Let's learn by an example:
CIX + CV + CCCXL = ?
109 + 105 + 340 = ? the Romans did not have the Arabic numbers
1. Substitute for any subtractives in the roman numerals; that is, "uncompact" them using only the additive notation.
Subtractive notation = a group of two numerals, one of a lower value preceding another larger one, the only allowed ones are: IV, IX, XL, XC, CD, CM, M(V), M(X), (X)(L), (X)(C), (C)(D), (C)(M) - to calculate the value subtract the first symbol from the second.
Additive notation = a group of two or more numerals, equal or sorted in descending order from high to low, largest symbol on the left, down to the smallest on the right - to calculate the value add up the symbols.
IX = X - I = V IIIII - I = V IIII = VIIII
CIX = CVIIII
XL = L - X = XXXXX - X = XXXX
CCCXL = CCCXXXX
2. Put the Roman numerals together, catenate them.
3. Sort the symbols in order from left-to-right with the largest symbol on the left, down to the smallest on the right.
4. Starting with the right end (smaller values), combine groups of the same symbols that can make a "larger" one and substitute the single larger one.
5. Rewrite the symbols written in excessive additive notation by using the substractive notation.
The numeral I should not repeat itself more than 3 times in a row, rewrite: