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

Let's learn by an example:

CIX + CV + CCCXL = ?

109 + 105 + 340 = ? the Romans did not have the Arabic numbers

Add and subtract Roman numerals, online calculator, with explanations

1. 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.

CIX:


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


CIX = CVIIII


CCCXL:


XL = L - X = XXXXX - X = XXXX


CCCXL = CCCXXXX


2. Put the Roman numerals together, catenate them.

CVIIII +


CV +


CCCXXXX =


CVIIIICVCCCXXXX


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

CVIIIICVCCCXXXX =


CCCCCXXXXVVIIII

4. 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.

CCCCCXXXXVVIIII =


CCCCCXXXXXIIII


CCCCCXXXXXIIII =


CCCCCLIIII


CCCCCLIIII =


DLIIII


5. 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:

DLIIII =


DLIV


Add and subtract Roman numerals, online calculator, with explanations

Final answer:

CIX + CV + CCCXL =


DLIV

109 + 105 + 340 = 554 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


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

Examples of converting Arabic numbers to Roman numerals


Roman numerals from 1 to 100

Roman numerals from 1 to 1000