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Re: Fractions and algebra
Posted:
Jun 27, 2006 9:58 PM


I like to teach fractions by looking forward to algebra. The reason the denominators have to be the same to add fractions is that anywhere in mathematics, when we add, we assume we are adding "like terms." 3 fourths + 1 fourth = 4 fourths, but 5 ninths + 3 eights are not like terms and cannot be added until some conversion is made to have the same unit. Similarly, the reason we line up the decimal for addition and subtraction is to line up the place values and add the pennies to the pennies, dimes to dimes, dollars to dollars, and so forth. Likewise, 1 in. + 7 in. = 8 in. but 7 cm + 3 in. is not equal to 10. Couching addition and subtraction of whole numbers and rational numbers written as fractions or in decimal form as combining like terms builds a large algebra concept.
At the other end, students have to understand fractions to comprehend the processes for adding, subtracting, multiplying and dividing rational expressions. They also have to use skill with adding and subtracting fractions in adding/subtracting coefficients to combine like terms. Although these types of problem may be contrived, I like to have students work some with fractional coefficients (and exponents) so that they really generalize processes. In calculus, I have had numerous students struggle with simple integration and differentiation because they have difficulty adding or subracting 1 to or from a fractional exponent.
Martha
Martha Haehl 8167594221 martha.haehl@mcckc.edu Metropolitan Community CollegePenn Valley 3201 S.W. Trafficway Kansas City, MO 64111
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