Let's learn by an example:
DCCCLXVIII - CXX - CCLVI - XL - X = ?
868 - 120 - 256 - 40 - 10 = ? The Romans did not have the Hindu-Arabic numbers
1. Simplify the operation.
Cross out the 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 subtractives.
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 of the same sign together.
Catenate the negative numerals together.
4. Combine groups of the same symbols together.
Starting on the right end (smaller values), combine groups of the same symbols into larger ones.
Combine the repetitive groups of symbols in the negative numeral.
XXXXX X =
5. Cross out the common symbols in the numerals of different signs.
Using the additive notation, convert larger symbols to smaller ones and cross out the common symbols.
Symbols converted, in additive notation:
D = CCCCLL; L = XXXXX;
6. Rewrite the repetitive symbols.
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: