Bài 1:
a) ${\frac{32}{80}=\frac{32:16}{80:16}=\frac{2}{5}}$
b) ${\frac{-1212}{2020}=\frac{-1212:404}{2020:404}=\frac{-3}{5}}$
c) ${\frac{-3.5.14}{6.10.7}=\frac{-3.5.2.7}{(-3).(-2).5.2.7}=\frac{1}{-2}}$
d) ${\frac{12.11.5}{-6.22.10}=\frac{(-6).(-2).11.5}{-6.11.2.5.2}=\frac{-1}{2}}$
Bài 2:
a) ${\frac{9.11+32.9}{23.15+12.23}=\frac{9.(11+32)}{23.(15+12)}=\frac{9.43}{23.27}=\frac{9.43}{23.9.3}=\frac{43}{23.3}=\frac{43}{69}}$
b) ${\frac{16.29-32}{16.37+32}=\frac{16.29-16.2}{16.37+16.2}=\frac{16.(29-2)}{16.(37+2)}=\frac{16.27}{16.39}=\frac{16.9.3}{16.3.13}=\frac{9}{13}}$
Bài 3:
$\text{ Theo bài ra ta có:}$
${\frac{29+n}{51+n}=\frac{2}{3}}$
⇒ ${ 3.(29+n)=2.(51+n)}$
⇒ ${ 87+3n=102+2n}$
⇒ ${ 3n-2n = 102-87}$
⇒${ n = 15}$
$\text{ Thử lại}$ ${\frac{29+15}{51+15}=\frac{44}{66}=\frac{2}{3}}$
$\text { Vậy n = 15}$