Đáp án:
1)
a)$\dfrac{5}{12}<\dfrac{7}{9}$
b)
$\dfrac{-7}{12}<\dfrac{-9}{16}$
c)
$\dfrac{7}{18}<\dfrac{5}{6}$
d)
$\dfrac{52}{195}<\dfrac{87}{24}$
e)
$\dfrac{1}{7}>\dfrac{-3}{38}$
2)
a)
$\dfrac{-2}{3}<\dfrac{-7}{18}<\dfrac{1}{2}<\dfrac{5}{6}$
b)
$\dfrac{-4}{5}<\dfrac{-7}{20}<0<\dfrac{3}{4}<\dfrac{3}{2}$
c)
$\dfrac{-14}{27}<\dfrac{-8}{27}<\dfrac{3}{5}<\dfrac{19}{20}<\dfrac{3}{2}$
3)
$a)\dfrac{-2}{3}\\
b)\dfrac{7}{15}\\
c)\dfrac{2}{3}\\
d)\dfrac{2}{9}\\
e)\dfrac{5}{7}\\
f)
-20$
Giải thích các bước giải:
$1)
a)\dfrac{7}{9}=\dfrac{28}{36}\\
\dfrac{5}{12}=\dfrac{15}{36}$
Vì $15<28\Rightarrow \dfrac{15}{36}<\dfrac{28}{36}$
Vậy $\dfrac{5}{12}<\dfrac{7}{9}$
b)
$\dfrac{-9}{16}=\dfrac{-27}{48}\\
\dfrac{-7}{12}=\dfrac{-28}{48}$
Vì $-28<-27\Rightarrow \dfrac{-28}{48}<\dfrac{-27}{48}$
Vậy $\dfrac{-7}{12}<\dfrac{-9}{16}$
c)
$\dfrac{5}{6}=\dfrac{15}{18}\\
\dfrac{7}{18}$
Vì $7<15\Rightarrow \dfrac{7}{18}<\dfrac{15}{18}$
Vậy $\dfrac{7}{18}<\dfrac{5}{6}$
d)
$\dfrac{87}{24}=\dfrac{29}{8}=\dfrac{435}{120}\\
\dfrac{52}{195}=\dfrac{4}{15}=\dfrac{32}{120}$
Vì $32<435\Rightarrow \dfrac{32}{120}<\dfrac{435}{120}$
Vậy $\dfrac{52}{195}<\dfrac{87}{24}$
e)
$\dfrac{-3}{38}=\dfrac{-21}{266}\\
\dfrac{1}{7}=\dfrac{38}{266}$
Vì $38>-21\Rightarrow \dfrac{38}{266}>\dfrac{-21}{266}$
Vậy $\dfrac{1}{7}>\dfrac{-3}{38}$
2)
a)
$\dfrac{-2}{3}=\dfrac{-12}{18}\\
\dfrac{-7}{18}\\
\dfrac{1}{2}=\dfrac{3}{6}\\
\dfrac{5}{6}$
Vì $-7>-12\Rightarrow \dfrac{-12}{18}<\dfrac{-7}{18}$
Vì $3<5\Rightarrow \dfrac{3}{6}<\dfrac{5}{6}$
Vậy $\dfrac{-2}{3}<\dfrac{-7}{18}<\dfrac{1}{2}<\dfrac{5}{6}$
b)
$\dfrac{-7}{20}\\
\dfrac{-4}{5}=\dfrac{-16}{20}\\
\dfrac{3}{2}=\dfrac{6}{4}\\
\dfrac{3}{4}\\
0=\dfrac{0}{4}$
Vì $-16<-7\Rightarrow \dfrac{-16}{20}<\dfrac{-7}{20}$
Vì $0<3<6\Rightarrow 0<\dfrac{3}{4}<\dfrac{6}{4}$
Vậy $\dfrac{-4}{5}<\dfrac{-7}{20}<0<\dfrac{3}{4}<\dfrac{3}{2}$
c)
$\dfrac{3}{5}=\dfrac{12}{20}\\
\dfrac{19}{20}\\
\dfrac{3}{2}=\dfrac{30}{20}\\
\dfrac{-14}{27}\\
\dfrac{8}{-27}=\dfrac{-8}{27}$
Vì $-14<-8\Rightarrow \dfrac{-14}{27}<\dfrac{-8}{27}$
$12<19<30\Rightarrow \dfrac{12}{20}<\dfrac{19}{20}<\dfrac{30}{20}$
Vậy $\dfrac{-14}{27}<\dfrac{-8}{27}<\dfrac{3}{5}<\dfrac{19}{20}<\dfrac{3}{2}$
3)
$a)\dfrac{-16}{24}=\dfrac{(-16):8}{24:8}=\dfrac{-2}{3}\\
b)\dfrac{-35}{-75}=\dfrac{(-35):5}{(-75):5}=\dfrac{7}{15}\\
c)\dfrac{7.18}{9.21}=\dfrac{7.3^2.2}{3^3.7.3}=\dfrac{2}{3}\\
d)\dfrac{5.14.9}{27.15.7}=\dfrac{5.7.2.3^2}{3^3.3.5.7}=\dfrac{2}{9}\\
e)\dfrac{5.16+5.23}{39.23-39.16}\\
=\dfrac{5.(16+23)}{39.(23-16)}\\
=\dfrac{5.39}{29.7}=\dfrac{5}{7}\\
f)
\dfrac{13.21-13}{4-17}\\
=\dfrac{13.(21-1)}{-13}\\
=-20$
