Adding and Subtracting Roman NumeralsDate: 10/26/1999 at 08:51:49 From: Greg Brennan Subject: Roman Numerals I would like to know how to add and subtract Roman Numerals without converting them to regular numbers. I tried looking for patterns in different problems like XXX + X = XXXX, which I know is written XL. A problem I can't find a pattern for is LX - XIV = XLVI. What did the Romans do to solve this kind of problem? Date: 10/26/1999 at 13:28:30 From: Doctor Rick Subject: Re: Roman Numerals Hi, Greg. You might want to look at the Roman Numerals page in our Dr. Math FAQ: http://mathforum.org/dr.math/faq/faq.roman.html I have read that Europeans didn't switch to Hindu-Arabic numerals for a long time because they didn't see a reason to do arithmetic on paper, using written numerals. They would set up the numbers on an abacus, do the math, then write down the answer. (It's a little like using a calculator and not bothering to learn to do arithmetic by hand.) Roman numerals are closely related to the abacus -- that was one reason they liked them. If you want to add and subtract Roman numerals, I suggest you do a little bit of conversion first: get rid of the subtraction rule. That is, rewrite XIV as XIIII. Then you can subtract like this: LX = XXXXX V IIIII - XIIII = - X IIII -------- ------------- XXXX V I Now you can resume using the subtraction rule, so that the answer is XLVI. I "borrowed" or "regrouped," sort of the way we do it in regular subtraction: I changed L into XXXXX so there would be enough X's, and I changed X into VV and one of the V's into IIIII so there would be enough I's. You can make shortcuts by remembering that V - IIII = I, for instance. This method is much like using an abacus. The abacus does not use the subtraction rule; 4 (IV) is represented by four beads (like IIII). An abacus uses the same principle of changing a bead in one column into two "5" beads in the column to the right, then changing a "5" bead into five "1" beads in the same column. When it comes to multiplication, forget it! The Egyptians had a similar kind of numeral system (without the subtraction principle), and they used a completely different method of multiplication from ours -- one that works something like the way computers do it. You can find information on Egyptian multiplication by searching our Dr. Math Web site. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ |
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