1,147 - 381 + 1,013 + 1,197 + 912 = ? the Romans did not have the Arabic numbers
All the Roman numerals are valid.
Steps and explanations below, without Arabic numbers.
1. Simplify the operation: cross out the common symbols in the numerals of different signs.
Matching numerals / symbols are colored the same.
MCXLVII - CCCLXXXI + MXIII + MCXCVII + CMXII =
MXLVI - CLX + MIII + MXCVII + CMII
When crossing out, do not mix subtractive and additive groups symbols: for example ...
2. Substitute for any subtractives in the roman numerals; that is, "uncompact" them using only the additive notation.
Subtractive notation, additive notation: more information ...
XL = L - X = XXXXX - X = XXXX
MXLVI = MXXXXVI
XC = C - X = L XXXXX - X = L XXXX = LXXXX
MXCVII = MLXXXXVII
CM = M - C = D CCCCC - C = D CCCC = DCCCC
CMII = DCCCCII
3. Put the Roman numerals together, as a string.
Catenate the positive numerals together:
4. Sort the symbols in order from left-to-right with the largest symbol on the left, down to the smallest on the right.
Sort the symbols of the positive numerals:
5. Cross out (remove) any symbols occurring in both strings.
6. Starting on the right end (smaller values), combine groups of the same symbols into larger ones.
MMMDCCCXXXXXXXVVIIIII III =
MMMDCCCXXXXXXXVV VIII =
MMMDCCCXXXXX XXXVIII =