How to subtract the Roman numerals: MCCC - MCCCXLIX - MMCXIII - DCXCVII - CMXXV = ? Solve the mathematical operation of subtraction like the Romans were calculating, without using Hindu-Arabic numbers
The operation written with Hindu-Arabic numerals:
1,300 - 1,349 - 2,113 - 697 - 925 = ?
The Romans did not have the Hindu-Arabic numbers.
Steps and explanations below, without using any Hindu-Arabic numbers.
1. Simplify the operation.
Cross out the common symbols in the numerals of different signs.
The matching numerals / symbols are colored the same.
MCCC - MCCCXLIX - MMCXIII - DCXCVII - CMXXV =
- XLIX - MMCXIII - DCXCVII - CMXXV 2. Substitute for subtractives.
Substitute for any subtractive groups of symbols in the roman numerals; that is, 'uncompact' them using only the additive notation.
XLIX:
XL = L - X = XXXXX - X = XXXX
IX = X - I = V IIIII - I = V IIII = VIIII
XLIX = XXXXVIIII
DCXCVII:
XC = C - X = L XXXXX - X = L XXXX = LXXXX
DCXCVII = DCLXXXXVII
CMXXV:
CM = M - C = D CCCCC - C = D CCCC = DCCCC
CMXXV = DCCCCXXV
3. Put the Roman numerals of the same sign together.
XXXXVIIII +
MMCXIII +
DCLXXXXVII +
DCCCCXXV =
XXXXVIIIIMMCXIIIDCLXXXXVIIDCCCCXXV
4. 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.
XXXXVIIIIMMCXIIIDCLXXXXVIIDCCCCXXV =
MMDDCCCCCCLXXXXXXXXXXXVVVIIIIIIIII
5. Merge the repeating symbols together.
Starting on the right end of the number (starting with the smaller values), merge the repeating symbols into larger ones.
MMDDCCCCCCLXXXXXXXXXXXVVVIIIIIIIII =
MMDDCCCCCCLXXXXXXXXXXXVVVIIIII IIII =
MMDDCCCCCCLXXXXXXXXXXXVVVVIIII =
MMDDCCCCCCLXXXXXXXXXXXVVVVIIII =
MMDDCCCCCCLXXXXXXXXXXXVV VVIIII =
MMDDCCCCCCLXXXXXXXXXXXXXIIII =
MMDDCCCCCCLXXXXXXXXXXXXXIIII =
MMDDCCCCCCLXXXXX XXXXX XXXIIII =
MMDDCCCCCCLLLXXXIIII =
MMDDCCCCCCLLLXXXIIII =
MMDDCCCCCCLL LXXXIIII =
MMDDCCCCCCCLXXXIIII =
MMDDCCCCCCCLXXXIIII =
MMDDCCCCC CCLXXXIIII =
MMDDDCCLXXXIIII =
MMDDDCCLXXXIIII =
MMDD DCCLXXXIIII =
MMMDCCLXXXIIII
6. Rewrite the recurring symbols.
Rewrite the symbols written in 'excessive additive notation' by using the subtractive notation.
The numeral I should not be repeated for more than 3 times in a row, rewrite:
MMMDCCLXXXIIII =
MMMDCCLXXXIV
MCCC - MCCCXLIX - MMCXIII - DCXCVII - CMXXV =
- MMMDCCLXXXIV
The operation written with Hindu-Arabic numerals:
1,300 - 1,349 - 2,113 - 697 - 925 = -3,784
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
Automatically perform simple math calculations with Roman numerals, using the online calculator. Learn how to add or subtract Roman numerals, the right way, like the Romans were calculating. Without the help of Hindu-Arabic numbers. Step-by-step explanations.