Sắp xếp các phân số sau theo thứ tự tăng dần:

a) \(\frac{2}{3};\,\,\frac{5}{4};\,\,\frac{3}{8};\,\,\frac{7}{5};\,\,\frac{6}{5}\)

b) \(\frac{3}{4};\,\,\frac{{11}}{8};\,\,\frac{5}{6};\,\,\frac{2}{9};\,\,\frac{8}{3}\)

c) \(\frac{{26}}{{15}};\,\,\frac{{215}}{{253}};\,\,\frac{{18}}{{18}};\,\,\frac{{26}}{{11}};\,\,\frac{{162}}{{253}}\)

a) \(\frac{3}{5}\) < 1 b) \(\frac{7}{6}\,\, > 1\)                            c) \(\frac{4}{5}\) < 1     d) \(\frac{9}{{14}}\) < 1

e) \(\frac{8}{3}\) > 1 f) \(\frac{{14}}{3}\, > \frac{{10}}{3}\)     g) \(\frac{5}{7} > \frac{3}{7}\)                      h) \(\frac{7}{5} < \frac{9}{5}\)

i) \(\frac{{218}}{{376}} < \frac{{218}}{{367}}\)                       j) \(\frac{{721}}{{218}} < \frac{{721}}{{215}}\)                         

k)

Vì: \(\frac{{1999}}{{2003}} < 1 < \frac{9}{8}\) Nên: \[\frac{{1999}}{{2003}} < \frac{9}{8}\]   

l)

Vì: \(\frac{{12}}{{31}} < 1 < \frac{{22}}{{21}}\) Nên: \[\frac{{12}}{{31}} < \frac{{22}}{{21}}\]

m)                            

Vì: \(\frac{{47}}{{52}} > \frac{{47}}{{58}} > \frac{{45}}{{58}}\) Nên: \(\frac{{47}}{{52}} > \frac{{45}}{{58}}\)

n)                             

\(\frac{{2015}}{{2011}} - 1 = \frac{4}{{2011}}\)

\(\frac{{1996}}{{1992}} - 1 = \frac{4}{{1992}}\)

Vì: \(\frac{4}{{2011}} < \frac{4}{{1992}}\) Nên: \(\frac{{2015}}{{2011}}\,\, < \frac{{1996}}{{1992}}\)

o)

Vì: \(\frac{{1998}}{{1995}} > 1 > \frac{{2015}}{{2016}}\) Nên: \(\frac{{1998}}{{1995}} > \frac{{2015}}{{2016}}\)

p)

Ta có:

\(\frac{{222}}{{333}} = \frac{{222:111}}{{333:111}} = \frac{2}{3} = 1 - \frac{1}{3}\)

\(\frac{{333}}{{444}} = \frac{{333:111}}{{444:111}} = \frac{3}{4} = 1 - \frac{1}{4}\)

Vì \(\frac{1}{3} > \frac{1}{4}\) nên \(\frac{2}{3} < \frac{3}{4}\) hay \(\frac{{222}}{{333}} < \frac{{333}}{{444}}\)

q)

Vì: \(\frac{{1313}}{{1515}} < \frac{{1326}}{{1515}} < \frac{{1326}}{{1428}}\) nên \(\frac{{1313}}{{1515}} < \frac{{1326}}{{1428}}\)

r)

\(\frac{{119}}{{120}} = 1 - \frac{1}{{120}}\)

\(\frac{{118}}{{119}} = 1 - \frac{1}{{119}}\)

Vì: \(\frac{1}{{120}} < \frac{1}{{119}}\) Nên: \(\frac{{119}}{{120}} > \frac{{118}}{{119}}\)

s)

\(\frac{{222}}{{555}} = \frac{{222:111}}{{555:111}} = \frac{2}{5}\)

\(\frac{{333}}{{444}} = \frac{{333:111}}{{444:111}} = \frac{3}{4}\)

Vì \(\frac{2}{5} < \frac{3}{5} < \frac{3}{4}\) nên \(\frac{2}{5} < \frac{3}{4}\) hay \(\frac{{222}}{{555}} < \frac{{333}}{{444}}\)