1,578 - 1,121 + 1,540 + 1,094 = ? 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.
MDLXXVIII - MCXXI + MDXL + MXCIV =
DLVII - C + MDXL + MXCIV
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
MDXL = MDXXXX
XC = C - X = L XXXXX - X = L XXXX = LXXXX
IV = V - I = IIIII - I = IIII
MXCIV = MLXXXXIIII
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. Starting on the right end (smaller values), combine groups of the same symbols into larger ones.
Combine the repetitive groups of symbols in the positive numeral:
MMDDLLXXXXXXXXVIIIII I =
MMDDLLXXXXX XXXXI =
MMDDLL LXXXXI =
6. Cross out (remove) any symbols occurring in both strings.
7. Rewrite the symbols written in excessive additive notation by using the substractive notation.
The numeral X should not repeat itself more than 3 times in a row, rewrite: