639 + 1,403 + 1,814 - 974 + 1,286 = ? 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.
DCXXXIX + MCDIII + MDCCCXIV - CMLXXIV + MCCLXXXVI =
DCXIX + MCDIII + MDCCCX - CM + MCCXXXVI
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 ...
IX = X - I = V IIIII - I = V IIII = VIIII
DCXIX = DCXVIIII
CD = D - C = CCCCC - C = CCCC
MCDIII = MCCCCIII
CM = M - C = D CCCCC - C = D CCCC = DCCCC
CM = DCCCC
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.
MMMDCCCCCCXXXXXVVIIIII III =
MMMDCCCCCCXXXXXVV VIII =
MMMDCCCCCCXXXXX XVIII =
MMMDCCCCC CLXVIII =
7. Rewrite the symbols written in excessive additive notation by using the substractive notation.
The numeral M should not repeat itself more than 3 times in a row, rewrite: