# How to add and subtract the Roman numerals: MDLXXVIII - MCXXI + MDXL + MXCIV = ? Solve the mathematical operation of addition and subtraction like the Romans calculated

## MDLXXVIII - MCXXI + MDXL + MXCIV = ?

### 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

MDXL:

MXCIV:

### 3. Put the Roman numerals together, as a string.

#### Catenate the positive numerals together:

DLVII +
MDXXXX +
MLXXXXIIII =
DLVIIMDXXXXMLXXXXIIII

### 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:

DLVIIMDXXXXMLXXXXIIII =
MMDDLLXXXXXXXXVIIIIII

### 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:

MMDDLLXXXXXXXXVIIIIII =
MMDDLLXXXXXXXXVIIIII I =
MMDDLLXXXXXXXXVVI =
MMDDLLXXXXXXXXVVI =
MMDDLLXXXXXXXXXI =
MMDDLLXXXXXXXXXI =
MMDDLLXXXXX XXXXI =
MMDDLLLXXXXI =
MMDDLLLXXXXI =
MMDDLL LXXXXI =
MMDDCLXXXXI =
MMDDCLXXXXI =
MMMCLXXXXI

MMMCLXXXXI -
C =
MMMLXXXXI

MMMLXXXXI =
MMMXCI

## The latest operations with Roman numerals (added or / and subtracted)

 MDLXXVIII - MCXXI + MDXL + MXCIV = ? Apr 04 05:21 UTC (GMT) MLXXXIII + MCMLXXXIV - MCDVII + MMCCLXI = ? Apr 04 05:21 UTC (GMT) MXV + DCCCXX = ? Apr 04 05:21 UTC (GMT) DCCCXCIX - MCCCXII + MCCXXVIII = ? Apr 04 05:21 UTC (GMT) CMLXI - CMXXXIV + MDCCXCI = ? Apr 04 05:21 UTC (GMT) DCLXXII - MMMCCLV + MDCXIII = ? Apr 04 05:20 UTC (GMT) CCXVI - CCLXXXIV - MXIV = ? Apr 04 05:20 UTC (GMT) MCXLVII - CCCLIV = ? Apr 04 05:20 UTC (GMT) CCXXVI + MLXXIX - MXLVII - DCLXXIII - MMMCCCLXXXII = ? Apr 04 05:20 UTC (GMT) DCCXLIV + CCXXXI - MLXXIII = ? Apr 04 05:20 UTC (GMT) MCCXIII + CCXLII - DCCLXIX = ? Apr 04 05:19 UTC (GMT) MMXCII - MDCXXXII + CMLXXXVI - MCCCXLVIII - MMLXXXI = ? Apr 04 05:19 UTC (GMT) CCVI - DXIII - CCCXXXV - CDV - DCCLX = ? Apr 04 05:19 UTC (GMT) All the Roman numerals calculations: what our visitors added or subtracted, online operations...

## How to add and subtract Roman numerals the right way, like the Romans calculated: steps and explanations.

• Let's learn by an example:
• #### XC + MCMLIII + CCXIX - MCCXLVIII - XC = ?

• 90 + 1.953 + 219 - 1.248 - 90 = ? the Romans did not have the Arabic numbers

#### 1. Cancel equal but different signs numerals.

• Matching numerals / symbols are colored the same.
• XC + MCMLIII + CCXIX - MCCXLVIII - XC = MCMLIII + CCXIX - MCCXLVIII;

#### 2. Simplify the operation: cross out the common symbols in the numerals of different signs.

• Matching numerals / symbols are colored the same.
• MCMLIII + CCXIX - MCCXLVIII = CML + XIX - XLV;

#### When crossing out, do not mix subtractive and additive groups symbols.

• 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.

#### 3. 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.
• CML: CM = M - C = D CCCCC - C = D CCCC = DCCCC; CML = DCCCCL;
• XIX: IX = X - I = V IIIII - I = V IIII = VIIII; XIX = XVIIII;
• XLV: XL = L - X = XXXXX - X = XXXX; XLV = XXXXV;

#### 4. Put the Roman numerals together, as a string.

• Catenate the positive numerals together.
• DCCCCL + XVIIII = DCCCCLXVIIII;

#### 5. Cross out (remove) any symbols occurring in both strings.

• DCCCCLXVIIII - XXXXV = DCCCCLIIII - XXX;

#### 6. Using the additive notation, convert larger symbols to smaller ones and cross out the common symbols.

• Symbols converted, in additive notation: L = XXXXX;
• DCCCCLIIII - XXX = DCCCCXXXXXIIII - XXX = DCCCCXXIIII;

#### 7. 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:
• DCCCCXXIIII = CMXXIIII;
• The numeral I should not repeat itself more than 3 times in a row, rewrite:
• CMXXIIII = CMXXIV

• #### XC + MCMLIII + CCXIX - MCCXLVIII - XC = CMXXIV;

• 90 + 1,953 + 219 - 1,248 - 90 = 924 the Romans did not have the Arabic numbers