Ta có : 999/556 = 999 : 556
= 1,7967625....
1000/577 = 1000 : 577
= 1,7331022....
Ta thấy : 1,7967625... > 1,7331022
Vậy : 999/556 > 1000/577
Ta có : \(\frac{999}{556}=1+\frac{443}{556}\)
\(\frac{1000}{577}=1+\frac{423}{577}\)
Ta thấy : \(\frac{443\cdot577}{556\cdot577}=\frac{443}{556}\)
\(\frac{423\cdot556}{577\cdot556}=\frac{423}{577}\)
Ta có : \(443\cdot577=443\cdot\left(556+21\right)=443\cdot556+443\cdot21\)
Ta thấy : \(423\cdot556\)< \(443.556+21\cdot556\)
=>\(\frac{423\cdot556}{577\cdot556}< \frac{443\cdot577}{556\cdot577}\)
=>\(\frac{1000}{577}< \frac{999}{556}\)
Vậy \(\frac{999}{556}>\frac{1000}{557}\)
