Bài 3:

\(-3=\frac{-3\cdot30}{30}=-\frac{90}{30};\frac{-14}{15}=\frac{-14\cdot2}{15\cdot2}=\frac{-28}{30};\frac{9}{-18}=\frac{-9}{18}=\frac{-1}{2}=\frac{-1\cdot15}{2\cdot15}=-\frac{15}{30}\)

mà -90<-28<-15

nên \(-3<-\frac{14}{15}<-\frac{9}{18}\)

=>\(0>-\frac{9}{18}>-\frac{14}{15}>-3\left(1\right)\)

\(\frac{25}{20}=\frac{25\cdot3}{20\cdot3}=\frac{75}{60};\frac{31}{30}=\frac{31\cdot2}{30\cdot2}=\frac{62}{60}\)

\(\frac{23}{10}=\frac{23\cdot6}{10\cdot6}=\frac{138}{60};7=\frac{7\cdot60}{60}=\frac{420}{60}\)

mà 420>138>75>62

nên \(7>\frac{23}{10}>\frac{25}{20}>\frac{31}{30}>0\left(2\right)\)

Từ (1),(2) suy ra \(7>\frac{23}{10}>\frac{25}{20}>\frac{31}{30}>-\frac{9}{18}>-\frac{14}{15}>-3\)

Bài 2:

\(-6<-3,5=-\frac72;-\frac72<-1<-\frac{5}{18}\)

Do đó: \(-6<-\frac72<-\frac{5}{18}\) <0(3)

Ta có: \(\frac49=\frac{4\cdot2}{9\cdot2}=\frac{8}{18};\frac{-5}{-3}=\frac53=\frac{5\cdot6}{3\cdot6}=\frac{30}{18}\)

\(\frac76=\frac{7\cdot3}{6\cdot3}=\frac{21}{18};\frac{50}{75}=\frac{50:25}{75:25}=\frac23=\frac{2\cdot6}{3\cdot6}=\frac{12}{18}\)

\(4=\frac{4\cdot18}{18}=\frac{72}{18}\)

mà 8<12<21<30<72

nên \(0<\frac49<\frac{50}{75}<\frac76<\frac{-5}{-3}<4\) (4)

Từ (3),(4) suy ra \(-6<-\frac72<-\frac{5}{18}<\frac49<\frac{50}{75}<\frac76<\frac{-5}{-3}<4\)

Bài 1:

a: \(\frac{11}{12}=1-\frac{1}{12};\frac{13}{14}=1-\frac{1}{14}\)

Ta có: 12<14

=>\(\frac{1}{12}>\frac{1}{14}\)

=>\(-\frac{1}{12}<-\frac{1}{14}\)

=>\(-\frac{1}{12}+1<-\frac{1}{14}+1\)

=>\(\frac{11}{12}<\frac{13}{14}\)

b: \(-\frac{7}{15}=\frac{-7\cdot8}{15\cdot8}=\frac{-56}{120};\frac{-13}{24}=\frac{-13\cdot5}{24\cdot5}=\frac{-65}{120}\)

mà -56>-65

nên \(-\frac{7}{15}>\frac{13}{-24}\)

c: \(\frac{-4}{-25}=\frac{4}{25}=\frac{4\cdot7}{25\cdot7}=\frac{28}{175};\frac{6}{35}=\frac{6\cdot5}{35\cdot5}=\frac{30}{175}\)

mà 28<30

nên \(\frac{-4}{-25}<\frac{6}{35}\)

d: \(\frac{-45}{75}=\frac{-45:15}{75:15}=\frac{-3}{5};\frac{54}{-90}=\frac{54:\left(-18\right)}{-90:\left(-18\right)}=\frac{-3}{5}\)

Do đó: \(\frac{-45}{75}=\frac{54}{-90}\)

e: \(\frac{56}{72}=\frac{56:8}{72:8}=\frac79;\frac{48}{54}=\frac{48:6}{54:6}=\frac89\)

mà 7<8

nên \(\frac{56}{72}<\frac{48}{54}\)

f: \(121<125\)

=>\(\frac{113}{121}>\frac{113}{125}\)
g: \(\frac{188}{189}<1;1<\frac{186}{185}\)

Do đó: \(\frac{188}{189}<\frac{186}{185}\)

h: \(\frac{106}{-133}<0;0<\frac{108}{131}\)

Do đó: \(\frac{106}{-133}<\frac{108}{131}\)