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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) = 1785

MDCCLXXVI+VIIII = MDCCLXXXV => 1776+9 = 1785

MDCCLXXVI-IX = MDCCLXVII => 1776-(10-1) = 1767

MDCCLXXVI-VIIII = MDCCLXVII => 1776-9 = 1767

Note that in mathematics -(10-1) changes to 1-10

QED

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Q: How would you work out 1776 plus 9 in two different ways and 1776 minus 9 in two different ways but working out all four calculations entirely in Roman numerals with explanations?

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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).

MIM + MMXIV = MMMXIII or MMCXCIX + MMXIII = MMMXIII There is only one way to write the solution (3013)

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.

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/

According to my calculations,mccxxix in Hindu Arabic numerals is 1229

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

The Romans did their calculations on an abacus counting device which was the equivalent to a primitive calculator.

Latin numeracy is the same as Roman numerals and under the modern rules now governing the Roman numeral system the equivalent of 549 when converted into Roman numerals is now considered to be DXLIX but there exist historical evidence to suggest that the ancient Romans would have worked it out on an abacus counting device as DXXXXVIIII which can be abridged to IDL thus expediating the speed and ease of the required calculations as follows:-MDCCLXXVI+IDL = MMCCCXXV => 1776+(550-1) = 2325MDCCLXXVI+DXXXXVIIII = MMCCCXXV => 1776-449 = 2325MDCCLXXVI-IDL = MCCXXVII => 1776-(550-1) = 1227MDCCLXXVI-DXXXXVIIII = MCCXXVII => 1776-549 = 1227QED

The rules as we know them today now governing the Roman numerals system had nothing to do with the Romans because they were introduced during the Middle Ages and as result of these rules the equivalent of 999 converted into Roman numerals is now considered to be CMXCIX which hardly lends itself quite easily for the purpose of mathematical operations but there exist credible evidence to show that the ancient Romans would have worked out the requested calculations as in the following formats:-MDCCLXXVI+IM = MMDCCLXXV => 1776+(1000-1) = 2775MDCCLXXVI+DCCCCLXXXXVIIII = MMDCCLXXV => 1776+999 = 2775MDCCLXXVI-IM = DCCLXXVII => 1776-(1000-1) = 777MDCCLXXVI-DCCCCLXXXXVIIII = DCCLXXVII => 1776-999 = 777Note that in mathematics -(1000-1) becomes 1-1000 and that the above calculations were fairly simple and straightforward to work out but for more advanced calculations the Romans would have used an abacus calculating device.QED

In today's modern conversion of Roman numerals 49 and 19 are now considered to be XLIX and XIX respectively but the ancient Romans would have probably worked out the above as follows:- IL+IXX = LXVIII => (50-1)+(20-1) = 68 XXXXVIIII+XVIIII = LXVIII => 49+19 = 68 IL-IXX = XXX => (50-1)-(20-1) = 30 XXXXVIIII-XVIIII => 49-19 = 30 For more complicated calculations the Romans would use an abacus calculating device.

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