I do believe that algebra sums are going to particularly difficult to work out
using decimal fractions.
For instance a linear equation such as:
21y x 8 = 1
...is going to take some monumental working out using decimals.
21y x 8 = 1
1 / 8 =1/8
1/8 / 21 = 1/168
y = 1/168
I know I haven't used the most elegant way of working this out, but I've just
done it this way to illustrate a point. Try getting to the conclusion that y =
5.952380952 - this was worked out using a calculator with a fraction converter,
by the way.
----- Original Message -----
From: Bill Hooper
To: U.S. Metric Association
Sent: Wednesday, August 19, 2009 12:46 AM
Subject: [USMA:45671] Re: Maths (or should that be "math?")
On Aug 13 , at 7:04 PM, James R. Frysinger wrote:
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.
In short, we must teach students to deal with both decimals and fractions.
Each representation has advantages and disadvantages.
While I wholeheartedly agree with the above, I would add one other thing. As
was pointed out a the start of this thread, the primary reason to use common
fractions (as opposed to decimal fractions) is the ease with which they make
certain kinds of ALGEBRAIC manipulations (and solutions) easier. Thus, while
agreeing that common fractions should be taught, I would suggest that they
should not be taught until algebra class (usually high school), not in
elementary school*. In elementary school, teach ONLY decimal fractions, along
with teaching ONLY metric measures.
Bill Hooper
1810 mm tall
Fernandina Beach, Florida, USA
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*I do realize that younger students will encounter a few common fractions in
daily life, esp. 1/2, 1/4, 3/4 and maybe 1/3 and 2/3. These students can learn
that these things (using 3/4 as an example) stand for "three of the pieces when
something is cut into four equal pieces". That may also be expressed as a
decimal fraction by simply treating "3/4" as "3 divided by 4", or 0.75. There
would certainly not be any pressing reason for them to start learning common
fraction arithmetic like adding and subtracting common fractions.
In the unlikely case where that need should arise, teach them to convert the
common fractions to decimal form and then do the arithmetic. If a student needs
to know how much pie he or she has when given 1/3 of one pie and 1/4 of another
pie, they don't need to go through the complicated process of converting 1/3
and 1/4 into fractions with a common denominator (4/12 + 3/12). (This also
requires learning the additional skill of how to find the least common
denominator). They would then have to do the additional step of adding 4/12 +
3/12 which is equal to 7/12. (One also has to teach how to do this additional
step - it's easy but not obvious. Many students want to add 1/3 + 1/4 to get
2/7, or 4/12+ 3/12 to get 7/24.)
Instead, just change the problem from "1/3 + 1/4" to "0.33 + 0.25" and get
the answer 0.58. I think that a 0.58 fraction of
a whole pie is easier to comprehend than 7/12 of a pie. (Who ever cuts a pie
into 12ths anyway? And even if they did, would getting 1/3 of one pie and 1/4
of another pie somehow magically turn the two given pieces into 7 pieces of pie
divided into 12 equal sized pieces?)
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SImplification Begins With SI.
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