\(\dfrac{97}{100}\)  và \(\dfrac{98}{99}\)

\(\dfrac{97}{100}=\dfrac{97\times99}{100\times99}=\dfrac{9603}{9900}\)

\(\dfrac{98}{99}=\dfrac{98\times100}{99\times100}=\dfrac{9800}{9900}\)

Vì: \(9603< 9800\)  nên => \(\dfrac{97}{100}< \dfrac{98}{99}\)

\(\dfrac{13}{17}\)  và \(\dfrac{131}{171}\)

\(\dfrac{13}{17}=\dfrac{13\times171}{17\times171}=\dfrac{2223}{2907}\)

\(\dfrac{131}{171}=\dfrac{131\times17}{171\times17}=\dfrac{2227}{2907}\)

Vì: \(2227>2223\)  nên: => \(\dfrac{13}{17}< \dfrac{131}{171}\)

\(\dfrac{51}{61}\)  và \(\dfrac{515}{616}\)

\(\dfrac{51}{61}=\dfrac{51\times616}{61\times616}=\dfrac{31416}{37576}\)

\(\dfrac{515}{616}=\dfrac{515\times61}{616\times61}=\dfrac{31415}{37576}\)

Vì: \(31416>31415\)  Nên => \(\dfrac{51}{61}>\dfrac{515}{616}\)

a/

$\frac{97}{100}< \frac{98}{100}< \frac{98}{99}$

c/

$\frac{131}{171}=1-\frac{40}{171}> 1-\frac{40}{170}=1-\frac{4}{17}=\frac{13}{17}$
d/

$\frac{51}{61}=1-\frac{10}{61}=1-\frac{100}{610}$

$\frac{515}{616}=1-\frac{101}{616}$

Xét hiệu:

$\frac{100}{610}-\frac{101}{616}=\frac{100.616-101.610}{610.616}$

$=\frac{100(610+6)-101.610}{610.616}$

$=\frac{600-610}{610.616}<0$

$\Rightarrow \frac{100}{610}< \frac{101}{616}$

$\Rightarrow 1-\frac{100}{610}> 1-\frac{101}{616}$

$\Rightarrow \frac{51}{61}> \frac{515}{616}$ 

Vì 5 < 1000

Nên 1/5>1/1000

Vậy 1/5>1/1000

\(\frac{-1}{8}>\frac{-1}{7}>\frac{2}{-7}\)

-1/8=-7/56

2/-7=-2/7=-16/56

vì -7>-16

=>-7/56>-16/56

=>-1/8>2/-7

Do đó 

Do đó 

Do đó