The rules as we now know them today governing the Roman numeral system had absolutely nothing to do with the ancient Romans because they were introduced during the Middle Ages but we can glean and extrapolate from historical sources that the Romans would have evaluated the equivalent of the given calculations as in any of the following formats and even more if so required:-
ILXXX+IXX+IL+III = CL => (-1+80)+(-1+20)+(-1+50)+3 = 150
LXXVIIII+XVIIII+XXXXVIIII+III = CL => 79+19+49+3 = 150
ILXXX+XVIIII+IL+III = CL
LXXVIIII+IXX+XXXXVIIII+III = CL
ILXXX-IXX-IL-III = VIII => (-1+80)-(-1+20)-(-1+50)-3 = 8
LXXVIIII-XVIIII-XXXXVIIII-III = VIII => 79-19-49-3 = 8
ILXXX-XVIIII-IL-III = VIII
LXXVIIII-IXX-XXXXVIIII-III = VIII
Note that in arithmetic -(1+20) becomes 1-20 which is -19 and that -(-1+50) becomes 1-50 which is -49
QED
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).
Nowadays 249 when converted into Roman numerals is now considered to be CCXLIX but the ancient Romans probably worked out the required calculations as follows:-MDCCLXXVI+ICCL = MMXXV => 1776+(250-1) = 2025MDCCLXXVI+CCXXXXVIIII = MMXXV => 1776+249 = 2025MDCCLXXVI-ICCL = MDXXVII => 1776-(250-1) = 1527MDCCLXXVI-CCXXXXVIIII = MDXXVII => 1776-249 = 1527For more complicated calculations the Romans would have made use of an abacus calculating device.QED
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
Both 1776 plus 444 added in two different ways will have sum of MMCCXX = 2220 and both 17,776 minus 444 subtracted in two different ways will have a difference of (XVII)CCCXXXII = 17,332
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
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).
No. Only if you're adding or subtracting and then only if the denominators are different.
Nowadays 249 when converted into Roman numerals is now considered to be CCXLIX but the ancient Romans probably worked out the required calculations as follows:-MDCCLXXVI+ICCL = MMXXV => 1776+(250-1) = 2025MDCCLXXVI+CCXXXXVIIII = MMXXV => 1776+249 = 2025MDCCLXXVI-ICCL = MDXXVII => 1776-(250-1) = 1527MDCCLXXVI-CCXXXXVIIII = MDXXVII => 1776-249 = 1527For more complicated calculations the Romans would have made use of an abacus calculating device.QED
Not withstanding today's modern notation of Roman numerals in as much that the ancient Romans would have probably worked out the required calculations as follows: MDCCLXXVI+IC = MDCCCLXXV => 1776+(100-1) = 1875 MDCCLXXVI+LXXXXVIIII = MDCCCLXXV => 1776+99 = 1875 MDCCLXXVI-IC = MDCLXXVII => 1776-(100-1) = 1677 MDCCLXXVI-LXXXXVIIII = MDCLXXVII => 1776-99 = 1677
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
Both 1776 plus 444 added in two different ways will have sum of MMCCXX = 2220 and both 17,776 minus 444 subtracted in two different ways will have a difference of (XVII)CCCXXXII = 17,332
Nowadays we think that the equivalent of 9 in Roman numerals is only IX whereas in fact IX is an abridged version of VIIII in ancient Roman numerals thus facilitating the conversion and calculations of the given Hindu-Arabic numerals into Roman numerals in several ways as follows:- MDCCLXVII+VIIII = MDCCLXXVI => 1767+9 = 1776 MDCCLXVII+IX = MDCCLXXVI => 1767+(-1+10) = 1776 MDCCLXVII-VIIII = MDCCLVIII => 1767-9 = 1758 MDCCLXVII-IX = MDCCLVIII => 1767-(-1+10) = 1758 Note that in mathematics that -(-1+10) is equivalent to +1-10 and so -(-I+X) is equivalent to -VIIII
Nowadays 999 when converted into Roman numerals is now considered to be CMXCIX which does not quite easily lend itself for the purpose of arithmetical operations but the ancient Romans would have probably worked out the given three calculations as follows:-IM+DCCLXXVII = MDCCLXXVI => (1000-1)+777 = 1776DCCCCLXXXXVIIII+DCCLXXVII = MDCCLXXVI => 999+777 = 1776DCCCCLXXXXVIIII-DCCLXXVII = CCXXII => 999-777 = 222QED
Under today's modern rules now governing the Roman numeral system the equivalent of 249 when converted into Roman numerals is now considered to be CCXLIX which does not lend itself quite easily to arithmetical operations but there exist credible evidence to suggest that the ancient Romans would have carried out the requested calculations as follows:-MDCCLXXVI+ICCL = MMXXV => 1776+(250-1) = 2025MDCCLXXVI+CCXXXXVIIII = MMXXV => 1776+249 = 2025MDCCLXXVI-ICCL = MDXXVII => 1776-(250-1) = 1527MDCCLXXVI-CCXXXXVIIII = MDXXVII => 1776-249 = 1527Note that in mathematics -(250-1) becomes -250+1 or as 1-250The above calculations were fairly simple and straight forward to work out but for more complicated calculations the Romans would make use of an abacus calculating device.QED
Not withstanding the rules as we now know them today governing the Roman numeral system, that were introduced during the Middle Ages, inasmuch that the ancient Romans would have probably worked out the given numbers into Roman numerals as in any of the following formats:- MDCCLXXVI+DCCCCLXXXXVIIII = MMDCCLXXV => 1776+999 = 2775 MDCCLXXVI+IM = MMDCCLXXV => 1776+(-1+1000) = 2775 MDCCLXXVI-DCCCCLXXXXVIIII = DCCLXXVII => 1776-999 = 777 MDCCLXXVI-IM = DCCLXXVII => 1776-(-1+1000) = 777 Note: IM is a logical abridged version of DCCCCLXXXXVIIII Note: In mathematics -(-1+1000) becomes +1-1000 Note: The equivalent symbol of zero was never needed in Roman numerals
For working out arithmetical calculations
It is now generally accepted that the modern way of expressing 1999 into Roman numerals is now MCMXCIX but the ancient Romans would have probably worked out the above as follows:- A: MDCCLXXVI+IMM = MMMDCCLXXV => 1776+(2000-1) = 3775 B: MDCCLXXVI+MDCCCCLXXXXVIIII = MMMDCCLXXV => 1776+1999 = 3775 C: MDCCCCLXXXXVIIII-MDCCLXXVI = CCXXIII => 1999-1776 = 223 The above calculations are fairly easy and straightforward but for more complicated calculations the Romans would have used an abacus counting device.