Ta có :

\(\frac{1313}{9191}\)= \(\frac{1}{7}\)= \(\frac{11}{77}\)

\(\frac{1111}{7373}\)= \(\frac{11}{73}\)

Vì \(\frac{11}{77}\)< \(\frac{11}{73}\)( 77>73)

=> \(\frac{1313}{9191}\)> \(\frac{1111}{7373}\)

\(\frac{1313}{9191}=\frac{1}{7}=\frac{1.11}{7.11}=\frac{11}{77}\)

\(\frac{1111}{7373}=\frac{11}{73}\)

\(\Rightarrow\frac{11}{77}< \frac{11}{73}\Rightarrow\frac{1313}{9191}>\frac{1111}{7373}\)

\(c\frac{1313}{9191}=\frac{1313:101}{9191:101}=\frac{13}{91}=\frac{1}{7}\)

\(\frac{1111}{7373}=\frac{1111:101}{7373:101}=\frac{11}{73}\)

\(mà\frac{1}{7}=\frac{1}{77}\Rightarrow\frac{11}{77}< \frac{11}{73}\)

vậy \(\frac{1313}{9191}< \frac{1111}{7373}\)

quy đồng các phân số sao cho chúng cùng mẫu là so sánh được

Ta có:

a)18/91=18:91=0,197802197

   23/114=23:114=0,201754386

Mà:0,197802197<0,201754386 nên 18/91<23/114

b)21/52=21:52=0,403846153

   213/523=213:523=0,407265774

Mà:0,403846153<0,407265774 nên 21/52<213/523

c)1313/9191=1313:9191=0,142857142

   1111/7373=1111:7373=0,150684931

Mà:0,142857142<0,150684931 nên 1313/9191<1111/7373

^^^^!~~~
 

a) \(\frac{18}{91}=18\div91=0,1978021978\)

\(\frac{23}{114}=23\div114=0,20175438596\)

Mà \(0,1978021978< 0,20175438596\)nên \(\frac{18}{91}< \frac{23}{114}\) 

b) Cũng tương tự như phần a.

c) Cũng tương tự như phần a.

a) <

b) >

c) <

a) Ta có :

\(\frac{18}{91}< \frac{18}{90}=\frac{1}{5}=\frac{23}{115}< \frac{23}{114}\)

\(\Rightarrow\frac{18}{91}< \frac{23}{114}\)

b) Ta có :

\(\frac{21}{52}=\frac{210}{520}=1-\frac{310}{520}\)

\(\frac{213}{523}=1-\frac{310}{523}\)

Mà \(1-\frac{310}{520}< 1-\frac{310}{523}\)

\(\Rightarrow\frac{21}{52}< \frac{213}{523}\)

c) Ta có : \(\frac{1313}{9191}=\frac{13}{91}=\frac{1}{7}=\frac{11}{77};\frac{1111}{7373}=\frac{11}{73}\)

Mà \(\frac{11}{77}< \frac{11}{73}\)nên \(\frac{1313}{9191}< \frac{1111}{7373}\)

d) Ta có :

\(\frac{n}{n+1}=\frac{n+1-1}{n+1}=1-\frac{1}{n+1}\)

\(\frac{n+2}{n+3}=\frac{n+3-1}{n+3}=1-\frac{1}{n+3}\)

Mà \(1-\frac{1}{n+1}< 1-\frac{1}{n+3}\)nên \(\frac{n}{n+1}< \frac{n+2}{n+3}\)

a) Ta có : \(\frac{18}{91}< \frac{18}{90}=\frac{1}{5}< \frac{23}{115}< \frac{23}{114}\)

\(\Rightarrow\)       \(\frac{18}{91}< \frac{23}{114}\)

Vậy \(\frac{18}{91}< \frac{23}{114}\)

b) Ta có : \(\frac{21}{52}< \frac{21}{56}=\frac{3}{8}< \frac{213}{568}< \frac{213}{523}\)

