three fractions between π and 22/7

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three fractions between π and 22/7

π=355/113 =3.14159
22/7=3.1428

using a/b 355/113<22/7
then a+b/c+d
1)
355+22/113+7 =377/120~ 3.14166
2)
377+22/12+7 =399/127~3.14173
3)
399+22/127+7 =421/134~3.14179

is the method correct?!