Addition. Learn with an example how to add Roman numbers (Roman numerals) the right way, like the Romans were calculating, without the use of the Hindu-Arabic numbers. Steps, explanations

Let's learn with an example:

CIX + CV + CCCXL = ?

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.

Add and subtract Roman numerals, online calculator, with explanations

1. Replace the groups written in subtractive notation.

Replace any groups written 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 in that group.


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.

CVIIII +


CV +


CCCXXXX =


CVIIIICVCCCXXXX


3. Sort the symbols in descending order of their values.

Sort the symbols in descending order of their values, from left-to-right, with the largest symbol to the left, down to the smallest to the right.


CVIIIICVCCCXXXX =


CCCCCXXXXVVIIII

4. Combine the repeating symbols together, in groups.

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


CCCCCXXXXVVIIII =


CCCCCXXXXXIIII


CCCCCXXXXXIIII =


CCCCCLIIII


CCCCCLIIII =


DLIIII


5. Rewrite the repeating symbols.

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

The final answer:

CIX + CV + CCCXL =


DLIV ( = 554)

109 + 105 + 340 = 554
The Romans did not have the Hindu-Arabic numbers.

Mathematical operations with Roman numerals:

I. Addition. Learn by an example how to add the Roman numerals the right way, like the Romans were calculating, without the use of the Hindu-Arabic numbers. Steps, explanations

II. Subtraction. Learn by an example how to subtract the Roman numerals the right way, like the Romans were calculating, without the use of the Hindu-Arabic numbers. Steps, explanations

III. Addition and subtraction. Learn by an example how to add and subtract the Roman numerals the right way, like the Romans were calculating, without the use of the Hindu-Arabic numbers. Steps, explanations

The reading rules of the Roman numerals, summary:

I. The set of the basic symbols of the Roman numerals

II. The rule of the repetition of the Roman numerals

III. The groups of the Roman numerals written in subtractive notation

IV. The additive notation of the Roman numerals


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

Examples of converting Hindu-Arabic numbers to Roman numerals

Two lists of the first Roman numerals (in ascending order):

The list of the first 100 Roman numerals: the Roman numerals from 1 to 100

The list of the first 1,000 Roman numerals: the Roman numerals from 1 to 1,000