How to Add and Subtract Roman Numerals 

without converting them to Arabic Numbers

When adding or subtracting roman numerals without converting them to Arabic numbers is quite straight forward. 

The first thing you have to remember is that there is NO number placement in roman numerals as there is with our ordinary Arabic system.

The Number 499 is represented by the roman numerals CDXCIX where the number 500 is represented by the symbol D.  Roman numerals simply get there value by combining ALL the values of the symbols present.  You do however have to be familiar with how to convert Roman numbers and the subtractive rule.

There are simply five steps to adding or subtracting any Roman Numeral

  1. Write the numbers to be added
  2. Identify any subtractives
  3. Expand the numbers (removing the subtractives)
  4. Combine all the same symbols (for subtraction you would reduce ?like? symbols)
  5. Regroup your new answer using the subtractive rule where necessary.

Take a look at this worked example

Step

Action to be taken

Worked Example

1

Write the numbers to be added.

CDXCIX + MMMCMLIX

2

Identify any subtractives
(I have highlighted the subtractives and separated the pairs for ease of viewing). CD XC IX + MMM CM L IX

3

Expand the numbers
(removing the subtractives)

  • The value of CD is 400 which is the same as 4 C's
  • The value of XC is 90 which is the same as 9 X's
  • The value of IX is 9 which is the same as 9 I's
  • The value of CM is 900 which is the same as 9 C's

CD becomes CCCC

XC becomes XXXXXXXXX

IX becomes IIIIIIIII

Don't expand MMM

CM becomes CCCCCCCCC

Don't expand L

IX becomes IIIIIIIII

4

Combine all the same symbols, starting with the largest.

MMMCCCCCCCCCCCCCL

XXXXXXXXXIIIIIIIIIIIIIIIIII

5

Regroup your new answer using the subtractive rule where necessary.

M'S (3):MMM
C'S (13):MCCC
L'S(1): L
X'S(9): XC
I'S (18): XVIII

Put it all together!

MMMMCCCLXCXVIII

This concludes our adding and subtracting Roman Numerals page. As you can see, it is indeed quite straigt forward, however it will ALWAYS be difficult if the symbols and their values cannot be remembered. It is impossible to do anything with Roman Numerals if you don't know these. Download our mnemonic to remember Roman Numbers to help your student retain these. And remember! Practice, practice, practice! Try some of our free printable worksheets - some of the crossword puzzles are quite challenging. 

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