How do you work out a quarter of 1999 in Roman numerals giving reasons for your answer?

Answer 1

Today we write out 1999 in Roman numerals as MCMXCIX and to perform any arithmetical operations with theses numerals is almost impossible.

However. the Romans themselves would have calculated the equivalent of 1999 on an abacus counting device as MDCCCCLXXXXVIIII and by placing I to both sides of these numerals simply wrote them out as IMM (-1+2000=1999)

A quarter of 1 is 1/4 which is the equivalent of :. as a Roman fraction because a dot or a dash represented 1/12 and :. is 3/12 which is a 1/4.

So it follows that a quarter of IMM would probably work out as :.D (-0.25+500=499.75) which is a simplification of CCCCLXXXXVIIIIS:. (499.75)

Roman fractions . is 1/12, : is 2/12, :. is 3/12, :: is 4/12, ::. is 5/12, S is 6/12, S. is 7/12, S: is 8/12, S:. is 9/12, S:: is 10/12, S::. is 11/12 and SS = 12/12 = 1

In Roman times there were 12 uncias to an as and 16 asses to a denarius from whence evolved our modern words for inches and ounces

In his fascinating reference book about early numeration systems entitled 'History of Mathematics' volume 2 by David Eugene Smith first pubblished in 1925 and ISBN 0486 204 308 he gives thorough details of how Roman numerals and fractions were once worked out.