212/1414 ; 121212/141414`

`12/14 = `$\dfrac{12 : 2}{14 : 2}$` = 6/7.`

`1212/1414 = `$\dfrac{1212 : 202}{1414 : 202}$` = 6/7.`

`121212/141414 = `$\dfrac{121212 : 20202}{141414 : 20202}$` = 6/7`

$\text{Vì }$`6/7 = 6/7 = 6/7`

`=> 12/14 = 1212/1414 =  121212/141414.`

`b) 24/35 ; 2424/3535 ; 242424/353535`

`2424/3535 = `$\dfrac{2424 : 101}{3535 : 101}$` = 24/35.`

`242424/353535 = `$\dfrac{242424 : 10101}{353535 : 10101}$` = 24/35.`

$\text{Vì }$`24/35 = 24/35 = 24/35`

`=> 24/35 = 2424/3535 =  242424/353535.`

`3. `

`a) 1995/1994 và 2003/2002`

`1995/1994 = 1 + 1/1994.`

`2003/2002 = 1 + 1/2002.`

`Vì 1/1994 > 1/2002`

`=> 1 + 1/1994 > 1 + 1/2002`

`=> 1995/1994 > 2003/2002.`

`b) 2003/2000 và 1999/1996`

`2003/2000 = 1 + 3/2000`

`1999/1996 = 1 + 3/1996`

`Vì 3/2000 < 3/1996`

`=> 1 + 3/2000 < 1 + 3/1996`

`=> 2003/2000 < 1999/1996.`

`c) 299/295 và 279/275`

`299/295 = 1 + 4/295`

`279/275 = 1 + 4/275`

`Vì 4/295 < 4/275`

`=> 1 + 4/295 < 1 + 4/275`

`=> 299/295 < 279/275.`