Roman numerals addition and subtraction online calculator: adding, subtracting numbers the right way, like the Romans calculated; steps, explanations

Roman numerals addition and subtraction online calculator

Learn how to add or subtract Roman numerals, step by step, with explanations:

Addition and subtraction. Learn by example how to add and subtract Roman numerals the right way, like the Romans calculated, steps, explanations.

Addition. Learn by example how to add Roman numerals the right way, like the Romans calculated, steps, explanations.

Subtraction. Learn by example how to subtract Roman numerals the right way, like the Romans calculated, steps, explanations.

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

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

Final answer:

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

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

Mathematical operations with Roman numerals:

I. Addition. Learn by example how to add Roman numerals the right way, like the Romans calculated, steps, explanations

II. Subtraction. Learn by example how to subtract Roman numerals the right way, like the Romans calculated, steps, explanations

III. Addition and subtraction. Learn by example how to add and subtract Roman numerals the right way, like the Romans calculated, steps, explanations

Roman numerals reading rules, summary:

I. The Roman numerals set of basic symbols

II. The rule of numerals repetition

III. Subtractive notation of the Roman numerals

IV. Additive notation of the Roman numerals


How to convert Arabic numbers to Roman numerals: breaking down into place value subgroups

Examples of converting Arabic numbers to Roman numerals


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