With all due respect, you need a better example. Multiplying out, 168y = 1, hence y = 1/168 which can either be regarded as a fraction or a command to carry out division. (I believe you missed a X10^-2 in your answer) Sets of linear equations with lovely integer coefficients mostly exist in alegebra class, not in real world engineering, where decimal coefficients are the norm. To avoid any rounding errors any fractions can be cleared by multiplying by the least common denominator. A fraction-educated person would do that so he could turn to a computer to solve the system. I'd have to think about how to explain the LCD concept to the fraction-uneducated. With a judicious solution method, the division can normally be deferred to the final solution step. I support the earlier recommendation to defer fractions to algebra, or the last math class before algebra. I would not teach kids to measure in common fractions (of course, not teaching them inches solves the problem)
--- On Wed, 8/19/09, Stephen Davis <[email protected]> wrote: From: Stephen Davis <[email protected]> Subject: [USMA:45677] Re: Maths (or should that be "math?") To: "U.S. Metric Association" <[email protected]> Date: Wednesday, August 19, 2009, 8:43 AM 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 ============================ *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?) ========================== SImplification Begins With SI. ==========================
