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Notwithstanding today's notation of 444 in Roman numerals inasmuch that they are considered to be CDXLIV which makes integration of them with other numerals impracticable.

But it can be conclusively proven that the Romans themselves in the past would have calculated the equivalent of 444 as CCCCXXXXIIII which can be, with systematical logic, reduced to IVLD (-56+500) hence making addition more practicable as follows:-

CCXXII+IVLD = DCLXVI (222)+(-56+500) = (666)

Alternatively:-

CCXXII+CCCCXXXXIIII = DCLXVI (222)+(444) = (666)

Note that: 5*I=V, 2*V=X, 5*X=L, 2*L=C, 5*C=D and 2*D=M

Roman numerals: M=1000, D=500, C=100, L=50, X=10, V=5 and I=1

QED

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Q: How would you actually add together in two different ways 222 and 444 using Roman numerals in both calculations?
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