How to subtract the Roman numerals: XLV - XCIX - IV - CXXIII = ? Solve the mathematical operation of subtraction like the Romans calculated

XLV - XCIX - IV - CXXIII = ?

45 - 99 - 4 - 123 = ? the Romans did not have the Arabic numbers
All the Roman numerals are valid.

Steps and explanations below, without Arabic numbers.

Reading rules


1. Substitute for any subtractives in the roman numerals; that is, "uncompact" them using only the additive notation.

Subtractive notation, additive notation: more information ...

XLV:

XL = L - X = XXXXX - X = XXXX
XLV = XXXXV


XCIX:

XC = C - X = L XXXXX - X = L XXXX = LXXXX

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


IV:

IV = V - I = IIIII - I = IIII
IV = IIII


2. Put the Roman numerals together, as a string.

Catenate the negative numerals together:

LXXXXVIIII +
IIII +
CXXIII =
LXXXXVIIIIIIIICXXIII

3. 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 negative numerals:

LXXXXVIIIIIIIICXXIII =
CLXXXXXXVIIIIIIIIIII

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

XXXXV -
CLXXXXXXVIIIIIIIIIII =
- CLXXIIIIIIIIIII

Romans 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...

5. Starting on the right end (smaller values), combine groups of the same symbols into larger ones.

CLXXIIIIIIIIIII =
CLXXIIIII IIIII I =
CLXXVVI =
CLXXVVI =
CLXXXI

Final answer:

XLV - XCIX - IV - CXXIII =


- CLXXXI

45 - 99 - 4 - 123 = -181 the Romans did not have the Arabic numbers

Romans 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...


Another one. How to subtract the Roman numerals:

CXXI - CXXXIV - I = ?

Roman numerals addition and subtraction online calculator

The latest operations with Roman numerals (added, 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


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