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

Let's learn by an example:

CCCXXXVIII + XC + CCCXLIII + CCCXIX - CXVII - CXLVIII - LVI - XC = ?

338 + 90 + 343 + 319 - 117 - 148 - 56 - 90 = ? the Romans did not have the Arabic numbers

CCCXXXVIII + XC + CCCXLIII + CCCXIX - CXVII - CXLVIII - LVI - XC = ?

Add and subtract Roman numerals, online calculator, with explanations

1. Cancel equal but different signs numerals.

Matching numerals / symbols are colored the same.

CCCXXXVIII + XC + CCCXLIII + CCCXIX - CXVII - CXLVIII - LVI - XC =


CCCXXXVIII + CCCXLIII + CCCXIX - CXVII - CXLVIII - LVI

2. Simplify the operation right away by crossing out common symbols in the numerals of different signs.

Matching numerals / symbols are colored the same.

CCCXXXVIII + CCCXLIII + CCCXIX - CXVII - CXLVIII - LVI =


CXX + CCC + CCCXIX - V - LV

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.

CCCXIX:


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


CCCXIX = CCCXVIIII


4. Put the Roman numerals together, catenate them.

Catenate all the positive numerals together.

CXX +


CCC +


CCCXVIIII =


CXXCCCCCCXVIIII


Catenate all the negative numerals together.

V +


LV =


VLV


5. 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.

CXXCCCCCCXVIIII =


CCCCCCCXXXVIIII

Sort the symbols of the negative numerals.

VLV =


LVV

6. Simply "cross out" (remove) any symbols occurring in both values.

CCCCCCCXXXVIIII -


LVV =


CCCCCCCXXXIIII -


LV

7. Using only the additive notation, convert larger value symbols to some smaller ones, a necessary step in order to cross out all the common symbols.

Replacements used, in additive notation:

C = LL; X = VV;


CCCCCCCXXXIIII -


LV =


CCCCCCLLXXVVIIII -


LV =


CCCCCCLXXVIIII

8. Starting with the right end (smaller values), combine groups of the same symbols that can make a "larger" one and substitute the single larger one.

CCCCCCLXXVIIII =


CCCCC CLXXVIIII =


DCLXXVIIII


9. Rewrite the symbols written in excessive additive notation by using the substractive notation.

The numeral I should not repeat itself more than 3 times in a row, rewrite:

DCLXXVIIII =


DCLXXIX


Add and subtract Roman numerals, online calculator, with explanations

Final answer:

CCCXXXVIII + XC + CCCXLIII + CCCXIX - CXVII - CXLVIII - LVI - XC =


DCLXXIX

338 + 90 + 343 + 319 - 117 - 148 - 56 - 90 = 679 the Romans did not have the Arabic numbers

Add and subtract Roman numerals, online calculator, with explanations

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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Examples of converting Arabic numbers to Roman numerals


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