How to subtract the Roman numerals: MDXXV - MMMCLXXXII - CCLXVI = ? Solve the mathematical operation of subtraction like the Romans were calculating, without using Hindu-Arabic numbers
The operation written with Hindu-Arabic numerals:
1,525 - 3,182 - 266 = ?
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.
MDXXV - MMMCLXXXII - CCLXVI =
D - MMCLXII - CCLXI 2. Put the Roman numerals of the same sign together.
Catenate the negative numerals together:
MMCLXII +
CCLXI =
MMCLXIICCLXI
3. 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:
MMCLXIICCLXI =
MMCCCLLXXIII
4. 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.
Merge the repeating symbols in the negative numeral:
MMCCCLLXXIII =
MMCCCCXXIII
5. 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 larger symbols that are being converted, written in additive notation:
M = DD;
D -
MMCCCCXXIII =
D -
MDDCCCCXXIII =
- MDCCCCXXIIIThe 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.
6. 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:
MDCCCCXXIII =
MCMXXIII
MDXXV - MMMCLXXXII - CCLXVI =
- MCMXXIII
The operation written with Hindu-Arabic numerals:
1,525 - 3,182 - 266 = -1,923
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.