How to subtract the Roman numerals: XIIMCXLIX - DCCCLXCCCXXI - MCMIV = ? Solve the mathematical operation of subtraction like the Romans were calculating, without using Hindu-Arabic numbers

Not all the Roman numerals are valid. Instead, we run this math operation of subtraction:

MCLIX - MCLXI - MCMIV = ?

The operation written with Hindu-Arabic numerals:
1,159 - 1,161 - 1,904 = ?

The Romans did not have the Hindu-Arabic numbers.
Steps and explanations below, without using any Hindu-Arabic numbers.

>> Roman numerals, reading rules


1. Are the numerals valid?

XIIMCXLIX is not a valid Roman numeral. See why. Using this number instead: MCLIX.

DCCCLXCCCXXI is not a valid Roman numeral. See why. Using this number instead: MCLXI.

Not all the Roman numerals are valid.
Instead, we run this math operation of subtraction:

MCLIX - MCLXI - MCMIV = ?

2. Simplify the operation.

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


The matching numerals / symbols are colored the same.


MCLIX - MCLXI - MCMIV =
IX - XI - MCMIV

When crossing out, do not mix
the symbols in the subtractive and additive groups:
for example ...


3. Substitute for subtractives.

Substitute for any subtractive groups of symbols in the roman numerals; that is, 'uncompact' them using only the additive notation.


The subtractive and the additive notation: Find out more info on this topic ...


IX:


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


IX = VIIII


MCMIV:


CM = M - C = D CCCCC - C = D CCCC = DCCCC


IV = V - I = IIIII - I = IIII


MCMIV = MDCCCCIIII


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

Catenate the negative numerals together:

XI +


MDCCCCIIII =


XIMDCCCCIIII


5. Sort out the symbols in descending order.

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

Sort out the symbols of the negative numerals:

XIMDCCCCIIII =


MDCCCCXIIIII


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

VIIII -


MDCCCCXIIIII =


V -


MDCCCCXI


7. Get rid of all the symbols in either string.

Using the additive notation, convert larger symbols to smaller ones and then cross out the common symbols that occur in both numbers.


The subtractive and the additive notation: Find out more info on this topic ...


The larger symbols that are being converted, written in additive notation:

X = VV;


V -
MDCCCCXI =
V -
MDCCCCVVI =
- MDCCCCVI

The 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.


8. Rewrite the recurring symbols.

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

The numeral C should not be repeated for more than 3 times in a row, rewrite:

MDCCCCVI =


MCMVI


The final answer:

MCLIX - MCLXI - MCMIV =


- MCMVI

The operation written with Hindu-Arabic numerals:
1,159 - 1,161 - 1,904 = -1,906

The Romans did not have the Hindu-Arabic numbers.

The 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.


Roman numerals addition and subtraction, online calculator

The latest operations with Roman numerals (added, subtracted)

How to subtract the Roman numerals: MCLIX - MCLXI - MCMIV = ? Dec 07 07:45 UTC (GMT)
How to subtract the Roman numerals: MCLIX - MCLXI - MCMIV = ? Dec 07 07:44 UTC (GMT)
How to add and subtract the Roman numerals: DCCXLVI - CLXXXII + DCXV + CCCLXXV = ? Dec 07 07:43 UTC (GMT)
How to add the Roman numerals: CCCXXX + XXX = ? Dec 07 07:43 UTC (GMT)
How to add and subtract the Roman numerals: CXXIII - CDXXXVI - XCVIII + XCVI = ? Dec 07 07:43 UTC (GMT)
How to add and subtract the Roman numerals: MDCCXVII - CMXLVIII + CCCLII + MCDXC = ? Dec 07 07:42 UTC (GMT)
How to add and subtract the Roman numerals: MLXXXIII + L - DCCLIV + CCCXCIX - XLIV = ? Dec 07 07:42 UTC (GMT)
How to add the Roman numerals: MDXVIII + DCLV + MMCMLXXXVII + CMLXXVII = ? Dec 07 07:41 UTC (GMT)
How to add and subtract the Roman numerals: CDLXVI - CCLXIX + DLXXXV = ? Dec 07 07:40 UTC (GMT)
How to add the Roman numerals: CLX + MDCCI = ? Dec 07 07:40 UTC (GMT)
How to add the Roman numerals: MMDCXV + CLXXVI = ? Dec 07 07:40 UTC (GMT)
How to add and subtract the Roman numerals: DCCVII - CXXII + XXXVI = ? Dec 07 07:40 UTC (GMT)
How to add and subtract the Roman numerals: DXVIII + LXXII - MLXXXIII + CMLXVII - MLXXX = ? Dec 07 07:39 UTC (GMT)
All the addition and subtraction operations with Roman numerals. Added and subtracted online

How to add and subtract Roman numerals the right way, like the Romans calculated, without the Hindu-Arabic numbers: steps and explanations

1. Cancel the numerals having the same value but different signs.

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

When crossing out,
do not mix the symbols in subtractive and additive groups.

3. Replace the groups in subtractive notation.

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

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

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

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

The final answer:

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