# How to add and subtract the Roman numerals: CMXCIII + MCXLVI - MMCLXXXVIII + MDCXLV - DCCCLXV = ? Solve the mathematical operation of addition and subtraction like the Romans calculated

## CMXCIII + MCXLVI - MMCLXXXVIII + MDCXLV - DCCCLXV = ?

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

#### Matching numerals / symbols are colored the same.

CMXCIII + MCXLVI - MMCLXXXVIII + MDCXLV - DCCCLXV =
CMXC + XLI - LXXX + XL - CCLX

CMXC:

XLI:

XL:

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

#### Catenate the positive numerals together:

DCCCCLXXXX +
XXXXI +
XXXX =
DCCCCLXXXXXXXXIXXXX

LXXX +
CCLX =
LXXXCCLX

### 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:

DCCCCLXXXXXXXXIXXXX =
DCCCCLXXXXXXXXXXXXI

LXXXCCLX =
CCLLXXXX

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

DCCCCLXXXXXXXXXXXXI -
CCLLXXXX =
DCCXXXXXXXXI -
L

DCCXXXXXXXXI -
L =
DCLLXXXXXXXXI -
L =
DCLXXXXXXXXI

DCLXXXXXXXXI =
DCLXXXXX XXXI =
DCLLXXXI =
DCLLXXXI =
DCCXXXI

## The latest operations with Roman numerals (added, subtracted)

 CMXCIII + MCXLVI - MMCLXXXVIII + MDCXLV - DCCCLXV = ? Oct 26 12:54 UTC (GMT) DCXC - MMCMXLVII - MCCXLVI + MMCLXIII - MMLXX = ? Oct 26 12:54 UTC (GMT) MCMXCIII - LXXVI = ? Oct 26 12:54 UTC (GMT) MCDXCVIII + MCCCIV - DCCCXVI - CDLXX = ? Oct 26 12:54 UTC (GMT) MMCDL - XXXVIII + MMDCCLXXI = ? Oct 26 12:54 UTC (GMT) CXXXIX + CXLVI = ? Oct 26 12:54 UTC (GMT) CXCII + MCCCXCV + MII = ? Oct 26 12:54 UTC (GMT) CXLIII - CXII - CXL + MDCXXIV + MCXLII = ? Oct 26 12:54 UTC (GMT) CVIII + XX = ? Oct 26 12:54 UTC (GMT) CLXX - CXI - LXXVI - XXIII = ? Oct 26 12:54 UTC (GMT) MXLVIII + MMXLII - DCII + MDCLXXXI + MMDXVI = ? Oct 26 12:53 UTC (GMT) CMLX - DCIX = ? Oct 26 12:53 UTC (GMT) DCXCV + CLIV + MCDXIII - DII + CDXXXIV = ? Oct 26 12:53 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