A. 13/5 = 2 + 3/5   ;  15/7 = 2 + 1/7

    3/5 > 1/7 =>  13/5 > 15/7

B. 2012/1999 = 1 + 13/1999  ;  1999/1986 = 1 + 13/1986

13/1999 < 13/1986 => 2012/1999 < 1999/1986

C. 33/17 = 1 + 16/17

    37/18 = 2 + 1/18

=> 33/17 < 37/18 =>  17/33 > 18/37

D. 405/203 = 1 + 202/203

    203/101 = 2 + 1/101

=> 405/203 < 203/101 => 203/405 > 101/203

Lời giải:
$\frac{53}{17}=\frac{51+2}{17}=\frac{51}{17}+\frac{2}{17}=3+\frac{2}{17}$

$>3+\frac{2}{23}=\frac{3.23+2}{23}=\frac{71}{23}$

Ai trả lời đc mình sẽ 👍 nha

\(a.\)

\(\dfrac{9}{7}=\dfrac{7+2}{7}=1+\dfrac{2}{7}\)

\(\dfrac{11}{13}=\dfrac{13-2}{13}=1-\dfrac{2}{13}\)

Ta có : \(\dfrac{2}{7}>\dfrac{-2}{13}\)

\(\Rightarrow\dfrac{9}{7}>\dfrac{11}{13}\)

a ) Ta có 

\(\frac{29}{33}>\frac{29}{37}\)( đồng tử khác mẫu )

\(\frac{22}{37}< \frac{29}{37}\)( đồng mẫu khác tử )

=> \(\frac{29}{33}>\frac{29}{37}>\frac{22}{37}\)

b )  \(\frac{163}{257}< \frac{163}{221}\)

  \(\frac{162}{257}>\frac{149}{257}\)

  \(\Rightarrow\frac{163}{221}>\frac{163}{257}>\frac{149}{257}\)

a) ta có: \(\frac{22}{37}< \frac{29}{37}\)

\(\frac{29}{33}>\frac{29}{37}\)

\(\Rightarrow\frac{22}{37}< \frac{29}{37}< \frac{29}{33}\)

b) ta có: \(\frac{163}{257}>\frac{149}{257}\)

\(\frac{163}{221}>\frac{163}{257}\)

\(\Rightarrow\frac{163}{221}>\frac{163}{257}>\frac{149}{257}\)

a. \(\dfrac{10}{21}>1\)

\(\dfrac{9}{23}< 1\)

\(\Rightarrow\dfrac{10}{21}>\dfrac{9}{23}\)

b. \(\dfrac{32}{33}>\dfrac{31}{33}>\dfrac{31}{34}\Rightarrow\dfrac{32}{33}>\dfrac{31}{34}\)

c. \(\dfrac{44}{47}< \dfrac{45}{47}< \dfrac{45}{46}\Rightarrow\dfrac{44}{47}< \dfrac{45}{46}\)

\(d.\dfrac{70}{117}< \dfrac{70}{115}=\dfrac{14}{23}\Rightarrow\dfrac{70}{117}< \dfrac{14}{23}< \dfrac{15}{23}\)

\(\Rightarrow\dfrac{70}{117}< \dfrac{15}{23}\)

\(\frac{23}{3}>\frac{15}{2}\)

\(\frac{14}{7}>\frac{2}{9}\)

\(\frac{12}{13}< \frac{13}{14}\)

\(\frac{17}{16}< \frac{16}{15}\)

\(\frac{8}{6}>\frac{42}{43}\)

\(\frac{18}{17}\)và \(\frac{17}{15}\)

Ta có : \(\frac{18}{17}=\frac{18\times2}{17\times2}=\frac{36}{34}\)và giữ nguyên phân số \(\frac{17}{15}\).

\(\frac{36}{34}-1=\frac{2}{34};\frac{17}{15}-1=\frac{2}{15}\)

Vì \(\frac{2}{34}< \frac{2}{15}\)nên \(\frac{36}{34}< \frac{17}{15}\)hay \(\frac{18}{17}< \frac{17}{15}\).

Chúc bạn hok tốt !

\(\frac{18}{17}=\frac{17}{17}+\frac{1}{17}=1+\frac{1}{17}\)

\(\frac{17}{15}=\frac{15}{15}+\frac{2}{15}=1+\frac{2}{15}\)

Có:  \(\frac{1}{17}< \frac{1}{15}\)

và      \(1< 2\)

=> \(1.\frac{1}{17}< 2.\frac{1}{15}\)

=> \(\frac{1}{17}< \frac{2}{15}\)

=> \(1+\frac{1}{17}< 1+\frac{2}{15}\)

=> \(\frac{18}{17}< \frac{17}{15}\)