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$\frac {111}{1234}=\frac {666}{7404}$
$\frac {666}{7404}>\frac {666}{7654}$
$\frac {111}{1234}>\frac {666}{7654}$
$1-\frac {4443}{4445}=\frac {2}{4445}$
$1-\frac {5554}{5556}=\frac {2}{5556}$
$\frac {2}{4445}>\frac {2}{5556},$则$\frac {4443}{4445}<\frac {5554}{5556}$
$\frac {223}{447}<\frac 12,\frac {395}{788}>\frac 12$
$\frac {223}{447}<\frac {395}{788}$
$\frac {2346}{2345}=1+\frac {1}{2345}$
$\frac {2347}{2346}=1+\frac {1}{2346}$
$\frac {1}{2345}>\frac {1}{2346},$则$\frac {2346}{2345}>\frac {2347}{2346}$
$ 2020×2024$
$=2020×(2023+1)$
$=2020×2023+2020$
$ 2023×2019$
$=2023×(2020-1)$
$=2023×2020-2023$
$2020×2024>2023×2019$
所以$\frac {2020}{2023}>\frac {2019}{2024}$
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