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

Let's learn by an example:

DCCCLXVIII - CXX - CCLVI - XL - X = ?

868 - 120 - 256 - 40 - 10 = ? The Romans did not have the Hindu-Arabic numbers

Add and subtract Roman numerals, online calculator, with explanations

1. Simplify the operation.

Cross out the common symbols in the numerals of different signs.


Matching numerals / symbols are colored the same.


DCCCLXVIII - CXX - CCLVI - XL - X =


DII - X - XL - X

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.

2. Substitute for subtractives.

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.


XL:


XL = L - X = XXXXX - X = XXXX


XL = XXXX


3. Put the Roman numerals of the same sign together.

Catenate the negative numerals together.

X +


XXXX +


X =


XXXXXX


4. Combine groups of the same symbols together.

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

Combine the repetitive groups of symbols in the negative numeral.

XXXXXX =


XXXXX X =


LX


5. Cross out the common symbols in the numerals of different signs.

Using the additive notation, convert larger symbols to smaller ones and cross out the common symbols.

Symbols converted, in additive notation:

D = CCCCLL; L = XXXXX;


DII -


LX =


CCCCLXXXXXII -


LX =


CCCCXXXXII

6. Rewrite the repetitive symbols.

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:

CCCCXXXXII =


CDXXXXII


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

CDXXXXII =


CDXLII


Add and subtract Roman numerals, online calculator, with explanations

Final answer:

DCCCLXVIII - CXX - CCLVI - XL - X =


CDXLII

868 - 120 - 256 - 40 - 10 = 442 The Romans did not have the Hindu-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 Hindu-Arabic numbers to Roman numerals: breaking down into place value subgroups

Examples of converting Hindu-Arabic numbers to Roman numerals


Roman numerals from 1 to 100

Roman numerals from 1 to 1000