Hey...I didn't say it was hard, I said it was a trick! :-)
----- Original Message -----
From: "James R. Frysinger" <[email protected]>
To: "Stephen Davis" <[email protected]>
Cc: "U.S. Metric Association" <[email protected]>
Sent: Friday, August 14, 2009 1:36 AM
Subject: Re: [USMA:45619] Re: Maths (or should that be "math?")
That's the sort of "trick" I learned in elementary school, but with
fractions. Since 1/5 = 2/10 (fraction math), just double the number then
slide the decimal point over one notch. Of course, dividing by 5 is not
terribly hard and since multiplying by 1/5 is the same as dividing by 5
(fraction math), one can take that approach as well.
Jim
Stephen Davis wrote:
I find certain fractions, such as fifths, easier to express as a decimal
or percentage such as 0.2 or 20 per cent. It helps to remember that
there are 5 '20s' in 100. A handy little trick to calculate fifths, I
find, is to double the number. One-fifth of 62:
62 + 62 = 124
124 / 10 = 12.4
Therefore, one-fifth, or 20 per cent of 62 = 12.4.
----- Original Message ----- From: "James R. Frysinger"
<[email protected]>
To: "U.S. Metric Association" <[email protected]>
Sent: Friday, August 14, 2009 12:04 AM
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
--
James R. Frysinger
632 Stony Point Mountain Road
Doyle, TN 38559-3030
(C) 931.212.0267
(H) 931.657.3107
(F) 931.657.3108
