I am the fortunate (perhaps?) position of teaching Chemistry simultaneously with Precalculus, and so often times I will come across an equation and wonder “can my Precalculus students do this?” Today’s equation I “simplified” (read: took away the decimals and made into integers ) into this:
At first it depressed me that my students didn’t intuitively know what to do and where to go, in addition to the fact that they were not at all confident in their answer. Soon after, I became more depressed by the fact that some couldn’t solve it on their own.
Our Alg II teacher told me that they were done a little early with their curriculum, and asked if there was anything that he wanted me for the upcoming Precal students to work on. I told him that I wanted them to be able to solve the above problem.
I wonder if my frustration is increased because of the fact that there are about half a dozen different ways to do this problem. Of course, about half of those involve stupid little tricks, which I don’t like because they don’t increase understanding, but there are more than a few legitimate ways of solving this without resorting to “cross multiplication” and “cancelling” (ugh, bad words).
After school, I had a few Chemistry students who were talking about solving that kind of equation (well, I brought it up), some of whom are Alg II students and others whom are Precal students. Some of the Alg II students could do the problem and others couldn’t, and likewise some of the Precal students could do the problem and others couldn’t. I used to think that students forgot how to do this kind of thing because they had a whole summer to forget how to do it, but now I’m realizing that students forget how to do this kind of thing because they have an entire school year to forget how to do it.
 As another teacher pointed out, it is really sad that making an equation have decimals rather than integers increases the complexity for students.