Let's learn by an example:
DCCCLXVIII - CXX - CCLVI - XL - X = ?
868 - 120 - 256 - 40 - 10 = ? the Romans did not have the Arabic numbers
1. Simplify the operation right away by crossing out common symbols in the numerals of different signs.
Matching numerals / symbols are colored the same.
DCCCLXVIII - CXX - CCLVI - XL - X =
DII - X - XL - X
For example, the numerals XI and IV:
XI is an additive group - largest symbol on the left, down to the smallest on the right - to calculate the value add up the symbols: XI = X + I = 10 + 1 = 11;
IV is a subtractive group - a smaller symbol precedes a larger one - to calculate the value subtract the first symbol from the second: IV = V - I = 5 - 1 = 4.
When subtracting the two numerals, XI - IV = (uncompact the subtractive) XI - IIII = X - III = VIIIII - III = VII (= 7), CORRECT. But if you cross out the common symbol regardless of the fact that it is part of a subtractive group: XI - IV = X - V = VV - V = V (= 5), WRONG.
2. 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.
XL = L - X = XXXXX - X = XXXX
XL = XXXX
3. Put the Roman numerals together, catenate them.
Catenate all the negative numerals together.
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.
Combine the repetitive groups of symbols in the negative numeral.
XXXXX X =
5. Using only the additive notation, convert larger value symbols to some smaller ones, a necessary step in order to cross out all the common symbols.
Replacements used, in additive notation:
D = CCCCLL; L = XXXXX;
6. Rewrite the symbols written in excessive additive notation by using the substractive notation.
The numeral C should not repeat itself more than 3 times in a row, rewrite:
The numeral X should not repeat itself more than 3 times in a row, rewrite: