Fractions: Fractions are fun, not practical

2010-06-21T07:30:00Z Fractions: Fractions are fun, not practical missoulian.com
June 21, 2010 7:30 am

Several recent letters about fractions are missing the larger parts of what fractions are related to. Fractions are a concept in pure math that have no units in either numerator or denominator. Ratios generally have different units, top and bottom, like miles per hour, so one naturally puts the result into a decimal form. In calculus, there are "constants of integration and differentiation" that go separately into the numerator or denominator, making the intermediate result look like a fraction.

Our English system of measurement is most cumbersome. We usually calculate in base 10, but fractional inches, 1/2, 1/4, 1/8. 1/16, etc, are a version of inverse base two. Pounds and ounces are base 16, quarts and gallons are base four. I've long suspected that some aversion to word problems in math class relates to having to convert those cumbersome units into something that can be readily calculated.

Engineering concepts such as viscosity and acceleration are fundamentally ratios of ratios that look like complex fractions but each layer has dimensional units that are retained upon decimalization, e.g. feet per second per second.

In chemistry, reactions between materials often occur in simple proportions, ratios that are not fractions. The universal gas constant combines units of temperature, pressure and amount that are fundamentally ratios of ratios that look like fractions.

Fractions were kind of fun in grade school, something like working out a Sudoku puzzle, more entertaining than useful. In my career of science and engineering I don't recall ever using fractions in the way I was taught in grade school. Were fractions a waste of time? I think the study of ratios, where different units are pertinent, would be better. That leads to practical concepts, readily applied to actual living and better preparing young minds for transition to science and technology.

Don Michels, Missoula

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