Giải:

a) \(\dfrac{-3}{7}\) và \(\dfrac{2}{-5}\) 

\(\dfrac{-3}{7}=\dfrac{-3.5}{7.5}=\dfrac{-15}{35}\) 

\(\dfrac{2}{-5}=\dfrac{-2}{5}=\dfrac{-2.7}{5.7}=\dfrac{-14}{35}\) 

Vì \(\dfrac{-15}{35}< \dfrac{-14}{35}\) nên \(\dfrac{-3}{7}< \dfrac{2}{-5}\) 

b) \(\dfrac{-6}{7}\) và \(\dfrac{19}{23}\) 

Vì \(\dfrac{-6}{7}\) là số âm mà \(\dfrac{19}{23}\) là số dương nên \(\dfrac{-6}{7}< \dfrac{19}{23}\) 

c) \(\dfrac{-11}{23}\) và \(\dfrac{-13}{21}\) 

\(\dfrac{-11}{23}=\dfrac{-11.13}{23.13}=\dfrac{-143}{299}\) 

\(\dfrac{-13}{21}=\dfrac{-13.11}{21.11}=\dfrac{-143}{231}\) 

Vì \(\dfrac{-143}{299}>\dfrac{-143}{231}\) nên \(\dfrac{-11}{23}>\dfrac{-13}{21}\) 

d) \(\dfrac{-1}{5}\) và \(\dfrac{1}{100}\) 

Vì \(\dfrac{-1}{5}\) là số âm mà \(\dfrac{1}{100}\) là số dương nên \(\dfrac{-1}{5}< \dfrac{1}{100}\) 

Giải: (tiếp)

e) \(\dfrac{267}{-268}\) và \(\dfrac{-1347}{1343}\) 

\(\dfrac{267}{-268}=\dfrac{-267}{268}=\dfrac{-267.449}{268.449}=\dfrac{-119883}{120332}\) 

\(\dfrac{-1347}{1343}=\dfrac{-1347.89}{1343.89}=\dfrac{-119883}{119527}\)  

Vì \(\dfrac{-119883}{120332}>\dfrac{-119883}{119527}\) nên \(\dfrac{267}{-268}>\dfrac{-1347}{1343}\)

f) \(\dfrac{-13}{38}\) và \(\dfrac{29}{-88}\) 

\(\dfrac{-13}{38}=\dfrac{-13.29}{38.29}=\dfrac{-377}{1102}\)  

\(\dfrac{29}{-88}=\dfrac{-29}{88}=\dfrac{-29.13}{88.13}=\dfrac{-377}{1144}\) 

Vì \(\dfrac{-377}{1102}< \dfrac{-377}{1144}\) nên \(\dfrac{-13}{38}< \dfrac{29}{-88}\) 

g) \(\dfrac{4}{9}\) và \(\dfrac{13}{18}\) 

\(\dfrac{4}{9}=\dfrac{4.2}{9.2}=\dfrac{8}{18}\) 

Vì \(\dfrac{8}{18}< \dfrac{13}{18}\) nên \(\dfrac{4}{9}< \dfrac{13}{18}\) 

h) \(\dfrac{-15}{7}\) và \(\dfrac{-6}{5}\) 

\(\dfrac{-15}{7}=\dfrac{-15.5}{7.5}=\dfrac{-75}{35}\) 

\(\dfrac{-6}{5}=\dfrac{-6.7}{5.7}=\dfrac{-42}{35}\) 

Vì \(\dfrac{-75}{35}< \dfrac{-42}{35}\) nên \(\dfrac{-15}{7}< \dfrac{-6}{5}\)

Giải:

i) \(\dfrac{278}{37}\) và \(\dfrac{287}{46}\) 

\(\dfrac{278}{37}=\dfrac{278.46}{37.46}=\dfrac{12788}{1702}\) 

\(\dfrac{287}{46}=\dfrac{287.37}{46.37}=\dfrac{10619}{1702}\) 

Vì \(\dfrac{12788}{1702}>\dfrac{10619}{1702}\) nên \(\dfrac{278}{37}>\dfrac{287}{46}\) 

k) \(\dfrac{4}{9}\) và \(\dfrac{16}{21}\) 

\(\dfrac{4}{9}=\dfrac{4.7}{9.7}=\dfrac{28}{63}\) 

\(\dfrac{16}{21}=\dfrac{16.3}{21.3}=\dfrac{48}{63}\) 

Vì \(\dfrac{28}{63}< \dfrac{48}{63}\) nên \(\dfrac{4}{9}< \dfrac{16}{21}\) 

l) \(\dfrac{-11}{5}\) và \(\dfrac{4}{13}\) 

Vì \(\dfrac{-11}{5}\) là số âm mà \(\dfrac{4}{13}\) là số dương nên \(\dfrac{-11}{5}< \dfrac{4}{13}\) 

m) \(\dfrac{36}{49}\) và \(\dfrac{23}{56}\) 

\(\dfrac{36}{49}=\dfrac{36.8}{49.8}=\dfrac{288}{392}\) 

\(\dfrac{23}{56}=\dfrac{23.7}{56.7}=\dfrac{161}{392}\) 

Vì \(\dfrac{288}{392}>\dfrac{161}{392}\) nên \(\dfrac{36}{49}>\dfrac{23}{56}\)