The modern way of expressing 19 in Roman numerals is now XIX but the ancient Romans would have expressed it as IXX or as XVIIII because their equivalent Latin words are 'undeviginti' and 'novemdecim' respectively but there is no Latin equivalent for XIX and thus it logically follows that:-
IXX+IX = XXVIII => (20-1)+(10-1) = 28
XVIIII+VIIII = XXVIII => 19+9 = 28
IXX-IX = X => (20-1)-(10-1) = 10
XVIIII-VIIII = X => 19-9 = 10
Remember that in mathematics --I = +I and that the above calculations can be considered to be mental arithmetic but for more serious calculations the Romans would have used an abacus calculating device.
QED
See answer to question: ' How do you add together 1666 and 1999 in two different ways using Roman numerals'
Roman numerals are entirely inappropriate for doing such calculations. I believe the people in Roman times did such calculations on an abacus or something similar - which is basically similar to converting them to the Arabic numbers we use. If you really want to do it in Roman numerals - which is basically NOT a good idea - you would have to keep the thousands, hundreds, etc. separate, and handle carry (for addition) and borrowing (for subtraction).
Since you ask how I would do it: I would forget about doing this in Roman; rather, I would convert everything to arabic numbers, which are much more appropriate for such calculations.
Numerals are used for mathematical calculations. Mathematical calculations are used in science. This is the way Roman numerals related to Roman science.
The equivalent of 0.5 or 1/2 as a Roman numeral is S and so therefore the required calculations are as follows:-SX+SIX = XVIII => (10-0.5)+(10-1.5)= 18VIIIIS+VIIIS = XVIII => 9.5+8.5 = 18SX-SIX = I => (10-0.5)-(10-1.5) = 1VIIIIS-VIIIS = I => 9.5-8.5 = 1Note that in mathematics -(10-1.5) changes to 1.5-10QED
When 9 is converted into Roman numerals it is IX which is an abridged version of VIIII and so the required calculations are as follows:-MDCCLXXVI+IX = MDCCLXXXV => 1776+(10-1) = 1785MDCCLXXVI+VIIII = MDCCLXXXV => 1776+9 = 1785MDCCLXXVI-IX = MDCCLXVII => 1776-(10-1) = 1767MDCCLXXVI-VIIII = MDCCLXVII => 1776-9 = 1767Note that in mathematics -(10-1) changes to 1-10QED
According to my calculations,mccxxix in Hindu Arabic numerals is 1229
Save yourself the trouble and convert the numbers to arabic numbers (the numbers we usually use).
The Romans did their calculations on an abacus counting device which was the equivalent to a primitive calculator.
Doing arithmetic with Roman numerals is exasperating, and imho a pointless waste of time, except to demonstrate the obvious superiority of our "normal numbers," which use base-10 radix / positional notation that includes a zero digit as a placeholder. I'd venture to say science & technology -- commerce, too -- could never have developed in recent centuries if we still used Roman numerals for calculations. However, this web site explains some methods: http://turner.faculty.swau.edu/mathematics/materialslibrary/roman/
The modern way of expressing 49 into Roman numerals is now XLIX but the ancient Romans would have probably worked out the equivalent of 49 on an abacus counting frame as XXXXVIIII and then wrote it out as IL thus expediently working out the required calculations as follows:-LII+IL = CI => 52+(50-1) = 101LII-IL = III => 52-(50-1) = 3Note that in mathematics -(50-1) becomes -50+1 and that if we were to use the longer version of 49 in the above calculations the results would be exactly the same.QED
Today's modern way of expressing 1449 as Roman numerals is now MCDXLIX which prohibits sensible interaction with other numerals but the ancient Romans would have worked out the equivalent of 1449 on an abacus counting device as MCCCCXXXXVIIII and probably abridged it to ILMD thus facilitating the speed and ease of calculations as follows:-MDCCLXXVI+ILMD = MMMCCXXV => 1776+(1500-51) = 3225MDCCLXXVI-ILMD = CCCXXVII => 1776-(1500-51) = 327Note that the results would be exactly the same if we were to use the longer version of the equivalent of 1449.QED