Question

Answer 1

a) \(\dfrac{39}{41}=\dfrac{39.71}{41.71}=\dfrac{2769}{2911},\dfrac{69}{71}=\dfrac{69.41}{71.41}=\dfrac{2829}{2911}\)

\(2769< 2829\Rightarrow\dfrac{2769}{2911}< \dfrac{2829}{2911}\Rightarrow\dfrac{39}{41}< \dfrac{69}{71}\)

b) \(\dfrac{59}{-58}=\dfrac{59.\left(-68\right)}{-58.\left(-68\right)}=\dfrac{-4012}{3944},\dfrac{-69}{68}=\dfrac{-69.58}{68.58}=\dfrac{-4002}{3944}\)

\(-4012< -4002\Rightarrow\dfrac{-4012}{3944}< \dfrac{-4002}{3944}\Rightarrow\dfrac{59}{-58}< \dfrac{-69}{68}\)

c) \(\dfrac{-49}{50}=\dfrac{-49.9}{50.9}=\dfrac{-441}{450},\dfrac{91}{-90}=\dfrac{91.\left(-5\right)}{-90.\left(-5\right)}=\dfrac{-455}{450}\)

\(-441>-455\Rightarrow\dfrac{-441}{450}>\dfrac{-455}{450}\Rightarrow\dfrac{-49}{50}>\dfrac{91}{-90}\)

d) \(\dfrac{1399}{-1411}=\dfrac{1399.\left(-1151\right)}{-1411.\left(-1151\right)}=\dfrac{-1610249}{1624061},\dfrac{1169}{-1151}=\dfrac{1169.\left(-1411\right)}{-1151\left(-1411\right)}=\dfrac{-1649459}{1624061}\)

\(-1610249>-1649459\Rightarrow\dfrac{-1610249}{1624061}>\dfrac{-1649459}{1624061}\Rightarrow\dfrac{1399}{-1411}>\dfrac{1169}{-1151}\)