Rational Expressions … Easy Reducing, or “They’re Just Symbols”

For our intermediate algebra course, I am grading the test on rational expressions; in general, this is my least favorite test to grade. One of my students provided a bit of unintentional humor, however; at least, it was funny for a minute.

Here is the problem and the student’s work:

So, what you are seeing here is that the student combined the numerators (fine) and added a half space in one term in the denominator, which caused “4k – 5” to be seen as “4 k-5”. Reducing fractions the easy way!!

Fortunately, most students are actually doing okay with this test. This problem has been on my tests before, and this is the first time I’ve seen that ‘method’. I think this illustrates a generality about our students and fractions of any kind:

Students will deal with fractions at the symbolic level only, whenever possible. Meanings are not attached, in general.

If you are curious, I start our work with rational expressions with an activity where we explore the meaning of the ‘fraction bar’ and the role of factors in simplifying. That activity does shift students thinking a bit towards the meaning, though clearly not always :).

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