a, \(\dfrac{17}{23}\ne\dfrac{1717}{-2323}\) vì:

\(\dfrac{1717}{-2323}=\dfrac{1717:101}{\left(-2323\right):101}=\dfrac{17}{-23}\)

và \(\dfrac{17}{23}\ne\dfrac{17}{-23}\) => Vậy \(\dfrac{17}{23}\ne\dfrac{1717}{-2323}\)

b, \(\dfrac{-31}{49}=\dfrac{-313131}{494949}\) vì:

\(\dfrac{-313131}{494949}=\dfrac{\left(-313131\right):10101}{494949:10101}=\dfrac{-31}{49}\)

và \(\dfrac{-31}{49}=\dfrac{-31}{49}\) => Vậy \(\dfrac{-31}{49}=\dfrac{-313131}{494949}\)

2323/3131 = 23 x 101/31 x 101 

232323/313131 = 23 x 1001/31 x 1001

23232323/31313131 = 23 x 10001/31 x 10001

vậy tất cả phân số đó bằng nhau 

So sánh 54,54×2323,23 và 23,23×5454,54

\(\frac{27}{31}=\frac{27x10101}{31x10101}=\frac{272727}{313131}\)

27/31 = 272727/313131

27/31 = 272727/313131

0,(31)=0,313131...

0,3(13)=0,313131...

vậy 0,(31) = 0,3(13)

\(0,\left(31\right)=\frac{31}{99}\)

\(0,3\left(13\right)=\frac{313-3}{990}=\frac{310}{990}=\frac{31}{99}\)

Vậy.......

dễ thế mà

Ta có:

\(\frac{-181818}{313131}=\frac{-181818:10101}{313131:10101}=\frac{-18}{31}\)

Vì \(\frac{-18}{31}=\frac{-18}{31}\)

\(\Rightarrow\frac{-18}{31}=\frac{-181818}{313131}\)

181818/313131=18/31

suy ra -18/31 < 181818/313131

Ta có : \(\frac{-18}{31}\) và   \(\frac{-181818}{313131}=\frac{\left(-181818\right):10101}{313131:10101}=\frac{-18}{31}\)

Vì \(\frac{-18}{31}=\frac{-18}{31}\)nên \(\frac{-18}{31}=\frac{-181818}{313131}\)

Vậy  \(\frac{-18}{31}=\frac{-181818}{313131}\)

Ta co :\(-\frac{18}{13}\&-\frac{181818}{313131}\)

\(\Rightarrow\frac{-181818}{313131}=-\frac{18}{31}\)

Vi :\(-\frac{18}{31}=-\frac{18}{31}\)

vay :\(-\frac{18}{31}=-\frac{181818}{313131}\)

-181818/313131=-18/31

vi-18/31=-18/31nen -18/31=-181818/313131

Ta có 0,(31) – 0,3(13) = 0,313131... - 0,31313 ... = 0

Vậy 0,(31) = 0,3(13)

Ta có: 2 . 8 = 16 ; 3 . 6 = 18 ≠ 16

Suy ra 

Ta có: 1 . 12 = 12 ; 3 . 4 = 12

Suy ra