\(\dfrac{97}{100}\)  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:

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

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

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

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

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

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

\(a,\frac{8}{9}< \frac{108}{109}\)

\(b,\frac{97}{100}< \frac{98}{99}\)

\(c,\frac{19}{18}>\frac{2017}{2016}\)

\(d,\frac{15}{16}>\frac{515}{616}\)

\(\frac{25}{49}>\frac{25}{50}=\frac{1}{2}=\frac{35}{70}>\frac{35}{71}\)

Do đó \(\frac{25}{49}>\frac{35}{71}\).

\(\frac{1997}{2003}=\frac{2003-6}{2003}=1-\frac{6}{2003}\)

\(\frac{1995}{2001}=\frac{2001-6}{2001}=1-\frac{6}{2001}\)

Có \(\frac{6}{2003}< \frac{6}{2001}\)do đó \(\frac{1997}{2003}>\frac{1995}{2001}\).

\(\frac{2020}{2018}=\frac{2018+2}{2018}=1+\frac{2}{2018}< 1+\frac{2}{2016}=\frac{2018}{2016}\)

a) \(\frac{8}{9}=1-\frac{1}{9}\)  

\(\frac{108}{109}=1-\frac{1}{109}\)  

Vì \(\frac{1}{9}>\frac{1}{109}\)  

Nên \(1-\frac{1}{9}< 1-\frac{1}{109}\)   

Vậy \(\frac{8}{9}< \frac{108}{109}\)  

b) 

\(\frac{97}{100}=\frac{97\cdot99}{100\cdot99}\)  

\(\frac{98}{99}=\frac{98\cdot100}{99\cdot100}\) 

\(\Rightarrow\frac{97}{100}< \frac{98}{99}\)

a) Phân số đó là: \(\frac{7}{20}\)

b) \(\frac{7}{8}=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}\)

c) Gập sợi dây 4 lần và cắt 1/4. Đoạn còn lại dài: \(\left(1-\frac{1}{4}\right)\times\frac{2}{3}=\frac{3}{4}\times\frac{2}{3}=\frac{1}{2}\left(m\right)\)

d) \(\frac{114}{121}=\frac{228}{242}>\frac{225}{242}\)

e) \(\frac{2001}{2003}>\frac{1999}{2003}>\frac{1999}{2006}\)

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