Division with Roman NumeralsDate: 03/02/2004 at 15:38:58 From: Trish Subject: Division using Greek, Roman or Egyptian I'm having real problems trying to divide using a non place system. I can think in the Hindu place system, but the concept of using letters rather than numbers is confusing me. Can you please give me an example of a division calculation? Date: 03/02/2004 at 16:55:13 From: Doctor Peterson Subject: Re: Division using Greek, Roman or Egyptian Hi, Trish. There is a demonstration of addition and subtraction in our FAQ: Roman numerals http://mathforum.org/dr.math/faq/faq.roman.html That also points out that the Romans and others probably wouldn't have bothered doing arithmetic with their numerals in the sense we think of doing it; they would put the number on an abacus and use that. The Egyptians did multiplication and division using a method of doubling and halving, which is described here: Egyptian Method of Multiplication http://mathforum.org/library/drmath/view/57542.html Egyptian Division http://mathforum.org/library/drmath/view/57574.html Egyptian Division, Shelley Walsh http://faculty.ed.umuc.edu/~swalsh/Math%20Articles/EgyptDivide.html That method didn't require memorizing multiplication tables (which would have to be different from one place to another). Actually, the idea that one could memorize such tables was considered preposterous, at least for most people, long after Hindu-Arabic numerals became popular. Each operation can in principle be done in any numeral system by thinking in terms of place value. For example, to add CIV and CCXCII, you would arrange each number in columns (as on an abacus, or in a place-value system) and add the columns: C IV + CC XC II ---------- CCC XC VI I can see why division would be the hardest to do this way; estimating a quotient requires some sort of familiarity with multiplication tables. Probably anything reasonable you do will amount to either translating (bit by bit) into Hindu-Arabic, or thinking in terms of an abacus, or using the Egyptian method. We could try to demonstrate several such techniques, but you get the idea: if you want to do as the Romans did, you won't bother! I'll just try the Egyptian division using Roman numerals, since you asked for a sample. Here is 153 / 9, as in the link above: I | IX * C L III X VI II | XVIII -C XL IV + I IV | XXXVI --------- ------ VIII | LXXII IX X VII XVI | CXLIV* I doubled starting at I and at IX until the next doubling would take me past CLIII; then subtracted each number in the second column that I could, marking those I used with *; then added the corresponding numbers in the first column to get my answer, XVII. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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