\(\Rightarrow\)      \(\frac{21}{52}< \frac{213}{523}\)

Vậy \(\frac{21}{52}< \frac{213}{523}\)

c) Ta có : \(\frac{1313}{9191}=\frac{1313:1313}{9191:1313}=\frac{1}{7}\)

               \(\frac{1111}{7373}=\frac{1111:101}{7373:101}=\frac{11}{73}\)

  Lại có :   \(\frac{1}{7}< \frac{11}{77}< \frac{11}{73}\)

\(\Rightarrow\)       \(\frac{1313}{9191}< \frac{1111}{7373}\)

Vậy \(\frac{1313}{9191}< \frac{1111}{7373}\)

d) Ta có : \(1-\frac{n}{n+1}=\frac{n+1}{n+1}-\frac{n}{n+1}=\frac{1}{n+1}\)

                \(1-\frac{n+2}{n+3}=\frac{n+3}{n+3}-\frac{n+2}{n+3}=\frac{1}{n+3}\)

      Vì \(n+1< n+3\)

\(\Rightarrow\)\(\frac{1}{n+1}>\frac{1}{n+3}\)

\(\Rightarrow\) \(\frac{n}{n+1}< \frac{n+2}{n+3}\)

Vậy \(\frac{n}{n+1}< \frac{n+2}{n+3}\)

                   Chúc m.n hok tốt ♡❤️

P/s : 

a)

Ta có : \(\frac{18}{91}< \frac{18}{90}=\frac{1}{5}< \frac{23}{115}< \frac{23}{114}\)

\(\Rightarrow\)       \(\frac{18}{91}< \frac{23}{114}\)

Vậy \(\frac{18}{91}< \frac{23}{114}\)

b)

Ta có : \(\frac{21}{52}< \frac{21}{56}=\frac{3}{8}< \frac{213}{568}< \frac{213}{523}\)

\(\Rightarrow\)      \(\frac{21}{52}< \frac{213}{523}\)

Vậy \(\frac{21}{52}< \frac{213}{523}\)

c)

Ta có : \(\frac{1313}{9191}=\frac{1313:1313}{9191:1313}=\frac{1}{7}\)

               \(\frac{1111}{7373}=\frac{1111:101}{7373:101}=\frac{11}{73}\)

  Lại có :   \(\frac{1}{7}< \frac{11}{77}< \frac{11}{73}\)

\(\Rightarrow\)       \(\frac{1313}{9191}< \frac{1111}{7373}\)

Vậy \(\frac{1313}{9191}< \frac{1111}{7373}\)

d )   

Ta có : 

\(\frac{n}{n+1}=\frac{n+1-1}{n+1}=1-\frac{1}{n+1}\)

\(\frac{n+2}{n+3}=\frac{n+3-1}{n+3}=1-\frac{1}{n+3}\)

Do \(\frac{1}{n+1}>\frac{1}{n+3}\left(n+1< n+3\right)\)

\(\Rightarrow1-\frac{1}{n+1}>1-\frac{1}{n+3}\)

\(\Rightarrow\frac{n}{n+1}>\frac{n+2}{n+3}\)

Vậy ...

~ Ủng hộ nha 

\(\frac{1313}{9191}=\frac{1313:1313}{9191:1313}=\frac{1}{7}=\frac{73}{511}\)

\(\frac{1111}{7373}=\frac{1111:101}{7373:101}=\frac{11}{73}=\frac{77}{511}\)

Vì \(\frac{73}{511}< \frac{77}{511}\) nên \(\frac{1313}{9191}< \frac{1111}{7373}\).

\(\frac{1313}{9191}=\frac{13}{91}=\frac{1}{7}=0.14...\)

\(\frac{1111}{7373}=\frac{11}{73}=0,15.....\)

MÀ 0, 14 <0, 15

=> \(\frac{1313}{9191}< \frac{1111}{7373}\)