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 \(\dfrac{36}{49}>\dfrac{23}{56}\)
Giải: (tiếp)
n) \(\dfrac{-24}{37}\) và \(\dfrac{-21}{38}\)
\(\dfrac{-24}{37}=\dfrac{-24.7}{37.7}=\dfrac{-168}{259}\)
\(\dfrac{-21}{38}=\dfrac{-21.8}{38.8}=\dfrac{-168}{304}\)
Vì \(\dfrac{-168}{259}< \dfrac{-168}{304}\) nên \(\dfrac{-24}{37}< \dfrac{-21}{38}\)
p) \(-2\dfrac{1}{5}\) và \(\dfrac{110}{-50}\)
\(-2\dfrac{1}{5}=\dfrac{-11}{5}\)
\(\dfrac{110}{-50}=\dfrac{-110}{50}=\dfrac{-11}{5}\)
Vì \(\dfrac{-11}{5}=\dfrac{-11}{5}\) nên \(-2\dfrac{1}{5}=\dfrac{110}{-50}\)
q) \(\dfrac{17}{20}\) và \(0,75\)
\(0,75=\dfrac{3}{4}=\dfrac{3.5}{4.5}=\dfrac{15}{20}\)
Vì \(\dfrac{17}{20}>\dfrac{15}{20}\) nên \(\dfrac{17}{20}>0,75\)
