How to add and subtract the Roman numerals: LXIV + XXII - XLIX = ? Solve the mathematical operation of addition and subtraction like the Romans were calculating, without using Hindu-Arabic numbers
The operation written with Hindu-Arabic numerals:
64 + 22 - 49 = ?
The Romans did not have the Hindu-Arabic numbers.
Steps and explanations below, without using any Hindu-Arabic numbers.
1. Substitute for subtractives.
Substitute for any subtractive groups of symbols in the roman numerals; that is, 'uncompact' them using only the additive notation.
LXIV:
IV = V - I = IIIII - I = IIII
LXIV = LXIIII
XLIX:
XL = L - X = XXXXX - X = XXXX
IX = X - I = V IIIII - I = V IIII = VIIII
XLIX = XXXXVIIII
2. Put the Roman numerals of the same sign together.
Catenate the positive numerals together:
LXIIII +
XXII =
LXIIIIXXII
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 positive numerals:
LXIIIIXXII =
LXXXIIIIII
4. Cross out (remove) any symbols occurring in both strings.
LXXXIIIIII -
XXXXVIIII =
LII -
XV
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:
L = XXXXX; X = VV;
LII -
XV =
XXXXVVII -
XV =
XXXVII LXIV + XXII - XLIX =
XXXVII
The operation written with Hindu-Arabic numerals:
64 + 22 - 49 = 37
The Romans did not have the Hindu-Arabic numbers.
The Romans also 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.