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.

Get Prepared For Summer.

If you want to learn how to put a stop to the dreaded Summer Math Loss and send your child back to school in September feeling like a math super-hero then watch this free video training.

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


Action to be taken

Worked Example


Write the numbers to be added.



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


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


    Combine all the same symbols, starting with the largest.




    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!


    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. 

    Keep In Touch!

    You can send me a quick message, subscribe to K6Math Fun & Update, or join my Facebook Page - K6Math. Choose all the options so you don't miss any of the new material added to this site.

    Move from adding roman numerals to my Roman Numerals starting page or explore all that printable math worksheets has to offer.