Roman Numerals: Division
Date: 11/05/2001 at 11:57:06 From: Chalina Mendoza Subject: Arithmetic of Roman Numerals (specifically division and subtraction) Dr. Math - I am in a math class and our assignment is to find out how to add, subtract, multiply, and divide Roman numerals. I have found information on how to add and multiply, but have not found any information on how to divide or subtract. Your information would greatly appreciated. Thanks. Chalina Mendoza
Date: 11/05/2001 at 13:17:47 From: Doctor Sarah Subject: Re: Arithmetic of Roman Numerals (specifically division and subtraction) Hi Chalina - thanks for writing to Dr. Math. In the Dr. Math FAQ on Roman Numerals you'll find rules for subtracting, with some examples. Jim Loy's page on division is temporarily unavailable on the Web; here is a cached version: ----------------------------- Division with Roman Numerals Copyright MCMXCVII, Jim Loy Roman numeral division can be very easy or fairly difficult, depending on the two numbers. Sometimes you can just write down the two numbers and do some division of pieces of the numerator: XCV / V=XIX (- II + XX + I) MMCCCXXII / CCX=XI + XII/CCX (the remainder was XII) In the first example, we had to deal with a borrow. But, that wasn't difficult. In the second example, MMC is X x CCX, so MMCCCX=XI x CCX. And we had to deal with a remainder. General method: The above method works fairly often, but is pure torture in general. Try CXLV / VI, if you need to be convinced that it is difficult. We need a general method. Division is repeated subtractions. Our method of long division, which we learn in grade school, is just a formalized way of using repeated subtractions. In the above example (CXLV / VI) we could just subtract VI over and over, keeping track of how many times we subtracted. But, there is a short cut, we can subtract LX (which is X x VI) a few times, first: CXLV - LX - LX=XXV So, CXLV / VI=LX / VI + LX / VI + XXV / VI CXLV / VI=XX + XXV / VI Now we can repeatedly subtract VI from XXV: XXV=VI + VI + VI + VI + I So, XXV / VI=IV + I/VI The solution, then, is: CXLV / VI=XXIV + I/VI Here, we had a remainder of I. This method works fine for all division problems. You may have to multiply the denominator by C or even M, just as we multiplied by X. Multiplying the denominator by V or L sometimes can help. But, usually, that only complicates the process. We see here that Roman numerals are not a lot more difficult to divide than dividing our Arabic numerals. There are more steps, and most of us are not as familiar with the process, so it is more tedious for us. -------------------------- - Doctor Sarah, The Math Forum http://mathforum.org/dr.math/
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