Would I be correct in deducing that the preference of fractions or decimals is tied to a preference of English units or metric units? >From my experience, the English system tends to be more fractional driven where the metric system is more decimal driven?
Someone may be looking for a reason or excuse not to use metric because they have a preference for fractions or think fractions are better. They are misled as there is no rule in SI (that I'm aware of) that says fractions used in math are wrong. SI makes claims as to how math is done. You said: "Some physical relationships make more sense with fractional coefficients or exponents than with decimal coefficients or exponents. There is a very real reason for saying that E = (1/2)mv^2 rather than E = 0.5mv^2. I'd be curious to know what that real reason is as I see no difference in the two. It just may be what you are use to seeing and are more comfortable with viewing. As far as I can see the decimalized description is just as valid. Even when written in decimal form (zero point five), there is no reason it can't be spoken as a fraction (one half). As you show in your text, you had to group the fraction in parentheses to prevent the formula from being wrongly read as a reciprocal of 2mv^2. Such a problem does not exist with the decimal expression. Of course this problem can be solved with a the form 1/2 written or typed as ½. This is fine when the font is large, but can be difficult and subject to error if the digits are too small and a 2 in the denominator can be made to look like something else. For me to provide that character I had to make an extra step of using Windows character map, locate the symbol and cut and paste it to this post. What a PITA. Do fractions really need to be taught as a separate subject in math class or can they be integrated as part of learning algebra? The only time I recall ever having a need to do fractional math was when solving an algebraic equation. Because I do may basic math using a calculator, I enter the numbers decimally. To bring this topic back to the issue of the metric system. How friendly is metric to fractional descriptions for those who prefer to use fractions over decimals? Would there be any problem in writing ½ L of water as opposed to 0.5 L or 500 mL? Half liter seems to roll of the tongue better then zero point five liter or five hundred milliliters. Simon -------------------------------------------------- From: "James R. Frysinger" <j...@metricmethods.com> Sent: Thursday, 2009-08-13 19:04 To: "U.S. Metric Association" <usma@colostate.edu> Subject: [USMA:45618] Re: Maths (or should that be "math?") > > I think that we must be careful here not to demand a "one size fits all" > answer. > > An advantage that fractions have over decimals is that some values can > be more easily expressed in fraction form. Take for example the number > 1/3. While for technical work one can carry the string 0.333 ... out as > far as needed for the desired precision, one can never express 1/3 > exactly as a decimal number. That is a problem for pure mathematics done > decimally. > > A second advantage that fractions have over decimals is that they help > the comprehension of ratios and proportions (essentially the same > thing). That skill is sorely lacking in many students and it is > problematic for comprehending physics (among other subjects), as pointed > out by Arnold Arons in his _A Guide to Teaching Introductory Physics_ . > > Some physical relationships make more sense with fractional coefficients > or exponents than with decimal coefficients or exponents. There is a > very real reason for saying that E = (1/2)mv^2 rather than E = 0.5mv^2. > (Forgive me for not trying to reproduce the italic form of quantity > symbols.) It makes no sense to say that the charge on an up quark is > 0.667 times the elementary charge, that is 0.667e, but it does make > sense to say that it is (2/3)e. (These look better with horizontal bar > typesetting of the fractions!) > > Decimals have an advantage over mathematics in the mechanization of > calculations by calculator or by computer. Also, they are easier to > multiply, divide, add, and subtract. These operations with fractions > (vulgar, compound, etc.) are more difficult for students to solve than > their decimal equivalents. > > However, if we do away with teaching the math skills needed to deal with > fractions of one form or another, students lose a whole sector of > understanding. > > My feeling is that **practical** calculations often, but not always, are > easier with decimals. Examples that come to mind here on my farm are > calculations of field areas, fertilizer rates, yield rates, > precipitation records, and so forth. But the ability to deal with > fractions must be taught as well to cover the needs of "pure" areas such > as physics, chemistry, etc. > > In short, we must teach students to deal with both decimals and > fractions. Each representation has advantages and disadvantages. > > Jim > > > Stephen Davis wrote: >> A little while ago, James Frysinger stated that metric helped in the >> teaching of maths. >> >> Does he, or anyone else on the USMA board, think metric, with its >> decimal graduations, is appropriate for use with algebra? Particularly >> linear equations? >> >> I imagine life would become rather difficullt if you tried to solve >> linear equations with decimals rather than with fractions? >> >> > > -- > James R. Frysinger > 632 Stony Point Mountain Road > Doyle, TN 38559-3030 > > (C) 931.212.0267 > (H) 931.657.3107 > (F) 931.657.3108 > >
