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Re: Fractions and algebra
Posted:
Jun 27, 2006 9:58 PM
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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
816-759-4221
martha.haehl@mcckc.edu
Metropolitan Community College-Penn Valley
3201 S.W. Trafficway
Kansas City, MO 64111
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