How to add and subtract the Roman numerals: CCCXXIX - XXVI + MCLXXII = ? Solve the mathematical operation of addition and subtraction like the Romans were calculating, without using Hindu-Arabic numbers

The operation written with Hindu-Arabic numerals:

329 - 26 + 1,172 = ?

The Romans did not have the Hindu-Arabic numbers.

Steps and explanations below, without using any Hindu-Arabic numbers.


» Roman numerals, reading rules


1. Simplify the operation.

Cross out the common symbols in the numerals of different signs.


The matching numerals / symbols are colored the same.


CCCXXIX - XXVI + MCLXXII =
CCCIX - V + MCLXXI

2. Substitute for subtractives.

Substitute for any subtractive groups of symbols in the roman numerals; that is, 'uncompact' them using only the additive notation.


» The subtractive and the additive notation: Find out more info on this topic.


CCCIX:


IX = X - I = V IIIII - I = V IIII = VIIII


CCCIX = CCCVIIII


3. Put the Roman numerals of the same sign together.

Catenate the positive numerals together:

CCCVIIII +


MCLXXI =


CCCVIIIIMCLXXI


4. Sort out the symbols in descending order.

Sort out the symbols in descending order from left-to-right with the largest symbol on the left, down to the smallest on the right.


Sort out the symbols of the positive numerals:

CCCVIIIIMCLXXI =


MCCCCLXXVIIIII


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

MCCCCLXXVIIIII -


V =


MCCCCLXXIIIII


6. Merge the repeating symbols together.

Starting on the right end of the number (starting with the smaller values), merge the repeating symbols into larger ones.


MCCCCLXXIIIII =


MCCCCLXXV


7. Rewrite the recurring symbols.

Rewrite the symbols written in 'excessive additive notation' by using the subtractive notation.


The numeral C should not be repeated for more than 3 times in a row, rewrite:

MCCCCLXXV =


MCDLXXV


CCCXXIX - XXVI + MCLXXII =


MCDLXXV

The operation written with Hindu-Arabic numerals:
329 - 26 + 1,172 = 1,475

The Romans did not have the Hindu-Arabic numbers.

The Romans also did not have the concept of negativity with their numeral system.

What we now consider to be a negative number for them was just another number, for example a debt owned, which would rather be a plus on the creditor's account.


Roman numerals addition and subtraction, online calculator

Automatically perform simple math calculations with Roman numerals, using the online calculator. Learn how to add or subtract Roman numerals, the right way, like the Romans were calculating. Without the help of Hindu-Arabic numbers. Step-by-step explanations.

The latest operations with Roman numerals (added, subtracted)

How to add and subtract Roman numerals the right way, like the Romans calculated, without the Hindu-Arabic numbers: steps and explanations

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

  • The Romans did not have the Hindu-Arabic numbers. So we will solve out this operation exactly the way the Romans were calculating it, without using the Hindu-Arabic numbers.

1. Cancel the numerals having the same value but different signs.

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

2. Cross out the common symbols in the numerals of different signs.

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

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

  • For example, the numerals XI and IV:
  • XI is a group in additive notation - the largest symbol is to the left, down to the smallest to the right - to calculate the value of the group simply add up the values of the symbols in the group: XI = X + I = 10 + 1 = 11
  • IV is a group in subtractive notation - a smaller symbol precedes a larger one - to calculate the value of the group subtract the value of the first symbol from the value of 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. Replace the groups in subtractive notation.

  • Replace any groups in subtractive notation in the roman numerals; that is, "uncompact" them using only the additive notation.
  • A group in subtractive notation = a group of two numerals, one of a lower value preceding another of larger value, 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 of the group subtract the value of the first symbol from the value of the second.
  • A group in additive notation = a group of two or more numerals, of equal value or sorted in descending order of their value, from high to low, the largest symbol to the left, down to the smallest to the right - to calculate the value of the group add up the values of all 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 of the same sign together.

  • 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.

  • The larger symbol that will be converted to additive notation: L = XXXXX;
  • DCCCCLIIII - XXX = DCCCCXXXXXIIII - XXX = DCCCCXXIIII;

7. Rewrite the symbols written in excessive additive notation by using the subtractive 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

The final answer:

  • XC + MCMLIII + CCXIX - MCCXLVIII - XC = CMXXIV ( = 924).

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